Bayesian inference based on dual generalized order statistics from the exponentiated Weibull model

NASA Astrophysics Data System (ADS)

Al Sobhi, Mashail M.

2015-02-01

Bayesian estimation for the two parameters and the reliability function of the exponentiated Weibull model are obtained based on dual generalized order statistics (DGOS). Also, Bayesian prediction bounds for future DGOS from exponentiated Weibull model are obtained. The symmetric and asymmetric loss functions are considered for Bayesian computations. The Markov chain Monte Carlo (MCMC) methods are used for computing the Bayes estimates and prediction bounds. The results have been specialized to the lower record values. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation.

Careful with Those Priors: A Note on Bayesian Estimation in Two-Parameter Logistic Item Response Theory Models

ERIC Educational Resources Information Center

Marcoulides, Katerina M.

2018-01-01

This study examined the use of Bayesian analysis methods for the estimation of item parameters in a two-parameter logistic item response theory model. Using simulated data under various design conditions with both informative and non-informative priors, the parameter recovery of Bayesian analysis methods were examined. Overall results showed that…

Case studies in Bayesian microbial risk assessments.

PubMed

Kennedy, Marc C; Clough, Helen E; Turner, Joanne

2009-12-21

The quantification of uncertainty and variability is a key component of quantitative risk analysis. Recent advances in Bayesian statistics make it ideal for integrating multiple sources of information, of different types and quality, and providing a realistic estimate of the combined uncertainty in the final risk estimates. We present two case studies related to foodborne microbial risks. In the first, we combine models to describe the sequence of events resulting in illness from consumption of milk contaminated with VTEC O157. We used Monte Carlo simulation to propagate uncertainty in some of the inputs to computer models describing the farm and pasteurisation process. Resulting simulated contamination levels were then assigned to consumption events from a dietary survey. Finally we accounted for uncertainty in the dose-response relationship and uncertainty due to limited incidence data to derive uncertainty about yearly incidences of illness in young children. Options for altering the risk were considered by running the model with different hypothetical policy-driven exposure scenarios. In the second case study we illustrate an efficient Bayesian sensitivity analysis for identifying the most important parameters of a complex computer code that simulated VTEC O157 prevalence within a managed dairy herd. This was carried out in 2 stages, first to screen out the unimportant inputs, then to perform a more detailed analysis on the remaining inputs. The method works by building a Bayesian statistical approximation to the computer code using a number of known code input/output pairs (training runs). We estimated that the expected total number of children aged 1.5-4.5 who become ill due to VTEC O157 in milk is 8.6 per year, with 95% uncertainty interval (0,11.5). The most extreme policy we considered was banning on-farm pasteurisation of milk, which reduced the estimate to 6.4 with 95% interval (0,11). In the second case study the effective number of inputs was reduced from 30 to 7 in the screening stage, and just 2 inputs were found to explain 82.8% of the output variance. A combined total of 500 runs of the computer code were used. These case studies illustrate the use of Bayesian statistics to perform detailed uncertainty and sensitivity analyses, integrating multiple information sources in a way that is both rigorous and efficient.

Compound estimation procedures in reliability

NASA Technical Reports Server (NTRS)

Barnes, Ron

1990-01-01

At NASA, components and subsystems of components in the Space Shuttle and Space Station generally go through a number of redesign stages. While data on failures for various design stages are sometimes available, the classical procedures for evaluating reliability only utilize the failure data on the present design stage of the component or subsystem. Often, few or no failures have been recorded on the present design stage. Previously, Bayesian estimators for the reliability of a single component, conditioned on the failure data for the present design, were developed. These new estimators permit NASA to evaluate the reliability, even when few or no failures have been recorded. Point estimates for the latter evaluation were not possible with the classical procedures. Since different design stages of a component (or subsystem) generally have a good deal in common, the development of new statistical procedures for evaluating the reliability, which consider the entire failure record for all design stages, has great intuitive appeal. A typical subsystem consists of a number of different components and each component has evolved through a number of redesign stages. The present investigations considered compound estimation procedures and related models. Such models permit the statistical consideration of all design stages of each component and thus incorporate all the available failure data to obtain estimates for the reliability of the present version of the component (or subsystem). A number of models were considered to estimate the reliability of a component conditioned on its total failure history from two design stages. It was determined that reliability estimators for the present design stage, conditioned on the complete failure history for two design stages have lower risk than the corresponding estimators conditioned only on the most recent design failure data. Several models were explored and preliminary models involving bivariate Poisson distribution and the Consael Process (a bivariate Poisson process) were developed. Possible short comings of the models are noted. An example is given to illustrate the procedures. These investigations are ongoing with the aim of developing estimators that extend to components (and subsystems) with three or more design stages.

The integration of probabilistic information during sensorimotor estimation is unimpaired in children with Cerebral Palsy

PubMed Central

Sokhey, Taegh; Gaebler-Spira, Deborah; Kording, Konrad P.

2017-01-01

Background It is important to understand the motor deficits of children with Cerebral Palsy (CP). Our understanding of this motor disorder can be enriched by computational models of motor control. One crucial stage in generating movement involves combining uncertain information from different sources, and deficits in this process could contribute to reduced motor function in children with CP. Healthy adults can integrate previously-learned information (prior) with incoming sensory information (likelihood) in a close-to-optimal way when estimating object location, consistent with the use of Bayesian statistics. However, there are few studies investigating how children with CP perform sensorimotor integration. We compare sensorimotor estimation in children with CP and age-matched controls using a model-based analysis to understand the process. Methods and findings We examined Bayesian sensorimotor integration in children with CP, aged between 5 and 12 years old, with Gross Motor Function Classification System (GMFCS) levels 1–3 and compared their estimation behavior with age-matched typically-developing (TD) children. We used a simple sensorimotor estimation task which requires participants to combine probabilistic information from different sources: a likelihood distribution (current sensory information) with a prior distribution (learned target information). In order to examine sensorimotor integration, we quantified how participants weighed statistical information from the two sources (prior and likelihood) and compared this to the statistical optimal weighting. We found that the weighing of statistical information in children with CP was as statistically efficient as that of TD children. Conclusions We conclude that Bayesian sensorimotor integration is not impaired in children with CP and therefore, does not contribute to their motor deficits. Future research has the potential to enrich our understanding of motor disorders by investigating the stages of motor processing set out by computational models. Therapeutic interventions should exploit the ability of children with CP to use statistical information. PMID:29186196

Comparing interval estimates for small sample ordinal CFA models

PubMed Central

Natesan, Prathiba

2015-01-01

Robust maximum likelihood (RML) and asymptotically generalized least squares (AGLS) methods have been recommended for fitting ordinal structural equation models. Studies show that some of these methods underestimate standard errors. However, these studies have not investigated the coverage and bias of interval estimates. An estimate with a reasonable standard error could still be severely biased. This can only be known by systematically investigating the interval estimates. The present study compares Bayesian, RML, and AGLS interval estimates of factor correlations in ordinal confirmatory factor analysis models (CFA) for small sample data. Six sample sizes, 3 factor correlations, and 2 factor score distributions (multivariate normal and multivariate mildly skewed) were studied. Two Bayesian prior specifications, informative and relatively less informative were studied. Undercoverage of confidence intervals and underestimation of standard errors was common in non-Bayesian methods. Underestimated standard errors may lead to inflated Type-I error rates. Non-Bayesian intervals were more positive biased than negatively biased, that is, most intervals that did not contain the true value were greater than the true value. Some non-Bayesian methods had non-converging and inadmissible solutions for small samples and non-normal data. Bayesian empirical standard error estimates for informative and relatively less informative priors were closer to the average standard errors of the estimates. The coverage of Bayesian credibility intervals was closer to what was expected with overcoverage in a few cases. Although some Bayesian credibility intervals were wider, they reflected the nature of statistical uncertainty that comes with the data (e.g., small sample). Bayesian point estimates were also more accurate than non-Bayesian estimates. The results illustrate the importance of analyzing coverage and bias of interval estimates, and how ignoring interval estimates can be misleading. Therefore, editors and policymakers should continue to emphasize the inclusion of interval estimates in research. PMID:26579002

Comparing interval estimates for small sample ordinal CFA models.

PubMed

Natesan, Prathiba

2015-01-01

Robust maximum likelihood (RML) and asymptotically generalized least squares (AGLS) methods have been recommended for fitting ordinal structural equation models. Studies show that some of these methods underestimate standard errors. However, these studies have not investigated the coverage and bias of interval estimates. An estimate with a reasonable standard error could still be severely biased. This can only be known by systematically investigating the interval estimates. The present study compares Bayesian, RML, and AGLS interval estimates of factor correlations in ordinal confirmatory factor analysis models (CFA) for small sample data. Six sample sizes, 3 factor correlations, and 2 factor score distributions (multivariate normal and multivariate mildly skewed) were studied. Two Bayesian prior specifications, informative and relatively less informative were studied. Undercoverage of confidence intervals and underestimation of standard errors was common in non-Bayesian methods. Underestimated standard errors may lead to inflated Type-I error rates. Non-Bayesian intervals were more positive biased than negatively biased, that is, most intervals that did not contain the true value were greater than the true value. Some non-Bayesian methods had non-converging and inadmissible solutions for small samples and non-normal data. Bayesian empirical standard error estimates for informative and relatively less informative priors were closer to the average standard errors of the estimates. The coverage of Bayesian credibility intervals was closer to what was expected with overcoverage in a few cases. Although some Bayesian credibility intervals were wider, they reflected the nature of statistical uncertainty that comes with the data (e.g., small sample). Bayesian point estimates were also more accurate than non-Bayesian estimates. The results illustrate the importance of analyzing coverage and bias of interval estimates, and how ignoring interval estimates can be misleading. Therefore, editors and policymakers should continue to emphasize the inclusion of interval estimates in research.

Iterative Bayesian Estimation of Travel Times on Urban Arterials: Fusing Loop Detector and Probe Vehicle Data.

PubMed

Liu, Kai; Cui, Meng-Ying; Cao, Peng; Wang, Jiang-Bo

2016-01-01

On urban arterials, travel time estimation is challenging especially from various data sources. Typically, fusing loop detector data and probe vehicle data to estimate travel time is a troublesome issue while considering the data issue of uncertain, imprecise and even conflicting. In this paper, we propose an improved data fusing methodology for link travel time estimation. Link travel times are simultaneously pre-estimated using loop detector data and probe vehicle data, based on which Bayesian fusion is then applied to fuse the estimated travel times. Next, Iterative Bayesian estimation is proposed to improve Bayesian fusion by incorporating two strategies: 1) substitution strategy which replaces the lower accurate travel time estimation from one sensor with the current fused travel time; and 2) specially-designed conditions for convergence which restrict the estimated travel time in a reasonable range. The estimation results show that, the proposed method outperforms probe vehicle data based method, loop detector based method and single Bayesian fusion, and the mean absolute percentage error is reduced to 4.8%. Additionally, iterative Bayesian estimation performs better for lighter traffic flows when the variability of travel time is practically higher than other periods.

Iterative Bayesian Estimation of Travel Times on Urban Arterials: Fusing Loop Detector and Probe Vehicle Data

PubMed Central

Cui, Meng-Ying; Cao, Peng; Wang, Jiang-Bo

2016-01-01

On urban arterials, travel time estimation is challenging especially from various data sources. Typically, fusing loop detector data and probe vehicle data to estimate travel time is a troublesome issue while considering the data issue of uncertain, imprecise and even conflicting. In this paper, we propose an improved data fusing methodology for link travel time estimation. Link travel times are simultaneously pre-estimated using loop detector data and probe vehicle data, based on which Bayesian fusion is then applied to fuse the estimated travel times. Next, Iterative Bayesian estimation is proposed to improve Bayesian fusion by incorporating two strategies: 1) substitution strategy which replaces the lower accurate travel time estimation from one sensor with the current fused travel time; and 2) specially-designed conditions for convergence which restrict the estimated travel time in a reasonable range. The estimation results show that, the proposed method outperforms probe vehicle data based method, loop detector based method and single Bayesian fusion, and the mean absolute percentage error is reduced to 4.8%. Additionally, iterative Bayesian estimation performs better for lighter traffic flows when the variability of travel time is practically higher than other periods. PMID:27362654

Estimating neural response functions from fMRI

PubMed Central

Kumar, Sukhbinder; Penny, William

2014-01-01

This paper proposes a methodology for estimating Neural Response Functions (NRFs) from fMRI data. These NRFs describe non-linear relationships between experimental stimuli and neuronal population responses. The method is based on a two-stage model comprising an NRF and a Hemodynamic Response Function (HRF) that are simultaneously fitted to fMRI data using a Bayesian optimization algorithm. This algorithm also produces a model evidence score, providing a formal model comparison method for evaluating alternative NRFs. The HRF is characterized using previously established “Balloon” and BOLD signal models. We illustrate the method with two example applications based on fMRI studies of the auditory system. In the first, we estimate the time constants of repetition suppression and facilitation, and in the second we estimate the parameters of population receptive fields in a tonotopic mapping study. PMID:24847246

A Bayesian-based two-stage inexact optimization method for supporting stream water quality management in the Three Gorges Reservoir region.

PubMed

Hu, X H; Li, Y P; Huang, G H; Zhuang, X W; Ding, X W

2016-05-01

In this study, a Bayesian-based two-stage inexact optimization (BTIO) method is developed for supporting water quality management through coupling Bayesian analysis with interval two-stage stochastic programming (ITSP). The BTIO method is capable of addressing uncertainties caused by insufficient inputs in water quality model as well as uncertainties expressed as probabilistic distributions and interval numbers. The BTIO method is applied to a real case of water quality management for the Xiangxi River basin in the Three Gorges Reservoir region to seek optimal water quality management schemes under various uncertainties. Interval solutions for production patterns under a range of probabilistic water quality constraints have been generated. Results obtained demonstrate compromises between the system benefit and the system failure risk due to inherent uncertainties that exist in various system components. Moreover, information about pollutant emission is accomplished, which would help managers to adjust production patterns of regional industry and local policies considering interactions of water quality requirement, economic benefit, and industry structure.

Quantifying the Uncertainty in Discharge Data Using Hydraulic Knowledge and Uncertain Gaugings

NASA Astrophysics Data System (ADS)

Renard, B.; Le Coz, J.; Bonnifait, L.; Branger, F.; Le Boursicaud, R.; Horner, I.; Mansanarez, V.; Lang, M.

2014-12-01

River discharge is a crucial variable for Hydrology: as the output variable of most hydrologic models, it is used for sensitivity analyses, model structure identification, parameter estimation, data assimilation, prediction, etc. A major difficulty stems from the fact that river discharge is not measured continuously. Instead, discharge time series used by hydrologists are usually based on simple stage-discharge relations (rating curves) calibrated using a set of direct stage-discharge measurements (gaugings). In this presentation, we present a Bayesian approach to build such hydrometric rating curves, to estimate the associated uncertainty and to propagate this uncertainty to discharge time series. The three main steps of this approach are described: (1) Hydraulic analysis: identification of the hydraulic controls that govern the stage-discharge relation, identification of the rating curve equation and specification of prior distributions for the rating curve parameters; (2) Rating curve estimation: Bayesian inference of the rating curve parameters, accounting for the individual uncertainties of available gaugings, which often differ according to the discharge measurement procedure and the flow conditions; (3) Uncertainty propagation: quantification of the uncertainty in discharge time series, accounting for both the rating curve uncertainties and the uncertainty of recorded stage values. In addition, we also discuss current research activities, including the treatment of non-univocal stage-discharge relationships (e.g. due to hydraulic hysteresis, vegetation growth, sudden change of the geometry of the section, etc.).

Bayesian analysis of stage-fall-discharge rating curves and their uncertainties

NASA Astrophysics Data System (ADS)

Mansanarez, Valentin; Le Coz, Jérôme; Renard, Benjamin; Lang, Michel; Pierrefeu, Gilles; Le Boursicaud, Raphaël; Pobanz, Karine

2016-04-01

Stage-fall-discharge (SFD) rating curves are traditionally used to compute streamflow records at sites where the energy slope of the flow is variable due to variable backwater effects. Building on existing Bayesian approaches, we introduce an original hydraulics-based method for developing SFD rating curves used at twin gauge stations and estimating their uncertainties. Conventional power functions for channel and section controls are used, and transition to a backwater-affected channel control is computed based on a continuity condition, solved either analytically or numerically. The difference between the reference levels at the two stations is estimated as another uncertain parameter of the SFD model. The method proposed in this presentation incorporates information from both the hydraulic knowledge (equations of channel or section controls) and the information available in the stage-fall-discharge observations (gauging data). The obtained total uncertainty combines the parametric uncertainty and the remnant uncertainty related to the model of rating curve. This method provides a direct estimation of the physical inputs of the rating curve (roughness, width, slope bed, distance between twin gauges, etc.). The performance of the new method is tested using an application case affected by the variable backwater of a run-of-the-river dam: the Rhône river at Valence, France. In particular, a sensitivity analysis to the prior information and to the gauging dataset is performed. At that site, the stage-fall-discharge domain is well documented with gaugings conducted over a range of backwater affected and unaffected conditions. The performance of the new model was deemed to be satisfactory. Notably, transition to uniform flow when the overall range of the auxiliary stage is gauged is correctly simulated. The resulting curves are in good agreement with the observations (gaugings) and their uncertainty envelopes are acceptable for computing streamflow records. Similar conclusions were drawn from the application to other similar sites.

Estimation of post-test probabilities by residents: Bayesian reasoning versus heuristics?

PubMed

Hall, Stacey; Phang, Sen Han; Schaefer, Jeffrey P; Ghali, William; Wright, Bruce; McLaughlin, Kevin

2014-08-01

Although the process of diagnosing invariably begins with a heuristic, we encourage our learners to support their diagnoses by analytical cognitive processes, such as Bayesian reasoning, in an attempt to mitigate the effects of heuristics on diagnosing. There are, however, limited data on the use ± impact of Bayesian reasoning on the accuracy of disease probability estimates. In this study our objective was to explore whether Internal Medicine residents use a Bayesian process to estimate disease probabilities by comparing their disease probability estimates to literature-derived Bayesian post-test probabilities. We gave 35 Internal Medicine residents four clinical vignettes in the form of a referral letter and asked them to estimate the post-test probability of the target condition in each case. We then compared these to literature-derived probabilities. For each vignette the estimated probability was significantly different from the literature-derived probability. For the two cases with low literature-derived probability our participants significantly overestimated the probability of these target conditions being the correct diagnosis, whereas for the two cases with high literature-derived probability the estimated probability was significantly lower than the calculated value. Our results suggest that residents generate inaccurate post-test probability estimates. Possible explanations for this include ineffective application of Bayesian reasoning, attribute substitution whereby a complex cognitive task is replaced by an easier one (e.g., a heuristic), or systematic rater bias, such as central tendency bias. Further studies are needed to identify the reasons for inaccuracy of disease probability estimates and to explore ways of improving accuracy.

Bayesian analysis and classification of two Enzyme-Linked Immunosorbent Assay (ELISA) tests without a gold standard

PubMed Central

Zhang, Jingyang; Chaloner, Kathryn; McLinden, James H.; Stapleton, Jack T.

2013-01-01

Reconciling two quantitative ELISA tests for an antibody to an RNA virus, in a situation without a gold standard and where false negatives may occur, is the motivation for this work. False negatives occur when access of the antibody to the binding site is blocked. Based on the mechanism of the assay, a mixture of four bivariate normal distributions is proposed with the mixture probabilities depending on a two-stage latent variable model including the prevalence of the antibody in the population and the probabilities of blocking on each test. There is prior information on the prevalence of the antibody, and also on the probability of false negatives, and so a Bayesian analysis is used. The dependence between the two tests is modeled to be consistent with the biological mechanism. Bayesian decision theory is utilized for classification. The proposed method is applied to the motivating data set to classify the data into two groups: those with and those without the antibody. Simulation studies describe the properties of the estimation and the classification. Sensitivity to the choice of the prior distribution is also addressed by simulation. The same model with two levels of latent variables is applicable in other testing procedures such as quantitative polymerase chain reaction tests where false negatives occur when there is a mutation in the primer sequence. PMID:23592433

Unification of field theory and maximum entropy methods for learning probability densities

NASA Astrophysics Data System (ADS)

Kinney, Justin B.

2015-09-01

The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship between them has remained unclear. Here I unify these two methods by showing that every maximum entropy density estimate can be recovered in the infinite smoothness limit of an appropriate Bayesian field theory. I also show that Bayesian field theory estimation can be performed without imposing any boundary conditions on candidate densities, and that the infinite smoothness limit of these theories recovers the most common types of maximum entropy estimates. Bayesian field theory thus provides a natural test of the maximum entropy null hypothesis and, furthermore, returns an alternative (lower entropy) density estimate when the maximum entropy hypothesis is falsified. The computations necessary for this approach can be performed rapidly for one-dimensional data, and software for doing this is provided.

Unification of field theory and maximum entropy methods for learning probability densities.

PubMed

Kinney, Justin B

2015-09-01

The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship between them has remained unclear. Here I unify these two methods by showing that every maximum entropy density estimate can be recovered in the infinite smoothness limit of an appropriate Bayesian field theory. I also show that Bayesian field theory estimation can be performed without imposing any boundary conditions on candidate densities, and that the infinite smoothness limit of these theories recovers the most common types of maximum entropy estimates. Bayesian field theory thus provides a natural test of the maximum entropy null hypothesis and, furthermore, returns an alternative (lower entropy) density estimate when the maximum entropy hypothesis is falsified. The computations necessary for this approach can be performed rapidly for one-dimensional data, and software for doing this is provided.

Bayesian Estimation of Combined Accuracy for Tests with Verification Bias

PubMed Central

Broemeling, Lyle D.

2011-01-01

This presentation will emphasize the estimation of the combined accuracy of two or more tests when verification bias is present. Verification bias occurs when some of the subjects are not subject to the gold standard. The approach is Bayesian where the estimation of test accuracy is based on the posterior distribution of the relevant parameter. Accuracy of two combined binary tests is estimated employing either “believe the positive” or “believe the negative” rule, then the true and false positive fractions for each rule are computed for two tests. In order to perform the analysis, the missing at random assumption is imposed, and an interesting example is provided by estimating the combined accuracy of CT and MRI to diagnose lung cancer. The Bayesian approach is extended to two ordinal tests when verification bias is present, and the accuracy of the combined tests is based on the ROC area of the risk function. An example involving mammography with two readers with extreme verification bias illustrates the estimation of the combined test accuracy for ordinal tests. PMID:26859487

Propagation of stage measurement uncertainties to streamflow time series

NASA Astrophysics Data System (ADS)

Horner, Ivan; Le Coz, Jérôme; Renard, Benjamin; Branger, Flora; McMillan, Hilary

2016-04-01

Streamflow uncertainties due to stage measurements errors are generally overlooked in the promising probabilistic approaches that have emerged in the last decade. We introduce an original error model for propagating stage uncertainties through a stage-discharge rating curve within a Bayesian probabilistic framework. The method takes into account both rating curve (parametric errors and structural errors) and stage uncertainty (systematic and non-systematic errors). Practical ways to estimate the different types of stage errors are also presented: (1) non-systematic errors due to instrument resolution and precision and non-stationary waves and (2) systematic errors due to gauge calibration against the staff gauge. The method is illustrated at a site where the rating-curve-derived streamflow can be compared with an accurate streamflow reference. The agreement between the two time series is overall satisfying. Moreover, the quantification of uncertainty is also satisfying since the streamflow reference is compatible with the streamflow uncertainty intervals derived from the rating curve and the stage uncertainties. Illustrations from other sites are also presented. Results are much contrasted depending on the site features. In some cases, streamflow uncertainty is mainly due to stage measurement errors. The results also show the importance of discriminating systematic and non-systematic stage errors, especially for long term flow averages. Perspectives for improving and validating the streamflow uncertainty estimates are eventually discussed.

Two-stage Bayesian model to evaluate the effect of air pollution on chronic respiratory diseases using drug prescriptions.

PubMed

Blangiardo, Marta; Finazzi, Francesco; Cameletti, Michela

2016-08-01

Exposure to high levels of air pollutant concentration is known to be associated with respiratory problems which can translate into higher morbidity and mortality rates. The link between air pollution and population health has mainly been assessed considering air quality and hospitalisation or mortality data. However, this approach limits the analysis to individuals characterised by severe conditions. In this paper we evaluate the link between air pollution and respiratory diseases using general practice drug prescriptions for chronic respiratory diseases, which allow to draw conclusions based on the general population. We propose a two-stage statistical approach: in the first stage we specify a space-time model to estimate the monthly NO2 concentration integrating several data sources characterised by different spatio-temporal resolution; in the second stage we link the concentration to the β2-agonists prescribed monthly by general practices in England and we model the prescription rates through a small area approach. Copyright © 2016 Elsevier Ltd. All rights reserved.

Quantum state estimation when qubits are lost: a no-data-left-behind approach

DOE PAGES

Williams, Brian P.; Lougovski, Pavel

2017-04-06

We present an approach to Bayesian mean estimation of quantum states using hyperspherical parametrization and an experiment-specific likelihood which allows utilization of all available data, even when qubits are lost. With this method, we report the first closed-form Bayesian mean and maximum likelihood estimates for the ideal single qubit. Due to computational constraints, we utilize numerical sampling to determine the Bayesian mean estimate for a photonic two-qubit experiment in which our novel analysis reduces burdens associated with experimental asymmetries and inefficiencies. This method can be applied to quantum states of any dimension and experimental complexity.

Construction cost estimation of spherical storage tanks: artificial neural networks and hybrid regression—GA algorithms

NASA Astrophysics Data System (ADS)

Arabzadeh, Vida; Niaki, S. T. A.; Arabzadeh, Vahid

2017-10-01

One of the most important processes in the early stages of construction projects is to estimate the cost involved. This process involves a wide range of uncertainties, which make it a challenging task. Because of unknown issues, using the experience of the experts or looking for similar cases are the conventional methods to deal with cost estimation. The current study presents data-driven methods for cost estimation based on the application of artificial neural network (ANN) and regression models. The learning algorithms of the ANN are the Levenberg-Marquardt and the Bayesian regulated. Moreover, regression models are hybridized with a genetic algorithm to obtain better estimates of the coefficients. The methods are applied in a real case, where the input parameters of the models are assigned based on the key issues involved in a spherical tank construction. The results reveal that while a high correlation between the estimated cost and the real cost exists; both ANNs could perform better than the hybridized regression models. In addition, the ANN with the Levenberg-Marquardt learning algorithm (LMNN) obtains a better estimation than the ANN with the Bayesian-regulated learning algorithm (BRNN). The correlation between real data and estimated values is over 90%, while the mean square error is achieved around 0.4. The proposed LMNN model can be effective to reduce uncertainty and complexity in the early stages of the construction project.

Direct Estimation of Optical Parameters From Photoacoustic Time Series in Quantitative Photoacoustic Tomography.

PubMed

Pulkkinen, Aki; Cox, Ben T; Arridge, Simon R; Goh, Hwan; Kaipio, Jari P; Tarvainen, Tanja

2016-11-01

Estimation of optical absorption and scattering of a target is an inverse problem associated with quantitative photoacoustic tomography. Conventionally, the problem is expressed as two folded. First, images of initial pressure distribution created by absorption of a light pulse are formed based on acoustic boundary measurements. Then, the optical properties are determined based on these photoacoustic images. The optical stage of the inverse problem can thus suffer from, for example, artefacts caused by the acoustic stage. These could be caused by imperfections in the acoustic measurement setting, of which an example is a limited view acoustic measurement geometry. In this work, the forward model of quantitative photoacoustic tomography is treated as a coupled acoustic and optical model and the inverse problem is solved by using a Bayesian approach. Spatial distribution of the optical properties of the imaged target are estimated directly from the photoacoustic time series in varying acoustic detection and optical illumination configurations. It is numerically demonstrated, that estimation of optical properties of the imaged target is feasible in limited view acoustic detection setting.

Influence of erroneous patient records on population pharmacokinetic modeling and individual bayesian estimation.

PubMed

van der Meer, Aize Franciscus; Touw, Daniël J; Marcus, Marco A E; Neef, Cornelis; Proost, Johannes H

2012-10-01

Observational data sets can be used for population pharmacokinetic (PK) modeling. However, these data sets are generally less precisely recorded than experimental data sets. This article aims to investigate the influence of erroneous records on population PK modeling and individual maximum a posteriori Bayesian (MAPB) estimation. A total of 1123 patient records of neonates who were administered vancomycin were used for population PK modeling by iterative 2-stage Bayesian (ITSB) analysis. Cut-off values for weighted residuals were tested for exclusion of records from the analysis. A simulation study was performed to assess the influence of erroneous records on population modeling and individual MAPB estimation. Also the cut-off values for weighted residuals were tested in the simulation study. Errors in registration have limited the influence on outcomes of population PK modeling but can have detrimental effects on individual MAPB estimation. A population PK model created from a data set with many registration errors has little influence on subsequent MAPB estimates for precisely recorded data. A weighted residual value of 2 for concentration measurements has good discriminative power for identification of erroneous records. ITSB analysis and its individual estimates are hardly affected by most registration errors. Large registration errors can be detected by weighted residuals of concentration.

Characterization of background concentrations of contaminants using a mixture of normal distributions.

PubMed

Qian, Song S; Lyons, Regan E

2006-10-01

We present a Bayesian approach for characterizing background contaminant concentration distributions using data from sites that may have been contaminated. Our method, focused on estimation, resolves several technical problems of the existing methods sanctioned by the U.S. Environmental Protection Agency (USEPA) (a hypothesis testing based method), resulting in a simple and quick procedure for estimating background contaminant concentrations. The proposed Bayesian method is applied to two data sets from a federal facility regulated under the Resource Conservation and Restoration Act. The results are compared to background distributions identified using existing methods recommended by the USEPA. The two data sets represent low and moderate levels of censorship in the data. Although an unbiased estimator is elusive, we show that the proposed Bayesian estimation method will have a smaller bias than the EPA recommended method.

A Bayesian hierarchical model with novel prior specifications for estimating HIV testing rates

PubMed Central

An, Qian; Kang, Jian; Song, Ruiguang; Hall, H. Irene

2016-01-01

Human immunodeficiency virus (HIV) infection is a severe infectious disease actively spreading globally, and acquired immunodeficiency syndrome (AIDS) is an advanced stage of HIV infection. The HIV testing rate, that is, the probability that an AIDS-free HIV infected person seeks a test for HIV during a particular time interval, given no previous positive test has been obtained prior to the start of the time, is an important parameter for public health. In this paper, we propose a Bayesian hierarchical model with two levels of hierarchy to estimate the HIV testing rate using annual AIDS and AIDS-free HIV diagnoses data. At level one, we model the latent number of HIV infections for each year using a Poisson distribution with the intensity parameter representing the HIV incidence rate. At level two, the annual numbers of AIDS and AIDS-free HIV diagnosed cases and all undiagnosed cases stratified by the HIV infections at different years are modeled using a multinomial distribution with parameters including the HIV testing rate. We propose a new class of priors for the HIV incidence rate and HIV testing rate taking into account the temporal dependence of these parameters to improve the estimation accuracy. We develop an efficient posterior computation algorithm based on the adaptive rejection metropolis sampling technique. We demonstrate our model using simulation studies and the analysis of the national HIV surveillance data in the USA. PMID:26567891

Multiple Imputation in Two-Stage Cluster Samples Using The Weighted Finite Population Bayesian Bootstrap.

PubMed

Zhou, Hanzhi; Elliott, Michael R; Raghunathan, Trivellore E

2016-06-01

Multistage sampling is often employed in survey samples for cost and convenience. However, accounting for clustering features when generating datasets for multiple imputation is a nontrivial task, particularly when, as is often the case, cluster sampling is accompanied by unequal probabilities of selection, necessitating case weights. Thus, multiple imputation often ignores complex sample designs and assumes simple random sampling when generating imputations, even though failing to account for complex sample design features is known to yield biased estimates and confidence intervals that have incorrect nominal coverage. In this article, we extend a recently developed, weighted, finite-population Bayesian bootstrap procedure to generate synthetic populations conditional on complex sample design data that can be treated as simple random samples at the imputation stage, obviating the need to directly model design features for imputation. We develop two forms of this method: one where the probabilities of selection are known at the first and second stages of the design, and the other, more common in public use files, where only the final weight based on the product of the two probabilities is known. We show that this method has advantages in terms of bias, mean square error, and coverage properties over methods where sample designs are ignored, with little loss in efficiency, even when compared with correct fully parametric models. An application is made using the National Automotive Sampling System Crashworthiness Data System, a multistage, unequal probability sample of U.S. passenger vehicle crashes, which suffers from a substantial amount of missing data in "Delta-V," a key crash severity measure.

Multiple Imputation in Two-Stage Cluster Samples Using The Weighted Finite Population Bayesian Bootstrap

PubMed Central

Zhou, Hanzhi; Elliott, Michael R.; Raghunathan, Trivellore E.

2017-01-01

Multistage sampling is often employed in survey samples for cost and convenience. However, accounting for clustering features when generating datasets for multiple imputation is a nontrivial task, particularly when, as is often the case, cluster sampling is accompanied by unequal probabilities of selection, necessitating case weights. Thus, multiple imputation often ignores complex sample designs and assumes simple random sampling when generating imputations, even though failing to account for complex sample design features is known to yield biased estimates and confidence intervals that have incorrect nominal coverage. In this article, we extend a recently developed, weighted, finite-population Bayesian bootstrap procedure to generate synthetic populations conditional on complex sample design data that can be treated as simple random samples at the imputation stage, obviating the need to directly model design features for imputation. We develop two forms of this method: one where the probabilities of selection are known at the first and second stages of the design, and the other, more common in public use files, where only the final weight based on the product of the two probabilities is known. We show that this method has advantages in terms of bias, mean square error, and coverage properties over methods where sample designs are ignored, with little loss in efficiency, even when compared with correct fully parametric models. An application is made using the National Automotive Sampling System Crashworthiness Data System, a multistage, unequal probability sample of U.S. passenger vehicle crashes, which suffers from a substantial amount of missing data in “Delta-V,” a key crash severity measure. PMID:29226161

Accounting for standard errors of vision-specific latent trait in regression models.

PubMed

Wong, Wan Ling; Li, Xiang; Li, Jialiang; Wong, Tien Yin; Cheng, Ching-Yu; Lamoureux, Ecosse L

2014-07-11

To demonstrate the effectiveness of Hierarchical Bayesian (HB) approach in a modeling framework for association effects that accounts for SEs of vision-specific latent traits assessed using Rasch analysis. A systematic literature review was conducted in four major ophthalmic journals to evaluate Rasch analysis performed on vision-specific instruments. The HB approach was used to synthesize the Rasch model and multiple linear regression model for the assessment of the association effects related to vision-specific latent traits. The effectiveness of this novel HB one-stage "joint-analysis" approach allows all model parameters to be estimated simultaneously and was compared with the frequently used two-stage "separate-analysis" approach in our simulation study (Rasch analysis followed by traditional statistical analyses without adjustment for SE of latent trait). Sixty-six reviewed articles performed evaluation and validation of vision-specific instruments using Rasch analysis, and 86.4% (n = 57) performed further statistical analyses on the Rasch-scaled data using traditional statistical methods; none took into consideration SEs of the estimated Rasch-scaled scores. The two models on real data differed for effect size estimations and the identification of "independent risk factors." Simulation results showed that our proposed HB one-stage "joint-analysis" approach produces greater accuracy (average of 5-fold decrease in bias) with comparable power and precision in estimation of associations when compared with the frequently used two-stage "separate-analysis" procedure despite accounting for greater uncertainty due to the latent trait. Patient-reported data, using Rasch analysis techniques, do not take into account the SE of latent trait in association analyses. The HB one-stage "joint-analysis" is a better approach, producing accurate effect size estimations and information about the independent association of exposure variables with vision-specific latent traits. Copyright 2014 The Association for Research in Vision and Ophthalmology, Inc.

Bayesian Estimation of the True Prevalence and of the Diagnostic Test Sensitivity and Specificity of Enteropathogenic Yersinia in Finnish Pig Serum Samples.

PubMed

Vilar, M J; Ranta, J; Virtanen, S; Korkeala, H

2015-01-01

Bayesian analysis was used to estimate the pig's and herd's true prevalence of enteropathogenic Yersinia in serum samples collected from Finnish pig farms. The sensitivity and specificity of the diagnostic test were also estimated for the commercially available ELISA which is used for antibody detection against enteropathogenic Yersinia. The Bayesian analysis was performed in two steps; the first step estimated the prior true prevalence of enteropathogenic Yersinia with data obtained from a systematic review of the literature. In the second step, data of the apparent prevalence (cross-sectional study data), prior true prevalence (first step), and estimated sensitivity and specificity of the diagnostic methods were used for building the Bayesian model. The true prevalence of Yersinia in slaughter-age pigs was 67.5% (95% PI 63.2-70.9). The true prevalence of Yersinia in sows was 74.0% (95% PI 57.3-82.4). The estimates of sensitivity and specificity values of the ELISA were 79.5% and 96.9%.

Tree Biomass Estimation of Chinese fir (Cunninghamia lanceolata) Based on Bayesian Method

PubMed Central

Zhang, Jianguo

2013-01-01

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass. PMID:24278198

Tree biomass estimation of Chinese fir (Cunninghamia lanceolata) based on Bayesian method.

PubMed

Zhang, Xiongqing; Duan, Aiguo; Zhang, Jianguo

2013-01-01

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation W = a(D2H)b was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass.

Rediscovery of Good-Turing estimators via Bayesian nonparametrics.

PubMed

Favaro, Stefano; Nipoti, Bernardo; Teh, Yee Whye

2016-03-01

The problem of estimating discovery probabilities originated in the context of statistical ecology, and in recent years it has become popular due to its frequent appearance in challenging applications arising in genetics, bioinformatics, linguistics, designs of experiments, machine learning, etc. A full range of statistical approaches, parametric and nonparametric as well as frequentist and Bayesian, has been proposed for estimating discovery probabilities. In this article, we investigate the relationships between the celebrated Good-Turing approach, which is a frequentist nonparametric approach developed in the 1940s, and a Bayesian nonparametric approach recently introduced in the literature. Specifically, under the assumption of a two parameter Poisson-Dirichlet prior, we show that Bayesian nonparametric estimators of discovery probabilities are asymptotically equivalent, for a large sample size, to suitably smoothed Good-Turing estimators. As a by-product of this result, we introduce and investigate a methodology for deriving exact and asymptotic credible intervals to be associated with the Bayesian nonparametric estimators of discovery probabilities. The proposed methodology is illustrated through a comprehensive simulation study and the analysis of Expressed Sequence Tags data generated by sequencing a benchmark complementary DNA library. © 2015, The International Biometric Society.

Magnetic resonance elastography is as accurate as liver biopsy for liver fibrosis staging.

PubMed

Morisaka, Hiroyuki; Motosugi, Utaroh; Ichikawa, Shintaro; Nakazawa, Tadao; Kondo, Tetsuo; Funayama, Satoshi; Matsuda, Masanori; Ichikawa, Tomoaki; Onishi, Hiroshi

2018-05-01

Liver MR elastography (MRE) is available for the noninvasive assessment of liver fibrosis; however, no previous studies have compared the diagnostic ability of MRE with that of liver biopsy. To compare the diagnostic accuracy of liver fibrosis staging between MRE-based methods and liver biopsy using the resected liver specimens as the reference standard. A retrospective study at a single institution. In all, 200 patients who underwent preoperative MRE and subsequent surgical liver resection were included in this study. Data from 80 patients were used to estimate cutoff and distributions of liver stiffness values measured by MRE for each liver fibrosis stage (F0-F4, METAVIR system). In the remaining 120 patients, liver biopsy specimens were obtained from the resected liver tissues using a standard biopsy needle. 2D liver MRE with gradient-echo based sequence on a 1.5 or 3T scanner was used. Two radiologists independently measured the liver stiffness value on MRE and two types of MRE-based methods (threshold and Bayesian prediction method) were applied. Two pathologists evaluated all biopsy samples independently to stage liver fibrosis. Surgically resected whole tissue specimens were used as the reference standard. The accuracy for liver fibrosis staging was compared between liver biopsy and MRE-based methods with a modified McNemar's test. Accurate fibrosis staging was achieved in 53.3% (64/120) and 59.1% (71/120) of patients using MRE with threshold and Bayesian methods, respectively, and in 51.6% (62/120) with liver biopsy. Accuracies of MRE-based methods for diagnoses of ≥F2 (90-91% [108-9/120]), ≥F3 (79-81% [95-97/120]), and F4 (82-85% [98-102/120]) were statistically equivalent to those of liver biopsy (≥F2, 79% [95/120], P ≤ 0.01; ≥F3, 88% [105/120], P ≤ 0.006; and F4, 82% [99/120], P ≤ 0.017). MRE can be an alternative to liver biopsy for fibrosis staging. 3. Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2018;47:1268-1275. © 2017 International Society for Magnetic Resonance in Medicine.

A Real-Time Brain-Machine Interface Combining Motor Target and Trajectory Intent Using an Optimal Feedback Control Design

PubMed Central

Shanechi, Maryam M.; Williams, Ziv M.; Wornell, Gregory W.; Hu, Rollin C.; Powers, Marissa; Brown, Emery N.

2013-01-01

Real-time brain-machine interfaces (BMI) have focused on either estimating the continuous movement trajectory or target intent. However, natural movement often incorporates both. Additionally, BMIs can be modeled as a feedback control system in which the subject modulates the neural activity to move the prosthetic device towards a desired target while receiving real-time sensory feedback of the state of the movement. We develop a novel real-time BMI using an optimal feedback control design that jointly estimates the movement target and trajectory of monkeys in two stages. First, the target is decoded from neural spiking activity before movement initiation. Second, the trajectory is decoded by combining the decoded target with the peri-movement spiking activity using an optimal feedback control design. This design exploits a recursive Bayesian decoder that uses an optimal feedback control model of the sensorimotor system to take into account the intended target location and the sensory feedback in its trajectory estimation from spiking activity. The real-time BMI processes the spiking activity directly using point process modeling. We implement the BMI in experiments consisting of an instructed-delay center-out task in which monkeys are presented with a target location on the screen during a delay period and then have to move a cursor to it without touching the incorrect targets. We show that the two-stage BMI performs more accurately than either stage alone. Correct target prediction can compensate for inaccurate trajectory estimation and vice versa. The optimal feedback control design also results in trajectories that are smoother and have lower estimation error. The two-stage decoder also performs better than linear regression approaches in offline cross-validation analyses. Our results demonstrate the advantage of a BMI design that jointly estimates the target and trajectory of movement and more closely mimics the sensorimotor control system. PMID:23593130

A Bayesian predictive two-stage design for phase II clinical trials.

PubMed

Sambucini, Valeria

2008-04-15

In this paper, we propose a Bayesian two-stage design for phase II clinical trials, which represents a predictive version of the single threshold design (STD) recently introduced by Tan and Machin. The STD two-stage sample sizes are determined specifying a minimum threshold for the posterior probability that the true response rate exceeds a pre-specified target value and assuming that the observed response rate is slightly higher than the target. Unlike the STD, we do not refer to a fixed experimental outcome, but take into account the uncertainty about future data. In both stages, the design aims to control the probability of getting a large posterior probability that the true response rate exceeds the target value. Such a probability is expressed in terms of prior predictive distributions of the data. The performance of the design is based on the distinction between analysis and design priors, recently introduced in the literature. The properties of the method are studied when all the design parameters vary.

Bayesian estimation and use of high-throughput remote sensing indices for quantitative genetic analyses of leaf growth.

PubMed

Baker, Robert L; Leong, Wen Fung; An, Nan; Brock, Marcus T; Rubin, Matthew J; Welch, Stephen; Weinig, Cynthia

2018-02-01

We develop Bayesian function-valued trait models that mathematically isolate genetic mechanisms underlying leaf growth trajectories by factoring out genotype-specific differences in photosynthesis. Remote sensing data can be used instead of leaf-level physiological measurements. Characterizing the genetic basis of traits that vary during ontogeny and affect plant performance is a major goal in evolutionary biology and agronomy. Describing genetic programs that specifically regulate morphological traits can be complicated by genotypic differences in physiological traits. We describe the growth trajectories of leaves using novel Bayesian function-valued trait (FVT) modeling approaches in Brassica rapa recombinant inbred lines raised in heterogeneous field settings. While frequentist approaches estimate parameter values by treating each experimental replicate discretely, Bayesian models can utilize information in the global dataset, potentially leading to more robust trait estimation. We illustrate this principle by estimating growth asymptotes in the face of missing data and comparing heritabilities of growth trajectory parameters estimated by Bayesian and frequentist approaches. Using pseudo-Bayes factors, we compare the performance of an initial Bayesian logistic growth model and a model that incorporates carbon assimilation (A max ) as a cofactor, thus statistically accounting for genotypic differences in carbon resources. We further evaluate two remotely sensed spectroradiometric indices, photochemical reflectance (pri2) and MERIS Terrestrial Chlorophyll Index (mtci) as covariates in lieu of A max , because these two indices were genetically correlated with A max across years and treatments yet allow much higher throughput compared to direct leaf-level gas-exchange measurements. For leaf lengths in uncrowded settings, including A max improves model fit over the initial model. The mtci and pri2 indices also outperform direct A max measurements. Of particular importance for evolutionary biologists and plant breeders, hierarchical Bayesian models estimating FVT parameters improve heritabilities compared to frequentist approaches.

Bayesian inference of Calibration curves: application to archaeomagnetism

NASA Astrophysics Data System (ADS)

Lanos, P.

2003-04-01

The range of errors that occur at different stages of the archaeomagnetic calibration process are modelled using a Bayesian hierarchical model. The archaeomagnetic data obtained from archaeological structures such as hearths, kilns or sets of bricks and tiles, exhibit considerable experimental errors and are typically more or less well dated by archaeological context, history or chronometric methods (14C, TL, dendrochronology, etc.). They can also be associated with stratigraphic observations which provide prior relative chronological information. The modelling we describe in this paper allows all these observations, on materials from a given period, to be linked together, and the use of penalized maximum likelihood for smoothing univariate, spherical or three-dimensional time series data allows representation of the secular variation of the geomagnetic field over time. The smooth curve we obtain (which takes the form of a penalized natural cubic spline) provides an adaptation to the effects of variability in the density of reference points over time. Since our model takes account of all the known errors in the archaeomagnetic calibration process, we are able to obtain a functional highest-posterior-density envelope on the new curve. With this new posterior estimate of the curve available to us, the Bayesian statistical framework then allows us to estimate the calendar dates of undated archaeological features (such as kilns) based on one, two or three geomagnetic parameters (inclination, declination and/or intensity). Date estimates are presented in much the same way as those that arise from radiocarbon dating. In order to illustrate the model and inference methods used, we will present results based on German archaeomagnetic data recently published by a German team.

Testing students' e-learning via Facebook through Bayesian structural equation modeling.

PubMed

Salarzadeh Jenatabadi, Hashem; Moghavvemi, Sedigheh; Wan Mohamed Radzi, Che Wan Jasimah Bt; Babashamsi, Parastoo; Arashi, Mohammad

2017-01-01

Learning is an intentional activity, with several factors affecting students' intention to use new learning technology. Researchers have investigated technology acceptance in different contexts by developing various theories/models and testing them by a number of means. Although most theories/models developed have been examined through regression or structural equation modeling, Bayesian analysis offers more accurate data analysis results. To address this gap, the unified theory of acceptance and technology use in the context of e-learning via Facebook are re-examined in this study using Bayesian analysis. The data (S1 Data) were collected from 170 students enrolled in a business statistics course at University of Malaya, Malaysia, and tested with the maximum likelihood and Bayesian approaches. The difference between the two methods' results indicates that performance expectancy and hedonic motivation are the strongest factors influencing the intention to use e-learning via Facebook. The Bayesian estimation model exhibited better data fit than the maximum likelihood estimator model. The results of the Bayesian and maximum likelihood estimator approaches are compared and the reasons for the result discrepancy are deliberated.

Testing students’ e-learning via Facebook through Bayesian structural equation modeling

PubMed Central

Moghavvemi, Sedigheh; Wan Mohamed Radzi, Che Wan Jasimah Bt; Babashamsi, Parastoo; Arashi, Mohammad

2017-01-01

Learning is an intentional activity, with several factors affecting students’ intention to use new learning technology. Researchers have investigated technology acceptance in different contexts by developing various theories/models and testing them by a number of means. Although most theories/models developed have been examined through regression or structural equation modeling, Bayesian analysis offers more accurate data analysis results. To address this gap, the unified theory of acceptance and technology use in the context of e-learning via Facebook are re-examined in this study using Bayesian analysis. The data (S1 Data) were collected from 170 students enrolled in a business statistics course at University of Malaya, Malaysia, and tested with the maximum likelihood and Bayesian approaches. The difference between the two methods’ results indicates that performance expectancy and hedonic motivation are the strongest factors influencing the intention to use e-learning via Facebook. The Bayesian estimation model exhibited better data fit than the maximum likelihood estimator model. The results of the Bayesian and maximum likelihood estimator approaches are compared and the reasons for the result discrepancy are deliberated. PMID:28886019

Phylogeography of the Western Lyresnake (Trimorphodon biscutatus): testing aridland biogeographical hypotheses across the Nearctic-Neotropical transition.

PubMed

Devitt, Thomas J

2006-12-01

The Western Lyresnake (Trimorphodon biscutatus) is a widespread, polytypic taxon inhabiting arid regions from the warm deserts of the southwestern United States southward along the Pacific versant of Mexico to the tropical deciduous forests of Mesoamerica. This broadly distributed species provides a unique opportunity to evaluate a priori biogeographical hypotheses spanning two major distinct biogeographical realms (the Nearctic and Neotropical) that are usually treated separately in phylogeographical analyses. I investigated the phylogeography of T. biscutatus using maximum likelihood and Bayesian phylogenetic analysis of mitochondrial DNA (mtDNA) from across this species' range. Phylogenetic analyses recovered five well-supported clades whose boundaries are concordant with existing geographical barriers, a pattern consistent with a model of vicariant allopatric divergence. Assuming a vicariance model, divergence times between mitochondrial lineages were estimated using Bayesian relaxed molecular clock methods calibrated using geological information from putative vicariant events. Divergence time point estimates were bounded by broad confidence intervals, and thus these highly conservative estimates should be considered tentative hypotheses at best. Comparison of mtDNA lineages and taxa traditionally recognized as subspecies based on morphology suggest this taxon is comprised of multiple independent lineages at various stages of divergence, ranging from putative secondary contact and hybridization to sympatry of 'subspecies'.

A two-stage model in a Bayesian framework to estimate a survival endpoint in the presence of confounding by indication.

PubMed

Bellera, Carine; Proust-Lima, Cécile; Joseph, Lawrence; Richaud, Pierre; Taylor, Jeremy; Sandler, Howard; Hanley, James; Mathoulin-Pélissier, Simone

2018-04-01

Background Biomarker series can indicate disease progression and predict clinical endpoints. When a treatment is prescribed depending on the biomarker, confounding by indication might be introduced if the treatment modifies the marker profile and risk of failure. Objective Our aim was to highlight the flexibility of a two-stage model fitted within a Bayesian Markov Chain Monte Carlo framework. For this purpose, we monitored the prostate-specific antigens in prostate cancer patients treated with external beam radiation therapy. In the presence of rising prostate-specific antigens after external beam radiation therapy, salvage hormone therapy can be prescribed to reduce both the prostate-specific antigens concentration and the risk of clinical failure, an illustration of confounding by indication. We focused on the assessment of the prognostic value of hormone therapy and prostate-specific antigens trajectory on the risk of failure. Methods We used a two-stage model within a Bayesian framework to assess the role of the prostate-specific antigens profile on clinical failure while accounting for a secondary treatment prescribed by indication. We modeled prostate-specific antigens using a hierarchical piecewise linear trajectory with a random changepoint. Residual prostate-specific antigens variability was expressed as a function of prostate-specific antigens concentration. Covariates in the survival model included hormone therapy, baseline characteristics, and individual predictions of the prostate-specific antigens nadir and timing and prostate-specific antigens slopes before and after the nadir as provided by the longitudinal process. Results We showed positive associations between an increased prostate-specific antigens nadir, an earlier changepoint and a steeper post-nadir slope with an increased risk of failure. Importantly, we highlighted a significant benefit of hormone therapy, an effect that was not observed when the prostate-specific antigens trajectory was not accounted for in the survival model. Conclusion Our modeling strategy was particularly flexible and accounted for multiple complex features of longitudinal and survival data, including the presence of a random changepoint and a time-dependent covariate.

A Bayesian Approach for Evaluation of Determinants of Health System Efficiency Using Stochastic Frontier Analysis and Beta Regression.

PubMed

Şenel, Talat; Cengiz, Mehmet Ali

2016-01-01

In today's world, Public expenditures on health are one of the most important issues for governments. These increased expenditures are putting pressure on public budgets. Therefore, health policy makers have focused on the performance of their health systems and many countries have introduced reforms to improve the performance of their health systems. This study investigates the most important determinants of healthcare efficiency for OECD countries using second stage approach for Bayesian Stochastic Frontier Analysis (BSFA). There are two steps in this study. First we measure 29 OECD countries' healthcare efficiency by BSFA using the data from the OECD Health Database. At second stage, we expose the multiple relationships between the healthcare efficiency and characteristics of healthcare systems across OECD countries using Bayesian beta regression.

Bayesian analysis of stage-fall-discharge rating curves and their uncertainties

NASA Astrophysics Data System (ADS)

Mansanarez, V.; Le Coz, J.; Renard, B.; Lang, M.; Pierrefeu, G.; Vauchel, P.

2016-09-01

Stage-fall-discharge (SFD) rating curves are traditionally used to compute streamflow records at sites where the energy slope of the flow is variable due to variable backwater effects. We introduce a model with hydraulically interpretable parameters for estimating SFD rating curves and their uncertainties. Conventional power functions for channel and section controls are used. The transition to a backwater-affected channel control is computed based on a continuity condition, solved either analytically or numerically. The practical use of the method is demonstrated with two real twin-gauge stations, the Rhône River at Valence, France, and the Guthusbekken stream at station 0003ṡ0033, Norway. Those stations are typical of a channel control and a section control, respectively, when backwater-unaffected conditions apply. The performance of the method is investigated through sensitivity analysis to prior information on controls and to observations (i.e., available gaugings) for the station of Valence. These analyses suggest that precisely identifying SFD rating curves requires adapted gauging strategy and/or informative priors. The Madeira River, one of the largest tributaries of the Amazon, provides a challenging case typical of large, flat, tropical river networks where bed roughness can also be variable in addition to slope. In this case, the difference in staff gauge reference levels must be estimated as another uncertain parameter of the SFD model. The proposed Bayesian method is a valuable alternative solution to the graphical and empirical techniques still proposed in hydrometry guidance and standards.

Probabilistic models in human sensorimotor control

PubMed Central

Wolpert, Daniel M.

2009-01-01

Sensory and motor uncertainty form a fundamental constraint on human sensorimotor control. Bayesian decision theory (BDT) has emerged as a unifying framework to understand how the central nervous system performs optimal estimation and control in the face of such uncertainty. BDT has two components: Bayesian statistics and decision theory. Here we review Bayesian statistics and show how it applies to estimating the state of the world and our own body. Recent results suggest that when learning novel tasks we are able to learn the statistical properties of both the world and our own sensory apparatus so as to perform estimation using Bayesian statistics. We review studies which suggest that humans can combine multiple sources of information to form maximum likelihood estimates, can incorporate prior beliefs about possible states of the world so as to generate maximum a posteriori estimates and can use Kalman filter-based processes to estimate time-varying states. Finally, we review Bayesian decision theory in motor control and how the central nervous system processes errors to determine loss functions and optimal actions. We review results that suggest we plan movements based on statistics of our actions that result from signal-dependent noise on our motor outputs. Taken together these studies provide a statistical framework for how the motor system performs in the presence of uncertainty. PMID:17628731

Spatiotemporal Bayesian analysis of Lyme disease in New York state, 1990-2000.

PubMed

Chen, Haiyan; Stratton, Howard H; Caraco, Thomas B; White, Dennis J

2006-07-01

Mapping ordinarily increases our understanding of nontrivial spatial and temporal heterogeneities in disease rates. However, the large number of parameters required by the corresponding statistical models often complicates detailed analysis. This study investigates the feasibility of a fully Bayesian hierarchical regression approach to the problem and identifies how it outperforms two more popular methods: crude rate estimates (CRE) and empirical Bayes standardization (EBS). In particular, we apply a fully Bayesian approach to the spatiotemporal analysis of Lyme disease incidence in New York state for the period 1990-2000. These results are compared with those obtained by CRE and EBS in Chen et al. (2005). We show that the fully Bayesian regression model not only gives more reliable estimates of disease rates than the other two approaches but also allows for tractable models that can accommodate more numerous sources of variation and unknown parameters.

Numerical Demons in Monte Carlo Estimation of Bayesian Model Evidence with Application to Soil Respiration Models

NASA Astrophysics Data System (ADS)

Elshall, A. S.; Ye, M.; Niu, G. Y.; Barron-Gafford, G.

2016-12-01

Bayesian multimodel inference is increasingly being used in hydrology. Estimating Bayesian model evidence (BME) is of central importance in many Bayesian multimodel analysis such as Bayesian model averaging and model selection. BME is the overall probability of the model in reproducing the data, accounting for the trade-off between the goodness-of-fit and the model complexity. Yet estimating BME is challenging, especially for high dimensional problems with complex sampling space. Estimating BME using the Monte Carlo numerical methods is preferred, as the methods yield higher accuracy than semi-analytical solutions (e.g. Laplace approximations, BIC, KIC, etc.). However, numerical methods are prone the numerical demons arising from underflow of round off errors. Although few studies alluded to this issue, to our knowledge this is the first study that illustrates these numerical demons. We show that the precision arithmetic can become a threshold on likelihood values and Metropolis acceptance ratio, which results in trimming parameter regions (when likelihood function is less than the smallest floating point number that a computer can represent) and corrupting of the empirical measures of the random states of the MCMC sampler (when using log-likelihood function). We consider two of the most powerful numerical estimators of BME that are the path sampling method of thermodynamic integration (TI) and the importance sampling method of steppingstone sampling (SS). We also consider the two most widely used numerical estimators, which are the prior sampling arithmetic mean (AS) and posterior sampling harmonic mean (HM). We investigate the vulnerability of these four estimators to the numerical demons. Interesting, the most biased estimator, namely the HM, turned out to be the least vulnerable. While it is generally assumed that AM is a bias-free estimator that will always approximate the true BME by investing in computational effort, we show that arithmetic underflow can hamper AM resulting in severe underestimation of BME. TI turned out to be the most vulnerable, resulting in BME overestimation. Finally, we show how SS can be largely invariant to rounding errors, yielding the most accurate and computational efficient results. These research results are useful for MC simulations to estimate Bayesian model evidence.

A Bayesian hierarchical model with novel prior specifications for estimating HIV testing rates.

PubMed

An, Qian; Kang, Jian; Song, Ruiguang; Hall, H Irene

2016-04-30

Human immunodeficiency virus (HIV) infection is a severe infectious disease actively spreading globally, and acquired immunodeficiency syndrome (AIDS) is an advanced stage of HIV infection. The HIV testing rate, that is, the probability that an AIDS-free HIV infected person seeks a test for HIV during a particular time interval, given no previous positive test has been obtained prior to the start of the time, is an important parameter for public health. In this paper, we propose a Bayesian hierarchical model with two levels of hierarchy to estimate the HIV testing rate using annual AIDS and AIDS-free HIV diagnoses data. At level one, we model the latent number of HIV infections for each year using a Poisson distribution with the intensity parameter representing the HIV incidence rate. At level two, the annual numbers of AIDS and AIDS-free HIV diagnosed cases and all undiagnosed cases stratified by the HIV infections at different years are modeled using a multinomial distribution with parameters including the HIV testing rate. We propose a new class of priors for the HIV incidence rate and HIV testing rate taking into account the temporal dependence of these parameters to improve the estimation accuracy. We develop an efficient posterior computation algorithm based on the adaptive rejection metropolis sampling technique. We demonstrate our model using simulation studies and the analysis of the national HIV surveillance data in the USA. Copyright © 2015 John Wiley & Sons, Ltd.

Introducing Computed Tomography Standards for Age Estimation of Modern Australian Subadults Using Postnatal Ossification Timings of Select Cranial and Cervical Sites(.).

PubMed

Lottering, Nicolene; MacGregor, Donna M; Alston, Clair L; Watson, Debbie; Gregory, Laura S

2016-01-01

Contemporary, population-specific ossification timings of the cranium are lacking in current literature due to challenges in obtaining large repositories of documented subadult material, forcing Australian practitioners to rely on North American, arguably antiquated reference standards for age estimation. This study assessed the temporal pattern of ossification of the cranium and provides recalibrated probabilistic information for age estimation of modern Australian children. Fusion status of the occipital and frontal bones, atlas, and axis was scored using a modified two- to four-tier system from cranial/cervical DICOM datasets of 585 children aged birth to 10 years. Transition analysis was applied to elucidate maximum-likelihood estimates between consecutive fusion stages, in conjunction with Bayesian statistics to calculate credible intervals for age estimation. Results demonstrate significant sex differences in skeletal maturation (p < 0.05) and earlier timings in comparison with major literary sources, underscoring the requisite of updated standards for age estimation of modern individuals. © 2015 American Academy of Forensic Sciences.

Application of Bayesian Maximum Entropy Filter in parameter calibration of groundwater flow model in PingTung Plain

NASA Astrophysics Data System (ADS)

Cheung, Shao-Yong; Lee, Chieh-Han; Yu, Hwa-Lung

2017-04-01

Due to the limited hydrogeological observation data and high levels of uncertainty within, parameter estimation of the groundwater model has been an important issue. There are many methods of parameter estimation, for example, Kalman filter provides a real-time calibration of parameters through measurement of groundwater monitoring wells, related methods such as Extended Kalman Filter and Ensemble Kalman Filter are widely applied in groundwater research. However, Kalman Filter method is limited to linearity. This study propose a novel method, Bayesian Maximum Entropy Filtering, which provides a method that can considers the uncertainty of data in parameter estimation. With this two methods, we can estimate parameter by given hard data (certain) and soft data (uncertain) in the same time. In this study, we use Python and QGIS in groundwater model (MODFLOW) and development of Extended Kalman Filter and Bayesian Maximum Entropy Filtering in Python in parameter estimation. This method may provide a conventional filtering method and also consider the uncertainty of data. This study was conducted through numerical model experiment to explore, combine Bayesian maximum entropy filter and a hypothesis for the architecture of MODFLOW groundwater model numerical estimation. Through the virtual observation wells to simulate and observe the groundwater model periodically. The result showed that considering the uncertainty of data, the Bayesian maximum entropy filter will provide an ideal result of real-time parameters estimation.

An elusive paleodemography? A comparison of two methods for estimating the adult age distribution of deaths at late Classic Copan, Honduras.

PubMed

Storey, Rebecca

2007-01-01

Comparison of different adult age estimation methods on the same skeletal sample with unknown ages could forward paleodemographic inference, while researchers sort out various controversies. The original aging method for the auricular surface (Lovejoy et al., 1985a) assigned an age estimation based on several separate characteristics. Researchers have found this original method hard to apply. It is usually forgotten that before assigning an age, there was a seriation, an ordering of all available individuals from youngest to oldest. Thus, age estimation reflected the place of an individual within its sample. A recent article (Buckberry and Chamberlain, 2002) proposed a revised method that scores theses various characteristics into age stages, which can then be used with a Bayesian method to estimate an adult age distribution for the sample. Both methods were applied to the adult auricular surfaces of a Pre-Columbian Maya skeletal population from Copan, Honduras and resulted in age distributions with significant numbers of older adults. However, contrary to the usual paleodemographic distribution, one Bayesian estimation based on uniform prior probabilities yielded a population with 57% of the ages at death over 65, while another based on a high mortality life table still had 12% of the individuals aged over 75 years. The seriation method yielded an age distribution more similar to that known from preindustrial historical situations, without excessive longevity of adults. Paleodemography must still wrestle with its elusive goal of accurate adult age estimation from skeletons, a necessary base for demographic study of past populations. (c) 2006 Wiley-Liss, Inc

Bayesian WLS/GLS regression for regional skewness analysis for regions with large crest stage gage networks

USGS Publications Warehouse

Veilleux, Andrea G.; Stedinger, Jery R.; Eash, David A.

2012-01-01

This paper summarizes methodological advances in regional log-space skewness analyses that support flood-frequency analysis with the log Pearson Type III (LP3) distribution. A Bayesian Weighted Least Squares/Generalized Least Squares (B-WLS/B-GLS) methodology that relates observed skewness coefficient estimators to basin characteristics in conjunction with diagnostic statistics represents an extension of the previously developed B-GLS methodology. B-WLS/B-GLS has been shown to be effective in two California studies. B-WLS/B-GLS uses B-WLS to generate stable estimators of model parameters and B-GLS to estimate the precision of those B-WLS regression parameters, as well as the precision of the model. The study described here employs this methodology to develop a regional skewness model for the State of Iowa. To provide cost effective peak-flow data for smaller drainage basins in Iowa, the U.S. Geological Survey operates a large network of crest stage gages (CSGs) that only record flow values above an identified recording threshold (thus producing a censored data record). CSGs are different from continuous-record gages, which record almost all flow values and have been used in previous B-GLS and B-WLS/B-GLS regional skewness studies. The complexity of analyzing a large CSG network is addressed by using the B-WLS/B-GLS framework along with the Expected Moments Algorithm (EMA). Because EMA allows for the censoring of low outliers, as well as the use of estimated interval discharges for missing, censored, and historic data, it complicates the calculations of effective record length (and effective concurrent record length) used to describe the precision of sample estimators because the peak discharges are no longer solely represented by single values. Thus new record length calculations were developed. The regional skewness analysis for the State of Iowa illustrates the value of the new B-WLS/BGLS methodology with these new extensions.

As-built design specification for proportion estimate software subsystem

NASA Technical Reports Server (NTRS)

Obrien, S. (Principal Investigator)

1980-01-01

The Proportion Estimate Processor evaluates four estimation techniques in order to get an improved estimate of the proportion of a scene that is planted in a selected crop. The four techniques to be evaluated were provided by the techniques development section and are: (1) random sampling; (2) proportional allocation, relative count estimate; (3) proportional allocation, Bayesian estimate; and (4) sequential Bayesian allocation. The user is given two options for computation of the estimated mean square error. These are referred to as the cluster calculation option and the segment calculation option. The software for the Proportion Estimate Processor is operational on the IBM 3031 computer.

A Bayesian approach for estimating under-reported dengue incidence with a focus on non-linear associations between climate and dengue in Dhaka, Bangladesh.

PubMed

Sharmin, Sifat; Glass, Kathryn; Viennet, Elvina; Harley, David

2018-04-01

Determining the relation between climate and dengue incidence is challenging due to under-reporting of disease and consequent biased incidence estimates. Non-linear associations between climate and incidence compound this. Here, we introduce a modelling framework to estimate dengue incidence from passive surveillance data while incorporating non-linear climate effects. We estimated the true number of cases per month using a Bayesian generalised linear model, developed in stages to adjust for under-reporting. A semi-parametric thin-plate spline approach was used to quantify non-linear climate effects. The approach was applied to data collected from the national dengue surveillance system of Bangladesh. The model estimated that only 2.8% (95% credible interval 2.7-2.8) of all cases in the capital Dhaka were reported through passive case reporting. The optimal mean monthly temperature for dengue transmission is 29℃ and average monthly rainfall above 15 mm decreases transmission. Our approach provides an estimate of true incidence and an understanding of the effects of temperature and rainfall on dengue transmission in Dhaka, Bangladesh.

Bayesian parameter estimation for chiral effective field theory

NASA Astrophysics Data System (ADS)

Wesolowski, Sarah; Furnstahl, Richard; Phillips, Daniel; Klco, Natalie

2016-09-01

The low-energy constants (LECs) of a chiral effective field theory (EFT) interaction in the two-body sector are fit to observable data using a Bayesian parameter estimation framework. By using Bayesian prior probability distributions (pdfs), we quantify relevant physical expectations such as LEC naturalness and include them in the parameter estimation procedure. The final result is a posterior pdf for the LECs, which can be used to propagate uncertainty resulting from the fit to data to the final observable predictions. The posterior pdf also allows an empirical test of operator redundancy and other features of the potential. We compare results of our framework with other fitting procedures, interpreting the underlying assumptions in Bayesian probabilistic language. We also compare results from fitting all partial waves of the interaction simultaneously to cross section data compared to fitting to extracted phase shifts, appropriately accounting for correlations in the data. Supported in part by the NSF and DOE.

Maximum a posteriori Bayesian estimation of mycophenolic Acid area under the concentration-time curve: is this clinically useful for dosage prediction yet?

PubMed

Staatz, Christine E; Tett, Susan E

2011-12-01

This review seeks to summarize the available data about Bayesian estimation of area under the plasma concentration-time curve (AUC) and dosage prediction for mycophenolic acid (MPA) and evaluate whether sufficient evidence is available for routine use of Bayesian dosage prediction in clinical practice. A literature search identified 14 studies that assessed the predictive performance of maximum a posteriori Bayesian estimation of MPA AUC and one report that retrospectively evaluated how closely dosage recommendations based on Bayesian forecasting achieved targeted MPA exposure. Studies to date have mostly been undertaken in renal transplant recipients, with limited investigation in patients treated with MPA for autoimmune disease or haematopoietic stem cell transplantation. All of these studies have involved use of the mycophenolate mofetil (MMF) formulation of MPA, rather than the enteric-coated mycophenolate sodium (EC-MPS) formulation. Bias associated with estimation of MPA AUC using Bayesian forecasting was generally less than 10%. However some difficulties with imprecision was evident, with values ranging from 4% to 34% (based on estimation involving two or more concentration measurements). Evaluation of whether MPA dosing decisions based on Bayesian forecasting (by the free website service https://pharmaco.chu-limoges.fr) achieved target drug exposure has only been undertaken once. When MMF dosage recommendations were applied by clinicians, a higher proportion (72-80%) of subsequent estimated MPA AUC values were within the 30-60 mg · h/L target range, compared with when dosage recommendations were not followed (only 39-57% within target range). Such findings provide evidence that Bayesian dosage prediction is clinically useful for achieving target MPA AUC. This study, however, was retrospective and focussed only on adult renal transplant recipients. Furthermore, in this study, Bayesian-generated AUC estimations and dosage predictions were not compared with a later full measured AUC but rather with a further AUC estimate based on a second Bayesian analysis. This study also provided some evidence that a useful monitoring schedule for MPA AUC following adult renal transplant would be every 2 weeks during the first month post-transplant, every 1-3 months between months 1 and 12, and each year thereafter. It will be interesting to see further validations in different patient groups using the free website service. In summary, the predictive performance of Bayesian estimation of MPA, comparing estimated with measured AUC values, has been reported in several studies. However, the next step of predicting dosages based on these Bayesian-estimated AUCs, and prospectively determining how closely these predicted dosages give drug exposure matching targeted AUCs, remains largely unaddressed. Further prospective studies are required, particularly in non-renal transplant patients and with the EC-MPS formulation. Other important questions remain to be answered, such as: do Bayesian forecasting methods devised to date use the best population pharmacokinetic models or most accurate algorithms; are the methods simple to use for routine clinical practice; do the algorithms actually improve dosage estimations beyond empirical recommendations in all groups that receive MPA therapy; and, importantly, do the dosage predictions, when followed, improve patient health outcomes?

A Bayesian approach to parameter and reliability estimation in the Poisson distribution.

NASA Technical Reports Server (NTRS)

Canavos, G. C.

1972-01-01

For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.

Modeling two strains of disease via aggregate-level infectivity curves.

PubMed

Romanescu, Razvan; Deardon, Rob

2016-04-01

Well formulated models of disease spread, and efficient methods to fit them to observed data, are powerful tools for aiding the surveillance and control of infectious diseases. Our project considers the problem of the simultaneous spread of two related strains of disease in a context where spatial location is the key driver of disease spread. We start our modeling work with the individual level models (ILMs) of disease transmission, and extend these models to accommodate the competing spread of the pathogens in a two-tier hierarchical population (whose levels we refer to as 'farm' and 'animal'). The postulated interference mechanism between the two strains is a period of cross-immunity following infection. We also present a framework for speeding up the computationally intensive process of fitting the ILM to data, typically done using Markov chain Monte Carlo (MCMC) in a Bayesian framework, by turning the inference into a two-stage process. First, we approximate the number of animals infected on a farm over time by infectivity curves. These curves are fit to data sampled from farms, using maximum likelihood estimation, then, conditional on the fitted curves, Bayesian MCMC inference proceeds for the remaining parameters. Finally, we use posterior predictive distributions of salient epidemic summary statistics, in order to assess the model fitted.

The multicategory case of the sequential Bayesian pixel selection and estimation procedure

NASA Technical Reports Server (NTRS)

Pore, M. D.; Dennis, T. B. (Principal Investigator)

1980-01-01

A Bayesian technique for stratified proportion estimation and a sampling based on minimizing the mean squared error of this estimator were developed and tested on LANDSAT multispectral scanner data using the beta density function to model the prior distribution in the two-class case. An extention of this procedure to the k-class case is considered. A generalization of the beta function is shown to be a density function for the general case which allows the procedure to be extended.

Bayesian structural equation modeling in sport and exercise psychology.

PubMed

Stenling, Andreas; Ivarsson, Andreas; Johnson, Urban; Lindwall, Magnus

2015-08-01

Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach.

Improving the quantification of contrast enhanced ultrasound using a Bayesian approach

NASA Astrophysics Data System (ADS)

Rizzo, Gaia; Tonietto, Matteo; Castellaro, Marco; Raffeiner, Bernd; Coran, Alessandro; Fiocco, Ugo; Stramare, Roberto; Grisan, Enrico

2017-03-01

Contrast Enhanced Ultrasound (CEUS) is a sensitive imaging technique to assess tissue vascularity, that can be useful in the quantification of different perfusion patterns. This can be particularly important in the early detection and staging of arthritis. In a recent study we have shown that a Gamma-variate can accurately quantify synovial perfusion and it is flexible enough to describe many heterogeneous patterns. Moreover, we have shown that through a pixel-by-pixel analysis the quantitative information gathered characterizes more effectively the perfusion. However, the SNR ratio of the data and the nonlinearity of the model makes the parameter estimation difficult. Using classical non-linear-leastsquares (NLLS) approach the number of unreliable estimates (those with an asymptotic coefficient of variation greater than a user-defined threshold) is significant, thus affecting the overall description of the perfusion kinetics and of its heterogeneity. In this work we propose to solve the parameter estimation at the pixel level within a Bayesian framework using Variational Bayes (VB), and an automatic and data-driven prior initialization. When evaluating the pixels for which both VB and NLLS provided reliable estimates, we demonstrated that the parameter values provided by the two methods are well correlated (Pearson's correlation between 0.85 and 0.99). Moreover, the mean number of unreliable pixels drastically reduces from 54% (NLLS) to 26% (VB), without increasing the computational time (0.05 s/pixel for NLLS and 0.07 s/pixel for VB). When considering the efficiency of the algorithms as computational time per reliable estimate, VB outperforms NLLS (0.11 versus 0.25 seconds per reliable estimate respectively).

Bayesian dose-response analysis for epidemiological studies with complex uncertainty in dose estimation.

PubMed

Kwon, Deukwoo; Hoffman, F Owen; Moroz, Brian E; Simon, Steven L

2016-02-10

Most conventional risk analysis methods rely on a single best estimate of exposure per person, which does not allow for adjustment for exposure-related uncertainty. Here, we propose a Bayesian model averaging method to properly quantify the relationship between radiation dose and disease outcomes by accounting for shared and unshared uncertainty in estimated dose. Our Bayesian risk analysis method utilizes multiple realizations of sets (vectors) of doses generated by a two-dimensional Monte Carlo simulation method that properly separates shared and unshared errors in dose estimation. The exposure model used in this work is taken from a study of the risk of thyroid nodules among a cohort of 2376 subjects who were exposed to fallout from nuclear testing in Kazakhstan. We assessed the performance of our method through an extensive series of simulations and comparisons against conventional regression risk analysis methods. When the estimated doses contain relatively small amounts of uncertainty, the Bayesian method using multiple a priori plausible draws of dose vectors gave similar results to the conventional regression-based methods of dose-response analysis. However, when large and complex mixtures of shared and unshared uncertainties are present, the Bayesian method using multiple dose vectors had significantly lower relative bias than conventional regression-based risk analysis methods and better coverage, that is, a markedly increased capability to include the true risk coefficient within the 95% credible interval of the Bayesian-based risk estimate. An evaluation of the dose-response using our method is presented for an epidemiological study of thyroid disease following radiation exposure. Copyright © 2015 John Wiley & Sons, Ltd.

Bayesian hierarchical models for smoothing in two-phase studies, with application to small area estimation.

PubMed

Ross, Michelle; Wakefield, Jon

2015-10-01

Two-phase study designs are appealing since they allow for the oversampling of rare sub-populations which improves efficiency. In this paper we describe a Bayesian hierarchical model for the analysis of two-phase data. Such a model is particularly appealing in a spatial setting in which random effects are introduced to model between-area variability. In such a situation, one may be interested in estimating regression coefficients or, in the context of small area estimation, in reconstructing the population totals by strata. The efficiency gains of the two-phase sampling scheme are compared to standard approaches using 2011 birth data from the research triangle area of North Carolina. We show that the proposed method can overcome small sample difficulties and improve on existing techniques. We conclude that the two-phase design is an attractive approach for small area estimation.

Uncertainty estimation of Intensity-Duration-Frequency relationships: A regional analysis

NASA Astrophysics Data System (ADS)

Mélèse, Victor; Blanchet, Juliette; Molinié, Gilles

2018-03-01

We propose in this article a regional study of uncertainties in IDF curves derived from point-rainfall maxima. We develop two generalized extreme value models based on the simple scaling assumption, first in the frequentist framework and second in the Bayesian framework. Within the frequentist framework, uncertainties are obtained i) from the Gaussian density stemming from the asymptotic normality theorem of the maximum likelihood and ii) with a bootstrap procedure. Within the Bayesian framework, uncertainties are obtained from the posterior densities. We confront these two frameworks on the same database covering a large region of 100, 000 km2 in southern France with contrasted rainfall regime, in order to be able to draw conclusion that are not specific to the data. The two frameworks are applied to 405 hourly stations with data back to the 1980's, accumulated in the range 3 h-120 h. We show that i) the Bayesian framework is more robust than the frequentist one to the starting point of the estimation procedure, ii) the posterior and the bootstrap densities are able to better adjust uncertainty estimation to the data than the Gaussian density, and iii) the bootstrap density give unreasonable confidence intervals, in particular for return levels associated to large return period. Therefore our recommendation goes towards the use of the Bayesian framework to compute uncertainty.

A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study.

PubMed

Kaplan, David; Chen, Jianshen

2012-07-01

A two-step Bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous Bayesian propensity score approaches. The corresponding variance estimators are also provided. The two-step Bayesian propensity score is provided for three methods of implementation: propensity score stratification, weighting, and optimal full matching. Three simulation studies and one case study are presented to elaborate the proposed two-step Bayesian propensity score approach. Results of the simulation studies reveal that greater precision in the propensity score equation yields better recovery of the frequentist-based treatment effect. A slight advantage is shown for the Bayesian approach in small samples. Results also reveal that greater precision around the wrong treatment effect can lead to seriously distorted results. However, greater precision around the correct treatment effect parameter yields quite good results, with slight improvement seen with greater precision in the propensity score equation. A comparison of coverage rates for the conventional frequentist approach and proposed Bayesian approach is also provided. The case study reveals that credible intervals are wider than frequentist confidence intervals when priors are non-informative.

Intraherd correlation coefficients and design effects for bovine viral diarrhoea, infectious bovine rhinotracheitis, leptospirosis and neosporosis in cow-calf system herds in North-eastern Mexico.

PubMed

Segura-Correa, J C; Domínguez-Díaz, D; Avalos-Ramírez, R; Argaez-Sosa, J

2010-09-01

Knowledge of the intraherd correlation coefficient (ICC) and design (D) effect for infectious diseases could be of interest in sample size calculation and to provide the correct standard errors of prevalence estimates in cluster or two-stage samplings surveys. Information on 813 animals from 48 non-vaccinated cow-calf herds from North-eastern Mexico was used. The ICC for the bovine viral diarrhoea (BVD), infectious bovine rhinotracheitis (IBR), leptospirosis and neosporosis diseases were calculated using a Bayesian approach adjusting for the sensitivity and specificity of the diagnostic tests. The ICC and D values for BVD, IBR, leptospirosis and neosporosis were 0.31 and 5.91, 0.18 and 3.88, 0.22 and 4.53, and 0.11 and 2.68, respectively. The ICC and D values were different from 0 and D greater than 1, therefore large sample sizes are required to obtain the same precision in prevalence estimates than for a random simple sampling design. The report of ICC and D values is of great help in planning and designing two-stage sampling studies. 2010 Elsevier B.V. All rights reserved.

A Bayesian approach to estimating variance components within a multivariate generalizability theory framework.

PubMed

Jiang, Zhehan; Skorupski, William

2017-12-12

In many behavioral research areas, multivariate generalizability theory (mG theory) has been typically used to investigate the reliability of certain multidimensional assessments. However, traditional mG-theory estimation-namely, using frequentist approaches-has limits, leading researchers to fail to take full advantage of the information that mG theory can offer regarding the reliability of measurements. Alternatively, Bayesian methods provide more information than frequentist approaches can offer. This article presents instructional guidelines on how to implement mG-theory analyses in a Bayesian framework; in particular, BUGS code is presented to fit commonly seen designs from mG theory, including single-facet designs, two-facet crossed designs, and two-facet nested designs. In addition to concrete examples that are closely related to the selected designs and the corresponding BUGS code, a simulated dataset is provided to demonstrate the utility and advantages of the Bayesian approach. This article is intended to serve as a tutorial reference for applied researchers and methodologists conducting mG-theory studies.

Identification of transmissivity fields using a Bayesian strategy and perturbative approach

NASA Astrophysics Data System (ADS)

Zanini, Andrea; Tanda, Maria Giovanna; Woodbury, Allan D.

2017-10-01

The paper deals with the crucial problem of the groundwater parameter estimation that is the basis for efficient modeling and reclamation activities. A hierarchical Bayesian approach is developed: it uses the Akaike's Bayesian Information Criteria in order to estimate the hyperparameters (related to the covariance model chosen) and to quantify the unknown noise variance. The transmissivity identification proceeds in two steps: the first, called empirical Bayesian interpolation, uses Y* (Y = lnT) observations to interpolate Y values on a specified grid; the second, called empirical Bayesian update, improve the previous Y estimate through the addition of hydraulic head observations. The relationship between the head and the lnT has been linearized through a perturbative solution of the flow equation. In order to test the proposed approach, synthetic aquifers from literature have been considered. The aquifers in question contain a variety of boundary conditions (both Dirichelet and Neuman type) and scales of heterogeneities (σY2 = 1.0 and σY2 = 5.3). The estimated transmissivity fields were compared to the true one. The joint use of Y* and head measurements improves the estimation of Y considering both degrees of heterogeneity. Even if the variance of the strong transmissivity field can be considered high for the application of the perturbative approach, the results show the same order of approximation of the non-linear methods proposed in literature. The procedure allows to compute the posterior probability distribution of the target quantities and to quantify the uncertainty in the model prediction. Bayesian updating has advantages related both to the Monte-Carlo (MC) and non-MC approaches. In fact, as the MC methods, Bayesian updating allows computing the direct posterior probability distribution of the target quantities and as non-MC methods it has computational times in the order of seconds.

Lithospheric architecture of NE China from joint Inversions of receiver functions and surface wave dispersion through Bayesian optimisation

NASA Astrophysics Data System (ADS)

Sebastian, Nita; Kim, Seongryong; Tkalčić, Hrvoje; Sippl, Christian

2017-04-01

The purpose of this study is to develop an integrated inference on the lithospheric structure of NE China using three passive seismic networks comprised of 92 stations. The NE China plain consists of complex lithospheric domains characterised by the co-existence of complex geodynamic processes such as crustal thinning, active intraplate cenozoic volcanism and low velocity anomalies. To estimate lithospheric structures with greater detail, we chose to perform the joint inversion of independent data sets such as receiver functions and surface wave dispersion curves (group and phase velocity). We perform a joint inversion based on principles of Bayesian transdimensional optimisation techniques (Kim etal., 2016). Unlike in the previous studies of NE China, the complexity of the model is determined from the data in the first stage of the inversion, and the data uncertainty is computed based on Bayesian statistics in the second stage of the inversion. The computed crustal properties are retrieved from an ensemble of probable models. We obtain major structural inferences with well constrained absolute velocity estimates, which are vital for inferring properties of the lithosphere and bulk crustal Vp/Vs ratio. The Vp/Vs estimate obtained from joint inversions confirms the high Vp/Vs ratio ( 1.98) obtained using the H-Kappa method beneath some stations. Moreover, we could confirm the existence of a lower crustal velocity beneath several stations (eg: station SHS) within the NE China plain. Based on these findings we attempt to identify a plausible origin for structural complexity. We compile a high-resolution 3D image of the lithospheric architecture of the NE China plain.

Quantum-Like Bayesian Networks for Modeling Decision Making

PubMed Central

Moreira, Catarina; Wichert, Andreas

2016-01-01

In this work, we explore an alternative quantum structure to perform quantum probabilistic inferences to accommodate the paradoxical findings of the Sure Thing Principle. We propose a Quantum-Like Bayesian Network, which consists in replacing classical probabilities by quantum probability amplitudes. However, since this approach suffers from the problem of exponential growth of quantum parameters, we also propose a similarity heuristic that automatically fits quantum parameters through vector similarities. This makes the proposed model general and predictive in contrast to the current state of the art models, which cannot be generalized for more complex decision scenarios and that only provide an explanatory nature for the observed paradoxes. In the end, the model that we propose consists in a nonparametric method for estimating inference effects from a statistical point of view. It is a statistical model that is simpler than the previous quantum dynamic and quantum-like models proposed in the literature. We tested the proposed network with several empirical data from the literature, mainly from the Prisoner's Dilemma game and the Two Stage Gambling game. The results obtained show that the proposed quantum Bayesian Network is a general method that can accommodate violations of the laws of classical probability theory and make accurate predictions regarding human decision-making in these scenarios. PMID:26858669

Bayesian enhancement two-stage design for single-arm phase II clinical trials with binary and time-to-event endpoints.

PubMed

Shi, Haolun; Yin, Guosheng

2018-02-21

Simon's two-stage design is one of the most commonly used methods in phase II clinical trials with binary endpoints. The design tests the null hypothesis that the response rate is less than an uninteresting level, versus the alternative hypothesis that the response rate is greater than a desirable target level. From a Bayesian perspective, we compute the posterior probabilities of the null and alternative hypotheses given that a promising result is declared in Simon's design. Our study reveals that because the frequentist hypothesis testing framework places its focus on the null hypothesis, a potentially efficacious treatment identified by rejecting the null under Simon's design could have only less than 10% posterior probability of attaining the desirable target level. Due to the indifference region between the null and alternative, rejecting the null does not necessarily mean that the drug achieves the desirable response level. To clarify such ambiguity, we propose a Bayesian enhancement two-stage (BET) design, which guarantees a high posterior probability of the response rate reaching the target level, while allowing for early termination and sample size saving in case that the drug's response rate is smaller than the clinically uninteresting level. Moreover, the BET design can be naturally adapted to accommodate survival endpoints. We conduct extensive simulation studies to examine the empirical performance of our design and present two trial examples as applications. © 2018, The International Biometric Society.

Bayesian calibration for forensic age estimation.

PubMed

Ferrante, Luigi; Skrami, Edlira; Gesuita, Rosaria; Cameriere, Roberto

2015-05-10

Forensic medicine is increasingly called upon to assess the age of individuals. Forensic age estimation is mostly required in relation to illegal immigration and identification of bodies or skeletal remains. A variety of age estimation methods are based on dental samples and use of regression models, where the age of an individual is predicted by morphological tooth changes that take place over time. From the medico-legal point of view, regression models, with age as the dependent random variable entail that age tends to be overestimated in the young and underestimated in the old. To overcome this bias, we describe a new full Bayesian calibration method (asymmetric Laplace Bayesian calibration) for forensic age estimation that uses asymmetric Laplace distribution as the probability model. The method was compared with three existing approaches (two Bayesian and a classical method) using simulated data. Although its accuracy was comparable with that of the other methods, the asymmetric Laplace Bayesian calibration appears to be significantly more reliable and robust in case of misspecification of the probability model. The proposed method was also applied to a real dataset of values of the pulp chamber of the right lower premolar measured on x-ray scans of individuals of known age. Copyright © 2015 John Wiley & Sons, Ltd.

Bayesian Correlation Analysis for Sequence Count Data

PubMed Central

Lau, Nelson; Perkins, Theodore J.

2016-01-01

Evaluating the similarity of different measured variables is a fundamental task of statistics, and a key part of many bioinformatics algorithms. Here we propose a Bayesian scheme for estimating the correlation between different entities’ measurements based on high-throughput sequencing data. These entities could be different genes or miRNAs whose expression is measured by RNA-seq, different transcription factors or histone marks whose expression is measured by ChIP-seq, or even combinations of different types of entities. Our Bayesian formulation accounts for both measured signal levels and uncertainty in those levels, due to varying sequencing depth in different experiments and to varying absolute levels of individual entities, both of which affect the precision of the measurements. In comparison with a traditional Pearson correlation analysis, we show that our Bayesian correlation analysis retains high correlations when measurement confidence is high, but suppresses correlations when measurement confidence is low—especially for entities with low signal levels. In addition, we consider the influence of priors on the Bayesian correlation estimate. Perhaps surprisingly, we show that naive, uniform priors on entities’ signal levels can lead to highly biased correlation estimates, particularly when different experiments have widely varying sequencing depths. However, we propose two alternative priors that provably mitigate this problem. We also prove that, like traditional Pearson correlation, our Bayesian correlation calculation constitutes a kernel in the machine learning sense, and thus can be used as a similarity measure in any kernel-based machine learning algorithm. We demonstrate our approach on two RNA-seq datasets and one miRNA-seq dataset. PMID:27701449

A Bayesian estimation of a stochastic predator-prey model of economic fluctuations

NASA Astrophysics Data System (ADS)

Dibeh, Ghassan; Luchinsky, Dmitry G.; Luchinskaya, Daria D.; Smelyanskiy, Vadim N.

2007-06-01

In this paper, we develop a Bayesian framework for the empirical estimation of the parameters of one of the best known nonlinear models of the business cycle: The Marx-inspired model of a growth cycle introduced by R. M. Goodwin. The model predicts a series of closed cycles representing the dynamics of labor's share and the employment rate in the capitalist economy. The Bayesian framework is used to empirically estimate a modified Goodwin model. The original model is extended in two ways. First, we allow for exogenous periodic variations of the otherwise steady growth rates of the labor force and productivity per worker. Second, we allow for stochastic variations of those parameters. The resultant modified Goodwin model is a stochastic predator-prey model with periodic forcing. The model is then estimated using a newly developed Bayesian estimation method on data sets representing growth cycles in France and Italy during the years 1960-2005. Results show that inference of the parameters of the stochastic Goodwin model can be achieved. The comparison of the dynamics of the Goodwin model with the inferred values of parameters demonstrates quantitative agreement with the growth cycle empirical data.

Parameter estimation of multivariate multiple regression model using bayesian with non-informative Jeffreys’ prior distribution

NASA Astrophysics Data System (ADS)

Saputro, D. R. S.; Amalia, F.; Widyaningsih, P.; Affan, R. C.

2018-05-01

Bayesian method is a method that can be used to estimate the parameters of multivariate multiple regression model. Bayesian method has two distributions, there are prior and posterior distributions. Posterior distribution is influenced by the selection of prior distribution. Jeffreys’ prior distribution is a kind of Non-informative prior distribution. This prior is used when the information about parameter not available. Non-informative Jeffreys’ prior distribution is combined with the sample information resulting the posterior distribution. Posterior distribution is used to estimate the parameter. The purposes of this research is to estimate the parameters of multivariate regression model using Bayesian method with Non-informative Jeffreys’ prior distribution. Based on the results and discussion, parameter estimation of β and Σ which were obtained from expected value of random variable of marginal posterior distribution function. The marginal posterior distributions for β and Σ are multivariate normal and inverse Wishart. However, in calculation of the expected value involving integral of a function which difficult to determine the value. Therefore, approach is needed by generating of random samples according to the posterior distribution characteristics of each parameter using Markov chain Monte Carlo (MCMC) Gibbs sampling algorithm.

Bayesian generalized least squares regression with application to log Pearson type 3 regional skew estimation

NASA Astrophysics Data System (ADS)

Reis, D. S.; Stedinger, J. R.; Martins, E. S.

2005-10-01

This paper develops a Bayesian approach to analysis of a generalized least squares (GLS) regression model for regional analyses of hydrologic data. The new approach allows computation of the posterior distributions of the parameters and the model error variance using a quasi-analytic approach. Two regional skew estimation studies illustrate the value of the Bayesian GLS approach for regional statistical analysis of a shape parameter and demonstrate that regional skew models can be relatively precise with effective record lengths in excess of 60 years. With Bayesian GLS the marginal posterior distribution of the model error variance and the corresponding mean and variance of the parameters can be computed directly, thereby providing a simple but important extension of the regional GLS regression procedures popularized by Tasker and Stedinger (1989), which is sensitive to the likely values of the model error variance when it is small relative to the sampling error in the at-site estimator.

ABrox-A user-friendly Python module for approximate Bayesian computation with a focus on model comparison.

PubMed

Mertens, Ulf Kai; Voss, Andreas; Radev, Stefan

2018-01-01

We give an overview of the basic principles of approximate Bayesian computation (ABC), a class of stochastic methods that enable flexible and likelihood-free model comparison and parameter estimation. Our new open-source software called ABrox is used to illustrate ABC for model comparison on two prominent statistical tests, the two-sample t-test and the Levene-Test. We further highlight the flexibility of ABC compared to classical Bayesian hypothesis testing by computing an approximate Bayes factor for two multinomial processing tree models. Last but not least, throughout the paper, we introduce ABrox using the accompanied graphical user interface.

Estimating abundance in the presence of species uncertainty

USGS Publications Warehouse

Chambert, Thierry A.; Hossack, Blake R.; Fishback, LeeAnn; Davenport, Jon M.

2016-01-01

1.N-mixture models have become a popular method for estimating abundance of free-ranging animals that are not marked or identified individually. These models have been used on count data for single species that can be identified with certainty. However, co-occurring species often look similar during one or more life stages, making it difficult to assign species for all recorded captures. This uncertainty creates problems for estimating species-specific abundance and it can often limit life stages to which we can make inference. 2.We present a new extension of N-mixture models that accounts for species uncertainty. In addition to estimating site-specific abundances and detection probabilities, this model allows estimating probability of correct assignment of species identity. We implement this hierarchical model in a Bayesian framework and provide all code for running the model in BUGS-language programs. 3.We present an application of the model on count data from two sympatric freshwater fishes, the brook stickleback (Culaea inconstans) and the ninespine stickleback (Pungitius pungitius), ad illustrate implementation of covariate effects (habitat characteristics). In addition, we used a simulation study to validate the model and illustrate potential sample size issues. We also compared, for both real and simulated data, estimates provided by our model to those obtained by a simple N-mixture model when captures of unknown species identification were discarded. In the latter case, abundance estimates appeared highly biased and very imprecise, while our new model provided unbiased estimates with higher precision. 4.This extension of the N-mixture model should be useful for a wide variety of studies and taxa, as species uncertainty is a common issue. It should notably help improve investigation of abundance and vital rate characteristics of organisms’ early life stages, which are sometimes more difficult to identify than adults.

Information loss in approximately bayesian data assimilation: a comparison of generative and discriminative approaches to estimating agricultural yield

USDA-ARS?s Scientific Manuscript database

Data assimilation and regression are two commonly used methods for predicting agricultural yield from remote sensing observations. Data assimilation is a generative approach because it requires explicit approximations of the Bayesian prior and likelihood to compute the probability density function...

New phiomorph rodents from the latest Eocene of Egypt, and the impact of Bayesian "clock"-based phylogenetic methods on estimates of basal hystricognath relationships and biochronology.

PubMed

Sallam, Hesham M; Seiffert, Erik R

2016-01-01

The Fayum Depression of Egypt has yielded fossils of hystricognathous rodents from multiple Eocene and Oligocene horizons that range in age from ∼37 to ∼30 Ma and document several phases in the early evolution of crown Hystricognathi and one of its major subclades, Phiomorpha. Here we describe two new genera and species of basal phiomorphs, Birkamys korai and Mubhammys vadumensis, based on rostra and maxillary and mandibular remains from the terminal Eocene (∼34 Ma) Fayum Locality 41 (L-41). Birkamys is the smallest known Paleogene hystricognath, has very simple molars, and, like derived Oligocene-to-Recent phiomorphs (but unlike contemporaneous and older taxa) apparently retained dP(4)∕4 late into life, with no evidence for P(4)∕4 eruption or formation. Mubhammys is very similar in dental morphology to Birkamys, and also shows no evidence for P(4)∕4 formation or eruption, but is considerably larger. Though parsimony analysis with all characters equally weighted places Birkamys and Mubhammys as sister taxa of extant Thryonomys to the exclusion of much younger relatives of that genus, all other methods (standard Bayesian inference, Bayesian "tip-dating," and parsimony analysis with scaled transitions between "fixed" and polymorphic states) place these species in more basal positions within Hystricognathi, as sister taxa of Oligocene-to-Recent phiomorphs. We also employ tip-dating as a means for estimating the ages of early hystricognath-bearing localities, many of which are not well-constrained by geological, geochronological, or biostratigraphic evidence. By simultaneously taking into account phylogeny, evolutionary rates, and uniform priors that appropriately encompass the range of possible ages for fossil localities, dating of tips in this Bayesian framework allows paleontologists to move beyond vague and assumption-laden "stage of evolution" arguments in biochronology to provide relatively rigorous age assessments of poorly-constrained faunas. This approach should become increasingly robust as estimates are combined from multiple independent analyses of distantly related clades, and is broadly applicable across the tree of life; as such it is deserving of paleontologists' close attention. Notably, in the example provided here, hystricognathous rodents from Libya and Namibia that are controversially considered to be of middle Eocene age are instead estimated to be of late Eocene and late Oligocene age, respectively. Finally, we reconstruct the evolution of first lower molar size among Paleogene African hystricognaths using a Bayesian approach; the results of this analysis reconstruct a rapid latest Eocene dwarfing event along the lineage leading to Birkamys.

Diagnostic accuracy of a bayesian latent group analysis for the detection of malingering-related poor effort.

PubMed

Ortega, Alonso; Labrenz, Stephan; Markowitsch, Hans J; Piefke, Martina

2013-01-01

In the last decade, different statistical techniques have been introduced to improve assessment of malingering-related poor effort. In this context, we have recently shown preliminary evidence that a Bayesian latent group model may help to optimize classification accuracy using a simulation research design. In the present study, we conducted two analyses. Firstly, we evaluated how accurately this Bayesian approach can distinguish between participants answering in an honest way (honest response group) and participants feigning cognitive impairment (experimental malingering group). Secondly, we tested the accuracy of our model in the differentiation between patients who had real cognitive deficits (cognitively impaired group) and participants who belonged to the experimental malingering group. All Bayesian analyses were conducted using the raw scores of a visual recognition forced-choice task (2AFC), the Test of Memory Malingering (TOMM, Trial 2), and the Word Memory Test (WMT, primary effort subtests). The first analysis showed 100% accuracy for the Bayesian model in distinguishing participants of both groups with all effort measures. The second analysis showed outstanding overall accuracy of the Bayesian model when estimates were obtained from the 2AFC and the TOMM raw scores. Diagnostic accuracy of the Bayesian model diminished when using the WMT total raw scores. Despite, overall diagnostic accuracy can still be considered excellent. The most plausible explanation for this decrement is the low performance in verbal recognition and fluency tasks of some patients of the cognitively impaired group. Additionally, the Bayesian model provides individual estimates, p(zi |D), of examinees' effort levels. In conclusion, both high classification accuracy levels and Bayesian individual estimates of effort may be very useful for clinicians when assessing for effort in medico-legal settings.

A note on the efficiencies of sampling strategies in two-stage Bayesian regional fine mapping of a quantitative trait.

PubMed

Chen, Zhijian; Craiu, Radu V; Bull, Shelley B

2014-11-01

In focused studies designed to follow up associations detected in a genome-wide association study (GWAS), investigators can proceed to fine-map a genomic region by targeted sequencing or dense genotyping of all variants in the region, aiming to identify a functional sequence variant. For the analysis of a quantitative trait, we consider a Bayesian approach to fine-mapping study design that incorporates stratification according to a promising GWAS tag SNP in the same region. Improved cost-efficiency can be achieved when the fine-mapping phase incorporates a two-stage design, with identification of a smaller set of more promising variants in a subsample taken in stage 1, followed by their evaluation in an independent stage 2 subsample. To avoid the potential negative impact of genetic model misspecification on inference we incorporate genetic model selection based on posterior probabilities for each competing model. Our simulation study shows that, compared to simple random sampling that ignores genetic information from GWAS, tag-SNP-based stratified sample allocation methods reduce the number of variants continuing to stage 2 and are more likely to promote the functional sequence variant into confirmation studies. © 2014 WILEY PERIODICALS, INC.

Sequential Bayesian Filters for Estimating Time Series of Wrapped and Unwrapped Angles with Hyperparameter Estimation

NASA Astrophysics Data System (ADS)

Umehara, Hiroaki; Okada, Masato; Naruse, Yasushi

2018-03-01

The estimation of angular time series data is a widespread issue relating to various situations involving rotational motion and moving objects. There are two kinds of problem settings: the estimation of wrapped angles, which are principal values in a circular coordinate system (e.g., the direction of an object), and the estimation of unwrapped angles in an unbounded coordinate system such as for the positioning and tracking of moving objects measured by the signal-wave phase. Wrapped angles have been estimated in previous studies by sequential Bayesian filtering; however, the hyperparameters that are to be solved and that control the properties of the estimation model were given a priori. The present study establishes a procedure of hyperparameter estimation from the observation data of angles only, using the framework of Bayesian inference completely as the maximum likelihood estimation. Moreover, the filter model is modified to estimate the unwrapped angles. It is proved that without noise our model reduces to the existing algorithm of Itoh's unwrapping transform. It is numerically confirmed that our model is an extension of unwrapping estimation from Itoh's unwrapping transform to the case with noise.

Statistical estimation via convex optimization for trending and performance monitoring

NASA Astrophysics Data System (ADS)

Samar, Sikandar

This thesis presents an optimization-based statistical estimation approach to find unknown trends in noisy data. A Bayesian framework is used to explicitly take into account prior information about the trends via trend models and constraints. The main focus is on convex formulation of the Bayesian estimation problem, which allows efficient computation of (globally) optimal estimates. There are two main parts of this thesis. The first part formulates trend estimation in systems described by known detailed models as a convex optimization problem. Statistically optimal estimates are then obtained by maximizing a concave log-likelihood function subject to convex constraints. We consider the problem of increasing problem dimension as more measurements become available, and introduce a moving horizon framework to enable recursive estimation of the unknown trend by solving a fixed size convex optimization problem at each horizon. We also present a distributed estimation framework, based on the dual decomposition method, for a system formed by a network of complex sensors with local (convex) estimation. Two specific applications of the convex optimization-based Bayesian estimation approach are described in the second part of the thesis. Batch estimation for parametric diagnostics in a flight control simulation of a space launch vehicle is shown to detect incipient fault trends despite the natural masking properties of feedback in the guidance and control loops. Moving horizon approach is used to estimate time varying fault parameters in a detailed nonlinear simulation model of an unmanned aerial vehicle. An excellent performance is demonstrated in the presence of winds and turbulence.

Lord's Wald Test for Detecting Dif in Multidimensional Irt Models: A Comparison of Two Estimation Approaches

ERIC Educational Resources Information Center

Lee, Soo; Suh, Youngsuk

2018-01-01

Lord's Wald test for differential item functioning (DIF) has not been studied extensively in the context of the multidimensional item response theory (MIRT) framework. In this article, Lord's Wald test was implemented using two estimation approaches, marginal maximum likelihood estimation and Bayesian Markov chain Monte Carlo estimation, to detect…

DOE Office of Scientific and Technical Information (OSTI.GOV)

La Russa, D

Purpose: The purpose of this project is to develop a robust method of parameter estimation for a Poisson-based TCP model using Bayesian inference. Methods: Bayesian inference was performed using the PyMC3 probabilistic programming framework written in Python. A Poisson-based TCP regression model that accounts for clonogen proliferation was fit to observed rates of local relapse as a function of equivalent dose in 2 Gy fractions for a population of 623 stage-I non-small-cell lung cancer patients. The Slice Markov Chain Monte Carlo sampling algorithm was used to sample the posterior distributions, and was initiated using the maximum of the posterior distributionsmore » found by optimization. The calculation of TCP with each sample step required integration over the free parameter α, which was performed using an adaptive 24-point Gauss-Legendre quadrature. Convergence was verified via inspection of the trace plot and posterior distribution for each of the fit parameters, as well as with comparisons of the most probable parameter values with their respective maximum likelihood estimates. Results: Posterior distributions for α, the standard deviation of α (σ), the average tumour cell-doubling time (Td), and the repopulation delay time (Tk), were generated assuming α/β = 10 Gy, and a fixed clonogen density of 10{sup 7} cm−{sup 3}. Posterior predictive plots generated from samples from these posterior distributions are in excellent agreement with the observed rates of local relapse used in the Bayesian inference. The most probable values of the model parameters also agree well with maximum likelihood estimates. Conclusion: A robust method of performing Bayesian inference of TCP data using a complex TCP model has been established.« less

Tmax Determined Using a Bayesian Estimation Deconvolution Algorithm Applied to Bolus Tracking Perfusion Imaging: A Digital Phantom Validation Study.

PubMed

Uwano, Ikuko; Sasaki, Makoto; Kudo, Kohsuke; Boutelier, Timothé; Kameda, Hiroyuki; Mori, Futoshi; Yamashita, Fumio

2017-01-10

The Bayesian estimation algorithm improves the precision of bolus tracking perfusion imaging. However, this algorithm cannot directly calculate Tmax, the time scale widely used to identify ischemic penumbra, because Tmax is a non-physiological, artificial index that reflects the tracer arrival delay (TD) and other parameters. We calculated Tmax from the TD and mean transit time (MTT) obtained by the Bayesian algorithm and determined its accuracy in comparison with Tmax obtained by singular value decomposition (SVD) algorithms. The TD and MTT maps were generated by the Bayesian algorithm applied to digital phantoms with time-concentration curves that reflected a range of values for various perfusion metrics using a global arterial input function. Tmax was calculated from the TD and MTT using constants obtained by a linear least-squares fit to Tmax obtained from the two SVD algorithms that showed the best benchmarks in a previous study. Correlations between the Tmax values obtained by the Bayesian and SVD methods were examined. The Bayesian algorithm yielded accurate TD and MTT values relative to the true values of the digital phantom. Tmax calculated from the TD and MTT values with the least-squares fit constants showed excellent correlation (Pearson's correlation coefficient = 0.99) and agreement (intraclass correlation coefficient = 0.99) with Tmax obtained from SVD algorithms. Quantitative analyses of Tmax values calculated from Bayesian-estimation algorithm-derived TD and MTT from a digital phantom correlated and agreed well with Tmax values determined using SVD algorithms.

Collinear Latent Variables in Multilevel Confirmatory Factor Analysis: A Comparison of Maximum Likelihood and Bayesian Estimations.

PubMed

Can, Seda; van de Schoot, Rens; Hox, Joop

2015-06-01

Because variables may be correlated in the social and behavioral sciences, multicollinearity might be problematic. This study investigates the effect of collinearity manipulated in within and between levels of a two-level confirmatory factor analysis by Monte Carlo simulation. Furthermore, the influence of the size of the intraclass correlation coefficient (ICC) and estimation method; maximum likelihood estimation with robust chi-squares and standard errors and Bayesian estimation, on the convergence rate are investigated. The other variables of interest were rate of inadmissible solutions and the relative parameter and standard error bias on the between level. The results showed that inadmissible solutions were obtained when there was between level collinearity and the estimation method was maximum likelihood. In the within level multicollinearity condition, all of the solutions were admissible but the bias values were higher compared with the between level collinearity condition. Bayesian estimation appeared to be robust in obtaining admissible parameters but the relative bias was higher than for maximum likelihood estimation. Finally, as expected, high ICC produced less biased results compared to medium ICC conditions.

Parameter Estimation of Partial Differential Equation Models.

PubMed

Xun, Xiaolei; Cao, Jiguo; Mallick, Bani; Carroll, Raymond J; Maity, Arnab

2013-01-01

Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE, and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from LIDAR data.

Estimation of insurance premiums for coverage against natural disaster risk: an application of Bayesian Inference

NASA Astrophysics Data System (ADS)

Paudel, Y.; Botzen, W. J. W.; Aerts, J. C. J. H.

2013-03-01

This study applies Bayesian Inference to estimate flood risk for 53 dyke ring areas in the Netherlands, and focuses particularly on the data scarcity and extreme behaviour of catastrophe risk. The probability density curves of flood damage are estimated through Monte Carlo simulations. Based on these results, flood insurance premiums are estimated using two different practical methods that each account in different ways for an insurer's risk aversion and the dispersion rate of loss data. This study is of practical relevance because insurers have been considering the introduction of flood insurance in the Netherlands, which is currently not generally available.

Bayesian-based estimation of acoustic surface impedance: Finite difference frequency domain approach.

PubMed

Bockman, Alexander; Fackler, Cameron; Xiang, Ning

2015-04-01

Acoustic performance for an interior requires an accurate description of the boundary materials' surface acoustic impedance. Analytical methods may be applied to a small class of test geometries, but inverse numerical methods provide greater flexibility. The parameter estimation problem requires minimizing prediction vice observed acoustic field pressure. The Bayesian-network sampling approach presented here mitigates other methods' susceptibility to noise inherent to the experiment, model, and numerics. A geometry agnostic method is developed here and its parameter estimation performance is demonstrated for an air-backed micro-perforated panel in an impedance tube. Good agreement is found with predictions from the ISO standard two-microphone, impedance-tube method, and a theoretical model for the material. Data by-products exclusive to a Bayesian approach are analyzed to assess sensitivity of the method to nuisance parameters.

Multilevel modeling of single-case data: A comparison of maximum likelihood and Bayesian estimation.

PubMed

Moeyaert, Mariola; Rindskopf, David; Onghena, Patrick; Van den Noortgate, Wim

2017-12-01

The focus of this article is to describe Bayesian estimation, including construction of prior distributions, and to compare parameter recovery under the Bayesian framework (using weakly informative priors) and the maximum likelihood (ML) framework in the context of multilevel modeling of single-case experimental data. Bayesian estimation results were found similar to ML estimation results in terms of the treatment effect estimates, regardless of the functional form and degree of information included in the prior specification in the Bayesian framework. In terms of the variance component estimates, both the ML and Bayesian estimation procedures result in biased and less precise variance estimates when the number of participants is small (i.e., 3). By increasing the number of participants to 5 or 7, the relative bias is close to 5% and more precise estimates are obtained for all approaches, except for the inverse-Wishart prior using the identity matrix. When a more informative prior was added, more precise estimates for the fixed effects and random effects were obtained, even when only 3 participants were included. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Measuring Learning Progressions Using Bayesian Modeling in Complex Assessments

ERIC Educational Resources Information Center

Rutstein, Daisy Wise

2012-01-01

This research examines issues regarding model estimation and robustness in the use of Bayesian Inference Networks (BINs) for measuring Learning Progressions (LPs). It provides background information on LPs and how they might be used in practice. Two simulation studies are performed, along with real data examples. The first study examines the case…

A Bayesian approach to the statistical analysis of device preference studies.

PubMed

Fu, Haoda; Qu, Yongming; Zhu, Baojin; Huster, William

2012-01-01

Drug delivery devices are required to have excellent technical specifications to deliver drugs accurately, and in addition, the devices should provide a satisfactory experience to patients because this can have a direct effect on drug compliance. To compare patients' experience with two devices, cross-over studies with patient-reported outcomes (PRO) as response variables are often used. Because of the strength of cross-over designs, each subject can directly compare the two devices by using the PRO variables, and variables indicating preference (preferring A, preferring B, or no preference) can be easily derived. Traditionally, methods based on frequentist statistics can be used to analyze such preference data, but there are some limitations for the frequentist methods. Recently, Bayesian methods are considered an acceptable method by the US Food and Drug Administration to design and analyze device studies. In this paper, we propose a Bayesian statistical method to analyze the data from preference trials. We demonstrate that the new Bayesian estimator enjoys some optimal properties versus the frequentist estimator. Copyright © 2012 John Wiley & Sons, Ltd.

Genetic selection for ovulation rate and litter size in rabbits: Estimation of genetic parameters and direct and correlated responses.

PubMed

Ziadi, C; Mocé, M L; Laborda, P; Blasco, A; Santacreu, M A

2013-07-01

The aim of this work was to estimate direct and correlated responses in survival rates in an experiment of selection for ovulation rate (OR) and litter size (LS) in a line of rabbits (OR_LS). From generation 0 to 6 (first selection period), females were selected only for second gestation OR estimated by laparoscopy. From generation 7 to 13 (second selection period), a 2-stage selection for OR and LS was performed. In stage 1, females having the greatest OR at second gestation were selected. In stage 2, selection was for the greatest average LS of the first 2 parities of the females selected in stage 1. Total selection pressure in females was about 30%. The line had approximately 17 males and 75 females per generation. Traits recorded were OR estimated as the number of corpora lutea in both ovaries, number of implanted embryos (IE) estimated as the number of implantation sites, LS estimated as total number of rabbits born recorded at each parity, embryo survival (ES) estimated as IE/OR, fetal survival (FS) estimated as LS/IE, and prenatal survival (PS) estimated as LS/OR. Data were analyzed using Bayesian methodology. The estimated heritabilities of LS, OR, IE, ES, FS, and PS were 0.07, 0.21, 0.10, 0.07, 0.12, and 0.16, respectively. Direct and correlated responses from this study were estimated in each period of selection as the difference between the average genetic values of last and first generation. In the first selection period, OR increased 1.36 ova, but no correlated response was observed in LS due to a decrease on FS. Correlated responses for IE, ES, FS, and PS in the first selection period were 1.11, 0.00, -0.04, and -0.01, respectively. After 7 generations of 2-stage selection for OR and LS, OR increased 1.0 ova and response in LS was 0.9 kits. Correlated responses for IE, ES, FS, and PS in the second selection period were 1.14, 0.02, 0.02, and 0.07, respectively. Two-stage selection for OR and LS can be a promising procedure to improve LS in rabbits.

Is Bayesian Estimation Proper for Estimating the Individual's Ability? Research Report 80-3.

ERIC Educational Resources Information Center

Samejima, Fumiko

The effect of prior information in Bayesian estimation is considered, mainly from the standpoint of objective testing. In the estimation of a parameter belonging to an individual, the prior information is, in most cases, the density function of the population to which the individual belongs. Bayesian estimation was compared with maximum likelihood…

The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective.

PubMed

Kruschke, John K; Liddell, Torrin M

2018-02-01

In the practice of data analysis, there is a conceptual distinction between hypothesis testing, on the one hand, and estimation with quantified uncertainty on the other. Among frequentists in psychology, a shift of emphasis from hypothesis testing to estimation has been dubbed "the New Statistics" (Cumming 2014). A second conceptual distinction is between frequentist methods and Bayesian methods. Our main goal in this article is to explain how Bayesian methods achieve the goals of the New Statistics better than frequentist methods. The article reviews frequentist and Bayesian approaches to hypothesis testing and to estimation with confidence or credible intervals. The article also describes Bayesian approaches to meta-analysis, randomized controlled trials, and power analysis.

Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Peng, E-mail: peng@ices.utexas.edu; Schwab, Christoph, E-mail: christoph.schwab@sam.math.ethz.ch

2016-07-01

We extend the reduced basis (RB) accelerated Bayesian inversion methods for affine-parametric, linear operator equations which are considered in [16,17] to non-affine, nonlinear parametric operator equations. We generalize the analysis of sparsity of parametric forward solution maps in [20] and of Bayesian inversion in [48,49] to the fully discrete setting, including Petrov–Galerkin high-fidelity (“HiFi”) discretization of the forward maps. We develop adaptive, stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold. The nonaffinity and nonlinearity with respect to (w.r.t.) the distributed, uncertain parameters and the unknown solution is collocated; specifically, by themore » so-called Empirical Interpolation Method (EIM). For the corresponding Bayesian inversion problems, computational efficiency is enhanced in two ways: first, expectations w.r.t. the posterior are computed by adaptive quadratures with dimension-independent convergence rates proposed in [49]; the present work generalizes [49] to account for the impact of the PG discretization in the forward maps on the convergence rates of the Quantities of Interest (QoI for short). Second, we propose to perform the Bayesian estimation only w.r.t. a parsimonious, RB approximation of the posterior density. Based on the approximation results in [49], the infinite-dimensional parametric, deterministic forward map and operator admit N-term RB and EIM approximations which converge at rates which depend only on the sparsity of the parametric forward map. In several numerical experiments, the proposed algorithms exhibit dimension-independent convergence rates which equal, at least, the currently known rate estimates for N-term approximation. We propose to accelerate Bayesian estimation by first offline construction of reduced basis surrogates of the Bayesian posterior density. The parsimonious surrogates can then be employed for online data assimilation and for Bayesian estimation. They also open a perspective for optimal experimental design.« less

Analyzing small data sets using Bayesian estimation: the case of posttraumatic stress symptoms following mechanical ventilation in burn survivors

PubMed Central

van de Schoot, Rens; Broere, Joris J.; Perryck, Koen H.; Zondervan-Zwijnenburg, Mariëlle; van Loey, Nancy E.

2015-01-01

Background The analysis of small data sets in longitudinal studies can lead to power issues and often suffers from biased parameter values. These issues can be solved by using Bayesian estimation in conjunction with informative prior distributions. By means of a simulation study and an empirical example concerning posttraumatic stress symptoms (PTSS) following mechanical ventilation in burn survivors, we demonstrate the advantages and potential pitfalls of using Bayesian estimation. Methods First, we show how to specify prior distributions and by means of a sensitivity analysis we demonstrate how to check the exact influence of the prior (mis-) specification. Thereafter, we show by means of a simulation the situations in which the Bayesian approach outperforms the default, maximum likelihood and approach. Finally, we re-analyze empirical data on burn survivors which provided preliminary evidence of an aversive influence of a period of mechanical ventilation on the course of PTSS following burns. Results Not suprisingly, maximum likelihood estimation showed insufficient coverage as well as power with very small samples. Only when Bayesian analysis, in conjunction with informative priors, was used power increased to acceptable levels. As expected, we showed that the smaller the sample size the more the results rely on the prior specification. Conclusion We show that two issues often encountered during analysis of small samples, power and biased parameters, can be solved by including prior information into Bayesian analysis. We argue that the use of informative priors should always be reported together with a sensitivity analysis. PMID:25765534

Analyzing small data sets using Bayesian estimation: the case of posttraumatic stress symptoms following mechanical ventilation in burn survivors.

PubMed

van de Schoot, Rens; Broere, Joris J; Perryck, Koen H; Zondervan-Zwijnenburg, Mariëlle; van Loey, Nancy E

2015-01-01

Background : The analysis of small data sets in longitudinal studies can lead to power issues and often suffers from biased parameter values. These issues can be solved by using Bayesian estimation in conjunction with informative prior distributions. By means of a simulation study and an empirical example concerning posttraumatic stress symptoms (PTSS) following mechanical ventilation in burn survivors, we demonstrate the advantages and potential pitfalls of using Bayesian estimation. Methods : First, we show how to specify prior distributions and by means of a sensitivity analysis we demonstrate how to check the exact influence of the prior (mis-) specification. Thereafter, we show by means of a simulation the situations in which the Bayesian approach outperforms the default, maximum likelihood and approach. Finally, we re-analyze empirical data on burn survivors which provided preliminary evidence of an aversive influence of a period of mechanical ventilation on the course of PTSS following burns. Results : Not suprisingly, maximum likelihood estimation showed insufficient coverage as well as power with very small samples. Only when Bayesian analysis, in conjunction with informative priors, was used power increased to acceptable levels. As expected, we showed that the smaller the sample size the more the results rely on the prior specification. Conclusion : We show that two issues often encountered during analysis of small samples, power and biased parameters, can be solved by including prior information into Bayesian analysis. We argue that the use of informative priors should always be reported together with a sensitivity analysis.

Impact of wildfires on regional air pollution | Science Inventory ...

EPA Pesticide Factsheets

We examine the impact of wildfires and agricultural/prescribed burning on regional air pollution and Air Quality Index (AQI) between 2006 and 2013. We define daily regional air pollution using monitoring sites for ozone (n=1595), PM2.5 collected by Federal Reference Method (n=1058), and constituents of PM2.5 from the Interagency Monitoring of PROtected Visual Environment (IMPROVE) network (n=264) and use satellite image analysis from the NOAA Hazard Mapping System (HMS) to determine days on which visible smoke plumes are detected in the vertical column of the monitoring site. To examine the impact of smoke from these fires on regional air pollution we use a two stage approach, accounting for within site (1st stage) and between site (2nd stage) variations. At the first stage we estimate a monitor-specific plume day effect describing the relative change in pollutant concentrations on the days impacted by smoke plume while accounting for confounding effects of season and temperature_. At the second stage we combine monitor-specific plume day effects with a Bayesian hierarchical model and estimate a pooled nationally-averaged effect. HMS visible smoke plumes were detected on 6% of ozone, 8% of PM2.5 and 6% of IMPROVE network monitoring days. Our preliminary results indicate that the long range transport of air pollutants from wildfires and prescribed burns increase ozone concentration by 11% and PM2.5 mass by 34%. On all of the days where monitoring sites were AQI

A new Bayesian recursive technique for parameter estimation

NASA Astrophysics Data System (ADS)

Kaheil, Yasir H.; Gill, M. Kashif; McKee, Mac; Bastidas, Luis

2006-08-01

The performance of any model depends on how well its associated parameters are estimated. In the current application, a localized Bayesian recursive estimation (LOBARE) approach is devised for parameter estimation. The LOBARE methodology is an extension of the Bayesian recursive estimation (BARE) method. It is applied in this paper on two different types of models: an artificial intelligence (AI) model in the form of a support vector machine (SVM) application for forecasting soil moisture and a conceptual rainfall-runoff (CRR) model represented by the Sacramento soil moisture accounting (SAC-SMA) model. Support vector machines, based on statistical learning theory (SLT), represent the modeling task as a quadratic optimization problem and have already been used in various applications in hydrology. They require estimation of three parameters. SAC-SMA is a very well known model that estimates runoff. It has a 13-dimensional parameter space. In the LOBARE approach presented here, Bayesian inference is used in an iterative fashion to estimate the parameter space that will most likely enclose a best parameter set. This is done by narrowing the sampling space through updating the "parent" bounds based on their fitness. These bounds are actually the parameter sets that were selected by BARE runs on subspaces of the initial parameter space. The new approach results in faster convergence toward the optimal parameter set using minimum training/calibration data and fewer sets of parameter values. The efficacy of the localized methodology is also compared with the previously used BARE algorithm.

Manifold absolute pressure estimation using neural network with hybrid training algorithm

PubMed Central

Selamat, Hazlina; Alimin, Ahmad Jais; Haniff, Mohamad Fadzli

2017-01-01

In a modern small gasoline engine fuel injection system, the load of the engine is estimated based on the measurement of the manifold absolute pressure (MAP) sensor, which took place in the intake manifold. This paper present a more economical approach on estimating the MAP by using only the measurements of the throttle position and engine speed, resulting in lower implementation cost. The estimation was done via two-stage multilayer feed-forward neural network by combining Levenberg-Marquardt (LM) algorithm, Bayesian Regularization (BR) algorithm and Particle Swarm Optimization (PSO) algorithm. Based on the results found in 20 runs, the second variant of the hybrid algorithm yields a better network performance than the first variant of hybrid algorithm, LM, LM with BR and PSO by estimating the MAP closely to the simulated MAP values. By using a valid experimental training data, the estimator network that trained with the second variant of the hybrid algorithm showed the best performance among other algorithms when used in an actual retrofit fuel injection system (RFIS). The performance of the estimator was also validated in steady-state and transient condition by showing a closer MAP estimation to the actual value. PMID:29190779

Bayesian Multi-Trait Analysis Reveals a Useful Tool to Increase Oil Concentration and to Decrease Toxicity in Jatropha curcas L.

PubMed Central

Silva Junqueira, Vinícius; de Azevedo Peixoto, Leonardo; Galvêas Laviola, Bruno; Lopes Bhering, Leonardo; Mendonça, Simone; Agostini Costa, Tania da Silveira; Antoniassi, Rosemar

2016-01-01

The biggest challenge for jatropha breeding is to identify superior genotypes that present high seed yield and seed oil content with reduced toxicity levels. Therefore, the objective of this study was to estimate genetic parameters for three important traits (weight of 100 seed, oil seed content, and phorbol ester concentration), and to select superior genotypes to be used as progenitors in jatropha breeding. Additionally, the genotypic values and the genetic parameters estimated under the Bayesian multi-trait approach were used to evaluate different selection indices scenarios of 179 half-sib families. Three different scenarios and economic weights were considered. It was possible to simultaneously reduce toxicity and increase seed oil content and weight of 100 seed by using index selection based on genotypic value estimated by the Bayesian multi-trait approach. Indeed, we identified two families that present these characteristics by evaluating genetic diversity using the Ward clustering method, which suggested nine homogenous clusters. Future researches must integrate the Bayesian multi-trait methods with realized relationship matrix, aiming to build accurate selection indices models. PMID:27281340

Bayesian effect estimation accounting for adjustment uncertainty.

PubMed

Wang, Chi; Parmigiani, Giovanni; Dominici, Francesca

2012-09-01

Model-based estimation of the effect of an exposure on an outcome is generally sensitive to the choice of which confounding factors are included in the model. We propose a new approach, which we call Bayesian adjustment for confounding (BAC), to estimate the effect of an exposure of interest on the outcome, while accounting for the uncertainty in the choice of confounders. Our approach is based on specifying two models: (1) the outcome as a function of the exposure and the potential confounders (the outcome model); and (2) the exposure as a function of the potential confounders (the exposure model). We consider Bayesian variable selection on both models and link the two by introducing a dependence parameter, ω, denoting the prior odds of including a predictor in the outcome model, given that the same predictor is in the exposure model. In the absence of dependence (ω= 1), BAC reduces to traditional Bayesian model averaging (BMA). In simulation studies, we show that BAC, with ω > 1, estimates the exposure effect with smaller bias than traditional BMA, and improved coverage. We, then, compare BAC, a recent approach of Crainiceanu, Dominici, and Parmigiani (2008, Biometrika 95, 635-651), and traditional BMA in a time series data set of hospital admissions, air pollution levels, and weather variables in Nassau, NY for the period 1999-2005. Using each approach, we estimate the short-term effects of on emergency admissions for cardiovascular diseases, accounting for confounding. This application illustrates the potentially significant pitfalls of misusing variable selection methods in the context of adjustment uncertainty. © 2012, The International Biometric Society.

Uncertainty estimation of a complex water quality model: The influence of Box-Cox transformation on Bayesian approaches and comparison with a non-Bayesian method

NASA Astrophysics Data System (ADS)

Freni, Gabriele; Mannina, Giorgio

In urban drainage modelling, uncertainty analysis is of undoubted necessity. However, uncertainty analysis in urban water-quality modelling is still in its infancy and only few studies have been carried out. Therefore, several methodological aspects still need to be experienced and clarified especially regarding water quality modelling. The use of the Bayesian approach for uncertainty analysis has been stimulated by its rigorous theoretical framework and by the possibility of evaluating the impact of new knowledge on the modelling predictions. Nevertheless, the Bayesian approach relies on some restrictive hypotheses that are not present in less formal methods like the Generalised Likelihood Uncertainty Estimation (GLUE). One crucial point in the application of Bayesian method is the formulation of a likelihood function that is conditioned by the hypotheses made regarding model residuals. Statistical transformations, such as the use of Box-Cox equation, are generally used to ensure the homoscedasticity of residuals. However, this practice may affect the reliability of the analysis leading to a wrong uncertainty estimation. The present paper aims to explore the influence of the Box-Cox equation for environmental water quality models. To this end, five cases were considered one of which was the “real” residuals distributions (i.e. drawn from available data). The analysis was applied to the Nocella experimental catchment (Italy) which is an agricultural and semi-urbanised basin where two sewer systems, two wastewater treatment plants and a river reach were monitored during both dry and wet weather periods. The results show that the uncertainty estimation is greatly affected by residual transformation and a wrong assumption may also affect the evaluation of model uncertainty. The use of less formal methods always provide an overestimation of modelling uncertainty with respect to Bayesian method but such effect is reduced if a wrong assumption is made regarding the residuals distribution. If residuals are not normally distributed, the uncertainty is over-estimated if Box-Cox transformation is not applied or non-calibrated parameter is used.

Uncertainty quantification for nuclear density functional theory and information content of new measurements.

PubMed

McDonnell, J D; Schunck, N; Higdon, D; Sarich, J; Wild, S M; Nazarewicz, W

2015-03-27

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squares optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. The example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.

A Bayesian Framework for Generalized Linear Mixed Modeling Identifies New Candidate Loci for Late-Onset Alzheimer’s Disease

PubMed Central

Wang, Xulong; Philip, Vivek M.; Ananda, Guruprasad; White, Charles C.; Malhotra, Ankit; Michalski, Paul J.; Karuturi, Krishna R. Murthy; Chintalapudi, Sumana R.; Acklin, Casey; Sasner, Michael; Bennett, David A.; De Jager, Philip L.; Howell, Gareth R.; Carter, Gregory W.

2018-01-01

Recent technical and methodological advances have greatly enhanced genome-wide association studies (GWAS). The advent of low-cost, whole-genome sequencing facilitates high-resolution variant identification, and the development of linear mixed models (LMM) allows improved identification of putatively causal variants. While essential for correcting false positive associations due to sample relatedness and population stratification, LMMs have commonly been restricted to quantitative variables. However, phenotypic traits in association studies are often categorical, coded as binary case-control or ordered variables describing disease stages. To address these issues, we have devised a method for genomic association studies that implements a generalized LMM (GLMM) in a Bayesian framework, called Bayes-GLMM. Bayes-GLMM has four major features: (1) support of categorical, binary, and quantitative variables; (2) cohesive integration of previous GWAS results for related traits; (3) correction for sample relatedness by mixed modeling; and (4) model estimation by both Markov chain Monte Carlo sampling and maximal likelihood estimation. We applied Bayes-GLMM to the whole-genome sequencing cohort of the Alzheimer’s Disease Sequencing Project. This study contains 570 individuals from 111 families, each with Alzheimer’s disease diagnosed at one of four confidence levels. Using Bayes-GLMM we identified four variants in three loci significantly associated with Alzheimer’s disease. Two variants, rs140233081 and rs149372995, lie between PRKAR1B and PDGFA. The coded proteins are localized to the glial-vascular unit, and PDGFA transcript levels are associated with Alzheimer’s disease-related neuropathology. In summary, this work provides implementation of a flexible, generalized mixed-model approach in a Bayesian framework for association studies. PMID:29507048

Bayesian Estimation of Multidimensional Item Response Models. A Comparison of Analytic and Simulation Algorithms

ERIC Educational Resources Information Center

Martin-Fernandez, Manuel; Revuelta, Javier

2017-01-01

This study compares the performance of two estimation algorithms of new usage, the Metropolis-Hastings Robins-Monro (MHRM) and the Hamiltonian MCMC (HMC), with two consolidated algorithms in the psychometric literature, the marginal likelihood via EM algorithm (MML-EM) and the Markov chain Monte Carlo (MCMC), in the estimation of multidimensional…

Critically evaluating the theory and performance of Bayesian analysis of macroevolutionary mixtures

PubMed Central

Moore, Brian R.; Höhna, Sebastian; May, Michael R.; Rannala, Bruce; Huelsenbeck, John P.

2016-01-01

Bayesian analysis of macroevolutionary mixtures (BAMM) has recently taken the study of lineage diversification by storm. BAMM estimates the diversification-rate parameters (speciation and extinction) for every branch of a study phylogeny and infers the number and location of diversification-rate shifts across branches of a tree. Our evaluation of BAMM reveals two major theoretical errors: (i) the likelihood function (which estimates the model parameters from the data) is incorrect, and (ii) the compound Poisson process prior model (which describes the prior distribution of diversification-rate shifts across branches) is incoherent. Using simulation, we demonstrate that these theoretical issues cause statistical pathologies; posterior estimates of the number of diversification-rate shifts are strongly influenced by the assumed prior, and estimates of diversification-rate parameters are unreliable. Moreover, the inability to correctly compute the likelihood or to correctly specify the prior for rate-variable trees precludes the use of Bayesian approaches for testing hypotheses regarding the number and location of diversification-rate shifts using BAMM. PMID:27512038

Physics of ultrasonic wave propagation in bone and heart characterized using Bayesian parameter estimation

NASA Astrophysics Data System (ADS)

Anderson, Christian Carl

This Dissertation explores the physics underlying the propagation of ultrasonic waves in bone and in heart tissue through the use of Bayesian probability theory. Quantitative ultrasound is a noninvasive modality used for clinical detection, characterization, and evaluation of bone quality and cardiovascular disease. Approaches that extend the state of knowledge of the physics underpinning the interaction of ultrasound with inherently inhomogeneous and isotropic tissue have the potential to enhance its clinical utility. Simulations of fast and slow compressional wave propagation in cancellous bone were carried out to demonstrate the plausibility of a proposed explanation for the widely reported anomalous negative dispersion in cancellous bone. The results showed that negative dispersion could arise from analysis that proceeded under the assumption that the data consist of only a single ultrasonic wave, when in fact two overlapping and interfering waves are present. The confounding effect of overlapping fast and slow waves was addressed by applying Bayesian parameter estimation to simulated data, to experimental data acquired on bone-mimicking phantoms, and to data acquired in vitro on cancellous bone. The Bayesian approach successfully estimated the properties of the individual fast and slow waves even when they strongly overlapped in the acquired data. The Bayesian parameter estimation technique was further applied to an investigation of the anisotropy of ultrasonic properties in cancellous bone. The degree to which fast and slow waves overlap is partially determined by the angle of insonation of ultrasound relative to the predominant direction of trabecular orientation. In the past, studies of anisotropy have been limited by interference between fast and slow waves over a portion of the range of insonation angles. Bayesian analysis estimated attenuation, velocity, and amplitude parameters over the entire range of insonation angles, allowing a more complete characterization of anisotropy. A novel piecewise linear model for the cyclic variation of ultrasonic backscatter from myocardium was proposed. Models of cyclic variation for 100 type 2 diabetes patients and 43 normal control subjects were constructed using Bayesian parameter estimation. Parameters determined from the model, specifically rise time and slew rate, were found to be more reliable in differentiating between subject groups than the previously employed magnitude parameter.

Bayesian estimation of seasonal course of canopy leaf area index from hyperspectral satellite data

NASA Astrophysics Data System (ADS)

Varvia, Petri; Rautiainen, Miina; Seppänen, Aku

2018-03-01

In this paper, Bayesian inversion of a physically-based forest reflectance model is investigated to estimate of boreal forest canopy leaf area index (LAI) from EO-1 Hyperion hyperspectral data. The data consist of multiple forest stands with different species compositions and structures, imaged in three phases of the growing season. The Bayesian estimates of canopy LAI are compared to reference estimates based on a spectral vegetation index. The forest reflectance model contains also other unknown variables in addition to LAI, for example leaf single scattering albedo and understory reflectance. In the Bayesian approach, these variables are estimated simultaneously with LAI. The feasibility and seasonal variation of these estimates is also examined. Credible intervals for the estimates are also calculated and evaluated. The results show that the Bayesian inversion approach is significantly better than using a comparable spectral vegetation index regression.

BayeSED: A General Approach to Fitting the Spectral Energy Distribution of Galaxies

NASA Astrophysics Data System (ADS)

Han, Yunkun; Han, Zhanwen

2014-11-01

We present a newly developed version of BayeSED, a general Bayesian approach to the spectral energy distribution (SED) fitting of galaxies. The new BayeSED code has been systematically tested on a mock sample of galaxies. The comparison between the estimated and input values of the parameters shows that BayeSED can recover the physical parameters of galaxies reasonably well. We then applied BayeSED to interpret the SEDs of a large Ks -selected sample of galaxies in the COSMOS/UltraVISTA field with stellar population synthesis models. Using the new BayeSED code, a Bayesian model comparison of stellar population synthesis models has been performed for the first time. We found that the 2003 model by Bruzual & Charlot, statistically speaking, has greater Bayesian evidence than the 2005 model by Maraston for the Ks -selected sample. In addition, while setting the stellar metallicity as a free parameter obviously increases the Bayesian evidence of both models, varying the initial mass function has a notable effect only on the Maraston model. Meanwhile, the physical parameters estimated with BayeSED are found to be generally consistent with those obtained using the popular grid-based FAST code, while the former parameters exhibit more natural distributions. Based on the estimated physical parameters of the galaxies in the sample, we qualitatively classified the galaxies in the sample into five populations that may represent galaxies at different evolution stages or in different environments. We conclude that BayeSED could be a reliable and powerful tool for investigating the formation and evolution of galaxies from the rich multi-wavelength observations currently available. A binary version of the BayeSED code parallelized with Message Passing Interface is publicly available at https://bitbucket.org/hanyk/bayesed.

BayeSED: A GENERAL APPROACH TO FITTING THE SPECTRAL ENERGY DISTRIBUTION OF GALAXIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Han, Yunkun; Han, Zhanwen, E-mail: hanyk@ynao.ac.cn, E-mail: zhanwenhan@ynao.ac.cn

2014-11-01

We present a newly developed version of BayeSED, a general Bayesian approach to the spectral energy distribution (SED) fitting of galaxies. The new BayeSED code has been systematically tested on a mock sample of galaxies. The comparison between the estimated and input values of the parameters shows that BayeSED can recover the physical parameters of galaxies reasonably well. We then applied BayeSED to interpret the SEDs of a large K{sub s} -selected sample of galaxies in the COSMOS/UltraVISTA field with stellar population synthesis models. Using the new BayeSED code, a Bayesian model comparison of stellar population synthesis models has beenmore » performed for the first time. We found that the 2003 model by Bruzual and Charlot, statistically speaking, has greater Bayesian evidence than the 2005 model by Maraston for the K{sub s} -selected sample. In addition, while setting the stellar metallicity as a free parameter obviously increases the Bayesian evidence of both models, varying the initial mass function has a notable effect only on the Maraston model. Meanwhile, the physical parameters estimated with BayeSED are found to be generally consistent with those obtained using the popular grid-based FAST code, while the former parameters exhibit more natural distributions. Based on the estimated physical parameters of the galaxies in the sample, we qualitatively classified the galaxies in the sample into five populations that may represent galaxies at different evolution stages or in different environments. We conclude that BayeSED could be a reliable and powerful tool for investigating the formation and evolution of galaxies from the rich multi-wavelength observations currently available. A binary version of the BayeSED code parallelized with Message Passing Interface is publicly available at https://bitbucket.org/hanyk/bayesed.« less

Estimation model of life insurance claims risk for cancer patients by using Bayesian method

NASA Astrophysics Data System (ADS)

Sukono; Suyudi, M.; Islamiyati, F.; Supian, S.

2017-01-01

This paper discussed the estimation model of the risk of life insurance claims for cancer patients using Bayesian method. To estimate the risk of the claim, the insurance participant data is grouped into two: the number of policies issued and the number of claims incurred. Model estimation is done using a Bayesian approach method. Further, the estimator model was used to estimate the risk value of life insurance claims each age group for each sex. The estimation results indicate that a large risk premium for insured males aged less than 30 years is 0.85; for ages 30 to 40 years is 3:58; for ages 41 to 50 years is 1.71; for ages 51 to 60 years is 2.96; and for those aged over 60 years is 7.82. Meanwhile, for insured women aged less than 30 years was 0:56; for ages 30 to 40 years is 3:21; for ages 41 to 50 years is 0.65; for ages 51 to 60 years is 3:12; and for those aged over 60 years is 9.99. This study is useful in determining the risk premium in homogeneous groups based on gender and age.

A Bayesian Analysis of the Post-seismic Deformation of the Great 11 March 2011 Tohoku-Oki (Mw 9.0) Earthquake: Implications for Future Earthquake Occurrence

NASA Astrophysics Data System (ADS)

Ortega Culaciati, F. H.; Simons, M.; Minson, S. E.; Owen, S. E.; Moore, A. W.; Hetland, E. A.

2011-12-01

We aim to quantify the spatial distribution of after-slip following the Great 11 March 2011 Tohoku-Oki (Mw 9.0) earthquake and its implications for the occurrence of a future Great Earthquake, particularly in the Ibaraki region of Japan. We use a Bayesian approach (CATMIP algorithm), constrained by on-land Geonet GPS time series, to infer models of after-slip to date in the Japan megathrust. Unlike traditional inverse methods, in which a single optimum model is found, the Bayesian approach allows a complete characterization of the model parameter space by searching a-posteriori estimates of the range of plausible models. We use the Kullback-Liebler information divergence as a metric of the information gain on each subsurface slip patch, to quantify the extent to which land-based geodetic observations can constrain the upper parts of the megathrust, where the Great Tohoku-Oki earthquake took place. We aim to understand the relationships of spatial distribution of fault slip behavior in the different stages of the seismic cycle. We compare our post-seismic slip distributions to inter- and co-seismic slip distributions obtained through a Bayesian methodology as well as through traditional (optimization) inverse estimates in the published literature. We discuss implications of these analyses for the occurrence of a large earthquake in the Japan megathrust regions adjacent to the Great Tohoku-Oki earthquake.

Performance of two predictive uncertainty estimation approaches for conceptual Rainfall-Runoff Model: Bayesian Joint Inference and Hydrologic Uncertainty Post-processing

NASA Astrophysics Data System (ADS)

Hernández-López, Mario R.; Romero-Cuéllar, Jonathan; Camilo Múnera-Estrada, Juan; Coccia, Gabriele; Francés, Félix

2017-04-01

It is noticeably important to emphasize the role of uncertainty particularly when the model forecasts are used to support decision-making and water management. This research compares two approaches for the evaluation of the predictive uncertainty in hydrological modeling. First approach is the Bayesian Joint Inference of hydrological and error models. Second approach is carried out through the Model Conditional Processor using the Truncated Normal Distribution in the transformed space. This comparison is focused on the predictive distribution reliability. The case study is applied to two basins included in the Model Parameter Estimation Experiment (MOPEX). These two basins, which have different hydrological complexity, are the French Broad River (North Carolina) and the Guadalupe River (Texas). The results indicate that generally, both approaches are able to provide similar predictive performances. However, the differences between them can arise in basins with complex hydrology (e.g. ephemeral basins). This is because obtained results with Bayesian Joint Inference are strongly dependent on the suitability of the hypothesized error model. Similarly, the results in the case of the Model Conditional Processor are mainly influenced by the selected model of tails or even by the selected full probability distribution model of the data in the real space, and by the definition of the Truncated Normal Distribution in the transformed space. In summary, the different hypotheses that the modeler choose on each of the two approaches are the main cause of the different results. This research also explores a proper combination of both methodologies which could be useful to achieve less biased hydrological parameter estimation. For this approach, firstly the predictive distribution is obtained through the Model Conditional Processor. Secondly, this predictive distribution is used to derive the corresponding additive error model which is employed for the hydrological parameter estimation with the Bayesian Joint Inference methodology.

Three-dimensional Stochastic Estimation of Porosity Distribution: Benefits of Using Ground-penetrating Radar Velocity Tomograms in Simulated-annealing-based or Bayesian Sequential Simulation Approaches

DTIC Science & Technology

2012-05-30

annealing-based or Bayesian sequential simulation approaches B. Dafflon1,2 and W. Barrash1 Received 13 May 2011; revised 12 March 2012; accepted 17 April 2012...the withheld porosity log are also withheld for this estimation process. For both cases we do this for two wells having locally variable stratigraphy ...borehole location is given at the bottom of each log comparison panel. For comparison with stratigraphy at the BHRS, contacts between Units 1 to 4

Introduction to Bayesian statistical approaches to compositional analyses of transgenic crops 1. Model validation and setting the stage.

PubMed

Harrison, Jay M; Breeze, Matthew L; Harrigan, George G

2011-08-01

Statistical comparisons of compositional data generated on genetically modified (GM) crops and their near-isogenic conventional (non-GM) counterparts typically rely on classical significance testing. This manuscript presents an introduction to Bayesian methods for compositional analysis along with recommendations for model validation. The approach is illustrated using protein and fat data from two herbicide tolerant GM soybeans (MON87708 and MON87708×MON89788) and a conventional comparator grown in the US in 2008 and 2009. Guidelines recommended by the US Food and Drug Administration (FDA) in conducting Bayesian analyses of clinical studies on medical devices were followed. This study is the first Bayesian approach to GM and non-GM compositional comparisons. The evaluation presented here supports a conclusion that a Bayesian approach to analyzing compositional data can provide meaningful and interpretable results. We further describe the importance of method validation and approaches to model checking if Bayesian approaches to compositional data analysis are to be considered viable by scientists involved in GM research and regulation. Copyright © 2011 Elsevier Inc. All rights reserved.

Bayesian Probability Theory

NASA Astrophysics Data System (ADS)

von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo

2014-06-01

Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.

Multivariate space-time modelling of multiple air pollutants and their health effects accounting for exposure uncertainty.

PubMed

Huang, Guowen; Lee, Duncan; Scott, E Marian

2018-03-30

The long-term health effects of air pollution are often estimated using a spatio-temporal ecological areal unit study, but this design leads to the following statistical challenges: (1) how to estimate spatially representative pollution concentrations for each areal unit; (2) how to allow for the uncertainty in these estimated concentrations when estimating their health effects; and (3) how to simultaneously estimate the joint effects of multiple correlated pollutants. This article proposes a novel 2-stage Bayesian hierarchical model for addressing these 3 challenges, with inference based on Markov chain Monte Carlo simulation. The first stage is a multivariate spatio-temporal fusion model for predicting areal level average concentrations of multiple pollutants from both monitored and modelled pollution data. The second stage is a spatio-temporal model for estimating the health impact of multiple correlated pollutants simultaneously, which accounts for the uncertainty in the estimated pollution concentrations. The novel methodology is motivated by a new study of the impact of both particulate matter and nitrogen dioxide concentrations on respiratory hospital admissions in Scotland between 2007 and 2011, and the results suggest that both pollutants exhibit substantial and independent health effects. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

A Simulation Study Comparison of Bayesian Estimation with Conventional Methods for Estimating Unknown Change Points

ERIC Educational Resources Information Center

Wang, Lijuan; McArdle, John J.

2008-01-01

The main purpose of this research is to evaluate the performance of a Bayesian approach for estimating unknown change points using Monte Carlo simulations. The univariate and bivariate unknown change point mixed models were presented and the basic idea of the Bayesian approach for estimating the models was discussed. The performance of Bayesian…

Bayesian Analysis of Item Response Curves. Research Report 84-1. Mathematical Sciences Technical Report No. 132.

ERIC Educational Resources Information Center

Tsutakawa, Robert K.; Lin, Hsin Ying

Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. The procedure is illustrated by data…

Objectively combining AR5 instrumental period and paleoclimate climate sensitivity evidence

NASA Astrophysics Data System (ADS)

Lewis, Nicholas; Grünwald, Peter

2018-03-01

Combining instrumental period evidence regarding equilibrium climate sensitivity with largely independent paleoclimate proxy evidence should enable a more constrained sensitivity estimate to be obtained. Previous, subjective Bayesian approaches involved selection of a prior probability distribution reflecting the investigators' beliefs about climate sensitivity. Here a recently developed approach employing two different statistical methods—objective Bayesian and frequentist likelihood-ratio—is used to combine instrumental period and paleoclimate evidence based on data presented and assessments made in the IPCC Fifth Assessment Report. Probabilistic estimates from each source of evidence are represented by posterior probability density functions (PDFs) of physically-appropriate form that can be uniquely factored into a likelihood function and a noninformative prior distribution. The three-parameter form is shown accurately to fit a wide range of estimated climate sensitivity PDFs. The likelihood functions relating to the probabilistic estimates from the two sources are multiplicatively combined and a prior is derived that is noninformative for inference from the combined evidence. A posterior PDF that incorporates the evidence from both sources is produced using a single-step approach, which avoids the order-dependency that would arise if Bayesian updating were used. Results are compared with an alternative approach using the frequentist signed root likelihood ratio method. Results from these two methods are effectively identical, and provide a 5-95% range for climate sensitivity of 1.1-4.05 K (median 1.87 K).

New phiomorph rodents from the latest Eocene of Egypt, and the impact of Bayesian “clock”-based phylogenetic methods on estimates of basal hystricognath relationships and biochronology

PubMed Central

2016-01-01

The Fayum Depression of Egypt has yielded fossils of hystricognathous rodents from multiple Eocene and Oligocene horizons that range in age from ∼37 to ∼30 Ma and document several phases in the early evolution of crown Hystricognathi and one of its major subclades, Phiomorpha. Here we describe two new genera and species of basal phiomorphs, Birkamys korai and Mubhammys vadumensis, based on rostra and maxillary and mandibular remains from the terminal Eocene (∼34 Ma) Fayum Locality 41 (L-41). Birkamys is the smallest known Paleogene hystricognath, has very simple molars, and, like derived Oligocene-to-Recent phiomorphs (but unlike contemporaneous and older taxa) apparently retained dP4∕4 late into life, with no evidence for P4∕4 eruption or formation. Mubhammys is very similar in dental morphology to Birkamys, and also shows no evidence for P4∕4 formation or eruption, but is considerably larger. Though parsimony analysis with all characters equally weighted places Birkamys and Mubhammys as sister taxa of extant Thryonomys to the exclusion of much younger relatives of that genus, all other methods (standard Bayesian inference, Bayesian “tip-dating,” and parsimony analysis with scaled transitions between “fixed” and polymorphic states) place these species in more basal positions within Hystricognathi, as sister taxa of Oligocene-to-Recent phiomorphs. We also employ tip-dating as a means for estimating the ages of early hystricognath-bearing localities, many of which are not well-constrained by geological, geochronological, or biostratigraphic evidence. By simultaneously taking into account phylogeny, evolutionary rates, and uniform priors that appropriately encompass the range of possible ages for fossil localities, dating of tips in this Bayesian framework allows paleontologists to move beyond vague and assumption-laden “stage of evolution” arguments in biochronology to provide relatively rigorous age assessments of poorly-constrained faunas. This approach should become increasingly robust as estimates are combined from multiple independent analyses of distantly related clades, and is broadly applicable across the tree of life; as such it is deserving of paleontologists’ close attention. Notably, in the example provided here, hystricognathous rodents from Libya and Namibia that are controversially considered to be of middle Eocene age are instead estimated to be of late Eocene and late Oligocene age, respectively. Finally, we reconstruct the evolution of first lower molar size among Paleogene African hystricognaths using a Bayesian approach; the results of this analysis reconstruct a rapid latest Eocene dwarfing event along the lineage leading to Birkamys. PMID:26966657

On the Relationships between Jeffreys Modal and Weighted Likelihood Estimation of Ability under Logistic IRT Models

ERIC Educational Resources Information Center

Magis, David; Raiche, Gilles

2012-01-01

This paper focuses on two estimators of ability with logistic item response theory models: the Bayesian modal (BM) estimator and the weighted likelihood (WL) estimator. For the BM estimator, Jeffreys' prior distribution is considered, and the corresponding estimator is referred to as the Jeffreys modal (JM) estimator. It is established that under…

Bayesian estimates of the incidence of rare cancers in Europe.

PubMed

Botta, Laura; Capocaccia, Riccardo; Trama, Annalisa; Herrmann, Christian; Salmerón, Diego; De Angelis, Roberta; Mallone, Sandra; Bidoli, Ettore; Marcos-Gragera, Rafael; Dudek-Godeau, Dorota; Gatta, Gemma; Cleries, Ramon

2018-04-21

The RARECAREnet project has updated the estimates of the burden of the 198 rare cancers in each European country. Suspecting that scant data could affect the reliability of statistical analysis, we employed a Bayesian approach to estimate the incidence of these cancers. We analyzed about 2,000,000 rare cancers diagnosed in 2000-2007 provided by 83 population-based cancer registries from 27 European countries. We considered European incidence rates (IRs), calculated over all the data available in RARECAREnet, as a valid a priori to merge with country-specific observed data. Therefore we provided (1) Bayesian estimates of IRs and the yearly numbers of cases of rare cancers in each country; (2) the expected time (T) in years needed to observe one new case; and (3) practical criteria to decide when to use the Bayesian approach. Bayesian and classical estimates did not differ much; substantial differences (>10%) ranged from 77 rare cancers in Iceland to 14 in England. The smaller the population the larger the number of rare cancers needing a Bayesian approach. Bayesian estimates were useful for cancers with fewer than 150 observed cases in a country during the study period; this occurred mostly when the population of the country is small. For the first time the Bayesian estimates of IRs and the yearly expected numbers of cases for each rare cancer in each individual European country were calculated. Moreover, the indicator T is useful to convey incidence estimates for exceptionally rare cancers and in small countries; it far exceeds the professional lifespan of a medical doctor. Copyright © 2018 Elsevier Ltd. All rights reserved.

Non-Spatial Analysis of Relative Risk of Dengue Disease in Bandung Using Poisson-gamma and Log-normal Models: A Case Study of Dengue Data from Santo Borromeus Hospital in 2013

NASA Astrophysics Data System (ADS)

Irawan, R.; Yong, B.; Kristiani, F.

2017-02-01

Bandung, one of the cities in Indonesia, is vulnerable to dengue disease for both early-stage (Dengue Fever) and severe-stage (Dengue Haemorrhagic Fever and Dengue Shock Syndrome). In 2013, there were 5,749 patients in Bandung and 2,032 of the patients were hospitalized in Santo Borromeus Hospital. In this paper, there are two models, Poisson-gamma and Log-normal models, that use Bayesian inference to estimate the value of the relative risk. The calculation is done by Markov Chain Monte Carlo method which is the simulation using Gibbs Sampling algorithm in WinBUGS 1.4.3 software. The analysis results for dengue disease of 30 sub-districts in Bandung in 2013 based on Santo Borromeus Hospital’s data are Coblong and Bandung Wetan sub-districts had the highest relative risk using both models for the early-stage, severe-stage, and all stages. Meanwhile, Cinambo sub-district had the lowest relative risk using both models for the severe-stage and all stages and BojongloaKaler sub-district had the lowest relative risk using both models for the early-stage. For the model comparison using DIC (Deviance Information Criterion) method, the Log-normal model is a better model for the early-stage and severe-stage, but for the all stages, the Poisson-gamma model is a better model which fits the data.

Bayesian aggregation versus majority vote in the characterization of non-specific arm pain based on quantitative needle electromyography

PubMed Central

2010-01-01

Background Methods for the calculation and application of quantitative electromyographic (EMG) statistics for the characterization of EMG data detected from forearm muscles of individuals with and without pain associated with repetitive strain injury are presented. Methods A classification procedure using a multi-stage application of Bayesian inference is presented that characterizes a set of motor unit potentials acquired using needle electromyography. The utility of this technique in characterizing EMG data obtained from both normal individuals and those presenting with symptoms of "non-specific arm pain" is explored and validated. The efficacy of the Bayesian technique is compared with simple voting methods. Results The aggregate Bayesian classifier presented is found to perform with accuracy equivalent to that of majority voting on the test data, with an overall accuracy greater than 0.85. Theoretical foundations of the technique are discussed, and are related to the observations found. Conclusions Aggregation of motor unit potential conditional probability distributions estimated using quantitative electromyographic analysis, may be successfully used to perform electrodiagnostic characterization of "non-specific arm pain." It is expected that these techniques will also be able to be applied to other types of electrodiagnostic data. PMID:20156353

A Comparison of a Bayesian and a Maximum Likelihood Tailored Testing Procedure.

ERIC Educational Resources Information Center

McKinley, Robert L.; Reckase, Mark D.

A study was conducted to compare tailored testing procedures based on a Bayesian ability estimation technique and on a maximum likelihood ability estimation technique. The Bayesian tailored testing procedure selected items so as to minimize the posterior variance of the ability estimate distribution, while the maximum likelihood tailored testing…

Gene selection in cancer classification using sparse logistic regression with Bayesian regularization.

PubMed

Cawley, Gavin C; Talbot, Nicola L C

2006-10-01

Gene selection algorithms for cancer classification, based on the expression of a small number of biomarker genes, have been the subject of considerable research in recent years. Shevade and Keerthi propose a gene selection algorithm based on sparse logistic regression (SLogReg) incorporating a Laplace prior to promote sparsity in the model parameters, and provide a simple but efficient training procedure. The degree of sparsity obtained is determined by the value of a regularization parameter, which must be carefully tuned in order to optimize performance. This normally involves a model selection stage, based on a computationally intensive search for the minimizer of the cross-validation error. In this paper, we demonstrate that a simple Bayesian approach can be taken to eliminate this regularization parameter entirely, by integrating it out analytically using an uninformative Jeffrey's prior. The improved algorithm (BLogReg) is then typically two or three orders of magnitude faster than the original algorithm, as there is no longer a need for a model selection step. The BLogReg algorithm is also free from selection bias in performance estimation, a common pitfall in the application of machine learning algorithms in cancer classification. The SLogReg, BLogReg and Relevance Vector Machine (RVM) gene selection algorithms are evaluated over the well-studied colon cancer and leukaemia benchmark datasets. The leave-one-out estimates of the probability of test error and cross-entropy of the BLogReg and SLogReg algorithms are very similar, however the BlogReg algorithm is found to be considerably faster than the original SLogReg algorithm. Using nested cross-validation to avoid selection bias, performance estimation for SLogReg on the leukaemia dataset takes almost 48 h, whereas the corresponding result for BLogReg is obtained in only 1 min 24 s, making BLogReg by far the more practical algorithm. BLogReg also demonstrates better estimates of conditional probability than the RVM, which are of great importance in medical applications, with similar computational expense. A MATLAB implementation of the sparse logistic regression algorithm with Bayesian regularization (BLogReg) is available from http://theoval.cmp.uea.ac.uk/~gcc/cbl/blogreg/

A Comparison of Japan and U.K. SF-6D Health-State Valuations Using a Non-Parametric Bayesian Method.

PubMed

Kharroubi, Samer A

2015-08-01

There is interest in the extent to which valuations of health may differ between different countries and cultures, but few studies have compared preference values of health states obtained in different countries. We sought to estimate and compare two directly elicited valuations for SF-6D health states between the Japan and U.K. general adult populations using Bayesian methods. We analysed data from two SF-6D valuation studies where, using similar standard gamble protocols, values for 241 and 249 states were elicited from representative samples of the Japan and U.K. general adult populations, respectively. We estimate a function applicable across both countries that explicitly accounts for the differences between them, and is estimated using data from both countries. The results suggest that differences in SF-6D health-state valuations between the Japan and U.K. general populations are potentially important. The magnitude of these country-specific differences in health-state valuation depended, however, in a complex way on the levels of individual dimensions. The new Bayesian non-parametric method is a powerful approach for analysing data from multiple nationalities or ethnic groups, to understand the differences between them and potentially to estimate the underlying utility functions more efficiently.

Invited commentary: Lost in estimation--searching for alternatives to markov chains to fit complex Bayesian models.

PubMed

Molitor, John

2012-03-01

Bayesian methods have seen an increase in popularity in a wide variety of scientific fields, including epidemiology. One of the main reasons for their widespread application is the power of the Markov chain Monte Carlo (MCMC) techniques generally used to fit these models. As a result, researchers often implicitly associate Bayesian models with MCMC estimation procedures. However, Bayesian models do not always require Markov-chain-based methods for parameter estimation. This is important, as MCMC estimation methods, while generally quite powerful, are complex and computationally expensive and suffer from convergence problems related to the manner in which they generate correlated samples used to estimate probability distributions for parameters of interest. In this issue of the Journal, Cole et al. (Am J Epidemiol. 2012;175(5):368-375) present an interesting paper that discusses non-Markov-chain-based approaches to fitting Bayesian models. These methods, though limited, can overcome some of the problems associated with MCMC techniques and promise to provide simpler approaches to fitting Bayesian models. Applied researchers will find these estimation approaches intuitively appealing and will gain a deeper understanding of Bayesian models through their use. However, readers should be aware that other non-Markov-chain-based methods are currently in active development and have been widely published in other fields.

Predictive distributions for between-study heterogeneity and simple methods for their application in Bayesian meta-analysis

PubMed Central

Turner, Rebecca M; Jackson, Dan; Wei, Yinghui; Thompson, Simon G; Higgins, Julian P T

2015-01-01

Numerous meta-analyses in healthcare research combine results from only a small number of studies, for which the variance representing between-study heterogeneity is estimated imprecisely. A Bayesian approach to estimation allows external evidence on the expected magnitude of heterogeneity to be incorporated. The aim of this paper is to provide tools that improve the accessibility of Bayesian meta-analysis. We present two methods for implementing Bayesian meta-analysis, using numerical integration and importance sampling techniques. Based on 14 886 binary outcome meta-analyses in the Cochrane Database of Systematic Reviews, we derive a novel set of predictive distributions for the degree of heterogeneity expected in 80 settings depending on the outcomes assessed and comparisons made. These can be used as prior distributions for heterogeneity in future meta-analyses. The two methods are implemented in R, for which code is provided. Both methods produce equivalent results to standard but more complex Markov chain Monte Carlo approaches. The priors are derived as log-normal distributions for the between-study variance, applicable to meta-analyses of binary outcomes on the log odds-ratio scale. The methods are applied to two example meta-analyses, incorporating the relevant predictive distributions as prior distributions for between-study heterogeneity. We have provided resources to facilitate Bayesian meta-analysis, in a form accessible to applied researchers, which allow relevant prior information on the degree of heterogeneity to be incorporated. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd. PMID:25475839

On estimating the accuracy of monitoring methods using Bayesian error propagation technique

NASA Astrophysics Data System (ADS)

Zonta, Daniele; Bruschetta, Federico; Cappello, Carlo; Zandonini, R.; Pozzi, Matteo; Wang, Ming; Glisic, B.; Inaudi, D.; Posenato, D.; Zhao, Y.

2014-04-01

This paper illustrates an application of Bayesian logic to monitoring data analysis and structural condition state inference. The case study is a 260 m long cable-stayed bridge spanning the Adige River 10 km north of the town of Trento, Italy. This is a statically indeterminate structure, having a composite steel-concrete deck, supported by 12 stay cables. Structural redundancy, possible relaxation losses and an as-built condition differing from design, suggest that long-term load redistribution between cables can be expected. To monitor load redistribution, the owner decided to install a monitoring system which combines built-on-site elasto-magnetic and fiber-optic sensors. In this note, we discuss a rational way to improve the accuracy of the load estimate from the EM sensors taking advantage of the FOS information. More specifically, we use a multi-sensor Bayesian data fusion approach which combines the information from the two sensing systems with the prior knowledge, including design information and the outcomes of laboratory calibration. Using the data acquired to date, we demonstrate that combining the two measurements allows a more accurate estimate of the cable load, to better than 50 kN.

Bayesian estimation of the discrete coefficient of determination.

PubMed

Chen, Ting; Braga-Neto, Ulisses M

2016-12-01

The discrete coefficient of determination (CoD) measures the nonlinear interaction between discrete predictor and target variables and has had far-reaching applications in Genomic Signal Processing. Previous work has addressed the inference of the discrete CoD using classical parametric and nonparametric approaches. In this paper, we introduce a Bayesian framework for the inference of the discrete CoD. We derive analytically the optimal minimum mean-square error (MMSE) CoD estimator, as well as a CoD estimator based on the Optimal Bayesian Predictor (OBP). For the latter estimator, exact expressions for its bias, variance, and root-mean-square (RMS) are given. The accuracy of both Bayesian CoD estimators with non-informative and informative priors, under fixed or random parameters, is studied via analytical and numerical approaches. We also demonstrate the application of the proposed Bayesian approach in the inference of gene regulatory networks, using gene-expression data from a previously published study on metastatic melanoma.

Multiscale Bayesian neural networks for soil water content estimation

NASA Astrophysics Data System (ADS)

Jana, Raghavendra B.; Mohanty, Binayak P.; Springer, Everett P.

2008-08-01

Artificial neural networks (ANN) have been used for some time now to estimate soil hydraulic parameters from other available or more easily measurable soil properties. However, most such uses of ANNs as pedotransfer functions (PTFs) have been at matching spatial scales (1:1) of inputs and outputs. This approach assumes that the outputs are only required at the same scale as the input data. Unfortunately, this is rarely true. Different hydrologic, hydroclimatic, and contaminant transport models require soil hydraulic parameter data at different spatial scales, depending upon their grid sizes. While conventional (deterministic) ANNs have been traditionally used in these studies, the use of Bayesian training of ANNs is a more recent development. In this paper, we develop a Bayesian framework to derive soil water retention function including its uncertainty at the point or local scale using PTFs trained with coarser-scale Soil Survey Geographic (SSURGO)-based soil data. The approach includes an ANN trained with Bayesian techniques as a PTF tool with training and validation data collected across spatial extents (scales) in two different regions in the United States. The two study areas include the Las Cruces Trench site in the Rio Grande basin of New Mexico, and the Southern Great Plains 1997 (SGP97) hydrology experimental region in Oklahoma. Each region-specific Bayesian ANN is trained using soil texture and bulk density data from the SSURGO database (scale 1:24,000), and predictions of the soil water contents at different pressure heads with point scale data (1:1) inputs are made. The resulting outputs are corrected for bias using both linear and nonlinear correction techniques. The results show good agreement between the soil water content values measured at the point scale and those predicted by the Bayesian ANN-based PTFs for both the study sites. Overall, Bayesian ANNs coupled with nonlinear bias correction are found to be very suitable tools for deriving soil hydraulic parameters at the local/fine scale from soil physical properties at coarser-scale and across different spatial extents. This approach could potentially be used for soil hydraulic properties estimation and downscaling.

Estimation of the latent mediated effect with ordinal data using the limited-information and Bayesian full-information approaches.

PubMed

Chen, Jinsong; Zhang, Dake; Choi, Jaehwa

2015-12-01

It is common to encounter latent variables with ordinal data in social or behavioral research. Although a mediated effect of latent variables (latent mediated effect, or LME) with ordinal data may appear to be a straightforward combination of LME with continuous data and latent variables with ordinal data, the methodological challenges to combine the two are not trivial. This research covers model structures as complex as LME and formulates both point and interval estimates of LME for ordinal data using the Bayesian full-information approach. We also combine weighted least squares (WLS) estimation with the bias-corrected bootstrapping (BCB; Efron Journal of the American Statistical Association, 82, 171-185, 1987) method or the traditional delta method as the limited-information approach. We evaluated the viability of these different approaches across various conditions through simulation studies, and provide an empirical example to illustrate the approaches. We found that the Bayesian approach with reasonably informative priors is preferred when both point and interval estimates are of interest and the sample size is 200 or above.

A Bayesian Assessment of Seismic Semi-Periodicity Forecasts

NASA Astrophysics Data System (ADS)

Nava, F.; Quinteros, C.; Glowacka, E.; Frez, J.

2016-01-01

Among the schemes for earthquake forecasting, the search for semi-periodicity during large earthquakes in a given seismogenic region plays an important role. When considering earthquake forecasts based on semi-periodic sequence identification, the Bayesian formalism is a useful tool for: (1) assessing how well a given earthquake satisfies a previously made forecast; (2) re-evaluating the semi-periodic sequence probability; and (3) testing other prior estimations of the sequence probability. A comparison of Bayesian estimates with updated estimates of semi-periodic sequences that incorporate new data not used in the original estimates shows extremely good agreement, indicating that: (1) the probability that a semi-periodic sequence is not due to chance is an appropriate estimate for the prior sequence probability estimate; and (2) the Bayesian formalism does a very good job of estimating corrected semi-periodicity probabilities, using slightly less data than that used for updated estimates. The Bayesian approach is exemplified explicitly by its application to the Parkfield semi-periodic forecast, and results are given for its application to other forecasts in Japan and Venezuela.

Fractal dimension based damage identification incorporating multi-task sparse Bayesian learning

NASA Astrophysics Data System (ADS)

Huang, Yong; Li, Hui; Wu, Stephen; Yang, Yongchao

2018-07-01

Sensitivity to damage and robustness to noise are critical requirements for the effectiveness of structural damage detection. In this study, a two-stage damage identification method based on the fractal dimension analysis and multi-task Bayesian learning is presented. The Higuchi’s fractal dimension (HFD) based damage index is first proposed, directly examining the time-frequency characteristic of local free vibration data of structures based on the irregularity sensitivity and noise robustness analysis of HFD. Katz’s fractal dimension is then presented to analyze the abrupt irregularity change of the spatial curve of the displacement mode shape along the structure. At the second stage, the multi-task sparse Bayesian learning technique is employed to infer the final damage localization vector, which borrow the dependent strength of the two fractal dimension based damage indication information and also incorporate the prior knowledge that structural damage occurs at a limited number of locations in a structure in the absence of its collapse. To validate the capability of the proposed method, a steel beam and a bridge, named Yonghe Bridge, are analyzed as illustrative examples. The damage identification results demonstrate that the proposed method is capable of localizing single and multiple damages regardless of its severity, and show superior robustness under heavy noise as well.

SensibleSleep: A Bayesian Model for Learning Sleep Patterns from Smartphone Events

PubMed Central

Sekara, Vedran; Jonsson, Håkan; Larsen, Jakob Eg; Lehmann, Sune

2017-01-01

We propose a Bayesian model for extracting sleep patterns from smartphone events. Our method is able to identify individuals’ daily sleep periods and their evolution over time, and provides an estimation of the probability of sleep and wake transitions. The model is fitted to more than 400 participants from two different datasets, and we verify the results against ground truth from dedicated armband sleep trackers. We show that the model is able to produce reliable sleep estimates with an accuracy of 0.89, both at the individual and at the collective level. Moreover the Bayesian model is able to quantify uncertainty and encode prior knowledge about sleep patterns. Compared with existing smartphone-based systems, our method requires only screen on/off events, and is therefore much less intrusive in terms of privacy and more battery-efficient. PMID:28076375

SensibleSleep: A Bayesian Model for Learning Sleep Patterns from Smartphone Events.

PubMed

Cuttone, Andrea; Bækgaard, Per; Sekara, Vedran; Jonsson, Håkan; Larsen, Jakob Eg; Lehmann, Sune

2017-01-01

We propose a Bayesian model for extracting sleep patterns from smartphone events. Our method is able to identify individuals' daily sleep periods and their evolution over time, and provides an estimation of the probability of sleep and wake transitions. The model is fitted to more than 400 participants from two different datasets, and we verify the results against ground truth from dedicated armband sleep trackers. We show that the model is able to produce reliable sleep estimates with an accuracy of 0.89, both at the individual and at the collective level. Moreover the Bayesian model is able to quantify uncertainty and encode prior knowledge about sleep patterns. Compared with existing smartphone-based systems, our method requires only screen on/off events, and is therefore much less intrusive in terms of privacy and more battery-efficient.

Uncertainty Quantification of Medium-Term Heat Storage From Short-Term Geophysical Experiments Using Bayesian Evidential Learning

NASA Astrophysics Data System (ADS)

Hermans, Thomas; Nguyen, Frédéric; Klepikova, Maria; Dassargues, Alain; Caers, Jef

2018-04-01

In theory, aquifer thermal energy storage (ATES) systems can recover in winter the heat stored in the aquifer during summer to increase the energy efficiency of the system. In practice, the energy efficiency is often lower than expected from simulations due to spatial heterogeneity of hydraulic properties or non-favorable hydrogeological conditions. A proper design of ATES systems should therefore consider the uncertainty of the prediction related to those parameters. We use a novel framework called Bayesian Evidential Learning (BEL) to estimate the heat storage capacity of an alluvial aquifer using a heat tracing experiment. BEL is based on two main stages: pre- and postfield data acquisition. Before data acquisition, Monte Carlo simulations and global sensitivity analysis are used to assess the information content of the data to reduce the uncertainty of the prediction. After data acquisition, prior falsification and machine learning based on the same Monte Carlo are used to directly assess uncertainty on key prediction variables from observations. The result is a full quantification of the posterior distribution of the prediction conditioned to observed data, without any explicit full model inversion. We demonstrate the methodology in field conditions and validate the framework using independent measurements.

Bayesian Framework for Water Quality Model Uncertainty Estimation and Risk Management

EPA Science Inventory

A formal Bayesian methodology is presented for integrated model calibration and risk-based water quality management using Bayesian Monte Carlo simulation and maximum likelihood estimation (BMCML). The primary focus is on lucid integration of model calibration with risk-based wat...

APPLICATION OF BAYESIAN MONTE CARLO ANALYSIS TO A LAGRANGIAN PHOTOCHEMICAL AIR QUALITY MODEL. (R824792)

EPA Science Inventory

Uncertainties in ozone concentrations predicted with a Lagrangian photochemical air quality model have been estimated using Bayesian Monte Carlo (BMC) analysis. Bayesian Monte Carlo analysis provides a means of combining subjective "prior" uncertainty estimates developed ...

Estimating Tree Height-Diameter Models with the Bayesian Method

PubMed Central

Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the “best” model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2. PMID:24711733

Estimating tree height-diameter models with the Bayesian method.

PubMed

Zhang, Xiongqing; Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the "best" model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2.

Uncertainty quantification for nuclear density functional theory and information content of new measurements

DOE PAGES

McDonnell, J. D.; Schunck, N.; Higdon, D.; ...

2015-03-24

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squaresmore » optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. In addition, the example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.« less

Uncertainty quantification for nuclear density functional theory and information content of new measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

McDonnell, J. D.; Schunck, N.; Higdon, D.

2015-03-24

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squaresmore » optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. As a result, the example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.« less

Statistical Bayesian method for reliability evaluation based on ADT data

NASA Astrophysics Data System (ADS)

Lu, Dawei; Wang, Lizhi; Sun, Yusheng; Wang, Xiaohong

2018-05-01

Accelerated degradation testing (ADT) is frequently conducted in the laboratory to predict the products’ reliability under normal operating conditions. Two kinds of methods, degradation path models and stochastic process models, are utilized to analyze degradation data and the latter one is the most popular method. However, some limitations like imprecise solution process and estimation result of degradation ratio still exist, which may affect the accuracy of the acceleration model and the extrapolation value. Moreover, the conducted solution of this problem, Bayesian method, lose key information when unifying the degradation data. In this paper, a new data processing and parameter inference method based on Bayesian method is proposed to handle degradation data and solve the problems above. First, Wiener process and acceleration model is chosen; Second, the initial values of degradation model and parameters of prior and posterior distribution under each level is calculated with updating and iteration of estimation values; Third, the lifetime and reliability values are estimated on the basis of the estimation parameters; Finally, a case study is provided to demonstrate the validity of the proposed method. The results illustrate that the proposed method is quite effective and accuracy in estimating the lifetime and reliability of a product.

Bayesian Retrieval of Complete Posterior PDFs of Oceanic Rain Rate From Microwave Observations

NASA Technical Reports Server (NTRS)

Chiu, J. Christine; Petty, Grant W.

2005-01-01

This paper presents a new Bayesian algorithm for retrieving surface rain rate from Tropical Rainfall Measurements Mission (TRMM) Microwave Imager (TMI) over the ocean, along with validations against estimates from the TRMM Precipitation Radar (PR). The Bayesian approach offers a rigorous basis for optimally combining multichannel observations with prior knowledge. While other rain rate algorithms have been published that are based at least partly on Bayesian reasoning, this is believed to be the first self-contained algorithm that fully exploits Bayes Theorem to yield not just a single rain rate, but rather a continuous posterior probability distribution of rain rate. To advance our understanding of theoretical benefits of the Bayesian approach, we have conducted sensitivity analyses based on two synthetic datasets for which the true conditional and prior distribution are known. Results demonstrate that even when the prior and conditional likelihoods are specified perfectly, biased retrievals may occur at high rain rates. This bias is not the result of a defect of the Bayesian formalism but rather represents the expected outcome when the physical constraint imposed by the radiometric observations is weak, due to saturation effects. It is also suggested that the choice of the estimators and the prior information are both crucial to the retrieval. In addition, the performance of our Bayesian algorithm is found to be comparable to that of other benchmark algorithms in real-world applications, while having the additional advantage of providing a complete continuous posterior probability distribution of surface rain rate.

Accurate Biomass Estimation via Bayesian Adaptive Sampling

NASA Technical Reports Server (NTRS)

Wheeler, Kevin R.; Knuth, Kevin H.; Castle, Joseph P.; Lvov, Nikolay

2005-01-01

The following concepts were introduced: a) Bayesian adaptive sampling for solving biomass estimation; b) Characterization of MISR Rahman model parameters conditioned upon MODIS landcover. c) Rigorous non-parametric Bayesian approach to analytic mixture model determination. d) Unique U.S. asset for science product validation and verification.

HIV Trends in the United States: Diagnoses and Estimated Incidence

PubMed Central

Song, Ruiguang; Tang, Tian; An, Qian; Prejean, Joseph; Dietz, Patricia; Hernandez, Angela L; Green, Timothy; Harris, Norma; McCray, Eugene; Mermin, Jonathan

2017-01-01

Background The best indicator of the impact of human immunodeficiency virus (HIV) prevention programs is the incidence of infection; however, HIV is a chronic infection and HIV diagnoses may include infections that occurred years before diagnosis. Alternative methods to estimate incidence use diagnoses, stage of disease, and laboratory assays of infection recency. Using a consistent, accurate method would allow for timely interpretation of HIV trends. Objective The objective of our study was to assess the recent progress toward reducing HIV infections in the United States overall and among selected population segments with available incidence estimation methods. Methods Data on cases of HIV infection reported to national surveillance for 2008-2013 were used to compare trends in HIV diagnoses, unadjusted and adjusted for reporting delay, and model-based incidence for the US population aged ≥13 years. Incidence was estimated using a biomarker for recency of infection (stratified extrapolation approach) and 2 back-calculation models (CD4 and Bayesian hierarchical models). HIV testing trends were determined from behavioral surveys for persons aged ≥18 years. Analyses were stratified by sex, race or ethnicity (black, Hispanic or Latino, and white), and transmission category (men who have sex with men, MSM). Results On average, HIV diagnoses decreased 4.0% per year from 48,309 in 2008 to 39,270 in 2013 (P<.001). Adjusting for reporting delays, diagnoses decreased 3.1% per year (P<.001). The CD4 model estimated an annual decrease in incidence of 4.6% (P<.001) and the Bayesian hierarchical model 2.6% (P<.001); the stratified extrapolation approach estimated a stable incidence. During these years, overall, the percentage of persons who ever had received an HIV test or had had a test within the past year remained stable; among MSM testing increased. For women, all 3 incidence models corroborated the decreasing trend in HIV diagnoses, and HIV diagnoses and 2 incidence models indicated decreases among blacks and whites. The CD4 and Bayesian hierarchical models, but not the stratified extrapolation approach, indicated decreases in incidence among MSM. Conclusions HIV diagnoses and CD4 and Bayesian hierarchical model estimates indicated decreases in HIV incidence overall, among both sexes and all race or ethnicity groups. Further progress depends on effectively reducing HIV incidence among MSM, among whom the majority of new infections occur. PMID:28159730

An economic growth model based on financial credits distribution to the government economy priority sectors of each regency in Indonesia using hierarchical Bayesian method

NASA Astrophysics Data System (ADS)

Yasmirullah, Septia Devi Prihastuti; Iriawan, Nur; Sipayung, Feronika Rosalinda

2017-11-01

The success of regional economic establishment could be measured by economic growth. Since the Act No. 32 of 2004 has been implemented, unbalance economic among the regency in Indonesia is increasing. This condition is contrary different with the government goal to build society welfare through the economic activity development in each region. This research aims to examine economic growth through the distribution of bank credits to each Indonesia's regency. The data analyzed in this research is hierarchically structured data which follow normal distribution in first level. Two modeling approaches are employed in this research, a global-one level Bayesian approach and two-level hierarchical Bayesian approach. The result shows that hierarchical Bayesian has succeeded to demonstrate a better estimation than a global-one level Bayesian. It proves that the different economic growth in each province is significantly influenced by the variations of micro level characteristics in each province. These variations are significantly affected by cities and province characteristics in second level.

MPN estimation of qPCR target sequence recoveries from whole cell calibrator samples.

PubMed

Sivaganesan, Mano; Siefring, Shawn; Varma, Manju; Haugland, Richard A

2011-12-01

DNA extracts from enumerated target organism cells (calibrator samples) have been used for estimating Enterococcus cell equivalent densities in surface waters by a comparative cycle threshold (Ct) qPCR analysis method. To compare surface water Enterococcus density estimates from different studies by this approach, either a consistent source of calibrator cells must be used or the estimates must account for any differences in target sequence recoveries from different sources of calibrator cells. In this report we describe two methods for estimating target sequence recoveries from whole cell calibrator samples based on qPCR analyses of their serially diluted DNA extracts and most probable number (MPN) calculation. The first method employed a traditional MPN calculation approach. The second method employed a Bayesian hierarchical statistical modeling approach and a Monte Carlo Markov Chain (MCMC) simulation method to account for the uncertainty in these estimates associated with different individual samples of the cell preparations, different dilutions of the DNA extracts and different qPCR analytical runs. The two methods were applied to estimate mean target sequence recoveries per cell from two different lots of a commercially available source of enumerated Enterococcus cell preparations. The mean target sequence recovery estimates (and standard errors) per cell from Lot A and B cell preparations by the Bayesian method were 22.73 (3.4) and 11.76 (2.4), respectively, when the data were adjusted for potential false positive results. Means were similar for the traditional MPN approach which cannot comparably assess uncertainty in the estimates. Cell numbers and estimates of recoverable target sequences in calibrator samples prepared from the two cell sources were also used to estimate cell equivalent and target sequence quantities recovered from surface water samples in a comparative Ct method. Our results illustrate the utility of the Bayesian method in accounting for uncertainty, the high degree of precision attainable by the MPN approach and the need to account for the differences in target sequence recoveries from different calibrator sample cell sources when they are used in the comparative Ct method. Published by Elsevier B.V.

Performance evaluation of two serological tests for contagious bovine pleuropneumonia (CBPP) detection in an enzootic area using a Bayesian framework.

PubMed

Sidibé, Cheick Abou Kounta; Grosbois, Vladimir; Thiaucourt, François; Niang, Mamadou; Lesnoff, Matthieu; Roger, François

2012-08-01

A Bayesian approach, allowing for conditional dependence between two tests was used to estimate without gold standard the sensitivities of complement fixation test (CFT) and competitive enzyme-linked immunosorbent assay test (cELISA) and the serological prevalence of CBPP in a cattle population of the Central Delta of the Niger River in Mali, where CBPP is enzootic and the true prevalence and animals serological state were unknown. A significant difference (P = 0.99) was observed between the sensitivities of the two tests, estimated at 73.7% (95% probability interval [PI], 63.4-82.7) for cELISA and 42.3% (95% PI, 33.3-53.7) for CFT. Individual-level serological prevalence in the study population was estimated at 14.1% (95% PI, 10.8-16.9). Our results indicate that in enzootic areas, cELISA performs better in terms of sensitivity than CFT. However, negative conditional sensitivity dependence between the two tests was detected, implying that to achieve maximum sensitivity, the two tests should be applied in parallel.

A Bayesian hierarchical model for mortality data from cluster-sampling household surveys in humanitarian crises.

PubMed

Heudtlass, Peter; Guha-Sapir, Debarati; Speybroeck, Niko

2018-05-31

The crude death rate (CDR) is one of the defining indicators of humanitarian emergencies. When data from vital registration systems are not available, it is common practice to estimate the CDR from household surveys with cluster-sampling design. However, sample sizes are often too small to compare mortality estimates to emergency thresholds, at least in a frequentist framework. Several authors have proposed Bayesian methods for health surveys in humanitarian crises. Here, we develop an approach specifically for mortality data and cluster-sampling surveys. We describe a Bayesian hierarchical Poisson-Gamma mixture model with generic (weakly informative) priors that could be used as default in absence of any specific prior knowledge, and compare Bayesian and frequentist CDR estimates using five different mortality datasets. We provide an interpretation of the Bayesian estimates in the context of an emergency threshold and demonstrate how to interpret parameters at the cluster level and ways in which informative priors can be introduced. With the same set of weakly informative priors, Bayesian CDR estimates are equivalent to frequentist estimates, for all practical purposes. The probability that the CDR surpasses the emergency threshold can be derived directly from the posterior of the mean of the mixing distribution. All observation in the datasets contribute to the estimation of cluster-level estimates, through the hierarchical structure of the model. In a context of sparse data, Bayesian mortality assessments have advantages over frequentist ones already when using only weakly informative priors. More informative priors offer a formal and transparent way of combining new data with existing data and expert knowledge and can help to improve decision-making in humanitarian crises by complementing frequentist estimates.

Statistical properties of four effect-size measures for mediation models.

PubMed

Miočević, Milica; O'Rourke, Holly P; MacKinnon, David P; Brown, Hendricks C

2018-02-01

This project examined the performance of classical and Bayesian estimators of four effect size measures for the indirect effect in a single-mediator model and a two-mediator model. Compared to the proportion and ratio mediation effect sizes, standardized mediation effect-size measures were relatively unbiased and efficient in the single-mediator model and the two-mediator model. Percentile and bias-corrected bootstrap interval estimates of ab/s Y , and ab(s X )/s Y in the single-mediator model outperformed interval estimates of the proportion and ratio effect sizes in terms of power, Type I error rate, coverage, imbalance, and interval width. For the two-mediator model, standardized effect-size measures were superior to the proportion and ratio effect-size measures. Furthermore, it was found that Bayesian point and interval summaries of posterior distributions of standardized effect-size measures reduced excessive relative bias for certain parameter combinations. The standardized effect-size measures are the best effect-size measures for quantifying mediated effects.

An introduction to Bayesian statistics in health psychology.

PubMed

Depaoli, Sarah; Rus, Holly M; Clifton, James P; van de Schoot, Rens; Tiemensma, Jitske

2017-09-01

The aim of the current article is to provide a brief introduction to Bayesian statistics within the field of health psychology. Bayesian methods are increasing in prevalence in applied fields, and they have been shown in simulation research to improve the estimation accuracy of structural equation models, latent growth curve (and mixture) models, and hierarchical linear models. Likewise, Bayesian methods can be used with small sample sizes since they do not rely on large sample theory. In this article, we discuss several important components of Bayesian statistics as they relate to health-based inquiries. We discuss the incorporation and impact of prior knowledge into the estimation process and the different components of the analysis that should be reported in an article. We present an example implementing Bayesian estimation in the context of blood pressure changes after participants experienced an acute stressor. We conclude with final thoughts on the implementation of Bayesian statistics in health psychology, including suggestions for reviewing Bayesian manuscripts and grant proposals. We have also included an extensive amount of online supplementary material to complement the content presented here, including Bayesian examples using many different software programmes and an extensive sensitivity analysis examining the impact of priors.

A tutorial on Bayesian bivariate meta-analysis of mixed binary-continuous outcomes with missing treatment effects.

PubMed

Gajic-Veljanoski, Olga; Cheung, Angela M; Bayoumi, Ahmed M; Tomlinson, George

2016-05-30

Bivariate random-effects meta-analysis (BVMA) is a method of data synthesis that accounts for treatment effects measured on two outcomes. BVMA gives more precise estimates of the population mean and predicted values than two univariate random-effects meta-analyses (UVMAs). BVMA also addresses bias from incomplete reporting of outcomes. A few tutorials have covered technical details of BVMA of categorical or continuous outcomes. Limited guidance is available on how to analyze datasets that include trials with mixed continuous-binary outcomes where treatment effects on one outcome or the other are not reported. Given the advantages of Bayesian BVMA for handling missing outcomes, we present a tutorial for Bayesian BVMA of incompletely reported treatment effects on mixed bivariate outcomes. This step-by-step approach can serve as a model for our intended audience, the methodologist familiar with Bayesian meta-analysis, looking for practical advice on fitting bivariate models. To facilitate application of the proposed methods, we include our WinBUGS code. As an example, we use aggregate-level data from published trials to demonstrate the estimation of the effects of vitamin K and bisphosphonates on two correlated bone outcomes, fracture, and bone mineral density. We present datasets where reporting of the pairs of treatment effects on both outcomes was 'partially' complete (i.e., pairs completely reported in some trials), and we outline steps for modeling the incompletely reported data. To assess what is gained from the additional work required by BVMA, we compare the resulting estimates to those from separate UVMAs. We discuss methodological findings and make four recommendations. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Sparsity-promoting and edge-preserving maximum a posteriori estimators in non-parametric Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Agapiou, Sergios; Burger, Martin; Dashti, Masoumeh; Helin, Tapio

2018-04-01

We consider the inverse problem of recovering an unknown functional parameter u in a separable Banach space, from a noisy observation vector y of its image through a known possibly non-linear map {{\\mathcal G}} . We adopt a Bayesian approach to the problem and consider Besov space priors (see Lassas et al (2009 Inverse Problems Imaging 3 87-122)), which are well-known for their edge-preserving and sparsity-promoting properties and have recently attracted wide attention especially in the medical imaging community. Our key result is to show that in this non-parametric setup the maximum a posteriori (MAP) estimates are characterized by the minimizers of a generalized Onsager-Machlup functional of the posterior. This is done independently for the so-called weak and strong MAP estimates, which as we show coincide in our context. In addition, we prove a form of weak consistency for the MAP estimators in the infinitely informative data limit. Our results are remarkable for two reasons: first, the prior distribution is non-Gaussian and does not meet the smoothness conditions required in previous research on non-parametric MAP estimates. Second, the result analytically justifies existing uses of the MAP estimate in finite but high dimensional discretizations of Bayesian inverse problems with the considered Besov priors.

What Is the Probability You Are a Bayesian?

ERIC Educational Resources Information Center

Wulff, Shaun S.; Robinson, Timothy J.

2014-01-01

Bayesian methodology continues to be widely used in statistical applications. As a result, it is increasingly important to introduce students to Bayesian thinking at early stages in their mathematics and statistics education. While many students in upper level probability courses can recite the differences in the Frequentist and Bayesian…

Space Shuttle RTOS Bayesian Network

NASA Technical Reports Server (NTRS)

Morris, A. Terry; Beling, Peter A.

2001-01-01

With shrinking budgets and the requirements to increase reliability and operational life of the existing orbiter fleet, NASA has proposed various upgrades for the Space Shuttle that are consistent with national space policy. The cockpit avionics upgrade (CAU), a high priority item, has been selected as the next major upgrade. The primary functions of cockpit avionics include flight control, guidance and navigation, communication, and orbiter landing support. Secondary functions include the provision of operational services for non-avionics systems such as data handling for the payloads and caution and warning alerts to the crew. Recently, a process to selection the optimal commercial-off-the-shelf (COTS) real-time operating system (RTOS) for the CAU was conducted by United Space Alliance (USA) Corporation, which is a joint venture between Boeing and Lockheed Martin, the prime contractor for space shuttle operations. In order to independently assess the RTOS selection, NASA has used the Bayesian network-based scoring methodology described in this paper. Our two-stage methodology addresses the issue of RTOS acceptability by incorporating functional, performance and non-functional software measures related to reliability, interoperability, certifiability, efficiency, correctness, business, legal, product history, cost and life cycle. The first stage of the methodology involves obtaining scores for the various measures using a Bayesian network. The Bayesian network incorporates the causal relationships between the various and often competing measures of interest while also assisting the inherently complex decision analysis process with its ability to reason under uncertainty. The structure and selection of prior probabilities for the network is extracted from experts in the field of real-time operating systems. Scores for the various measures are computed using Bayesian probability. In the second stage, multi-criteria trade-off analyses are performed between the scores. Using a prioritization of measures from the decision-maker, trade-offs between the scores are used to rank order the available set of RTOS candidates.

A Re-Evaluation of the Size of the White Shark (Carcharodon carcharias) Population off California, USA

PubMed Central

Burgess, George H.; Bruce, Barry D.; Cailliet, Gregor M.; Goldman, Kenneth J.; Grubbs, R. Dean; Lowe, Christopher G.; MacNeil, M. Aaron; Mollet, Henry F.; Weng, Kevin C.; O'Sullivan, John B.

2014-01-01

White sharks are highly migratory and segregate by sex, age and size. Unlike marine mammals, they neither surface to breathe nor frequent haul-out sites, hindering generation of abundance data required to estimate population size. A recent tag-recapture study used photographic identifications of white sharks at two aggregation sites to estimate abundance in “central California” at 219 mature and sub-adult individuals. They concluded this represented approximately one-half of the total abundance of mature and sub-adult sharks in the entire eastern North Pacific Ocean (ENP). This low estimate generated great concern within the conservation community, prompting petitions for governmental endangered species designations. We critically examine that study and find violations of model assumptions that, when considered in total, lead to population underestimates. We also use a Bayesian mixture model to demonstrate that the inclusion of transient sharks, characteristic of white shark aggregation sites, would substantially increase abundance estimates for the adults and sub-adults in the surveyed sub-population. Using a dataset obtained from the same sampling locations and widely accepted demographic methodology, our analysis indicates a minimum all-life stages population size of >2000 individuals in the California subpopulation is required to account for the number and size range of individual sharks observed at the two sampled sites. Even accounting for methodological and conceptual biases, an extrapolation of these data to estimate the white shark population size throughout the ENP is inappropriate. The true ENP white shark population size is likely several-fold greater as both our study and the original published estimate exclude non-aggregating sharks and those that independently aggregate at other important ENP sites. Accurately estimating the central California and ENP white shark population size requires methodologies that account for biases introduced by sampling a limited number of sites and that account for all life history stages across the species' range of habitats. PMID:24932483

A re-evaluation of the size of the white shark (Carcharodon carcharias) population off California, USA.

PubMed

Burgess, George H; Bruce, Barry D; Cailliet, Gregor M; Goldman, Kenneth J; Grubbs, R Dean; Lowe, Christopher G; MacNeil, M Aaron; Mollet, Henry F; Weng, Kevin C; O'Sullivan, John B

2014-01-01

White sharks are highly migratory and segregate by sex, age and size. Unlike marine mammals, they neither surface to breathe nor frequent haul-out sites, hindering generation of abundance data required to estimate population size. A recent tag-recapture study used photographic identifications of white sharks at two aggregation sites to estimate abundance in "central California" at 219 mature and sub-adult individuals. They concluded this represented approximately one-half of the total abundance of mature and sub-adult sharks in the entire eastern North Pacific Ocean (ENP). This low estimate generated great concern within the conservation community, prompting petitions for governmental endangered species designations. We critically examine that study and find violations of model assumptions that, when considered in total, lead to population underestimates. We also use a Bayesian mixture model to demonstrate that the inclusion of transient sharks, characteristic of white shark aggregation sites, would substantially increase abundance estimates for the adults and sub-adults in the surveyed sub-population. Using a dataset obtained from the same sampling locations and widely accepted demographic methodology, our analysis indicates a minimum all-life stages population size of >2000 individuals in the California subpopulation is required to account for the number and size range of individual sharks observed at the two sampled sites. Even accounting for methodological and conceptual biases, an extrapolation of these data to estimate the white shark population size throughout the ENP is inappropriate. The true ENP white shark population size is likely several-fold greater as both our study and the original published estimate exclude non-aggregating sharks and those that independently aggregate at other important ENP sites. Accurately estimating the central California and ENP white shark population size requires methodologies that account for biases introduced by sampling a limited number of sites and that account for all life history stages across the species' range of habitats.

Bayesian analysis of the flutter margin method in aeroelasticity

DOE PAGES

Khalil, Mohammad; Poirel, Dominique; Sarkar, Abhijit

2016-08-27

A Bayesian statistical framework is presented for Zimmerman and Weissenburger flutter margin method which considers the uncertainties in aeroelastic modal parameters. The proposed methodology overcomes the limitations of the previously developed least-square based estimation technique which relies on the Gaussian approximation of the flutter margin probability density function (pdf). Using the measured free-decay responses at subcritical (preflutter) airspeeds, the joint non-Gaussain posterior pdf of the modal parameters is sampled using the Metropolis–Hastings (MH) Markov chain Monte Carlo (MCMC) algorithm. The posterior MCMC samples of the modal parameters are then used to obtain the flutter margin pdfs and finally the fluttermore » speed pdf. The usefulness of the Bayesian flutter margin method is demonstrated using synthetic data generated from a two-degree-of-freedom pitch-plunge aeroelastic model. The robustness of the statistical framework is demonstrated using different sets of measurement data. In conclusion, it will be shown that the probabilistic (Bayesian) approach reduces the number of test points required in providing a flutter speed estimate for a given accuracy and precision.« less

Using a web-based application to define the accuracy of diagnostic tests when the gold standard is imperfect.

PubMed

Lim, Cherry; Wannapinij, Prapass; White, Lisa; Day, Nicholas P J; Cooper, Ben S; Peacock, Sharon J; Limmathurotsakul, Direk

2013-01-01

Estimates of the sensitivity and specificity for new diagnostic tests based on evaluation against a known gold standard are imprecise when the accuracy of the gold standard is imperfect. Bayesian latent class models (LCMs) can be helpful under these circumstances, but the necessary analysis requires expertise in computational programming. Here, we describe open-access web-based applications that allow non-experts to apply Bayesian LCMs to their own data sets via a user-friendly interface. Applications for Bayesian LCMs were constructed on a web server using R and WinBUGS programs. The models provided (http://mice.tropmedres.ac) include two Bayesian LCMs: the two-tests in two-population model (Hui and Walter model) and the three-tests in one-population model (Walter and Irwig model). Both models are available with simplified and advanced interfaces. In the former, all settings for Bayesian statistics are fixed as defaults. Users input their data set into a table provided on the webpage. Disease prevalence and accuracy of diagnostic tests are then estimated using the Bayesian LCM, and provided on the web page within a few minutes. With the advanced interfaces, experienced researchers can modify all settings in the models as needed. These settings include correlation among diagnostic test results and prior distributions for all unknown parameters. The web pages provide worked examples with both models using the original data sets presented by Hui and Walter in 1980, and by Walter and Irwig in 1988. We also illustrate the utility of the advanced interface using the Walter and Irwig model on a data set from a recent melioidosis study. The results obtained from the web-based applications were comparable to those published previously. The newly developed web-based applications are open-access and provide an important new resource for researchers worldwide to evaluate new diagnostic tests.

Estimating virus occurrence using Bayesian modeling in multiple drinking water systems of the United States

USGS Publications Warehouse

Varughese, Eunice A.; Brinkman, Nichole E; Anneken, Emily M; Cashdollar, Jennifer S; Fout, G. Shay; Furlong, Edward T.; Kolpin, Dana W.; Glassmeyer, Susan T.; Keely, Scott P

2017-01-01

incorporated into a Bayesian model to more accurately determine viral load in both source and treated water. Results of the Bayesian model indicated that viruses are present in source water and treated water. By using a Bayesian framework that incorporates inhibition, as well as many other parameters that affect viral detection, this study offers an approach for more accurately estimating the occurrence of viral pathogens in environmental waters.

Spatio-temporal interpolation of precipitation during monsoon periods in Pakistan

NASA Astrophysics Data System (ADS)

Hussain, Ijaz; Spöck, Gunter; Pilz, Jürgen; Yu, Hwa-Lung

2010-08-01

Spatio-temporal estimation of precipitation over a region is essential to the modeling of hydrologic processes for water resources management. The changes of magnitude and space-time heterogeneity of rainfall observations make space-time estimation of precipitation a challenging task. In this paper we propose a Box-Cox transformed hierarchical Bayesian multivariate spatio-temporal interpolation method for the skewed response variable. The proposed method is applied to estimate space-time monthly precipitation in the monsoon periods during 1974-2000, and 27-year monthly average precipitation data are obtained from 51 stations in Pakistan. The results of transformed hierarchical Bayesian multivariate spatio-temporal interpolation are compared to those of non-transformed hierarchical Bayesian interpolation by using cross-validation. The software developed by [11] is used for Bayesian non-stationary multivariate space-time interpolation. It is observed that the transformed hierarchical Bayesian method provides more accuracy than the non-transformed hierarchical Bayesian method.

Bayesian Sensitivity Analysis of Statistical Models with Missing Data

PubMed Central

ZHU, HONGTU; IBRAHIM, JOSEPH G.; TANG, NIANSHENG

2013-01-01

Methods for handling missing data depend strongly on the mechanism that generated the missing values, such as missing completely at random (MCAR) or missing at random (MAR), as well as other distributional and modeling assumptions at various stages. It is well known that the resulting estimates and tests may be sensitive to these assumptions as well as to outlying observations. In this paper, we introduce various perturbations to modeling assumptions and individual observations, and then develop a formal sensitivity analysis to assess these perturbations in the Bayesian analysis of statistical models with missing data. We develop a geometric framework, called the Bayesian perturbation manifold, to characterize the intrinsic structure of these perturbations. We propose several intrinsic influence measures to perform sensitivity analysis and quantify the effect of various perturbations to statistical models. We use the proposed sensitivity analysis procedure to systematically investigate the tenability of the non-ignorable missing at random (NMAR) assumption. Simulation studies are conducted to evaluate our methods, and a dataset is analyzed to illustrate the use of our diagnostic measures. PMID:24753718

A menu-driven software package of Bayesian nonparametric (and parametric) mixed models for regression analysis and density estimation.

PubMed

Karabatsos, George

2017-02-01

Most of applied statistics involves regression analysis of data. In practice, it is important to specify a regression model that has minimal assumptions which are not violated by data, to ensure that statistical inferences from the model are informative and not misleading. This paper presents a stand-alone and menu-driven software package, Bayesian Regression: Nonparametric and Parametric Models, constructed from MATLAB Compiler. Currently, this package gives the user a choice from 83 Bayesian models for data analysis. They include 47 Bayesian nonparametric (BNP) infinite-mixture regression models; 5 BNP infinite-mixture models for density estimation; and 31 normal random effects models (HLMs), including normal linear models. Each of the 78 regression models handles either a continuous, binary, or ordinal dependent variable, and can handle multi-level (grouped) data. All 83 Bayesian models can handle the analysis of weighted observations (e.g., for meta-analysis), and the analysis of left-censored, right-censored, and/or interval-censored data. Each BNP infinite-mixture model has a mixture distribution assigned one of various BNP prior distributions, including priors defined by either the Dirichlet process, Pitman-Yor process (including the normalized stable process), beta (two-parameter) process, normalized inverse-Gaussian process, geometric weights prior, dependent Dirichlet process, or the dependent infinite-probits prior. The software user can mouse-click to select a Bayesian model and perform data analysis via Markov chain Monte Carlo (MCMC) sampling. After the sampling completes, the software automatically opens text output that reports MCMC-based estimates of the model's posterior distribution and model predictive fit to the data. Additional text and/or graphical output can be generated by mouse-clicking other menu options. This includes output of MCMC convergence analyses, and estimates of the model's posterior predictive distribution, for selected functionals and values of covariates. The software is illustrated through the BNP regression analysis of real data.

Missing-value estimation using linear and non-linear regression with Bayesian gene selection.

PubMed

Zhou, Xiaobo; Wang, Xiaodong; Dougherty, Edward R

2003-11-22

Data from microarray experiments are usually in the form of large matrices of expression levels of genes under different experimental conditions. Owing to various reasons, there are frequently missing values. Estimating these missing values is important because they affect downstream analysis, such as clustering, classification and network design. Several methods of missing-value estimation are in use. The problem has two parts: (1) selection of genes for estimation and (2) design of an estimation rule. We propose Bayesian variable selection to obtain genes to be used for estimation, and employ both linear and nonlinear regression for the estimation rule itself. Fast implementation issues for these methods are discussed, including the use of QR decomposition for parameter estimation. The proposed methods are tested on data sets arising from hereditary breast cancer and small round blue-cell tumors. The results compare very favorably with currently used methods based on the normalized root-mean-square error. The appendix is available from http://gspsnap.tamu.edu/gspweb/zxb/missing_zxb/ (user: gspweb; passwd: gsplab).

Bayesian probabilistic population projections for all countries.

PubMed

Raftery, Adrian E; Li, Nan; Ševčíková, Hana; Gerland, Patrick; Heilig, Gerhard K

2012-08-28

Projections of countries' future populations, broken down by age and sex, are widely used for planning and research. They are mostly done deterministically, but there is a widespread need for probabilistic projections. We propose a bayesian method for probabilistic population projections for all countries. The total fertility rate and female and male life expectancies at birth are projected probabilistically using bayesian hierarchical models estimated via Markov chain Monte Carlo using United Nations population data for all countries. These are then converted to age-specific rates and combined with a cohort component projection model. This yields probabilistic projections of any population quantity of interest. The method is illustrated for five countries of different demographic stages, continents and sizes. The method is validated by an out of sample experiment in which data from 1950-1990 are used for estimation, and applied to predict 1990-2010. The method appears reasonably accurate and well calibrated for this period. The results suggest that the current United Nations high and low variants greatly underestimate uncertainty about the number of oldest old from about 2050 and that they underestimate uncertainty for high fertility countries and overstate uncertainty for countries that have completed the demographic transition and whose fertility has started to recover towards replacement level, mostly in Europe. The results also indicate that the potential support ratio (persons aged 20-64 per person aged 65+) will almost certainly decline dramatically in most countries over the coming decades.

Fast and Accurate Learning When Making Discrete Numerical Estimates.

PubMed

Sanborn, Adam N; Beierholm, Ulrik R

2016-04-01

Many everyday estimation tasks have an inherently discrete nature, whether the task is counting objects (e.g., a number of paint buckets) or estimating discretized continuous variables (e.g., the number of paint buckets needed to paint a room). While Bayesian inference is often used for modeling estimates made along continuous scales, discrete numerical estimates have not received as much attention, despite their common everyday occurrence. Using two tasks, a numerosity task and an area estimation task, we invoke Bayesian decision theory to characterize how people learn discrete numerical distributions and make numerical estimates. Across three experiments with novel stimulus distributions we found that participants fell between two common decision functions for converting their uncertain representation into a response: drawing a sample from their posterior distribution and taking the maximum of their posterior distribution. While this was consistent with the decision function found in previous work using continuous estimation tasks, surprisingly the prior distributions learned by participants in our experiments were much more adaptive: When making continuous estimates, participants have required thousands of trials to learn bimodal priors, but in our tasks participants learned discrete bimodal and even discrete quadrimodal priors within a few hundred trials. This makes discrete numerical estimation tasks good testbeds for investigating how people learn and make estimates.

Fast and Accurate Learning When Making Discrete Numerical Estimates

PubMed Central

Sanborn, Adam N.; Beierholm, Ulrik R.

2016-01-01

Many everyday estimation tasks have an inherently discrete nature, whether the task is counting objects (e.g., a number of paint buckets) or estimating discretized continuous variables (e.g., the number of paint buckets needed to paint a room). While Bayesian inference is often used for modeling estimates made along continuous scales, discrete numerical estimates have not received as much attention, despite their common everyday occurrence. Using two tasks, a numerosity task and an area estimation task, we invoke Bayesian decision theory to characterize how people learn discrete numerical distributions and make numerical estimates. Across three experiments with novel stimulus distributions we found that participants fell between two common decision functions for converting their uncertain representation into a response: drawing a sample from their posterior distribution and taking the maximum of their posterior distribution. While this was consistent with the decision function found in previous work using continuous estimation tasks, surprisingly the prior distributions learned by participants in our experiments were much more adaptive: When making continuous estimates, participants have required thousands of trials to learn bimodal priors, but in our tasks participants learned discrete bimodal and even discrete quadrimodal priors within a few hundred trials. This makes discrete numerical estimation tasks good testbeds for investigating how people learn and make estimates. PMID:27070155

iSEDfit: Bayesian spectral energy distribution modeling of galaxies

NASA Astrophysics Data System (ADS)

Moustakas, John

2017-08-01

iSEDfit uses Bayesian inference to extract the physical properties of galaxies from their observed broadband photometric spectral energy distribution (SED). In its default mode, the inputs to iSEDfit are the measured photometry (fluxes and corresponding inverse variances) and a measurement of the galaxy redshift. Alternatively, iSEDfit can be used to estimate photometric redshifts from the input photometry alone. After the priors have been specified, iSEDfit calculates the marginalized posterior probability distributions for the physical parameters of interest, including the stellar mass, star-formation rate, dust content, star formation history, and stellar metallicity. iSEDfit also optionally computes K-corrections and produces multiple "quality assurance" (QA) plots at each stage of the modeling procedure to aid in the interpretation of the prior parameter choices and subsequent fitting results. The software is distributed as part of the impro IDL suite.

Bayesian design criteria: computation, comparison, and application to a pharmacokinetic and a pharmacodynamic model.

PubMed

Merlé, Y; Mentré, F

1995-02-01

In this paper 3 criteria to design experiments for Bayesian estimation of the parameters of nonlinear models with respect to their parameters, when a prior distribution is available, are presented: the determinant of the Bayesian information matrix, the determinant of the pre-posterior covariance matrix, and the expected information provided by an experiment. A procedure to simplify the computation of these criteria is proposed in the case of continuous prior distributions and is compared with the criterion obtained from a linearization of the model about the mean of the prior distribution for the parameters. This procedure is applied to two models commonly encountered in the area of pharmacokinetics and pharmacodynamics: the one-compartment open model with bolus intravenous single-dose injection and the Emax model. They both involve two parameters. Additive as well as multiplicative gaussian measurement errors are considered with normal prior distributions. Various combinations of the variances of the prior distribution and of the measurement error are studied. Our attention is restricted to designs with limited numbers of measurements (1 or 2 measurements). This situation often occurs in practice when Bayesian estimation is performed. The optimal Bayesian designs that result vary with the variances of the parameter distribution and with the measurement error. The two-point optimal designs sometimes differ from the D-optimal designs for the mean of the prior distribution and may consist of replicating measurements. For the studied cases, the determinant of the Bayesian information matrix and its linearized form lead to the same optimal designs. In some cases, the pre-posterior covariance matrix can be far from its lower bound, namely, the inverse of the Bayesian information matrix, especially for the Emax model and a multiplicative measurement error. The expected information provided by the experiment and the determinant of the pre-posterior covariance matrix generally lead to the same designs except for the Emax model and the multiplicative measurement error. Results show that these criteria can be easily computed and that they could be incorporated in modules for designing experiments.

[Evaluation of estimation of prevalence ratio using bayesian log-binomial regression model].

PubMed

Gao, W L; Lin, H; Liu, X N; Ren, X W; Li, J S; Shen, X P; Zhu, S L

2017-03-10

To evaluate the estimation of prevalence ratio ( PR ) by using bayesian log-binomial regression model and its application, we estimated the PR of medical care-seeking prevalence to caregivers' recognition of risk signs of diarrhea in their infants by using bayesian log-binomial regression model in Openbugs software. The results showed that caregivers' recognition of infant' s risk signs of diarrhea was associated significantly with a 13% increase of medical care-seeking. Meanwhile, we compared the differences in PR 's point estimation and its interval estimation of medical care-seeking prevalence to caregivers' recognition of risk signs of diarrhea and convergence of three models (model 1: not adjusting for the covariates; model 2: adjusting for duration of caregivers' education, model 3: adjusting for distance between village and township and child month-age based on model 2) between bayesian log-binomial regression model and conventional log-binomial regression model. The results showed that all three bayesian log-binomial regression models were convergence and the estimated PRs were 1.130(95 %CI : 1.005-1.265), 1.128(95 %CI : 1.001-1.264) and 1.132(95 %CI : 1.004-1.267), respectively. Conventional log-binomial regression model 1 and model 2 were convergence and their PRs were 1.130(95 % CI : 1.055-1.206) and 1.126(95 % CI : 1.051-1.203), respectively, but the model 3 was misconvergence, so COPY method was used to estimate PR , which was 1.125 (95 %CI : 1.051-1.200). In addition, the point estimation and interval estimation of PRs from three bayesian log-binomial regression models differed slightly from those of PRs from conventional log-binomial regression model, but they had a good consistency in estimating PR . Therefore, bayesian log-binomial regression model can effectively estimate PR with less misconvergence and have more advantages in application compared with conventional log-binomial regression model.

Hierarchical structure of the Sicilian goats revealed by Bayesian analyses of microsatellite information.

PubMed

Siwek, M; Finocchiaro, R; Curik, I; Portolano, B

2011-02-01

Genetic structure and relationship amongst the main goat populations in Sicily (Girgentana, Derivata di Siria, Maltese and Messinese) were analysed using information from 19 microsatellite markers genotyped on 173 individuals. A posterior Bayesian approach implemented in the program STRUCTURE revealed a hierarchical structure with two clusters at the first level (Girgentana vs. Messinese, Derivata di Siria and Maltese), explaining 4.8% of variation (amovaФ(ST) estimate). Seven clusters nested within these first two clusters (further differentiations of Girgentana, Derivata di Siria and Maltese), explaining 8.5% of variation (amovaФ(SC) estimate). The analyses and methods applied in this study indicate their power to detect subtle population structure. © 2010 The Authors, Animal Genetics © 2010 Stichting International Foundation for Animal Genetics.

Rigorous Approach in Investigation of Seismic Structure and Source Characteristicsin Northeast Asia: Hierarchical and Trans-dimensional Bayesian Inversion

NASA Astrophysics Data System (ADS)

Mustac, M.; Kim, S.; Tkalcic, H.; Rhie, J.; Chen, Y.; Ford, S. R.; Sebastian, N.

2015-12-01

Conventional approaches to inverse problems suffer from non-linearity and non-uniqueness in estimations of seismic structures and source properties. Estimated results and associated uncertainties are often biased by applied regularizations and additional constraints, which are commonly introduced to solve such problems. Bayesian methods, however, provide statistically meaningful estimations of models and their uncertainties constrained by data information. In addition, hierarchical and trans-dimensional (trans-D) techniques are inherently implemented in the Bayesian framework to account for involved error statistics and model parameterizations, and, in turn, allow more rigorous estimations of the same. Here, we apply Bayesian methods throughout the entire inference process to estimate seismic structures and source properties in Northeast Asia including east China, the Korean peninsula, and the Japanese islands. Ambient noise analysis is first performed to obtain a base three-dimensional (3-D) heterogeneity model using continuous broadband waveforms from more than 300 stations. As for the tomography of surface wave group and phase velocities in the 5-70 s band, we adopt a hierarchical and trans-D Bayesian inversion method using Voronoi partition. The 3-D heterogeneity model is further improved by joint inversions of teleseismic receiver functions and dispersion data using a newly developed high-efficiency Bayesian technique. The obtained model is subsequently used to prepare 3-D structural Green's functions for the source characterization. A hierarchical Bayesian method for point source inversion using regional complete waveform data is applied to selected events from the region. The seismic structure and source characteristics with rigorously estimated uncertainties from the novel Bayesian methods provide enhanced monitoring and discrimination of seismic events in northeast Asia.

Phylogeny and Bayesian divergence time estimations of small-headed flies (Diptera: Acroceridae) using multiple molecular markers.

PubMed

Winterton, Shaun L; Wiegmann, Brian M; Schlinger, Evert I

2007-06-01

The first formal analysis of phylogenetic relationships among small-headed flies (Acroceridae) is presented based on DNA sequence data from two ribosomal (16S and 28S) and two protein-encoding genes: carbomoylphosphate synthase (CPS) domain of CAD (i.e., rudimentary locus) and cytochrome oxidase I (COI). DNA sequences from 40 species in 22 genera of Acroceridae (representing all three subfamilies) were compared with outgroup exemplars from Nemestrinidae, Stratiomyidae, Tabanidae, and Xylophagidae. Parsimony and Bayesian simultaneous analyses of the full data set recover a well-resolved and strongly supported hypothesis of phylogenetic relationships for major lineages within the family. Molecular evidence supports the monophyly of traditionally recognised subfamilies Philopotinae and Panopinae, but Acrocerinae are polyphyletic. Panopinae, sometimes considered "primitive" based on morphology and host-use, are always placed in a more derived position in the current study. Furthermore, these data support emerging morphological evidence that the type genus Acrocera Meigen, and its sister genus Sphaerops, are atypical acrocerids, comprising a sister lineage to all other Acroceridae. Based on the phylogeny generated in the simultaneous analysis, historical divergence times were estimated using Bayesian methodology constrained with fossil data. These estimates indicate Acroceridae likely evolved during the late Triassic but did not diversify greatly until the Cretaceous.

Efficient estimation of abundance for patchily distributed populations via two-phase, adaptive sampling.

USGS Publications Warehouse

Conroy, M.J.; Runge, J.P.; Barker, R.J.; Schofield, M.R.; Fonnesbeck, C.J.

2008-01-01

Many organisms are patchily distributed, with some patches occupied at high density, others at lower densities, and others not occupied. Estimation of overall abundance can be difficult and is inefficient via intensive approaches such as capture-mark-recapture (CMR) or distance sampling. We propose a two-phase sampling scheme and model in a Bayesian framework to estimate abundance for patchily distributed populations. In the first phase, occupancy is estimated by binomial detection samples taken on all selected sites, where selection may be of all sites available, or a random sample of sites. Detection can be by visual surveys, detection of sign, physical captures, or other approach. At the second phase, if a detection threshold is achieved, CMR or other intensive sampling is conducted via standard procedures (grids or webs) to estimate abundance. Detection and CMR data are then used in a joint likelihood to model probability of detection in the occupancy sample via an abundance-detection model. CMR modeling is used to estimate abundance for the abundance-detection relationship, which in turn is used to predict abundance at the remaining sites, where only detection data are collected. We present a full Bayesian modeling treatment of this problem, in which posterior inference on abundance and other parameters (detection, capture probability) is obtained under a variety of assumptions about spatial and individual sources of heterogeneity. We apply the approach to abundance estimation for two species of voles (Microtus spp.) in Montana, USA. We also use a simulation study to evaluate the frequentist properties of our procedure given known patterns in abundance and detection among sites as well as design criteria. For most population characteristics and designs considered, bias and mean-square error (MSE) were low, and coverage of true parameter values by Bayesian credibility intervals was near nominal. Our two-phase, adaptive approach allows efficient estimation of abundance of rare and patchily distributed species and is particularly appropriate when sampling in all patches is impossible, but a global estimate of abundance is required.

Estimating Bayesian Phylogenetic Information Content

PubMed Central

Lewis, Paul O.; Chen, Ming-Hui; Kuo, Lynn; Lewis, Louise A.; Fučíková, Karolina; Neupane, Suman; Wang, Yu-Bo; Shi, Daoyuan

2016-01-01

Measuring the phylogenetic information content of data has a long history in systematics. Here we explore a Bayesian approach to information content estimation. The entropy of the posterior distribution compared with the entropy of the prior distribution provides a natural way to measure information content. If the data have no information relevant to ranking tree topologies beyond the information supplied by the prior, the posterior and prior will be identical. Information in data discourages consideration of some hypotheses allowed by the prior, resulting in a posterior distribution that is more concentrated (has lower entropy) than the prior. We focus on measuring information about tree topology using marginal posterior distributions of tree topologies. We show that both the accuracy and the computational efficiency of topological information content estimation improve with use of the conditional clade distribution, which also allows topological information content to be partitioned by clade. We explore two important applications of our method: providing a compelling definition of saturation and detecting conflict among data partitions that can negatively affect analyses of concatenated data. [Bayesian; concatenation; conditional clade distribution; entropy; information; phylogenetics; saturation.] PMID:27155008

Bayesian Assessment of the Uncertainties of Estimates of a Conceptual Rainfall-Runoff Model Parameters

NASA Astrophysics Data System (ADS)

Silva, F. E. O. E.; Naghettini, M. D. C.; Fernandes, W.

2014-12-01

This paper evaluated the uncertainties associated with the estimation of the parameters of a conceptual rainfall-runoff model, through the use of Bayesian inference techniques by Monte Carlo simulation. The Pará River sub-basin, located in the upper São Francisco river basin, in southeastern Brazil, was selected for developing the studies. In this paper, we used the Rio Grande conceptual hydrologic model (EHR/UFMG, 2001) and the Markov Chain Monte Carlo simulation method named DREAM (VRUGT, 2008a). Two probabilistic models for the residues were analyzed: (i) the classic [Normal likelihood - r ≈ N (0, σ²)]; and (ii) a generalized likelihood (SCHOUPS & VRUGT, 2010), in which it is assumed that the differences between observed and simulated flows are correlated, non-stationary, and distributed as a Skew Exponential Power density. The assumptions made for both models were checked to ensure that the estimation of uncertainties in the parameters was not biased. The results showed that the Bayesian approach proved to be adequate to the proposed objectives, enabling and reinforcing the importance of assessing the uncertainties associated with hydrological modeling.

A biologically inspired neural model for visual and proprioceptive integration including sensory training.

PubMed

Saidi, Maryam; Towhidkhah, Farzad; Gharibzadeh, Shahriar; Lari, Abdolaziz Azizi

2013-12-01

Humans perceive the surrounding world by integration of information through different sensory modalities. Earlier models of multisensory integration rely mainly on traditional Bayesian and causal Bayesian inferences for single causal (source) and two causal (for two senses such as visual and auditory systems), respectively. In this paper a new recurrent neural model is presented for integration of visual and proprioceptive information. This model is based on population coding which is able to mimic multisensory integration of neural centers in the human brain. The simulation results agree with those achieved by casual Bayesian inference. The model can also simulate the sensory training process of visual and proprioceptive information in human. Training process in multisensory integration is a point with less attention in the literature before. The effect of proprioceptive training on multisensory perception was investigated through a set of experiments in our previous study. The current study, evaluates the effect of both modalities, i.e., visual and proprioceptive training and compares them with each other through a set of new experiments. In these experiments, the subject was asked to move his/her hand in a circle and estimate its position. The experiments were performed on eight subjects with proprioception training and eight subjects with visual training. Results of the experiments show three important points: (1) visual learning rate is significantly more than that of proprioception; (2) means of visual and proprioceptive errors are decreased by training but statistical analysis shows that this decrement is significant for proprioceptive error and non-significant for visual error, and (3) visual errors in training phase even in the beginning of it, is much less than errors of the main test stage because in the main test, the subject has to focus on two senses. The results of the experiments in this paper is in agreement with the results of the neural model simulation.

A Bayesian multi-stage cost-effectiveness design for animal studies in stroke research

PubMed Central

Cai, Chunyan; Ning, Jing; Huang, Xuelin

2017-01-01

Much progress has been made in the area of adaptive designs for clinical trials. However, little has been done regarding adaptive designs to identify optimal treatment strategies in animal studies. Motivated by an animal study of a novel strategy for treating strokes, we propose a Bayesian multi-stage cost-effectiveness design to simultaneously identify the optimal dose and determine the therapeutic treatment window for administrating the experimental agent. We consider a non-monotonic pattern for the dose-schedule-efficacy relationship and develop an adaptive shrinkage algorithm to assign more cohorts to admissible strategies. We conduct simulation studies to evaluate the performance of the proposed design by comparing it with two standard designs. These simulation studies show that the proposed design yields a significantly higher probability of selecting the optimal strategy, while it is generally more efficient and practical in terms of resource usage. PMID:27405325

Bayesian and “Anti-Bayesian” Biases in Sensory Integration for Action and Perception in the Size–Weight Illusion

PubMed Central

Brayanov, Jordan B.

2010-01-01

Which is heavier: a pound of lead or a pound of feathers? This classic trick question belies a simple but surprising truth: when lifted, the pound of lead feels heavier—a phenomenon known as the size–weight illusion. To estimate the weight of an object, our CNS combines two imperfect sources of information: a prior expectation, based on the object's appearance, and direct sensory information from lifting it. Bayes' theorem (or Bayes' law) defines the statistically optimal way to combine multiple information sources for maximally accurate estimation. Here we asked whether the mechanisms for combining these information sources produce statistically optimal weight estimates for both perceptions and actions. We first studied the ability of subjects to hold one hand steady when the other removed an object from it, under conditions in which sensory information about the object's weight sometimes conflicted with prior expectations based on its size. Since the ability to steady the supporting hand depends on the generation of a motor command that accounts for lift timing and object weight, hand motion can be used to gauge biases in weight estimation by the motor system. We found that these motor system weight estimates reflected the integration of prior expectations with real-time proprioceptive information in a Bayesian, statistically optimal fashion that discounted unexpected sensory information. This produces a motor size–weight illusion that consistently biases weight estimates toward prior expectations. In contrast, when subjects compared the weights of two objects, their perceptions defied Bayes' law, exaggerating the value of unexpected sensory information. This produces a perceptual size–weight illusion that biases weight perceptions away from prior expectations. We term this effect “anti-Bayesian” because the bias is opposite that seen in Bayesian integration. Our findings suggest that two fundamentally different strategies for the integration of prior expectations with sensory information coexist in the nervous system for weight estimation. PMID:20089821

Trans-dimensional and hierarchical Bayesian approaches toward rigorous estimation of seismic sources and structures in the Northeast Asia

NASA Astrophysics Data System (ADS)

Kim, Seongryong; Tkalčić, Hrvoje; Mustać, Marija; Rhie, Junkee; Ford, Sean

2016-04-01

A framework is presented within which we provide rigorous estimations for seismic sources and structures in the Northeast Asia. We use Bayesian inversion methods, which enable statistical estimations of models and their uncertainties based on data information. Ambiguities in error statistics and model parameterizations are addressed by hierarchical and trans-dimensional (trans-D) techniques, which can be inherently implemented in the Bayesian inversions. Hence reliable estimation of model parameters and their uncertainties is possible, thus avoiding arbitrary regularizations and parameterizations. Hierarchical and trans-D inversions are performed to develop a three-dimensional velocity model using ambient noise data. To further improve the model, we perform joint inversions with receiver function data using a newly developed Bayesian method. For the source estimation, a novel moment tensor inversion method is presented and applied to regional waveform data of the North Korean nuclear explosion tests. By the combination of new Bayesian techniques and the structural model, coupled with meaningful uncertainties related to each of the processes, more quantitative monitoring and discrimination of seismic events is possible.

Bayesian Estimation of Small Effects in Exercise and Sports Science.

PubMed

Mengersen, Kerrie L; Drovandi, Christopher C; Robert, Christian P; Pyne, David B; Gore, Christopher J

2016-01-01

The aim of this paper is to provide a Bayesian formulation of the so-called magnitude-based inference approach to quantifying and interpreting effects, and in a case study example provide accurate probabilistic statements that correspond to the intended magnitude-based inferences. The model is described in the context of a published small-scale athlete study which employed a magnitude-based inference approach to compare the effect of two altitude training regimens (live high-train low (LHTL), and intermittent hypoxic exposure (IHE)) on running performance and blood measurements of elite triathletes. The posterior distributions, and corresponding point and interval estimates, for the parameters and associated effects and comparisons of interest, were estimated using Markov chain Monte Carlo simulations. The Bayesian analysis was shown to provide more direct probabilistic comparisons of treatments and able to identify small effects of interest. The approach avoided asymptotic assumptions and overcame issues such as multiple testing. Bayesian analysis of unscaled effects showed a probability of 0.96 that LHTL yields a substantially greater increase in hemoglobin mass than IHE, a 0.93 probability of a substantially greater improvement in running economy and a greater than 0.96 probability that both IHE and LHTL yield a substantially greater improvement in maximum blood lactate concentration compared to a Placebo. The conclusions are consistent with those obtained using a 'magnitude-based inference' approach that has been promoted in the field. The paper demonstrates that a fully Bayesian analysis is a simple and effective way of analysing small effects, providing a rich set of results that are straightforward to interpret in terms of probabilistic statements.

A Bayesian Analysis of a Randomized Clinical Trial Comparing Antimetabolite Therapies for Non-Infectious Uveitis.

PubMed

Browne, Erica N; Rathinam, Sivakumar R; Kanakath, Anuradha; Thundikandy, Radhika; Babu, Manohar; Lietman, Thomas M; Acharya, Nisha R

2017-02-01

To conduct a Bayesian analysis of a randomized clinical trial (RCT) for non-infectious uveitis using expert opinion as a subjective prior belief. A RCT was conducted to determine which antimetabolite, methotrexate or mycophenolate mofetil, is more effective as an initial corticosteroid-sparing agent for the treatment of intermediate, posterior, and pan-uveitis. Before the release of trial results, expert opinion on the relative effectiveness of these two medications was collected via online survey. Members of the American Uveitis Society executive committee were invited to provide an estimate for the relative decrease in efficacy with a 95% credible interval (CrI). A prior probability distribution was created from experts' estimates. A Bayesian analysis was performed using the constructed expert prior probability distribution and the trial's primary outcome. A total of 11 of the 12 invited uveitis specialists provided estimates. Eight of 11 experts (73%) believed mycophenolate mofetil is more effective. The group prior belief was that the odds of treatment success for patients taking mycophenolate mofetil were 1.4-fold the odds of those taking methotrexate (95% CrI 0.03-45.0). The odds of treatment success with mycophenolate mofetil compared to methotrexate was 0.4 from the RCT (95% confidence interval 0.1-1.2) and 0.7 (95% CrI 0.2-1.7) from the Bayesian analysis. A Bayesian analysis combining expert belief with the trial's result did not indicate preference for one drug. However, the wide credible interval leaves open the possibility of a substantial treatment effect. This suggests clinical equipoise necessary to allow a larger, more definitive RCT.

A Gentle Introduction to Bayesian Analysis: Applications to Developmental Research

ERIC Educational Resources Information Center

van de Schoot, Rens; Kaplan, David; Denissen, Jaap; Asendorpf, Jens B.; Neyer, Franz J.; van Aken, Marcel A. G.

2014-01-01

Bayesian statistical methods are becoming ever more popular in applied and fundamental research. In this study a gentle introduction to Bayesian analysis is provided. It is shown under what circumstances it is attractive to use Bayesian estimation, and how to interpret properly the results. First, the ingredients underlying Bayesian methods are…

Bayesian estimation inherent in a Mexican-hat-type neural network

NASA Astrophysics Data System (ADS)

Takiyama, Ken

2016-05-01

Brain functions, such as perception, motor control and learning, and decision making, have been explained based on a Bayesian framework, i.e., to decrease the effects of noise inherent in the human nervous system or external environment, our brain integrates sensory and a priori information in a Bayesian optimal manner. However, it remains unclear how Bayesian computations are implemented in the brain. Herein, I address this issue by analyzing a Mexican-hat-type neural network, which was used as a model of the visual cortex, motor cortex, and prefrontal cortex. I analytically demonstrate that the dynamics of an order parameter in the model corresponds exactly to a variational inference of a linear Gaussian state-space model, a Bayesian estimation, when the strength of recurrent synaptic connectivity is appropriately stronger than that of an external stimulus, a plausible condition in the brain. This exact correspondence can reveal the relationship between the parameters in the Bayesian estimation and those in the neural network, providing insight for understanding brain functions.

Fast genomic predictions via Bayesian G-BLUP and multilocus models of threshold traits including censored Gaussian data.

PubMed

Kärkkäinen, Hanni P; Sillanpää, Mikko J

2013-09-04

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed.

Fast Genomic Predictions via Bayesian G-BLUP and Multilocus Models of Threshold Traits Including Censored Gaussian Data

PubMed Central

Kärkkäinen, Hanni P.; Sillanpää, Mikko J.

2013-01-01

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed. PMID:23821618

SPATIO-TEMPORAL MODELING OF AGRICULTURAL YIELD DATA WITH AN APPLICATION TO PRICING CROP INSURANCE CONTRACTS

PubMed Central

Ozaki, Vitor A.; Ghosh, Sujit K.; Goodwin, Barry K.; Shirota, Ricardo

2009-01-01

This article presents a statistical model of agricultural yield data based on a set of hierarchical Bayesian models that allows joint modeling of temporal and spatial autocorrelation. This method captures a comprehensive range of the various uncertainties involved in predicting crop insurance premium rates as opposed to the more traditional ad hoc, two-stage methods that are typically based on independent estimation and prediction. A panel data set of county-average yield data was analyzed for 290 counties in the State of Paraná (Brazil) for the period of 1990 through 2002. Posterior predictive criteria are used to evaluate different model specifications. This article provides substantial improvements in the statistical and actuarial methods often applied to the calculation of insurance premium rates. These improvements are especially relevant to situations where data are limited. PMID:19890450

Asteroid orbital error analysis: Theory and application

NASA Technical Reports Server (NTRS)

Muinonen, K.; Bowell, Edward

1992-01-01

We present a rigorous Bayesian theory for asteroid orbital error estimation in which the probability density of the orbital elements is derived from the noise statistics of the observations. For Gaussian noise in a linearized approximation the probability density is also Gaussian, and the errors of the orbital elements at a given epoch are fully described by the covariance matrix. The law of error propagation can then be applied to calculate past and future positional uncertainty ellipsoids (Cappellari et al. 1976, Yeomans et al. 1987, Whipple et al. 1991). To our knowledge, this is the first time a Bayesian approach has been formulated for orbital element estimation. In contrast to the classical Fisherian school of statistics, the Bayesian school allows a priori information to be formally present in the final estimation. However, Bayesian estimation does give the same results as Fisherian estimation when no priori information is assumed (Lehtinen 1988, and reference therein).

Bayesian Factor Analysis as a Variable Selection Problem: Alternative Priors and Consequences

PubMed Central

Lu, Zhao-Hua; Chow, Sy-Miin; Loken, Eric

2016-01-01

Factor analysis is a popular statistical technique for multivariate data analysis. Developments in the structural equation modeling framework have enabled the use of hybrid confirmatory/exploratory approaches in which factor loading structures can be explored relatively flexibly within a confirmatory factor analysis (CFA) framework. Recently, a Bayesian structural equation modeling (BSEM) approach (Muthén & Asparouhov, 2012) has been proposed as a way to explore the presence of cross-loadings in CFA models. We show that the issue of determining factor loading patterns may be formulated as a Bayesian variable selection problem in which Muthén and Asparouhov’s approach can be regarded as a BSEM approach with ridge regression prior (BSEM-RP). We propose another Bayesian approach, denoted herein as the Bayesian structural equation modeling with spike and slab prior (BSEM-SSP), which serves as a one-stage alternative to the BSEM-RP. We review the theoretical advantages and disadvantages of both approaches and compare their empirical performance relative to two modification indices-based approaches and exploratory factor analysis with target rotation. A teacher stress scale data set (Byrne, 2012; Pettegrew & Wolf, 1982) is used to demonstrate our approach. PMID:27314566

Good fences make for good neighbors but bad science: a review of what improves Bayesian reasoning and why

PubMed Central

Brase, Gary L.; Hill, W. Trey

2015-01-01

Bayesian reasoning, defined here as the updating of a posterior probability following new information, has historically been problematic for humans. Classic psychology experiments have tested human Bayesian reasoning through the use of word problems and have evaluated each participant’s performance against the normatively correct answer provided by Bayes’ theorem. The standard finding is of generally poor performance. Over the past two decades, though, progress has been made on how to improve Bayesian reasoning. Most notably, research has demonstrated that the use of frequencies in a natural sampling framework—as opposed to single-event probabilities—can improve participants’ Bayesian estimates. Furthermore, pictorial aids and certain individual difference factors also can play significant roles in Bayesian reasoning success. The mechanics of how to build tasks which show these improvements is not under much debate. The explanations for why naturally sampled frequencies and pictures help Bayesian reasoning remain hotly contested, however, with many researchers falling into ingrained “camps” organized around two dominant theoretical perspectives. The present paper evaluates the merits of these theoretical perspectives, including the weight of empirical evidence, theoretical coherence, and predictive power. By these criteria, the ecological rationality approach is clearly better than the heuristics and biases view. Progress in the study of Bayesian reasoning will depend on continued research that honestly, vigorously, and consistently engages across these different theoretical accounts rather than staying “siloed” within one particular perspective. The process of science requires an understanding of competing points of view, with the ultimate goal being integration. PMID:25873904

Good fences make for good neighbors but bad science: a review of what improves Bayesian reasoning and why.

PubMed

Brase, Gary L; Hill, W Trey

2015-01-01

Bayesian reasoning, defined here as the updating of a posterior probability following new information, has historically been problematic for humans. Classic psychology experiments have tested human Bayesian reasoning through the use of word problems and have evaluated each participant's performance against the normatively correct answer provided by Bayes' theorem. The standard finding is of generally poor performance. Over the past two decades, though, progress has been made on how to improve Bayesian reasoning. Most notably, research has demonstrated that the use of frequencies in a natural sampling framework-as opposed to single-event probabilities-can improve participants' Bayesian estimates. Furthermore, pictorial aids and certain individual difference factors also can play significant roles in Bayesian reasoning success. The mechanics of how to build tasks which show these improvements is not under much debate. The explanations for why naturally sampled frequencies and pictures help Bayesian reasoning remain hotly contested, however, with many researchers falling into ingrained "camps" organized around two dominant theoretical perspectives. The present paper evaluates the merits of these theoretical perspectives, including the weight of empirical evidence, theoretical coherence, and predictive power. By these criteria, the ecological rationality approach is clearly better than the heuristics and biases view. Progress in the study of Bayesian reasoning will depend on continued research that honestly, vigorously, and consistently engages across these different theoretical accounts rather than staying "siloed" within one particular perspective. The process of science requires an understanding of competing points of view, with the ultimate goal being integration.

Estimation of parameter uncertainty for an activated sludge model using Bayesian inference: a comparison with the frequentist method.

PubMed

Zonta, Zivko J; Flotats, Xavier; Magrí, Albert

2014-08-01

The procedure commonly used for the assessment of the parameters included in activated sludge models (ASMs) relies on the estimation of their optimal value within a confidence region (i.e. frequentist inference). Once optimal values are estimated, parameter uncertainty is computed through the covariance matrix. However, alternative approaches based on the consideration of the model parameters as probability distributions (i.e. Bayesian inference), may be of interest. The aim of this work is to apply (and compare) both Bayesian and frequentist inference methods when assessing uncertainty for an ASM-type model, which considers intracellular storage and biomass growth, simultaneously. Practical identifiability was addressed exclusively considering respirometric profiles based on the oxygen uptake rate and with the aid of probabilistic global sensitivity analysis. Parameter uncertainty was thus estimated according to both the Bayesian and frequentist inferential procedures. Results were compared in order to evidence the strengths and weaknesses of both approaches. Since it was demonstrated that Bayesian inference could be reduced to a frequentist approach under particular hypotheses, the former can be considered as a more generalist methodology. Hence, the use of Bayesian inference is encouraged for tackling inferential issues in ASM environments.

Bayesian parameter estimation for nonlinear modelling of biological pathways.

PubMed

Ghasemi, Omid; Lindsey, Merry L; Yang, Tianyi; Nguyen, Nguyen; Huang, Yufei; Jin, Yu-Fang

2011-01-01

The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC) method. We applied this approach to the biological pathways involved in the left ventricle (LV) response to myocardial infarction (MI) and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly parameterized dynamic systems. Our proposed Bayesian algorithm successfully estimated parameters in nonlinear mathematical models for biological pathways. This method can be further extended to high order systems and thus provides a useful tool to analyze biological dynamics and extract information using temporal data.

An Excel sheet for inferring children's number-knower levels from give-N data.

PubMed

Negen, James; Sarnecka, Barbara W; Lee, Michael D

2012-03-01

Number-knower levels are a series of stages of number concept development in early childhood. A child's number-knower level is typically assessed using the give-N task. Although the task procedure has been highly refined, the standard ways of analyzing give-N data remain somewhat crude. Lee and Sarnecka (Cogn Sci 34:51-67, 2010, in press) have developed a Bayesian model of children's performance on the give-N task that allows knower level to be inferred in a more principled way. However, this model requires considerable expertise and computational effort to implement and apply to data. Here, we present an approximation to the model's inference that can be computed with Microsoft Excel. We demonstrate the accuracy of the approximation and provide instructions for its use. This makes the powerful inferential capabilities of the Bayesian model accessible to developmental researchers interested in estimating knower levels from give-N data.

Model selection and model averaging in phylogenetics: advantages of akaike information criterion and bayesian approaches over likelihood ratio tests.

PubMed

Posada, David; Buckley, Thomas R

2004-10-01

Model selection is a topic of special relevance in molecular phylogenetics that affects many, if not all, stages of phylogenetic inference. Here we discuss some fundamental concepts and techniques of model selection in the context of phylogenetics. We start by reviewing different aspects of the selection of substitution models in phylogenetics from a theoretical, philosophical and practical point of view, and summarize this comparison in table format. We argue that the most commonly implemented model selection approach, the hierarchical likelihood ratio test, is not the optimal strategy for model selection in phylogenetics, and that approaches like the Akaike Information Criterion (AIC) and Bayesian methods offer important advantages. In particular, the latter two methods are able to simultaneously compare multiple nested or nonnested models, assess model selection uncertainty, and allow for the estimation of phylogenies and model parameters using all available models (model-averaged inference or multimodel inference). We also describe how the relative importance of the different parameters included in substitution models can be depicted. To illustrate some of these points, we have applied AIC-based model averaging to 37 mitochondrial DNA sequences from the subgenus Ohomopterus(genus Carabus) ground beetles described by Sota and Vogler (2001).

Approximate Bayesian estimation of extinction rate in the Finnish Daphnia magna metapopulation.

PubMed

Robinson, John D; Hall, David W; Wares, John P

2013-05-01

Approximate Bayesian computation (ABC) is useful for parameterizing complex models in population genetics. In this study, ABC was applied to simultaneously estimate parameter values for a model of metapopulation coalescence and test two alternatives to a strict metapopulation model in the well-studied network of Daphnia magna populations in Finland. The models shared four free parameters: the subpopulation genetic diversity (θS), the rate of gene flow among patches (4Nm), the founding population size (N0) and the metapopulation extinction rate (e) but differed in the distribution of extinction rates across habitat patches in the system. The three models had either a constant extinction rate in all populations (strict metapopulation), one population that was protected from local extinction (i.e. a persistent source), or habitat-specific extinction rates drawn from a distribution with specified mean and variance. Our model selection analysis favoured the model including a persistent source population over the two alternative models. Of the closest 750,000 data sets in Euclidean space, 78% were simulated under the persistent source model (estimated posterior probability = 0.769). This fraction increased to more than 85% when only the closest 150,000 data sets were considered (estimated posterior probability = 0.774). Approximate Bayesian computation was then used to estimate parameter values that might produce the observed set of summary statistics. Our analysis provided posterior distributions for e that included the point estimate obtained from previous data from the Finnish D. magna metapopulation. Our results support the use of ABC and population genetic data for testing the strict metapopulation model and parameterizing complex models of demography. © 2013 Blackwell Publishing Ltd.

Applications of Bayesian Statistics to Problems in Gamma-Ray Bursts

NASA Technical Reports Server (NTRS)

Meegan, Charles A.

1997-01-01

This presentation will describe two applications of Bayesian statistics to Gamma Ray Bursts (GRBS). The first attempts to quantify the evidence for a cosmological versus galactic origin of GRBs using only the observations of the dipole and quadrupole moments of the angular distribution of bursts. The cosmological hypothesis predicts isotropy, while the galactic hypothesis is assumed to produce a uniform probability distribution over positive values for these moments. The observed isotropic distribution indicates that the Bayes factor for the cosmological hypothesis over the galactic hypothesis is about 300. Another application of Bayesian statistics is in the estimation of chance associations of optical counterparts with galaxies. The Bayesian approach is preferred to frequentist techniques here because the Bayesian approach easily accounts for galaxy mass distributions and because one can incorporate three disjoint hypotheses: (1) bursts come from galactic centers, (2) bursts come from galaxies in proportion to luminosity, and (3) bursts do not come from external galaxies. This technique was used in the analysis of the optical counterpart to GRB970228.

2D VARIABLY SATURATED FLOWS: PHYSICAL SCALING AND BAYESIAN ESTIMATION

EPA Science Inventory

A novel dimensionless formulation for water flow in two-dimensional variably saturated media is presented. It shows that scaling physical systems requires conservation of the ratio between capillary forces and gravity forces. A direct result of this finding is that for two phys...

On the importance of avoiding shortcuts in applying cognitive models to hierarchical data.

PubMed

Boehm, Udo; Marsman, Maarten; Matzke, Dora; Wagenmakers, Eric-Jan

2018-06-12

Psychological experiments often yield data that are hierarchically structured. A number of popular shortcut strategies in cognitive modeling do not properly accommodate this structure and can result in biased conclusions. To gauge the severity of these biases, we conducted a simulation study for a two-group experiment. We first considered a modeling strategy that ignores the hierarchical data structure. In line with theoretical results, our simulations showed that Bayesian and frequentist methods that rely on this strategy are biased towards the null hypothesis. Secondly, we considered a modeling strategy that takes a two-step approach by first obtaining participant-level estimates from a hierarchical cognitive model and subsequently using these estimates in a follow-up statistical test. Methods that rely on this strategy are biased towards the alternative hypothesis. Only hierarchical models of the multilevel data lead to correct conclusions. Our results are particularly relevant for the use of hierarchical Bayesian parameter estimates in cognitive modeling.

Robust Bayesian Fluorescence Lifetime Estimation, Decay Model Selection and Instrument Response Determination for Low-Intensity FLIM Imaging

PubMed Central

Rowley, Mark I.; Coolen, Anthonius C. C.; Vojnovic, Borivoj; Barber, Paul R.

2016-01-01

We present novel Bayesian methods for the analysis of exponential decay data that exploit the evidence carried by every detected decay event and enables robust extension to advanced processing. Our algorithms are presented in the context of fluorescence lifetime imaging microscopy (FLIM) and particular attention has been paid to model the time-domain system (based on time-correlated single photon counting) with unprecedented accuracy. We present estimates of decay parameters for mono- and bi-exponential systems, offering up to a factor of two improvement in accuracy compared to previous popular techniques. Results of the analysis of synthetic and experimental data are presented, and areas where the superior precision of our techniques can be exploited in Förster Resonance Energy Transfer (FRET) experiments are described. Furthermore, we demonstrate two advanced processing methods: decay model selection to choose between differing models such as mono- and bi-exponential, and the simultaneous estimation of instrument and decay parameters. PMID:27355322

Bayesian segregation analysis of production traits in two strains of laying chickens.

PubMed

Szydłowski, M; Szwaczkowski, T

2001-02-01

A bayesian marker-free segregation analysis was applied to search for evidence of segregating genes affecting production traits in two strains of laying hens under long-term selection. The study used data from 6 generations of Leghorn (H77) and New Hampshire (N88) breeding nuclei. Estimation of marginal posterior means of variance components and parameters of a single autosomal locus was performed by use of the Gibbs sampler. The results showed evidence for a mixed major gene: -polygenic inheritance of BW and age at sexual maturity (ASM) in both strains. Single genes affecting BW and ASM explained one-third of the genetic variance. For ASM large overdominance effect at single locus was estimated. Initial egg production (IEP) and average egg weight (EW) showed a polygenic model of inheritance. The polygenic heritability estimates for BW, ASM, IEP, and EW were 0.32, 0.25, 0.23, and 0.08 in Strain H77 and 0.25, 0.24, 0.11, and 0.38 in Strain N88, respectively.

Evaluation of Oceanic Transport Statistics By Use of Transient Tracers and Bayesian Methods

NASA Astrophysics Data System (ADS)

Trossman, D. S.; Thompson, L.; Mecking, S.; Bryan, F.; Peacock, S.

2013-12-01

Key variables that quantify the time scales over which atmospheric signals penetrate into the oceanic interior and their uncertainties are computed using Bayesian methods and transient tracers from both models and observations. First, the mean residence times, subduction rates, and formation rates of Subtropical Mode Water (STMW) and Subpolar Mode Water (SPMW) in the North Atlantic and Subantarctic Mode Water (SAMW) in the Southern Ocean are estimated by combining a model and observations of chlorofluorocarbon-11 (CFC-11) via Bayesian Model Averaging (BMA), statistical technique that weights model estimates according to how close they agree with observations. Second, a Bayesian method is presented to find two oceanic transport parameters associated with the age distribution of ocean waters, the transit-time distribution (TTD), by combining an eddying global ocean model's estimate of the TTD with hydrographic observations of CFC-11, temperature, and salinity. Uncertainties associated with objectively mapping irregularly spaced bottle data are quantified by making use of a thin-plate spline and then propagated via the two Bayesian techniques. It is found that the subduction of STMW, SPMW, and SAMW is mostly an advective process, but up to about one-third of STMW subduction likely owes to non-advective processes. Also, while the formation of STMW is mostly due to subduction, the formation of SPMW is mostly due to other processes. About half of the formation of SAMW is due to subduction and half is due to other processes. A combination of air-sea flux, acting on relatively short time scales, and turbulent mixing, acting on a wide range of time scales, is likely the dominant SPMW erosion mechanism. Air-sea flux is likely responsible for most STMW erosion, and turbulent mixing is likely responsible for most SAMW erosion. Two oceanic transport parameters, the mean age of a water parcel and the half-variance associated with the TTD, estimated using the model's tracers as data (BayesPOP) and those estimated using tracer observations as data (BayesObs) provide information about the sources of model biases, and give a more nuanced picture than can be found by comparing the simulated CFC-11 concentrations with observed CFC-11 concentrations. Using the differences between the two oceanic transport parameters from BayesObs and those from BayesPOP with and without a constant Peclet number assumption along each of the hydrographic cross-sections considered here, it is found that the model's diffusivity tensor biases lead to larger model errors than the model's mean advection time biases. However, it is also found that mean advection time biases in the model are statistically significant at the 95% level where mode water is found.

Toward an ecological analysis of Bayesian inferences: how task characteristics influence responses

PubMed Central

Hafenbrädl, Sebastian; Hoffrage, Ulrich

2015-01-01

In research on Bayesian inferences, the specific tasks, with their narratives and characteristics, are typically seen as exchangeable vehicles that merely transport the structure of the problem to research participants. In the present paper, we explore whether, and possibly how, task characteristics that are usually ignored influence participants’ responses in these tasks. We focus on both quantitative dimensions of the tasks, such as their base rates, hit rates, and false-alarm rates, as well as qualitative characteristics, such as whether the task involves a norm violation or not, whether the stakes are high or low, and whether the focus is on the individual case or on the numbers. Using a data set of 19 different tasks presented to 500 different participants who provided a total of 1,773 responses, we analyze these responses in two ways: first, on the level of the numerical estimates themselves, and second, on the level of various response strategies, Bayesian and non-Bayesian, that might have produced the estimates. We identified various contingencies, and most of the task characteristics had an influence on participants’ responses. Typically, this influence has been stronger when the numerical information in the tasks was presented in terms of probabilities or percentages, compared to natural frequencies – and this effect cannot be fully explained by a higher proportion of Bayesian responses when natural frequencies were used. One characteristic that did not seem to influence participants’ response strategy was the numerical value of the Bayesian solution itself. Our exploratory study is a first step toward an ecological analysis of Bayesian inferences, and highlights new avenues for future research. PMID:26300791

Competing risk models in reliability systems, a weibull distribution model with bayesian analysis approach

NASA Astrophysics Data System (ADS)

Iskandar, Ismed; Satria Gondokaryono, Yudi

2016-02-01

In reliability theory, the most important problem is to determine the reliability of a complex system from the reliability of its components. The weakness of most reliability theories is that the systems are described and explained as simply functioning or failed. In many real situations, the failures may be from many causes depending upon the age and the environment of the system and its components. Another problem in reliability theory is one of estimating the parameters of the assumed failure models. The estimation may be based on data collected over censored or uncensored life tests. In many reliability problems, the failure data are simply quantitatively inadequate, especially in engineering design and maintenance system. The Bayesian analyses are more beneficial than the classical one in such cases. The Bayesian estimation analyses allow us to combine past knowledge or experience in the form of an apriori distribution with life test data to make inferences of the parameter of interest. In this paper, we have investigated the application of the Bayesian estimation analyses to competing risk systems. The cases are limited to the models with independent causes of failure by using the Weibull distribution as our model. A simulation is conducted for this distribution with the objectives of verifying the models and the estimators and investigating the performance of the estimators for varying sample size. The simulation data are analyzed by using Bayesian and the maximum likelihood analyses. The simulation results show that the change of the true of parameter relatively to another will change the value of standard deviation in an opposite direction. For a perfect information on the prior distribution, the estimation methods of the Bayesian analyses are better than those of the maximum likelihood. The sensitivity analyses show some amount of sensitivity over the shifts of the prior locations. They also show the robustness of the Bayesian analysis within the range between the true value and the maximum likelihood estimated value lines.

HIV Trends in the United States: Diagnoses and Estimated Incidence.

PubMed

Hall, H Irene; Song, Ruiguang; Tang, Tian; An, Qian; Prejean, Joseph; Dietz, Patricia; Hernandez, Angela L; Green, Timothy; Harris, Norma; McCray, Eugene; Mermin, Jonathan

2017-02-03

The best indicator of the impact of human immunodeficiency virus (HIV) prevention programs is the incidence of infection; however, HIV is a chronic infection and HIV diagnoses may include infections that occurred years before diagnosis. Alternative methods to estimate incidence use diagnoses, stage of disease, and laboratory assays of infection recency. Using a consistent, accurate method would allow for timely interpretation of HIV trends. The objective of our study was to assess the recent progress toward reducing HIV infections in the United States overall and among selected population segments with available incidence estimation methods. Data on cases of HIV infection reported to national surveillance for 2008-2013 were used to compare trends in HIV diagnoses, unadjusted and adjusted for reporting delay, and model-based incidence for the US population aged ≥13 years. Incidence was estimated using a biomarker for recency of infection (stratified extrapolation approach) and 2 back-calculation models (CD4 and Bayesian hierarchical models). HIV testing trends were determined from behavioral surveys for persons aged ≥18 years. Analyses were stratified by sex, race or ethnicity (black, Hispanic or Latino, and white), and transmission category (men who have sex with men, MSM). On average, HIV diagnoses decreased 4.0% per year from 48,309 in 2008 to 39,270 in 2013 (P<.001). Adjusting for reporting delays, diagnoses decreased 3.1% per year (P<.001). The CD4 model estimated an annual decrease in incidence of 4.6% (P<.001) and the Bayesian hierarchical model 2.6% (P<.001); the stratified extrapolation approach estimated a stable incidence. During these years, overall, the percentage of persons who ever had received an HIV test or had had a test within the past year remained stable; among MSM testing increased. For women, all 3 incidence models corroborated the decreasing trend in HIV diagnoses, and HIV diagnoses and 2 incidence models indicated decreases among blacks and whites. The CD4 and Bayesian hierarchical models, but not the stratified extrapolation approach, indicated decreases in incidence among MSM. HIV diagnoses and CD4 and Bayesian hierarchical model estimates indicated decreases in HIV incidence overall, among both sexes and all race or ethnicity groups. Further progress depends on effectively reducing HIV incidence among MSM, among whom the majority of new infections occur. ©H Irene Hall, Ruiguang Song, Tian Tang, Qian An, Joseph Prejean, Patricia Dietz, Angela L Hernandez, Timothy Green, Norma Harris, Eugene McCray, Jonathan Mermin. Originally published in JMIR Public Health and Surveillance (http://publichealth.jmir.org), 03.02.2017.

Bayesian model selection: Evidence estimation based on DREAM simulation and bridge sampling

NASA Astrophysics Data System (ADS)

Volpi, Elena; Schoups, Gerrit; Firmani, Giovanni; Vrugt, Jasper A.

2017-04-01

Bayesian inference has found widespread application in Earth and Environmental Systems Modeling, providing an effective tool for prediction, data assimilation, parameter estimation, uncertainty analysis and hypothesis testing. Under multiple competing hypotheses, the Bayesian approach also provides an attractive alternative to traditional information criteria (e.g. AIC, BIC) for model selection. The key variable for Bayesian model selection is the evidence (or marginal likelihood) that is the normalizing constant in the denominator of Bayes theorem; while it is fundamental for model selection, the evidence is not required for Bayesian inference. It is computed for each hypothesis (model) by averaging the likelihood function over the prior parameter distribution, rather than maximizing it as by information criteria; the larger a model evidence the more support it receives among a collection of hypothesis as the simulated values assign relatively high probability density to the observed data. Hence, the evidence naturally acts as an Occam's razor, preferring simpler and more constrained models against the selection of over-fitted ones by information criteria that incorporate only the likelihood maximum. Since it is not particularly easy to estimate the evidence in practice, Bayesian model selection via the marginal likelihood has not yet found mainstream use. We illustrate here the properties of a new estimator of the Bayesian model evidence, which provides robust and unbiased estimates of the marginal likelihood; the method is coined Gaussian Mixture Importance Sampling (GMIS). GMIS uses multidimensional numerical integration of the posterior parameter distribution via bridge sampling (a generalization of importance sampling) of a mixture distribution fitted to samples of the posterior distribution derived from the DREAM algorithm (Vrugt et al., 2008; 2009). Some illustrative examples are presented to show the robustness and superiority of the GMIS estimator with respect to other commonly used approaches in the literature.

Quantifying sleep architecture dynamics and individual differences using big data and Bayesian networks

PubMed Central

Shelton, Christian; Mednick, Sara C.

2018-01-01

The pattern of sleep stages across a night (sleep architecture) is influenced by biological, behavioral, and clinical variables. However, traditional measures of sleep architecture such as stage proportions, fail to capture sleep dynamics. Here we quantify the impact of individual differences on the dynamics of sleep architecture and determine which factors or set of factors best predict the next sleep stage from current stage information. We investigated the influence of age, sex, body mass index, time of day, and sleep time on static (e.g. minutes in stage, sleep efficiency) and dynamic measures of sleep architecture (e.g. transition probabilities and stage duration distributions) using a large dataset of 3202 nights from a non-clinical population. Multi-level regressions show that sex effects duration of all Non-Rapid Eye Movement (NREM) stages, and age has a curvilinear relationship for Wake After Sleep Onset (WASO) and slow wave sleep (SWS) minutes. Bayesian network modeling reveals sleep architecture depends on time of day, total sleep time, age and sex, but not BMI. Older adults, and particularly males, have shorter bouts (more fragmentation) of Stage 2, SWS, and they transition less frequently to these stages. Additionally, we showed that the next sleep stage and its duration can be optimally predicted by the prior 2 stages and age. Our results demonstrate the potential benefit of big data and Bayesian network approaches in quantifying static and dynamic architecture of normal sleep. PMID:29641599

Quantifying sleep architecture dynamics and individual differences using big data and Bayesian networks.

PubMed

Yetton, Benjamin D; McDevitt, Elizabeth A; Cellini, Nicola; Shelton, Christian; Mednick, Sara C

2018-01-01

The pattern of sleep stages across a night (sleep architecture) is influenced by biological, behavioral, and clinical variables. However, traditional measures of sleep architecture such as stage proportions, fail to capture sleep dynamics. Here we quantify the impact of individual differences on the dynamics of sleep architecture and determine which factors or set of factors best predict the next sleep stage from current stage information. We investigated the influence of age, sex, body mass index, time of day, and sleep time on static (e.g. minutes in stage, sleep efficiency) and dynamic measures of sleep architecture (e.g. transition probabilities and stage duration distributions) using a large dataset of 3202 nights from a non-clinical population. Multi-level regressions show that sex effects duration of all Non-Rapid Eye Movement (NREM) stages, and age has a curvilinear relationship for Wake After Sleep Onset (WASO) and slow wave sleep (SWS) minutes. Bayesian network modeling reveals sleep architecture depends on time of day, total sleep time, age and sex, but not BMI. Older adults, and particularly males, have shorter bouts (more fragmentation) of Stage 2, SWS, and they transition less frequently to these stages. Additionally, we showed that the next sleep stage and its duration can be optimally predicted by the prior 2 stages and age. Our results demonstrate the potential benefit of big data and Bayesian network approaches in quantifying static and dynamic architecture of normal sleep.

Bayesian forecasting and uncertainty quantifying of stream flows using Metropolis-Hastings Markov Chain Monte Carlo algorithm

NASA Astrophysics Data System (ADS)

Wang, Hongrui; Wang, Cheng; Wang, Ying; Gao, Xiong; Yu, Chen

2017-06-01

This paper presents a Bayesian approach using Metropolis-Hastings Markov Chain Monte Carlo algorithm and applies this method for daily river flow rate forecast and uncertainty quantification for Zhujiachuan River using data collected from Qiaotoubao Gage Station and other 13 gage stations in Zhujiachuan watershed in China. The proposed method is also compared with the conventional maximum likelihood estimation (MLE) for parameter estimation and quantification of associated uncertainties. While the Bayesian method performs similarly in estimating the mean value of daily flow rate, it performs over the conventional MLE method on uncertainty quantification, providing relatively narrower reliable interval than the MLE confidence interval and thus more precise estimation by using the related information from regional gage stations. The Bayesian MCMC method might be more favorable in the uncertainty analysis and risk management.

Bayesian characterization of uncertainty in species interaction strengths.

PubMed

Wolf, Christopher; Novak, Mark; Gitelman, Alix I

2017-06-01

Considerable effort has been devoted to the estimation of species interaction strengths. This effort has focused primarily on statistical significance testing and obtaining point estimates of parameters that contribute to interaction strength magnitudes, leaving the characterization of uncertainty associated with those estimates unconsidered. We consider a means of characterizing the uncertainty of a generalist predator's interaction strengths by formulating an observational method for estimating a predator's prey-specific per capita attack rates as a Bayesian statistical model. This formulation permits the explicit incorporation of multiple sources of uncertainty. A key insight is the informative nature of several so-called non-informative priors that have been used in modeling the sparse data typical of predator feeding surveys. We introduce to ecology a new neutral prior and provide evidence for its superior performance. We use a case study to consider the attack rates in a New Zealand intertidal whelk predator, and we illustrate not only that Bayesian point estimates can be made to correspond with those obtained by frequentist approaches, but also that estimation uncertainty as described by 95% intervals is more useful and biologically realistic using the Bayesian method. In particular, unlike in bootstrap confidence intervals, the lower bounds of the Bayesian posterior intervals for attack rates do not include zero when a predator-prey interaction is in fact observed. We conclude that the Bayesian framework provides a straightforward, probabilistic characterization of interaction strength uncertainty, enabling future considerations of both the deterministic and stochastic drivers of interaction strength and their impact on food webs.

Generalizability of Evidence-Based Assessment Recommendations for Pediatric Bipolar Disorder

PubMed Central

Jenkins, Melissa M.; Youngstrom, Eric A.; Youngstrom, Jennifer Kogos; Feeny, Norah C.; Findling, Robert L.

2013-01-01

Bipolar disorder is frequently clinically diagnosed in youths who do not actually satisfy DSM-IV criteria, yet cases that would satisfy full DSM-IV criteria are often undetected clinically. Evidence-based assessment methods that incorporate Bayesian reasoning have demonstrated improved diagnostic accuracy, and consistency; however, their clinical utility is largely unexplored. The present study examines the effectiveness of promising evidence-based decision-making compared to the clinical gold standard. Participants were 562 youth, ages 5-17 and predominantly African American, drawn from a community mental health clinic. Research diagnoses combined semi-structured interview with youths’ psychiatric, developmental, and family mental health histories. Independent Bayesian estimates relied on published risk estimates from other samples discriminated bipolar diagnoses, Area Under Curve=.75, p<.00005. The Bayes and confidence ratings correlated rs =.30. Agreement about an evidence-based assessment intervention “threshold model” (wait/assess/treat) had K=.24, p<.05. No potential moderators of agreement between the Bayesian estimates and confidence ratings, including type of bipolar illness, were significant. Bayesian risk estimates were highly correlated with logistic regression estimates using optimal sample weights, r=.81, p<.0005. Clinical and Bayesian approaches agree in terms of overall concordance and deciding next clinical action, even when Bayesian predictions are based on published estimates from clinically and demographically different samples. Evidence-based assessment methods may be useful in settings that cannot routinely employ gold standard assessments, and they may help decrease rates of overdiagnosis while promoting earlier identification of true cases. PMID:22004538

Bayesian Modeling of Perceived Surface Slant from Actively-Generated and Passively-Observed Optic Flow

PubMed Central

Caudek, Corrado; Fantoni, Carlo; Domini, Fulvio

2011-01-01

We measured perceived depth from the optic flow (a) when showing a stationary physical or virtual object to observers who moved their head at a normal or slower speed, and (b) when simulating the same optic flow on a computer and presenting it to stationary observers. Our results show that perceived surface slant is systematically distorted, for both the active and the passive viewing of physical or virtual surfaces. These distortions are modulated by head translation speed, with perceived slant increasing directly with the local velocity gradient of the optic flow. This empirical result allows us to determine the relative merits of two alternative approaches aimed at explaining perceived surface slant in active vision: an “inverse optics” model that takes head motion information into account, and a probabilistic model that ignores extra-retinal signals. We compare these two approaches within the framework of the Bayesian theory. The “inverse optics” Bayesian model produces veridical slant estimates if the optic flow and the head translation velocity are measured with no error; because of the influence of a “prior” for flatness, the slant estimates become systematically biased as the measurement errors increase. The Bayesian model, which ignores the observer's motion, always produces distorted estimates of surface slant. Interestingly, the predictions of this second model, not those of the first one, are consistent with our empirical findings. The present results suggest that (a) in active vision perceived surface slant may be the product of probabilistic processes which do not guarantee the correct solution, and (b) extra-retinal signals may be mainly used for a better measurement of retinal information. PMID:21533197

Bayesian depth estimation from monocular natural images.

PubMed

Su, Che-Chun; Cormack, Lawrence K; Bovik, Alan C

2017-05-01

Estimating an accurate and naturalistic dense depth map from a single monocular photographic image is a difficult problem. Nevertheless, human observers have little difficulty understanding the depth structure implied by photographs. Two-dimensional (2D) images of the real-world environment contain significant statistical information regarding the three-dimensional (3D) structure of the world that the vision system likely exploits to compute perceived depth, monocularly as well as binocularly. Toward understanding how this might be accomplished, we propose a Bayesian model of monocular depth computation that recovers detailed 3D scene structures by extracting reliable, robust, depth-sensitive statistical features from single natural images. These features are derived using well-accepted univariate natural scene statistics (NSS) models and recent bivariate/correlation NSS models that describe the relationships between 2D photographic images and their associated depth maps. This is accomplished by building a dictionary of canonical local depth patterns from which NSS features are extracted as prior information. The dictionary is used to create a multivariate Gaussian mixture (MGM) likelihood model that associates local image features with depth patterns. A simple Bayesian predictor is then used to form spatial depth estimates. The depth results produced by the model, despite its simplicity, correlate well with ground-truth depths measured by a current-generation terrestrial light detection and ranging (LIDAR) scanner. Such a strong form of statistical depth information could be used by the visual system when creating overall estimated depth maps incorporating stereopsis, accommodation, and other conditions. Indeed, even in isolation, the Bayesian predictor delivers depth estimates that are competitive with state-of-the-art "computer vision" methods that utilize highly engineered image features and sophisticated machine learning algorithms.

BAYESIAN ANALYSIS TO EVALUATE TESTS FOR THE DETECTION OF MYCOBACTERIUM BOVIS INFECTION IN FREE-RANGING WILD BISON (BISON BISON ATHABASCAE) IN THE ABSENCE OF A GOLD STANDARD.

PubMed

Chapinal, Núria; Schumaker, Brant A; Joly, Damien O; Elkin, Brett T; Stephen, Craig

2015-07-01

We estimated the sensitivity and specificity of the caudal-fold skin test (CFT), the fluorescent polarization assay (FPA), and the rapid lateral-flow test (RT) for the detection of Mycobacterium bovis in free-ranging wild wood bison (Bison bison athabascae), in the absence of a gold standard, by using Bayesian analysis, and then used those estimates to forecast the performance of a pairwise combination of tests in parallel. In 1998-99, 212 wood bison from Wood Buffalo National Park (Canada) were tested for M. bovis infection using CFT and two serologic tests (FPA and RT). The sensitivity and specificity of each test were estimated using a three-test, one-population, Bayesian model allowing for conditional dependence between FPA and RT. The sensitivity and specificity of the combination of CFT and each serologic test in parallel were calculated assuming conditional independence. The test performance estimates were influenced by the prior values chosen. However, the rank of tests and combinations of tests based on those estimates remained constant. The CFT was the most sensitive test and the FPA was the least sensitive, whereas RT was the most specific test and CFT was the least specific. In conclusion, given the fact that gold standards for the detection of M. bovis are imperfect and difficult to obtain in the field, Bayesian analysis holds promise as a tool to rank tests and combinations of tests based on their performance. Combining a skin test with an animal-side serologic test, such as RT, increases sensitivity in the detection of M. bovis and is a good approach to enhance disease eradication or control in wild bison.

Population pharmacokinetics and maximum a posteriori probability Bayesian estimator of abacavir: application of individualized therapy in HIV-infected infants and toddlers

PubMed Central

Zhao, Wei; Cella, Massimo; Della Pasqua, Oscar; Burger, David; Jacqz-Aigrain, Evelyne

2012-01-01

AIMS To develop a population pharmacokinetic model for abacavir in HIV-infected infants and toddlers, which will be used to describe both once and twice daily pharmacokinetic profiles, identify covariates that explain variability and propose optimal time points to optimize the area under the concentration–time curve (AUC) targeted dosage and individualize therapy. METHODS The pharmacokinetics of abacavir was described with plasma concentrations from 23 patients using nonlinear mixed-effects modelling (NONMEM) software. A two-compartment model with first-order absorption and elimination was developed. The final model was validated using bootstrap, visual predictive check and normalized prediction distribution errors. The Bayesian estimator was validated using the cross-validation and simulation–estimation method. RESULTS The typical population pharmacokinetic parameters and relative standard errors (RSE) were apparent systemic clearance (CL) 13.4 l h−1 (RSE 6.3%), apparent central volume of distribution 4.94 l (RSE 28.7%), apparent peripheral volume of distribution 8.12 l (RSE14.2%), apparent intercompartment clearance 1.25 l h−1 (RSE 16.9%) and absorption rate constant 0.758 h−1 (RSE 5.8%). The covariate analysis identified weight as the individual factor influencing the apparent oral clearance: CL = 13.4 × (weight/12)1.14. The maximum a posteriori probability Bayesian estimator, based on three concentrations measured at 0, 1 or 2, and 3 h after drug intake allowed predicting individual AUC0–t. CONCLUSIONS The population pharmacokinetic model developed for abacavir in HIV-infected infants and toddlers accurately described both once and twice daily pharmacokinetic profiles. The maximum a posteriori probability Bayesian estimator of AUC0–t was developed from the final model and can be used routinely to optimize individual dosing. PMID:21988586

Genealogical Working Distributions for Bayesian Model Testing with Phylogenetic Uncertainty

PubMed Central

Baele, Guy; Lemey, Philippe; Suchard, Marc A.

2016-01-01

Marginal likelihood estimates to compare models using Bayes factors frequently accompany Bayesian phylogenetic inference. Approaches to estimate marginal likelihoods have garnered increased attention over the past decade. In particular, the introduction of path sampling (PS) and stepping-stone sampling (SS) into Bayesian phylogenetics has tremendously improved the accuracy of model selection. These sampling techniques are now used to evaluate complex evolutionary and population genetic models on empirical data sets, but considerable computational demands hamper their widespread adoption. Further, when very diffuse, but proper priors are specified for model parameters, numerical issues complicate the exploration of the priors, a necessary step in marginal likelihood estimation using PS or SS. To avoid such instabilities, generalized SS (GSS) has recently been proposed, introducing the concept of “working distributions” to facilitate—or shorten—the integration process that underlies marginal likelihood estimation. However, the need to fix the tree topology currently limits GSS in a coalescent-based framework. Here, we extend GSS by relaxing the fixed underlying tree topology assumption. To this purpose, we introduce a “working” distribution on the space of genealogies, which enables estimating marginal likelihoods while accommodating phylogenetic uncertainty. We propose two different “working” distributions that help GSS to outperform PS and SS in terms of accuracy when comparing demographic and evolutionary models applied to synthetic data and real-world examples. Further, we show that the use of very diffuse priors can lead to a considerable overestimation in marginal likelihood when using PS and SS, while still retrieving the correct marginal likelihood using both GSS approaches. The methods used in this article are available in BEAST, a powerful user-friendly software package to perform Bayesian evolutionary analyses. PMID:26526428

Syzygies, Pluricanonical Maps, and the Birational Geometry of Varieties of Maximal Albanese Dimension

NASA Astrophysics Data System (ADS)

Tesfagiorgis, Kibrewossen B.

Satellite Precipitation Estimates (SPEs) may be the only available source of information for operational hydrologic and flash flood prediction due to spatial limitations of radar and gauge products in mountainous regions. The present work develops an approach to seamlessly blend satellite, available radar, climatological and gauge precipitation products to fill gaps in ground-based radar precipitation field. To mix different precipitation products, the error of any of the products relative to each other should be removed. For bias correction, the study uses a new ensemble-based method which aims to estimate spatially varying multiplicative biases in SPEs using a radar-gauge precipitation product. Bias factors were calculated for a randomly selected sample of rainy pixels in the study area. Spatial fields of estimated bias were generated taking into account spatial variation and random errors in the sampled values. In addition to biases, sometimes there is also spatial error between the radar and satellite precipitation estimates; one of them has to be geometrically corrected with reference to the other. A set of corresponding raining points between SPE and radar products are selected to apply linear registration using a regularized least square technique to minimize the dislocation error in SPEs with respect to available radar products. A weighted Successive Correction Method (SCM) is used to make the merging between error corrected satellite and radar precipitation estimates. In addition to SCM, we use a combination of SCM and Bayesian spatial method for merging the rain gauges and climatological precipitation sources with radar and SPEs. We demonstrated the method using two satellite-based, CPC Morphing (CMORPH) and Hydro-Estimator (HE), two radar-gauge based, Stage-II and ST-IV, a climatological product PRISM and rain gauge dataset for several rain events from 2006 to 2008 over different geographical locations of the United States. Results show that: (a) the method of ensembles helped reduce biases in SPEs significantly; (b) the SCM method in combination with the Bayesian spatial model produced a precipitation product in good agreement with independent measurements .The study implies that using the available radar pixels surrounding the gap area, rain gauge, PRISM and satellite products, a radar like product is achievable over radar gap areas that benefits the operational meteorology and hydrology community.

Bayesian probabilistic population projections for all countries

PubMed Central

Raftery, Adrian E.; Li, Nan; Ševčíková, Hana; Gerland, Patrick; Heilig, Gerhard K.

2012-01-01

Projections of countries’ future populations, broken down by age and sex, are widely used for planning and research. They are mostly done deterministically, but there is a widespread need for probabilistic projections. We propose a Bayesian method for probabilistic population projections for all countries. The total fertility rate and female and male life expectancies at birth are projected probabilistically using Bayesian hierarchical models estimated via Markov chain Monte Carlo using United Nations population data for all countries. These are then converted to age-specific rates and combined with a cohort component projection model. This yields probabilistic projections of any population quantity of interest. The method is illustrated for five countries of different demographic stages, continents and sizes. The method is validated by an out of sample experiment in which data from 1950–1990 are used for estimation, and applied to predict 1990–2010. The method appears reasonably accurate and well calibrated for this period. The results suggest that the current United Nations high and low variants greatly underestimate uncertainty about the number of oldest old from about 2050 and that they underestimate uncertainty for high fertility countries and overstate uncertainty for countries that have completed the demographic transition and whose fertility has started to recover towards replacement level, mostly in Europe. The results also indicate that the potential support ratio (persons aged 20–64 per person aged 65+) will almost certainly decline dramatically in most countries over the coming decades. PMID:22908249

Robust power spectral estimation for EEG data

PubMed Central

Melman, Tamar; Victor, Jonathan D.

2016-01-01

Background Typical electroencephalogram (EEG) recordings often contain substantial artifact. These artifacts, often large and intermittent, can interfere with quantification of the EEG via its power spectrum. To reduce the impact of artifact, EEG records are typically cleaned by a preprocessing stage that removes individual segments or components of the recording. However, such preprocessing can introduce bias, discard available signal, and be labor-intensive. With this motivation, we present a method that uses robust statistics to reduce dependence on preprocessing by minimizing the effect of large intermittent outliers on the spectral estimates. New method Using the multitaper method[1] as a starting point, we replaced the final step of the standard power spectrum calculation with a quantile-based estimator, and the Jackknife approach to confidence intervals with a Bayesian approach. The method is implemented in provided MATLAB modules, which extend the widely used Chronux toolbox. Results Using both simulated and human data, we show that in the presence of large intermittent outliers, the robust method produces improved estimates of the power spectrum, and that the Bayesian confidence intervals yield close-to-veridical coverage factors. Comparison to existing method The robust method, as compared to the standard method, is less affected by artifact: inclusion of outliers produces fewer changes in the shape of the power spectrum as well as in the coverage factor. Conclusion In the presence of large intermittent outliers, the robust method can reduce dependence on data preprocessing as compared to standard methods of spectral estimation. PMID:27102041

Robust power spectral estimation for EEG data.

PubMed

Melman, Tamar; Victor, Jonathan D

2016-08-01

Typical electroencephalogram (EEG) recordings often contain substantial artifact. These artifacts, often large and intermittent, can interfere with quantification of the EEG via its power spectrum. To reduce the impact of artifact, EEG records are typically cleaned by a preprocessing stage that removes individual segments or components of the recording. However, such preprocessing can introduce bias, discard available signal, and be labor-intensive. With this motivation, we present a method that uses robust statistics to reduce dependence on preprocessing by minimizing the effect of large intermittent outliers on the spectral estimates. Using the multitaper method (Thomson, 1982) as a starting point, we replaced the final step of the standard power spectrum calculation with a quantile-based estimator, and the Jackknife approach to confidence intervals with a Bayesian approach. The method is implemented in provided MATLAB modules, which extend the widely used Chronux toolbox. Using both simulated and human data, we show that in the presence of large intermittent outliers, the robust method produces improved estimates of the power spectrum, and that the Bayesian confidence intervals yield close-to-veridical coverage factors. The robust method, as compared to the standard method, is less affected by artifact: inclusion of outliers produces fewer changes in the shape of the power spectrum as well as in the coverage factor. In the presence of large intermittent outliers, the robust method can reduce dependence on data preprocessing as compared to standard methods of spectral estimation. Copyright © 2016 Elsevier B.V. All rights reserved.

A Bayesian Semiparametric Approach for Incorporating Longitudinal Information on Exposure History for Inference in Case-Control Studies

PubMed Central

Bhadra, Dhiman; Daniels, Michael J.; Kim, Sungduk; Ghosh, Malay; Mukherjee, Bhramar

2014-01-01

In a typical case-control study, exposure information is collected at a single time-point for the cases and controls. However, case-control studies are often embedded in existing cohort studies containing a wealth of longitudinal exposure history on the participants. Recent medical studies have indicated that incorporating past exposure history, or a constructed summary measure of cumulative exposure derived from the past exposure history, when available, may lead to more precise and clinically meaningful estimates of the disease risk. In this paper, we propose a flexible Bayesian semiparametric approach to model the longitudinal exposure profiles of the cases and controls and then use measures of cumulative exposure based on a weighted integral of this trajectory in the final disease risk model. The estimation is done via a joint likelihood. In the construction of the cumulative exposure summary, we introduce an influence function, a smooth function of time to characterize the association pattern of the exposure profile on the disease status with different time windows potentially having differential influence/weights. This enables us to analyze how the present disease status of a subject is influenced by his/her past exposure history conditional on the current ones. The joint likelihood formulation allows us to properly account for uncertainties associated with both stages of the estimation process in an integrated manner. Analysis is carried out in a hierarchical Bayesian framework using Reversible jump Markov chain Monte Carlo (RJMCMC) algorithms. The proposed methodology is motivated by, and applied to a case-control study of prostate cancer where longitudinal biomarker information is available for the cases and controls. PMID:22313248

A Bayesian inverse modeling approach to estimate soil hydraulic properties of a toposequence in southeastern Amazonia.

NASA Astrophysics Data System (ADS)

Stucchi Boschi, Raquel; Qin, Mingming; Gimenez, Daniel; Cooper, Miguel

2016-04-01

Modeling is an important tool for better understanding and assessing land use impacts on landscape processes. A key point for environmental modeling is the knowledge of soil hydraulic properties. However, direct determination of soil hydraulic properties is difficult and costly, particularly in vast and remote regions such as one constituting the Amazon Biome. One way to overcome this problem is to extrapolate accurately estimated data to pedologically similar sites. The van Genuchten (VG) parametric equation is the most commonly used for modeling SWRC. The use of a Bayesian approach in combination with the Markov chain Monte Carlo to estimate the VG parameters has several advantages compared to the widely used global optimization techniques. The Bayesian approach provides posterior distributions of parameters that are independent from the initial values and allow for uncertainty analyses. The main objectives of this study were: i) to estimate hydraulic parameters from data of pasture and forest sites by the Bayesian inverse modeling approach; and ii) to investigate the extrapolation of the estimated VG parameters to a nearby toposequence with pedologically similar soils to those used for its estimate. The parameters were estimated from volumetric water content and tension observations obtained after rainfall events during a 207-day period from pasture and forest sites located in the southeastern Amazon region. These data were used to run HYDRUS-1D under a Differential Evolution Adaptive Metropolis (DREAM) scheme 10,000 times, and only the last 2,500 times were used to calculate the posterior distributions of each hydraulic parameter along with 95% confidence intervals (CI) of volumetric water content and tension time series. Then, the posterior distributions were used to generate hydraulic parameters for two nearby toposequences composed by six soil profiles, three are under forest and three are under pasture. The parameters of the nearby site were accepted when the predicted tension time series were within the 95% CI which is derived from the calibration site using DREAM scheme.

Univariate and bivariate likelihood-based meta-analysis methods performed comparably when marginal sensitivity and specificity were the targets of inference.

PubMed

Dahabreh, Issa J; Trikalinos, Thomas A; Lau, Joseph; Schmid, Christopher H

2017-03-01

To compare statistical methods for meta-analysis of sensitivity and specificity of medical tests (e.g., diagnostic or screening tests). We constructed a database of PubMed-indexed meta-analyses of test performance from which 2 × 2 tables for each included study could be extracted. We reanalyzed the data using univariate and bivariate random effects models fit with inverse variance and maximum likelihood methods. Analyses were performed using both normal and binomial likelihoods to describe within-study variability. The bivariate model using the binomial likelihood was also fit using a fully Bayesian approach. We use two worked examples-thoracic computerized tomography to detect aortic injury and rapid prescreening of Papanicolaou smears to detect cytological abnormalities-to highlight that different meta-analysis approaches can produce different results. We also present results from reanalysis of 308 meta-analyses of sensitivity and specificity. Models using the normal approximation produced sensitivity and specificity estimates closer to 50% and smaller standard errors compared to models using the binomial likelihood; absolute differences of 5% or greater were observed in 12% and 5% of meta-analyses for sensitivity and specificity, respectively. Results from univariate and bivariate random effects models were similar, regardless of estimation method. Maximum likelihood and Bayesian methods produced almost identical summary estimates under the bivariate model; however, Bayesian analyses indicated greater uncertainty around those estimates. Bivariate models produced imprecise estimates of the between-study correlation of sensitivity and specificity. Differences between methods were larger with increasing proportion of studies that were small or required a continuity correction. The binomial likelihood should be used to model within-study variability. Univariate and bivariate models give similar estimates of the marginal distributions for sensitivity and specificity. Bayesian methods fully quantify uncertainty and their ability to incorporate external evidence may be useful for imprecisely estimated parameters. Copyright © 2017 Elsevier Inc. All rights reserved.

Inferring late-Holocene climate in the Ecuadorian Andes using a chironomid-based temperature inference model

NASA Astrophysics Data System (ADS)

Matthews-Bird, Frazer; Brooks, Stephen J.; Holden, Philip B.; Montoya, Encarni; Gosling, William D.

2016-06-01

Presented here is the first chironomid calibration data set for tropical South America. Surface sediments were collected from 59 lakes across Bolivia (15 lakes), Peru (32 lakes), and Ecuador (12 lakes) between 2004 and 2013 over an altitudinal gradient from 150 m above sea level (a.s.l) to 4655 m a.s.l, between 0-17° S and 64-78° W. The study sites cover a mean annual temperature (MAT) gradient of 25 °C. In total, 55 chironomid taxa were identified in the 59 calibration data set lakes. When used as a single explanatory variable, MAT explains 12.9 % of the variance (λ1/λ2 = 1.431). Two inference models were developed using weighted averaging (WA) and Bayesian methods. The best-performing model using conventional statistical methods was a WA (inverse) model (R2jack = 0.890; RMSEPjack = 2.404 °C, RMSEP - root mean squared error of prediction; mean biasjack = -0.017 °C; max biasjack = 4.665 °C). The Bayesian method produced a model with R2jack = 0.909, RMSEPjack = 2.373 °C, mean biasjack = 0.598 °C, and max biasjack = 3.158 °C. Both models were used to infer past temperatures from a ca. 3000-year record from the tropical Andes of Ecuador, Laguna Pindo. Inferred temperatures fluctuated around modern-day conditions but showed significant departures at certain intervals (ca. 1600 cal yr BP; ca. 3000-2500 cal yr BP). Both methods (WA and Bayesian) showed similar patterns of temperature variability; however, the magnitude of fluctuations differed. In general the WA method was more variable and often underestimated Holocene temperatures (by ca. -7 ± 2.5 °C relative to the modern period). The Bayesian method provided temperature anomaly estimates for cool periods that lay within the expected range of the Holocene (ca. -3 ± 3.4 °C). The error associated with both reconstructions is consistent with a constant temperature of 20 °C for the past 3000 years. We would caution, however, against an over-interpretation at this stage. The reconstruction can only currently be deemed qualitative and requires more research before quantitative estimates can be generated with confidence. Increasing the number, and spread, of lakes in the calibration data set would enable the detection of smaller climate signals.

Hierarchical Bayesian Model (HBM)-Derived Estimates of Air Quality for 2004 - Annual Report

EPA Science Inventory

This report describes EPA's Hierarchical Bayesian model-generated (HBM) estimates of O₃ and PM_2.5 concentrations throughout the continental United States during the 2004 calendar year. HBM estimates provide the spatial and temporal variance of O₃ ...

Bayesian Estimation Supersedes the "t" Test

ERIC Educational Resources Information Center

Kruschke, John K.

2013-01-01

Bayesian estimation for 2 groups provides complete distributions of credible values for the effect size, group means and their difference, standard deviations and their difference, and the normality of the data. The method handles outliers. The decision rule can accept the null value (unlike traditional "t" tests) when certainty in the estimate is…

Bayesian and Frequentist Methods for Estimating Joint Uncertainty of Freundlich Adsorption Isotherm Fitting Parameters

EPA Science Inventory

In this paper, we present methods for estimating Freundlich isotherm fitting parameters (K and N) and their joint uncertainty, which have been implemented into the freeware software platforms R and WinBUGS. These estimates were determined by both Frequentist and Bayesian analyse...

A Bayesian hierarchical diffusion model decomposition of performance in Approach–Avoidance Tasks

PubMed Central

Krypotos, Angelos-Miltiadis; Beckers, Tom; Kindt, Merel; Wagenmakers, Eric-Jan

2015-01-01

Common methods for analysing response time (RT) tasks, frequently used across different disciplines of psychology, suffer from a number of limitations such as the failure to directly measure the underlying latent processes of interest and the inability to take into account the uncertainty associated with each individual's point estimate of performance. Here, we discuss a Bayesian hierarchical diffusion model and apply it to RT data. This model allows researchers to decompose performance into meaningful psychological processes and to account optimally for individual differences and commonalities, even with relatively sparse data. We highlight the advantages of the Bayesian hierarchical diffusion model decomposition by applying it to performance on Approach–Avoidance Tasks, widely used in the emotion and psychopathology literature. Model fits for two experimental data-sets demonstrate that the model performs well. The Bayesian hierarchical diffusion model overcomes important limitations of current analysis procedures and provides deeper insight in latent psychological processes of interest. PMID:25491372

Estimating the Effective Sample Size of Tree Topologies from Bayesian Phylogenetic Analyses

PubMed Central

Lanfear, Robert; Hua, Xia; Warren, Dan L.

2016-01-01

Bayesian phylogenetic analyses estimate posterior distributions of phylogenetic tree topologies and other parameters using Markov chain Monte Carlo (MCMC) methods. Before making inferences from these distributions, it is important to assess their adequacy. To this end, the effective sample size (ESS) estimates how many truly independent samples of a given parameter the output of the MCMC represents. The ESS of a parameter is frequently much lower than the number of samples taken from the MCMC because sequential samples from the chain can be non-independent due to autocorrelation. Typically, phylogeneticists use a rule of thumb that the ESS of all parameters should be greater than 200. However, we have no method to calculate an ESS of tree topology samples, despite the fact that the tree topology is often the parameter of primary interest and is almost always central to the estimation of other parameters. That is, we lack a method to determine whether we have adequately sampled one of the most important parameters in our analyses. In this study, we address this problem by developing methods to estimate the ESS for tree topologies. We combine these methods with two new diagnostic plots for assessing posterior samples of tree topologies, and compare their performance on simulated and empirical data sets. Combined, the methods we present provide new ways to assess the mixing and convergence of phylogenetic tree topologies in Bayesian MCMC analyses. PMID:27435794

Bayesian Model Averaging for Propensity Score Analysis

ERIC Educational Resources Information Center

Kaplan, David; Chen, Jianshen

2013-01-01

The purpose of this study is to explore Bayesian model averaging in the propensity score context. Previous research on Bayesian propensity score analysis does not take into account model uncertainty. In this regard, an internally consistent Bayesian framework for model building and estimation must also account for model uncertainty. The…

Flood quantile estimation at ungauged sites by Bayesian networks

NASA Astrophysics Data System (ADS)

Mediero, L.; Santillán, D.; Garrote, L.

2012-04-01

Estimating flood quantiles at a site for which no observed measurements are available is essential for water resources planning and management. Ungauged sites have no observations about the magnitude of floods, but some site and basin characteristics are known. The most common technique used is the multiple regression analysis, which relates physical and climatic basin characteristic to flood quantiles. Regression equations are fitted from flood frequency data and basin characteristics at gauged sites. Regression equations are a rigid technique that assumes linear relationships between variables and cannot take the measurement errors into account. In addition, the prediction intervals are estimated in a very simplistic way from the variance of the residuals in the estimated model. Bayesian networks are a probabilistic computational structure taken from the field of Artificial Intelligence, which have been widely and successfully applied to many scientific fields like medicine and informatics, but application to the field of hydrology is recent. Bayesian networks infer the joint probability distribution of several related variables from observations through nodes, which represent random variables, and links, which represent causal dependencies between them. A Bayesian network is more flexible than regression equations, as they capture non-linear relationships between variables. In addition, the probabilistic nature of Bayesian networks allows taking the different sources of estimation uncertainty into account, as they give a probability distribution as result. A homogeneous region in the Tagus Basin was selected as case study. A regression equation was fitted taking the basin area, the annual maximum 24-hour rainfall for a given recurrence interval and the mean height as explanatory variables. Flood quantiles at ungauged sites were estimated by Bayesian networks. Bayesian networks need to be learnt from a huge enough data set. As observational data are reduced, a stochastic generator of synthetic data was developed. Synthetic basin characteristics were randomised, keeping the statistical properties of observed physical and climatic variables in the homogeneous region. The synthetic flood quantiles were stochastically generated taking the regression equation as basis. The learnt Bayesian network was validated by the reliability diagram, the Brier Score and the ROC diagram, which are common measures used in the validation of probabilistic forecasts. Summarising, the flood quantile estimations through Bayesian networks supply information about the prediction uncertainty as a probability distribution function of discharges is given as result. Therefore, the Bayesian network model has application as a decision support for water resources and planning management.

Bayesian-MCMC-based parameter estimation of stealth aircraft RCS models

NASA Astrophysics Data System (ADS)

Xia, Wei; Dai, Xiao-Xia; Feng, Yuan

2015-12-01

When modeling a stealth aircraft with low RCS (Radar Cross Section), conventional parameter estimation methods may cause a deviation from the actual distribution, owing to the fact that the characteristic parameters are estimated via directly calculating the statistics of RCS. The Bayesian-Markov Chain Monte Carlo (Bayesian-MCMC) method is introduced herein to estimate the parameters so as to improve the fitting accuracies of fluctuation models. The parameter estimations of the lognormal and the Legendre polynomial models are reformulated in the Bayesian framework. The MCMC algorithm is then adopted to calculate the parameter estimates. Numerical results show that the distribution curves obtained by the proposed method exhibit improved consistence with the actual ones, compared with those fitted by the conventional method. The fitting accuracy could be improved by no less than 25% for both fluctuation models, which implies that the Bayesian-MCMC method might be a good candidate among the optimal parameter estimation methods for stealth aircraft RCS models. Project supported by the National Natural Science Foundation of China (Grant No. 61101173), the National Basic Research Program of China (Grant No. 613206), the National High Technology Research and Development Program of China (Grant No. 2012AA01A308), the State Scholarship Fund by the China Scholarship Council (CSC), and the Oversea Academic Training Funds, and University of Electronic Science and Technology of China (UESTC).

Combined state and parameter identification of nonlinear structural dynamical systems based on Rao-Blackwellization and Markov chain Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Abhinav, S.; Manohar, C. S.

2018-03-01

The problem of combined state and parameter estimation in nonlinear state space models, based on Bayesian filtering methods, is considered. A novel approach, which combines Rao-Blackwellized particle filters for state estimation with Markov chain Monte Carlo (MCMC) simulations for parameter identification, is proposed. In order to ensure successful performance of the MCMC samplers, in situations involving large amount of dynamic measurement data and (or) low measurement noise, the study employs a modified measurement model combined with an importance sampling based correction. The parameters of the process noise covariance matrix are also included as quantities to be identified. The study employs the Rao-Blackwellization step at two stages: one, associated with the state estimation problem in the particle filtering step, and, secondly, in the evaluation of the ratio of likelihoods in the MCMC run. The satisfactory performance of the proposed method is illustrated on three dynamical systems: (a) a computational model of a nonlinear beam-moving oscillator system, (b) a laboratory scale beam traversed by a loaded trolley, and (c) an earthquake shake table study on a bending-torsion coupled nonlinear frame subjected to uniaxial support motion.

Development and comparison in uncertainty assessment based Bayesian modularization method in hydrological modeling

NASA Astrophysics Data System (ADS)

Li, Lu; Xu, Chong-Yu; Engeland, Kolbjørn

2013-04-01

SummaryWith respect to model calibration, parameter estimation and analysis of uncertainty sources, various regression and probabilistic approaches are used in hydrological modeling. A family of Bayesian methods, which incorporates different sources of information into a single analysis through Bayes' theorem, is widely used for uncertainty assessment. However, none of these approaches can well treat the impact of high flows in hydrological modeling. This study proposes a Bayesian modularization uncertainty assessment approach in which the highest streamflow observations are treated as suspect information that should not influence the inference of the main bulk of the model parameters. This study includes a comprehensive comparison and evaluation of uncertainty assessments by our new Bayesian modularization method and standard Bayesian methods using the Metropolis-Hastings (MH) algorithm with the daily hydrological model WASMOD. Three likelihood functions were used in combination with standard Bayesian method: the AR(1) plus Normal model independent of time (Model 1), the AR(1) plus Normal model dependent on time (Model 2) and the AR(1) plus Multi-normal model (Model 3). The results reveal that the Bayesian modularization method provides the most accurate streamflow estimates measured by the Nash-Sutcliffe efficiency and provide the best in uncertainty estimates for low, medium and entire flows compared to standard Bayesian methods. The study thus provides a new approach for reducing the impact of high flows on the discharge uncertainty assessment of hydrological models via Bayesian method.

Bayesian inference for disease prevalence using negative binomial group testing

PubMed Central

Pritchard, Nicholas A.; Tebbs, Joshua M.

2011-01-01

Group testing, also known as pooled testing, and inverse sampling are both widely used methods of data collection when the goal is to estimate a small proportion. Taking a Bayesian approach, we consider the new problem of estimating disease prevalence from group testing when inverse (negative binomial) sampling is used. Using different distributions to incorporate prior knowledge of disease incidence and different loss functions, we derive closed form expressions for posterior distributions and resulting point and credible interval estimators. We then evaluate our new estimators, on Bayesian and classical grounds, and apply our methods to a West Nile Virus data set. PMID:21259308

Bayesian Estimation and Inference Using Stochastic Electronics

PubMed Central

Thakur, Chetan Singh; Afshar, Saeed; Wang, Runchun M.; Hamilton, Tara J.; Tapson, Jonathan; van Schaik, André

2016-01-01

In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker), demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM) to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise) probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND), we show how inference can be performed in a Directed Acyclic Graph (DAG) using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC) technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream. PMID:27047326

Bayesian Estimation and Inference Using Stochastic Electronics.

PubMed

Thakur, Chetan Singh; Afshar, Saeed; Wang, Runchun M; Hamilton, Tara J; Tapson, Jonathan; van Schaik, André

2016-01-01

In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker), demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM) to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise) probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND), we show how inference can be performed in a Directed Acyclic Graph (DAG) using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC) technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.

A Bayesian Analysis of a Randomized Clinical Trial Comparing Antimetabolite Therapies for Non-Infectious Uveitis

PubMed Central

Browne, Erica N; Rathinam, Sivakumar R; Kanakath, Anuradha; Thundikandy, Radhika; Babu, Manohar; Lietman, Thomas M; Acharya, Nisha R

2017-01-01

Purpose To conduct a Bayesian analysis of a randomized clinical trial (RCT) for non-infectious uveitis using expert opinion as a subjective prior belief. Methods A RCT was conducted to determine which antimetabolite, methotrexate or mycophenolate mofetil, is more effective as an initial corticosteroid-sparing agent for the treatment of intermediate, posterior, and pan- uveitis. Before the release of trial results, expert opinion on the relative effectiveness of these two medications was collected via online survey. Members of the American Uveitis Society executive committee were invited to provide an estimate for the relative decrease in efficacy with a 95% credible interval (CrI). A prior probability distribution was created from experts’ estimates. A Bayesian analysis was performed using the constructed expert prior probability distribution and the trial’s primary outcome. Results 11 of 12 invited uveitis specialists provided estimates. Eight of 11 experts (73%) believed mycophenolate mofetil is more effective. The group prior belief was that the odds of treatment success for patients taking mycophenolate mofetil were 1.4-fold the odds of those taking methotrexate (95% CrI 0.03 – 45.0). The odds of treatment success with mycophenolate mofetil compared to methotrexate was 0.4 from the RCT (95% confidence interval 0.1–1.2) and 0.7 (95% CrI 0.2–1.7) from the Bayesian analysis. Conclusions A Bayesian analysis combining expert belief with the trial’s result did not indicate preference for one drug. However, the wide credible interval leaves open the possibility of a substantial treatment effect. This suggests clinical equipoise necessary to allow a larger, more definitive RCT. PMID:27982726

From bridewealth to dowry? : A bayesian estimation of ancestral states of marriage transfers in Indo-European groups.

PubMed

Fortunato, Laura; Holden, Clare; Mace, Ruth

2006-12-01

Significant amounts of wealth have been exchanged as part of marriage settlements throughout history. Although various models have been proposed for interpreting these practices, their development over time has not been investigated systematically. In this paper we use a Bayesian MCMC phylogenetic comparative approach to reconstruct the evolution of two forms of wealth transfers at marriage, dowry and bridewealth, for 51 Indo-European cultural groups. Results indicate that dowry is more likely to have been the ancestral practice, and that a minimum of four changes to bridewealth is necessary to explain the observed distribution of the two states across the cultural groups.

Bayesian forecasting and uncertainty quantifying of stream flows using Metropolis–Hastings Markov Chain Monte Carlo algorithm

DOE PAGES

Wang, Hongrui; Wang, Cheng; Wang, Ying; ...

2017-04-05

This paper presents a Bayesian approach using Metropolis-Hastings Markov Chain Monte Carlo algorithm and applies this method for daily river flow rate forecast and uncertainty quantification for Zhujiachuan River using data collected from Qiaotoubao Gage Station and other 13 gage stations in Zhujiachuan watershed in China. The proposed method is also compared with the conventional maximum likelihood estimation (MLE) for parameter estimation and quantification of associated uncertainties. While the Bayesian method performs similarly in estimating the mean value of daily flow rate, it performs over the conventional MLE method on uncertainty quantification, providing relatively narrower reliable interval than the MLEmore » confidence interval and thus more precise estimation by using the related information from regional gage stations. As a result, the Bayesian MCMC method might be more favorable in the uncertainty analysis and risk management.« less

Survival Bayesian Estimation of Exponential-Gamma Under Linex Loss Function

NASA Astrophysics Data System (ADS)

Rizki, S. W.; Mara, M. N.; Sulistianingsih, E.

2017-06-01

This paper elaborates a research of the cancer patients after receiving a treatment in cencored data using Bayesian estimation under Linex Loss function for Survival Model which is assumed as an exponential distribution. By giving Gamma distribution as prior and likelihood function produces a gamma distribution as posterior distribution. The posterior distribution is used to find estimatior {\\hat{λ }}BL by using Linex approximation. After getting {\\hat{λ }}BL, the estimators of hazard function {\\hat{h}}BL and survival function {\\hat{S}}BL can be found. Finally, we compare the result of Maximum Likelihood Estimation (MLE) and Linex approximation to find the best method for this observation by finding smaller MSE. The result shows that MSE of hazard and survival under MLE are 2.91728E-07 and 0.000309004 and by using Bayesian Linex worths 2.8727E-07 and 0.000304131, respectively. It concludes that the Bayesian Linex is better than MLE.

A Bayesian approach to tracking patients having changing pharmacokinetic parameters

NASA Technical Reports Server (NTRS)

Bayard, David S.; Jelliffe, Roger W.

2004-01-01

This paper considers the updating of Bayesian posterior densities for pharmacokinetic models associated with patients having changing parameter values. For estimation purposes it is proposed to use the Interacting Multiple Model (IMM) estimation algorithm, which is currently a popular algorithm in the aerospace community for tracking maneuvering targets. The IMM algorithm is described, and compared to the multiple model (MM) and Maximum A-Posteriori (MAP) Bayesian estimation methods, which are presently used for posterior updating when pharmacokinetic parameters do not change. Both the MM and MAP Bayesian estimation methods are used in their sequential forms, to facilitate tracking of changing parameters. Results indicate that the IMM algorithm is well suited for tracking time-varying pharmacokinetic parameters in acutely ill and unstable patients, incurring only about half of the integrated error compared to the sequential MM and MAP methods on the same example.

Bayesian approach to the assessment of the population-specific risk of inhibitors in hemophilia A patients: a case study

PubMed Central

Cheng, Ji; Iorio, Alfonso; Marcucci, Maura; Romanov, Vadim; Pullenayegum, Eleanor M; Marshall, John K; Thabane, Lehana

2016-01-01

Background Developing inhibitors is a rare event during the treatment of hemophilia A. The multifacets and uncertainty surrounding the development of inhibitors further complicate the process of estimating inhibitor rate from the limited data. Bayesian statistical modeling provides a useful tool in generating, enhancing, and exploring the evidence through incorporating all the available information. Methods We built our Bayesian analysis using three study cases to estimate the inhibitor rates of patients with hemophilia A in three different scenarios: Case 1, a single cohort of previously treated patients (PTPs) or previously untreated patients; Case 2, a meta-analysis of PTP cohorts; and Case 3, a previously unexplored patient population – patients with baseline low-titer inhibitor or history of inhibitor development. The data used in this study were extracted from three published ADVATE (antihemophilic factor [recombinant] is a product of Baxter for treating hemophilia A) post-authorization surveillance studies. Noninformative and informative priors were applied to Bayesian standard (Case 1) or random-effects (Case 2 and Case 3) logistic models. Bayesian probabilities of satisfying three meaningful thresholds of the risk of developing a clinical significant inhibitor (10/100, 5/100 [high rates], and 1/86 [the Food and Drug Administration mandated cutoff rate in PTPs]) were calculated. The effect of discounting prior information or scaling up the study data was evaluated. Results Results based on noninformative priors were similar to the classical approach. Using priors from PTPs lowered the point estimate and narrowed the 95% credible intervals (Case 1: from 1.3 [0.5, 2.7] to 0.8 [0.5, 1.1]; Case 2: from 1.9 [0.6, 6.0] to 0.8 [0.5, 1.1]; Case 3: 2.3 [0.5, 6.8] to 0.7 [0.5, 1.1]). All probabilities of satisfying a threshold of 1/86 were above 0.65. Increasing the number of patients by two and ten times substantially narrowed the credible intervals for the single cohort study (1.4 [0.7, 2.3] and 1.4 [1.1, 1.8], respectively). Increasing the number of studies by two and ten times for the multiple study scenarios (Case 2: 1.9 [0.6, 4.0] and 1.9 [1.5, 2.6]; Case 3: 2.4 [0.9, 5.0] and 2.6 [1.9, 3.5], respectively) had a similar effect. Conclusion Bayesian approach as a robust, transparent, and reproducible analytic method can be efficiently used to estimate the inhibitor rate of hemophilia A in complex clinical settings. PMID:27822129

Bayesian approach to the assessment of the population-specific risk of inhibitors in hemophilia A patients: a case study.

PubMed

Cheng, Ji; Iorio, Alfonso; Marcucci, Maura; Romanov, Vadim; Pullenayegum, Eleanor M; Marshall, John K; Thabane, Lehana

2016-01-01

Developing inhibitors is a rare event during the treatment of hemophilia A. The multifacets and uncertainty surrounding the development of inhibitors further complicate the process of estimating inhibitor rate from the limited data. Bayesian statistical modeling provides a useful tool in generating, enhancing, and exploring the evidence through incorporating all the available information. We built our Bayesian analysis using three study cases to estimate the inhibitor rates of patients with hemophilia A in three different scenarios: Case 1, a single cohort of previously treated patients (PTPs) or previously untreated patients; Case 2, a meta-analysis of PTP cohorts; and Case 3, a previously unexplored patient population - patients with baseline low-titer inhibitor or history of inhibitor development. The data used in this study were extracted from three published ADVATE (antihemophilic factor [recombinant] is a product of Baxter for treating hemophilia A) post-authorization surveillance studies. Noninformative and informative priors were applied to Bayesian standard (Case 1) or random-effects (Case 2 and Case 3) logistic models. Bayesian probabilities of satisfying three meaningful thresholds of the risk of developing a clinical significant inhibitor (10/100, 5/100 [high rates], and 1/86 [the Food and Drug Administration mandated cutoff rate in PTPs]) were calculated. The effect of discounting prior information or scaling up the study data was evaluated. Results based on noninformative priors were similar to the classical approach. Using priors from PTPs lowered the point estimate and narrowed the 95% credible intervals (Case 1: from 1.3 [0.5, 2.7] to 0.8 [0.5, 1.1]; Case 2: from 1.9 [0.6, 6.0] to 0.8 [0.5, 1.1]; Case 3: 2.3 [0.5, 6.8] to 0.7 [0.5, 1.1]). All probabilities of satisfying a threshold of 1/86 were above 0.65. Increasing the number of patients by two and ten times substantially narrowed the credible intervals for the single cohort study (1.4 [0.7, 2.3] and 1.4 [1.1, 1.8], respectively). Increasing the number of studies by two and ten times for the multiple study scenarios (Case 2: 1.9 [0.6, 4.0] and 1.9 [1.5, 2.6]; Case 3: 2.4 [0.9, 5.0] and 2.6 [1.9, 3.5], respectively) had a similar effect. Bayesian approach as a robust, transparent, and reproducible analytic method can be efficiently used to estimate the inhibitor rate of hemophilia A in complex clinical settings.

Physics-based, Bayesian sequential detection method and system for radioactive contraband

DOEpatents

Candy, James V; Axelrod, Michael C; Breitfeller, Eric F; Chambers, David H; Guidry, Brian L; Manatt, Douglas R; Meyer, Alan W; Sale, Kenneth E

2014-03-18

A distributed sequential method and system for detecting and identifying radioactive contraband from highly uncertain (noisy) low-count, radionuclide measurements, i.e. an event mode sequence (EMS), using a statistical approach based on Bayesian inference and physics-model-based signal processing based on the representation of a radionuclide as a monoenergetic decomposition of monoenergetic sources. For a given photon event of the EMS, the appropriate monoenergy processing channel is determined using a confidence interval condition-based discriminator for the energy amplitude and interarrival time and parameter estimates are used to update a measured probability density function estimate for a target radionuclide. A sequential likelihood ratio test is then used to determine one of two threshold conditions signifying that the EMS is either identified as the target radionuclide or not, and if not, then repeating the process for the next sequential photon event of the EMS until one of the two threshold conditions is satisfied.

A Bayesian Approach to More Stable Estimates of Group-Level Effects in Contextual Studies.

PubMed

Zitzmann, Steffen; Lüdtke, Oliver; Robitzsch, Alexander

2015-01-01

Multilevel analyses are often used to estimate the effects of group-level constructs. However, when using aggregated individual data (e.g., student ratings) to assess a group-level construct (e.g., classroom climate), the observed group mean might not provide a reliable measure of the unobserved latent group mean. In the present article, we propose a Bayesian approach that can be used to estimate a multilevel latent covariate model, which corrects for the unreliable assessment of the latent group mean when estimating the group-level effect. A simulation study was conducted to evaluate the choice of different priors for the group-level variance of the predictor variable and to compare the Bayesian approach with the maximum likelihood approach implemented in the software Mplus. Results showed that, under problematic conditions (i.e., small number of groups, predictor variable with a small ICC), the Bayesian approach produced more accurate estimates of the group-level effect than the maximum likelihood approach did.

Ozone and childhood respiratory disease in three US cities: evaluation of effect measure modification by neighborhood socioeconomic status using a Bayesian hierarchical approach.

PubMed

O' Lenick, Cassandra R; Chang, Howard H; Kramer, Michael R; Winquist, Andrea; Mulholland, James A; Friberg, Mariel D; Sarnat, Stefanie Ebelt

2017-04-05

Ground-level ozone is a potent airway irritant and a determinant of respiratory morbidity. Susceptibility to the health effects of ambient ozone may be influenced by both intrinsic and extrinsic factors, such as neighborhood socioeconomic status (SES). Questions remain regarding the manner and extent that factors such as SES influence ozone-related health effects, particularly across different study areas. Using a 2-stage modeling approach we evaluated neighborhood SES as a modifier of ozone-related pediatric respiratory morbidity in Atlanta, Dallas, & St. Louis. We acquired multi-year data on emergency department (ED) visits among 5-18 year olds with a primary diagnosis of respiratory disease in each city. Daily concentrations of 8-h maximum ambient ozone were estimated for all ZIP Code Tabulation Areas (ZCTA) in each city by fusing observed concentration data from available network monitors with simulations from an emissions-based chemical transport model. In the first stage, we used conditional logistic regression to estimate ZCTA-specific odds ratios (OR) between ozone and respiratory ED visits, controlling for temporal trends and meteorology. In the second stage, we combined ZCTA-level estimates in a Bayesian hierarchical model to assess overall associations and effect modification by neighborhood SES considering categorical and continuous SES indicators (e.g., ZCTA-specific levels of poverty). We estimated ORs and 95% posterior intervals (PI) for a 25 ppb increase in ozone. The hierarchical model combined effect estimates from 179 ZCTAs in Atlanta, 205 ZCTAs in Dallas, and 151 ZCTAs in St. Louis. The strongest overall association of ozone and pediatric respiratory disease was in Atlanta (OR = 1.08, 95% PI: 1.06, 1.11), followed by Dallas (OR = 1.04, 95% PI: 1.01, 1.07) and St. Louis (OR = 1.03, 95% PI: 0.99, 1.07). Patterns of association across levels of neighborhood SES in each city suggested stronger ORs in low compared to high SES areas, with some evidence of non-linear effect modification. Results suggest that ozone is associated with pediatric respiratory morbidity in multiple US cities; neighborhood SES may modify this association in a non-linear manner. In each city, children living in low SES environments appear to be especially vulnerable given positive ORs and high underlying rates of respiratory morbidity.

The evolutionary relationships and age of Homo naledi: An assessment using dated Bayesian phylogenetic methods.

PubMed

Dembo, Mana; Radovčić, Davorka; Garvin, Heather M; Laird, Myra F; Schroeder, Lauren; Scott, Jill E; Brophy, Juliet; Ackermann, Rebecca R; Musiba, Chares M; de Ruiter, Darryl J; Mooers, Arne Ø; Collard, Mark

2016-08-01

Homo naledi is a recently discovered species of fossil hominin from South Africa. A considerable amount is already known about H. naledi but some important questions remain unanswered. Here we report a study that addressed two of them: "Where does H. naledi fit in the hominin evolutionary tree?" and "How old is it?" We used a large supermatrix of craniodental characters for both early and late hominin species and Bayesian phylogenetic techniques to carry out three analyses. First, we performed a dated Bayesian analysis to generate estimates of the evolutionary relationships of fossil hominins including H. naledi. Then we employed Bayes factor tests to compare the strength of support for hypotheses about the relationships of H. naledi suggested by the best-estimate trees. Lastly, we carried out a resampling analysis to assess the accuracy of the age estimate for H. naledi yielded by the dated Bayesian analysis. The analyses strongly supported the hypothesis that H. naledi forms a clade with the other Homo species and Australopithecus sediba. The analyses were more ambiguous regarding the position of H. naledi within the (Homo, Au. sediba) clade. A number of hypotheses were rejected, but several others were not. Based on the available craniodental data, Homo antecessor, Asian Homo erectus, Homo habilis, Homo floresiensis, Homo sapiens, and Au. sediba could all be the sister taxon of H. naledi. According to the dated Bayesian analysis, the most likely age for H. naledi is 912 ka. This age estimate was supported by the resampling analysis. Our findings have a number of implications. Most notably, they support the assignment of the new specimens to Homo, cast doubt on the claim that H. naledi is simply a variant of H. erectus, and suggest H. naledi is younger than has been previously proposed. Copyright © 2016 Elsevier Ltd. All rights reserved.

Estimating the extent and distribution of new-onset adult asthma in British Columbia using frequentist and Bayesian approaches.

PubMed

Beach, Jeremy; Burstyn, Igor; Cherry, Nicola

2012-07-01

We previously described a method to identify the incidence of new-onset adult asthma (NOAA) in Alberta by industry and occupation, utilizing Workers' Compensation Board (WCB) and physician billing data. The aim of this study was to extend this method to data from British Columbia (BC) so as to compare the two provinces and to incorporate Bayesian methodology into estimates of risk. WCB claims for any reason 1995-2004 were linked to physician billing data. NOAA was defined as a billing for asthma (ICD-9 493) in the 12 months before a WCB claim without asthma in the previous 3 years. Incidence was calculated by occupation and industry. In a matched case-referent analysis, associations with exposures were examined using an asthma-specific job exposure matrix (JEM). Posterior distributions from the Alberta analysis and estimated misclassification parameters were used as priors in the Bayesian analysis of the BC data. Among 1 118 239 eligible WCB claims the incidence of NOAA was 1.4%. Sixteen occupations and 44 industries had a significantly increased risk; six industries had a decreased risk. The JEM identified wood dust [odds ratio (OR) 1.55, 95% confidence interval (CI) 1.08-2.24] and animal antigens (OR 1.66, 95% CI 1.17-2.36) as related to an increased risk of NOAA. Exposure to isocyanates was associated with decreased risk (OR 0.57, 95% CI 0.39-0.85). Bayesian analyses taking account of exposure misclassification and informative priors resulted in posterior distributions of ORs with lower boundary of 95% credible intervals >1.00 for almost all exposures. The distribution of NOAA in BC appeared somewhat similar to that in Alberta, except for isocyanates. Bayesian analyses allowed incorporation of prior evidence into risk estimates, permitting reconsideration of the apparently protective effect of isocyanate exposure.

A Bayesian random effects discrete-choice model for resource selection: Population-level selection inference

USGS Publications Warehouse

Thomas, D.L.; Johnson, D.; Griffith, B.

2006-01-01

Modeling the probability of use of land units characterized by discrete and continuous measures, we present a Bayesian random-effects model to assess resource selection. This model provides simultaneous estimation of both individual- and population-level selection. Deviance information criterion (DIC), a Bayesian alternative to AIC that is sample-size specific, is used for model selection. Aerial radiolocation data from 76 adult female caribou (Rangifer tarandus) and calf pairs during 1 year on an Arctic coastal plain calving ground were used to illustrate models and assess population-level selection of landscape attributes, as well as individual heterogeneity of selection. Landscape attributes included elevation, NDVI (a measure of forage greenness), and land cover-type classification. Results from the first of a 2-stage model-selection procedure indicated that there is substantial heterogeneity among cow-calf pairs with respect to selection of the landscape attributes. In the second stage, selection of models with heterogeneity included indicated that at the population-level, NDVI and land cover class were significant attributes for selection of different landscapes by pairs on the calving ground. Population-level selection coefficients indicate that the pairs generally select landscapes with higher levels of NDVI, but the relationship is quadratic. The highest rate of selection occurs at values of NDVI less than the maximum observed. Results for land cover-class selections coefficients indicate that wet sedge, moist sedge, herbaceous tussock tundra, and shrub tussock tundra are selected at approximately the same rate, while alpine and sparsely vegetated landscapes are selected at a lower rate. Furthermore, the variability in selection by individual caribou for moist sedge and sparsely vegetated landscapes is large relative to the variability in selection of other land cover types. The example analysis illustrates that, while sometimes computationally intense, a Bayesian hierarchical discrete-choice model for resource selection can provide managers with 2 components of population-level inference: average population selection and variability of selection. Both components are necessary to make sound management decisions based on animal selection.

Bayesian Estimation of Panel Data Fractional Response Models with Endogeneity: An Application to Standardized Test Rates

ERIC Educational Resources Information Center

Kessler, Lawrence M.

2013-01-01

In this paper I propose Bayesian estimation of a nonlinear panel data model with a fractional dependent variable (bounded between 0 and 1). Specifically, I estimate a panel data fractional probit model which takes into account the bounded nature of the fractional response variable. I outline estimation under the assumption of strict exogeneity as…

A Bayesian observer replicates convexity context effects in figure-ground perception.

PubMed

Goldreich, Daniel; Peterson, Mary A

2012-01-01

Peterson and Salvagio (2008) demonstrated convexity context effects in figure-ground perception. Subjects shown displays consisting of unfamiliar alternating convex and concave regions identified the convex regions as foreground objects progressively more frequently as the number of regions increased; this occurred only when the concave regions were homogeneously colored. The origins of these effects have been unclear. Here, we present a two-free-parameter Bayesian observer that replicates convexity context effects. The Bayesian observer incorporates two plausible expectations regarding three-dimensional scenes: (1) objects tend to be convex rather than concave, and (2) backgrounds tend (more than foreground objects) to be homogeneously colored. The Bayesian observer estimates the probability that a depicted scene is three-dimensional, and that the convex regions are figures. It responds stochastically by sampling from its posterior distributions. Like human observers, the Bayesian observer shows convexity context effects only for images with homogeneously colored concave regions. With optimal parameter settings, it performs similarly to the average human subject on the four display types tested. We propose that object convexity and background color homogeneity are environmental regularities exploited by human visual perception; vision achieves figure-ground perception by interpreting ambiguous images in light of these and other expected regularities in natural scenes.

Relating Memory To Functional Performance In Normal Aging to Dementia Using Hierarchical Bayesian Cognitive Processing Models

PubMed Central

Shankle, William R.; Pooley, James P.; Steyvers, Mark; Hara, Junko; Mangrola, Tushar; Reisberg, Barry; Lee, Michael D.

2012-01-01

Determining how cognition affects functional abilities is important in Alzheimer’s disease and related disorders (ADRD). 280 patients (normal or ADRD) received a total of 1,514 assessments using the Functional Assessment Staging Test (FAST) procedure and the MCI Screen (MCIS). A hierarchical Bayesian cognitive processing (HBCP) model was created by embedding a signal detection theory (SDT) model of the MCIS delayed recognition memory task into a hierarchical Bayesian framework. The SDT model used latent parameters of discriminability (memory process) and response bias (executive function) to predict, simultaneously, recognition memory performance for each patient and each FAST severity group. The observed recognition memory data did not distinguish the six FAST severity stages, but the latent parameters completely separated them. The latent parameters were also used successfully to transform the ordinal FAST measure into a continuous measure reflecting the underlying continuum of functional severity. HBCP models applied to recognition memory data from clinical practice settings accurately translated a latent measure of cognition to a continuous measure of functional severity for both individuals and FAST groups. Such a translation links two levels of brain information processing, and may enable more accurate correlations with other levels, such as those characterized by biomarkers. PMID:22407225

Effects of subchronic exposures to concentrated ambient particles (CAPs) in mice. III. Acute and chronic effects of CAPs on heart rate, heart-rate fluctuation, and body temperature.

PubMed

Hwang, Jing-Shiang; Nadziejko, Christine; Chen, Lung Chi

2005-04-01

Normal mice (C57) and mice prone to develop atherosclerosis (ApoE-/-) were implanted with electrocardiograph (EKG), core body temperature, and motion transmitters were exposed daily for 6 h to Tuxedo, NY, concentrated ambient particles (CAPs) for 5 day/wk during the spring and summer of 2003. The series of 5-min EKG monitoring and body-temperature measurements were obtained for each animal in the CAPs and filtered air sham exposure groups. Our hypothesis was that chronic exposure could cause cumulative health effects. We used our recently developed nonparametric method to estimate the daily time periods that mean heart rates (HR), body temperature, and physical activity differed significantly between the CAPs and sham exposed group. CAPs exposure most affected heart rate between 1:30 a.m. and 4:30 a.m. With the response variables being the average heart rate, body temperature, and physical activity, we adopted a two-stage modeling approach to obtain the estimates of chronic and acute effects on the changes of these three response variables. In the first stage, a time-varying model estimated daily crude effects. In the second stage, the true means of the estimated crude effects were modeled with a polynominal function of time for chronic effects, a linear term of daily CAPs exposure concentrations for acute effects, and a random component for unknown noise. A Bayesian framework combined these two stages. There were significant decreasing patterns of HR, body temperature, and physical activity for the ApoE-/- mice over the 5 mo of CAPs exposure, with smaller and nonsignificant changes for the C57 mice. The chronic effect changes of the three response variables for ApoE-/- mice were maximal in the last few weeks. There was also a significant relationship between CAPs exposure concentration and short-term changes of heart rate in ApoE-/- mice during exposure. Response variables were also defined for examining fluctuations of 5-min heart rates within long (i.e., 3-6 h) and short time periods (i.e., approximately 15 min). The results for the ApoE-/- mice showed that heart-rate fluctuation within the longer periods increased to 1.35-fold by the end of exposure experiment, while the heart-rate fluctuation within 15 min decreased to 0.7-fold.

Improving the quantification of flash flood hydrographs and reducing their uncertainty using noncontact streamgauging methods

NASA Astrophysics Data System (ADS)

Branger, Flora; Dramais, Guillaume; Horner, Ivan; Le Boursicaud, Raphaël; Le Coz, Jérôme; Renard, Benjamin

2015-04-01

Continuous river discharge data are crucial for the study and management of floods. In most river discharge monitoring networks, these data are obtained at gauging stations, where the stage-discharge relation is modelled with a rating curve to derive discharge from the measurement of water level in the river. Rating curves are usually established using individual ratings (or gaugings). However, using traditional gauging methods during flash floods is challenging for many reasons including hazardous flow conditions (for both equipment and people), short duration of the flood events, transient flows during the time needed to perform the gauging, etc. The lack of gaugings implies that the rating curve is often extrapolated well beyond the gauged range for the highest floods, inducing large uncertainties in the computed discharges. We deployed two remote techniques for gauging floods and improving stage-discharge relations for high flow conditions at several hydrometric stations throughout the Ardèche river catchment in France : (1) permanent video-recording stations enabling the implementation of the image analysis LS-PIV technique (Large Scale Particle Image Velocimetry) ; (2) and mobile gaugings using handheld Surface Velocity Radars (SVR). These gaugings were used to estimate the rating curve and its uncertainty using the Bayesian method BaRatin (Le Coz et al., 2014). Importantly, this method explicitly accounts for the uncertainty of individual gaugings, which is especially relevant for remote gaugings since their uncertainty is generally much higher than that of standard intrusive gauging methods. Then, the uncertainty of streamflow records was derived by combining the uncertainty of the rating curve and the uncertainty of stage records. We assessed the impact of these methodological developments for peak flow estimation and for flood descriptors at various time steps. The combination of field measurement innovation and statistical developments allows efficiently quantifying and reducing the uncertainties of flood peak estimates and flood descriptors at gauging stations. The noncontact streamgauging techniques used in our field campaign strategy have complementary interests. Permanent LSPIV stations, once installed and calibrated, can monitor floods automatically and perform many gaugings during a single event, thus documenting the rise, peak and recession of floods. SVR gaugings are more "one shot" gaugings but can be deployed quickly and at minimal cost over a large territory. Both of these noncontact techniques contribute to a significant reduction of uncertainty on peak hydrographs and flood descriptors at different time steps for a given catchment. Le Coz, J.; Renard, B.; Bonnifait, L.; Branger, F. & Le Boursicaud, R. (2014), 'Combining hydraulic knowledge and uncertain gaugings in the estimation of hydrometric rating curves: A Bayesian approach', Journal of Hydrology 509, 573-587.

Correlation Between Hierarchical Bayesian and Aerosol Optical Depth PM2.5 Data and Respiratory-Cardiovascular Chronic Diseases

EPA Science Inventory

Tools to estimate PM2.5 mass have expanded in recent years, and now include: 1) stationary monitor readings, 2) Community Multi-Scale Air Quality (CMAQ) model estimates, 3) Hierarchical Bayesian (HB) estimates from combined stationary monitor readings and CMAQ model output; and, ...

BMDS: A Collection of R Functions for Bayesian Multidimensional Scaling

ERIC Educational Resources Information Center

Okada, Kensuke; Shigemasu, Kazuo

2009-01-01

Bayesian multidimensional scaling (MDS) has attracted a great deal of attention because: (1) it provides a better fit than do classical MDS and ALSCAL; (2) it provides estimation errors of the distances; and (3) the Bayesian dimension selection criterion, MDSIC, provides a direct indication of optimal dimensionality. However, Bayesian MDS is not…

Bayes and empirical Bayes estimators of abundance and density from spatial capture-recapture data

USGS Publications Warehouse

Dorazio, Robert M.

2013-01-01

In capture-recapture and mark-resight surveys, movements of individuals both within and between sampling periods can alter the susceptibility of individuals to detection over the region of sampling. In these circumstances spatially explicit capture-recapture (SECR) models, which incorporate the observed locations of individuals, allow population density and abundance to be estimated while accounting for differences in detectability of individuals. In this paper I propose two Bayesian SECR models, one for the analysis of recaptures observed in trapping arrays and another for the analysis of recaptures observed in area searches. In formulating these models I used distinct submodels to specify the distribution of individual home-range centers and the observable recaptures associated with these individuals. This separation of ecological and observational processes allowed me to derive a formal connection between Bayes and empirical Bayes estimators of population abundance that has not been established previously. I showed that this connection applies to every Poisson point-process model of SECR data and provides theoretical support for a previously proposed estimator of abundance based on recaptures in trapping arrays. To illustrate results of both classical and Bayesian methods of analysis, I compared Bayes and empirical Bayes esimates of abundance and density using recaptures from simulated and real populations of animals. Real populations included two iconic datasets: recaptures of tigers detected in camera-trap surveys and recaptures of lizards detected in area-search surveys. In the datasets I analyzed, classical and Bayesian methods provided similar – and often identical – inferences, which is not surprising given the sample sizes and the noninformative priors used in the analyses.

Bayes and empirical Bayes estimators of abundance and density from spatial capture-recapture data.

PubMed

Dorazio, Robert M

2013-01-01

In capture-recapture and mark-resight surveys, movements of individuals both within and between sampling periods can alter the susceptibility of individuals to detection over the region of sampling. In these circumstances spatially explicit capture-recapture (SECR) models, which incorporate the observed locations of individuals, allow population density and abundance to be estimated while accounting for differences in detectability of individuals. In this paper I propose two Bayesian SECR models, one for the analysis of recaptures observed in trapping arrays and another for the analysis of recaptures observed in area searches. In formulating these models I used distinct submodels to specify the distribution of individual home-range centers and the observable recaptures associated with these individuals. This separation of ecological and observational processes allowed me to derive a formal connection between Bayes and empirical Bayes estimators of population abundance that has not been established previously. I showed that this connection applies to every Poisson point-process model of SECR data and provides theoretical support for a previously proposed estimator of abundance based on recaptures in trapping arrays. To illustrate results of both classical and Bayesian methods of analysis, I compared Bayes and empirical Bayes esimates of abundance and density using recaptures from simulated and real populations of animals. Real populations included two iconic datasets: recaptures of tigers detected in camera-trap surveys and recaptures of lizards detected in area-search surveys. In the datasets I analyzed, classical and Bayesian methods provided similar - and often identical - inferences, which is not surprising given the sample sizes and the noninformative priors used in the analyses.

Using SAS PROC MCMC for Item Response Theory Models

PubMed Central

Samonte, Kelli

2014-01-01

Interest in using Bayesian methods for estimating item response theory models has grown at a remarkable rate in recent years. This attentiveness to Bayesian estimation has also inspired a growth in available software such as WinBUGS, R packages, BMIRT, MPLUS, and SAS PROC MCMC. This article intends to provide an accessible overview of Bayesian methods in the context of item response theory to serve as a useful guide for practitioners in estimating and interpreting item response theory (IRT) models. Included is a description of the estimation procedure used by SAS PROC MCMC. Syntax is provided for estimation of both dichotomous and polytomous IRT models, as well as a discussion on how to extend the syntax to accommodate more complex IRT models. PMID:29795834

A Bayesian perspective on magnitude estimation.

PubMed

Petzschner, Frederike H; Glasauer, Stefan; Stephan, Klaas E

2015-05-01

Our representation of the physical world requires judgments of magnitudes, such as loudness, distance, or time. Interestingly, magnitude estimates are often not veridical but subject to characteristic biases. These biases are strikingly similar across different sensory modalities, suggesting common processing mechanisms that are shared by different sensory systems. However, the search for universal neurobiological principles of magnitude judgments requires guidance by formal theories. Here, we discuss a unifying Bayesian framework for understanding biases in magnitude estimation. This Bayesian perspective enables a re-interpretation of a range of established psychophysical findings, reconciles seemingly incompatible classical views on magnitude estimation, and can guide future investigations of magnitude estimation and its neurobiological mechanisms in health and in psychiatric diseases, such as schizophrenia. Copyright © 2015 Elsevier Ltd. All rights reserved.

Effects of error covariance structure on estimation of model averaging weights and predictive performance

USGS Publications Warehouse

Lu, Dan; Ye, Ming; Meyer, Philip D.; Curtis, Gary P.; Shi, Xiaoqing; Niu, Xu-Feng; Yabusaki, Steve B.

2013-01-01

When conducting model averaging for assessing groundwater conceptual model uncertainty, the averaging weights are often evaluated using model selection criteria such as AIC, AICc, BIC, and KIC (Akaike Information Criterion, Corrected Akaike Information Criterion, Bayesian Information Criterion, and Kashyap Information Criterion, respectively). However, this method often leads to an unrealistic situation in which the best model receives overwhelmingly large averaging weight (close to 100%), which cannot be justified by available data and knowledge. It was found in this study that this problem was caused by using the covariance matrix, CE, of measurement errors for estimating the negative log likelihood function common to all the model selection criteria. This problem can be resolved by using the covariance matrix, Cek, of total errors (including model errors and measurement errors) to account for the correlation between the total errors. An iterative two-stage method was developed in the context of maximum likelihood inverse modeling to iteratively infer the unknown Cek from the residuals during model calibration. The inferred Cek was then used in the evaluation of model selection criteria and model averaging weights. While this method was limited to serial data using time series techniques in this study, it can be extended to spatial data using geostatistical techniques. The method was first evaluated in a synthetic study and then applied to an experimental study, in which alternative surface complexation models were developed to simulate column experiments of uranium reactive transport. It was found that the total errors of the alternative models were temporally correlated due to the model errors. The iterative two-stage method using Cekresolved the problem that the best model receives 100% model averaging weight, and the resulting model averaging weights were supported by the calibration results and physical understanding of the alternative models. Using Cek obtained from the iterative two-stage method also improved predictive performance of the individual models and model averaging in both synthetic and experimental studies.

Predictability of extreme weather events for NE U.S.: improvement of the numerical prediction using a Bayesian regression approach

NASA Astrophysics Data System (ADS)

Yang, J.; Astitha, M.; Anagnostou, E. N.; Hartman, B.; Kallos, G. B.

2015-12-01

Weather prediction accuracy has become very important for the Northeast U.S. given the devastating effects of extreme weather events in the recent years. Weather forecasting systems are used towards building strategies to prevent catastrophic losses for human lives and the environment. Concurrently, weather forecast tools and techniques have evolved with improved forecast skill as numerical prediction techniques are strengthened by increased super-computing resources. In this study, we examine the combination of two state-of-the-science atmospheric models (WRF and RAMS/ICLAMS) by utilizing a Bayesian regression approach to improve the prediction of extreme weather events for NE U.S. The basic concept behind the Bayesian regression approach is to take advantage of the strengths of two atmospheric modeling systems and, similar to the multi-model ensemble approach, limit their weaknesses which are related to systematic and random errors in the numerical prediction of physical processes. The first part of this study is focused on retrospective simulations of seventeen storms that affected the region in the period 2004-2013. Optimal variances are estimated by minimizing the root mean square error and are applied to out-of-sample weather events. The applicability and usefulness of this approach are demonstrated by conducting an error analysis based on in-situ observations from meteorological stations of the National Weather Service (NWS) for wind speed and wind direction, and NCEP Stage IV radar data, mosaicked from the regional multi-sensor for precipitation. The preliminary results indicate a significant improvement in the statistical metrics of the modeled-observed pairs for meteorological variables using various combinations of the sixteen events as predictors of the seventeenth. This presentation will illustrate the implemented methodology and the obtained results for wind speed, wind direction and precipitation, as well as set the research steps that will be followed in the future.

Analysis of the Bayesian Cramér-Rao lower bound in astrometry. Studying the impact of prior information in the location of an object

NASA Astrophysics Data System (ADS)

Echeverria, Alex; Silva, Jorge F.; Mendez, Rene A.; Orchard, Marcos

2016-10-01

Context. The best precision that can be achieved to estimate the location of a stellar-like object is a topic of permanent interest in the astrometric community. Aims: We analyze bounds for the best position estimation of a stellar-like object on a CCD detector array in a Bayesian setting where the position is unknown, but where we have access to a prior distribution. In contrast to a parametric setting where we estimate a parameter from observations, the Bayesian approach estimates a random object (I.e., the position is a random variable) from observations that are statistically dependent on the position. Methods: We characterize the Bayesian Cramér-Rao (CR) that bounds the minimum mean square error (MMSE) of the best estimator of the position of a point source on a linear CCD-like detector, as a function of the properties of detector, the source, and the background. Results: We quantify and analyze the increase in astrometric performance from the use of a prior distribution of the object position, which is not available in the classical parametric setting. This gain is shown to be significant for various observational regimes, in particular in the case of faint objects or when the observations are taken under poor conditions. Furthermore, we present numerical evidence that the MMSE estimator of this problem tightly achieves the Bayesian CR bound. This is a remarkable result, demonstrating that all the performance gains presented in our analysis can be achieved with the MMSE estimator. Conclusions: The Bayesian CR bound can be used as a benchmark indicator of the expected maximum positional precision of a set of astrometric measurements in which prior information can be incorporated. This bound can be achieved through the conditional mean estimator, in contrast to the parametric case where no unbiased estimator precisely reaches the CR bound.

A default Bayesian hypothesis test for mediation.

PubMed

Nuijten, Michèle B; Wetzels, Ruud; Matzke, Dora; Dolan, Conor V; Wagenmakers, Eric-Jan

2015-03-01

In order to quantify the relationship between multiple variables, researchers often carry out a mediation analysis. In such an analysis, a mediator (e.g., knowledge of a healthy diet) transmits the effect from an independent variable (e.g., classroom instruction on a healthy diet) to a dependent variable (e.g., consumption of fruits and vegetables). Almost all mediation analyses in psychology use frequentist estimation and hypothesis-testing techniques. A recent exception is Yuan and MacKinnon (Psychological Methods, 14, 301-322, 2009), who outlined a Bayesian parameter estimation procedure for mediation analysis. Here we complete the Bayesian alternative to frequentist mediation analysis by specifying a default Bayesian hypothesis test based on the Jeffreys-Zellner-Siow approach. We further extend this default Bayesian test by allowing a comparison to directional or one-sided alternatives, using Markov chain Monte Carlo techniques implemented in JAGS. All Bayesian tests are implemented in the R package BayesMed (Nuijten, Wetzels, Matzke, Dolan, & Wagenmakers, 2014).

Development of a population pharmacokinetic model for carbamazepine based on sparse therapeutic monitoring data from pediatric patients with epilepsy.

PubMed

Carlsson, Kristin Cecilie; Hoem, Nils Ove; Glauser, Tracy; Vinks, Alexander A

2005-05-01

Population models can be important extensions of therapeutic drug monitoring (TDM), as they allow estimation of individual pharmacokinetic parameters based on a small number of measured drug concentrations. This study used a Bayesian approach to explore the utility of routinely collected and sparse TDM data (1 sample per patient) for carbamazepine (CBZ) monotherapy in developing a population pharmacokinetic (PPK) model for CBZ in pediatric patients that would allow prediction of CBZ concentrations for both immediate- and controlled-release formulations. Patient and TDM data were obtained from a pediatric neurology outpatient database. Data were analyzed using an iterative 2-stage Bayesian algorithm and a nonparametric adaptive grid algorithm. Models were compared by final log likelihood, mean error (ME) as a measure of bias, and root mean squared error (RMSE) as a measure of precision. Fifty-seven entries with data on CBZ monotherapy were identified from the database and used in the analysis (36 from males, 21 from females; mean [SD] age, 9.1 [4.4] years [range, 2-21 years]). Preliminary models estimating clearance (Cl) or the elimination rate constant (K(el)) gave good prediction of serum concentrations compared with measured serum concentrations, but estimates of Cl and K(el) were highly correlated with estimates of volume of distribution (V(d)). Different covariate models were then tested. The selected model had zero-order input and had age and body weight as covariates. Cl (L/h) was calculated as K(el) . V(d), where K(el) = [K(i) - (K(s) . age)] and V(d) = [V(i) + (V(s) . body weight)]. Median parameter estimates were V(i) (intercept) = 11.5 L (fixed); V(s) (slope) = 0.3957 L/kg (range, 0.01200-1.5730); K(i) (intercept) = 0.173 h(-1) (fixed); and K(s) (slope) = 0.004487 h(-1) . y(-1) (range, 0.0001800-0.02969). The fit was good for estimates of steady-state serum concentrations based on prior values (population median estimates) (R = 0.468; R(2) = 0.219) but was even better for predictions based on individual Bayesian posterior values (R(2) = 0.991), with little bias (ME = -0.079) and good precision (RMSE = 0.055). Based on the findings of this study, sparse TDM data can be used for PPK modeling of CBZ clearance in children with epilepsy, and these models can be used to predict Cl at steady state in pediatric patients. However, to estimate additional pharmacokinetic model parameters (eg, the absorption rate constant and V(d)), it would be necessary to combine sparse TDM data with additional well-timed samples. This would allow development of more informative PPK models that could be used as part of Bayesian dose-individualization strategies.

Bayesian sparse channel estimation

NASA Astrophysics Data System (ADS)

Chen, Chulong; Zoltowski, Michael D.

2012-05-01

In Orthogonal Frequency Division Multiplexing (OFDM) systems, the technique used to estimate and track the time-varying multipath channel is critical to ensure reliable, high data rate communications. It is recognized that wireless channels often exhibit a sparse structure, especially for wideband and ultra-wideband systems. In order to exploit this sparse structure to reduce the number of pilot tones and increase the channel estimation quality, the application of compressed sensing to channel estimation is proposed. In this article, to make the compressed channel estimation more feasible for practical applications, it is investigated from a perspective of Bayesian learning. Under the Bayesian learning framework, the large-scale compressed sensing problem, as well as large time delay for the estimation of the doubly selective channel over multiple consecutive OFDM symbols, can be avoided. Simulation studies show a significant improvement in channel estimation MSE and less computing time compared to the conventional compressed channel estimation techniques.

Age estimation by assessment of pulp chamber volume: a Bayesian network for the evaluation of dental evidence.

PubMed

Sironi, Emanuele; Taroni, Franco; Baldinotti, Claudio; Nardi, Cosimo; Norelli, Gian-Aristide; Gallidabino, Matteo; Pinchi, Vilma

2017-11-14

The present study aimed to investigate the performance of a Bayesian method in the evaluation of dental age-related evidence collected by means of a geometrical approximation procedure of the pulp chamber volume. Measurement of this volume was based on three-dimensional cone beam computed tomography images. The Bayesian method was applied by means of a probabilistic graphical model, namely a Bayesian network. Performance of that method was investigated in terms of accuracy and bias of the decisional outcomes. Influence of an informed elicitation of the prior belief of chronological age was also studied by means of a sensitivity analysis. Outcomes in terms of accuracy were adequate with standard requirements for forensic adult age estimation. Findings also indicated that the Bayesian method does not show a particular tendency towards under- or overestimation of the age variable. Outcomes of the sensitivity analysis showed that results on estimation are improved with a ration elicitation of the prior probabilities of age.

Bayesian phylogenetic estimation of fossil ages.

PubMed

Drummond, Alexei J; Stadler, Tanja

2016-07-19

Recent advances have allowed for both morphological fossil evidence and molecular sequences to be integrated into a single combined inference of divergence dates under the rule of Bayesian probability. In particular, the fossilized birth-death tree prior and the Lewis-Mk model of discrete morphological evolution allow for the estimation of both divergence times and phylogenetic relationships between fossil and extant taxa. We exploit this statistical framework to investigate the internal consistency of these models by producing phylogenetic estimates of the age of each fossil in turn, within two rich and well-characterized datasets of fossil and extant species (penguins and canids). We find that the estimation accuracy of fossil ages is generally high with credible intervals seldom excluding the true age and median relative error in the two datasets of 5.7% and 13.2%, respectively. The median relative standard error (RSD) was 9.2% and 7.2%, respectively, suggesting good precision, although with some outliers. In fact, in the two datasets we analyse, the phylogenetic estimate of fossil age is on average less than 2 Myr from the mid-point age of the geological strata from which it was excavated. The high level of internal consistency found in our analyses suggests that the Bayesian statistical model employed is an adequate fit for both the geological and morphological data, and provides evidence from real data that the framework used can accurately model the evolution of discrete morphological traits coded from fossil and extant taxa. We anticipate that this approach will have diverse applications beyond divergence time dating, including dating fossils that are temporally unconstrained, testing of the 'morphological clock', and for uncovering potential model misspecification and/or data errors when controversial phylogenetic hypotheses are obtained based on combined divergence dating analyses.This article is part of the themed issue 'Dating species divergences using rocks and clocks'. © 2016 The Authors.

Bayesian phylogenetic estimation of fossil ages

PubMed Central

Drummond, Alexei J.; Stadler, Tanja

2016-01-01

Recent advances have allowed for both morphological fossil evidence and molecular sequences to be integrated into a single combined inference of divergence dates under the rule of Bayesian probability. In particular, the fossilized birth–death tree prior and the Lewis-Mk model of discrete morphological evolution allow for the estimation of both divergence times and phylogenetic relationships between fossil and extant taxa. We exploit this statistical framework to investigate the internal consistency of these models by producing phylogenetic estimates of the age of each fossil in turn, within two rich and well-characterized datasets of fossil and extant species (penguins and canids). We find that the estimation accuracy of fossil ages is generally high with credible intervals seldom excluding the true age and median relative error in the two datasets of 5.7% and 13.2%, respectively. The median relative standard error (RSD) was 9.2% and 7.2%, respectively, suggesting good precision, although with some outliers. In fact, in the two datasets we analyse, the phylogenetic estimate of fossil age is on average less than 2 Myr from the mid-point age of the geological strata from which it was excavated. The high level of internal consistency found in our analyses suggests that the Bayesian statistical model employed is an adequate fit for both the geological and morphological data, and provides evidence from real data that the framework used can accurately model the evolution of discrete morphological traits coded from fossil and extant taxa. We anticipate that this approach will have diverse applications beyond divergence time dating, including dating fossils that are temporally unconstrained, testing of the ‘morphological clock', and for uncovering potential model misspecification and/or data errors when controversial phylogenetic hypotheses are obtained based on combined divergence dating analyses. This article is part of the themed issue ‘Dating species divergences using rocks and clocks’. PMID:27325827

An algebraic aspect of Pareto mixture parameter estimation using censored sample: A Bayesian approach.

PubMed

Saleem, Muhammad; Sharif, Kashif; Fahmi, Aliya

2018-04-27

Applications of Pareto distribution are common in reliability, survival and financial studies. In this paper, A Pareto mixture distribution is considered to model a heterogeneous population comprising of two subgroups. Each of two subgroups is characterized by the same functional form with unknown distinct shape and scale parameters. Bayes estimators have been derived using flat and conjugate priors using squared error loss function. Standard errors have also been derived for the Bayes estimators. An interesting feature of this study is the preparation of components of Fisher Information matrix.

Bayesian approach to estimate AUC, partition coefficient and drug targeting index for studies with serial sacrifice design.

PubMed

Wang, Tianli; Baron, Kyle; Zhong, Wei; Brundage, Richard; Elmquist, William

2014-03-01

The current study presents a Bayesian approach to non-compartmental analysis (NCA), which provides the accurate and precise estimate of AUC 0 (∞) and any AUC 0 (∞) -based NCA parameter or derivation. In order to assess the performance of the proposed method, 1,000 simulated datasets were generated in different scenarios. A Bayesian method was used to estimate the tissue and plasma AUC 0 (∞) s and the tissue-to-plasma AUC 0 (∞) ratio. The posterior medians and the coverage of 95% credible intervals for the true parameter values were examined. The method was applied to laboratory data from a mice brain distribution study with serial sacrifice design for illustration. Bayesian NCA approach is accurate and precise in point estimation of the AUC 0 (∞) and the partition coefficient under a serial sacrifice design. It also provides a consistently good variance estimate, even considering the variability of the data and the physiological structure of the pharmacokinetic model. The application in the case study obtained a physiologically reasonable posterior distribution of AUC, with a posterior median close to the value estimated by classic Bailer-type methods. This Bayesian NCA approach for sparse data analysis provides statistical inference on the variability of AUC 0 (∞) -based parameters such as partition coefficient and drug targeting index, so that the comparison of these parameters following destructive sampling becomes statistically feasible.

A unified Bayesian semiparametric approach to assess discrimination ability in survival analysis

PubMed Central

Zhao, Lili; Feng, Dai; Chen, Guoan; Taylor, Jeremy M.G.

2015-01-01

Summary The discriminatory ability of a marker for censored survival data is routinely assessed by the time-dependent ROC curve and the c-index. The time-dependent ROC curve evaluates the ability of a biomarker to predict whether a patient lives past a particular time t. The c-index measures the global concordance of the marker and the survival time regardless of the time point. We propose a Bayesian semiparametric approach to estimate these two measures. The proposed estimators are based on the conditional distribution of the survival time given the biomarker and the empirical biomarker distribution. The conditional distribution is estimated by a linear dependent Dirichlet process mixture model. The resulting ROC curve is smooth as it is estimated by a mixture of parametric functions. The proposed c-index estimator is shown to be more efficient than the commonly used Harrell's c-index since it uses all pairs of data rather than only informative pairs. The proposed estimators are evaluated through simulations and illustrated using a lung cancer dataset. PMID:26676324

Collinear Latent Variables in Multilevel Confirmatory Factor Analysis

PubMed Central

van de Schoot, Rens; Hox, Joop

2014-01-01

Because variables may be correlated in the social and behavioral sciences, multicollinearity might be problematic. This study investigates the effect of collinearity manipulated in within and between levels of a two-level confirmatory factor analysis by Monte Carlo simulation. Furthermore, the influence of the size of the intraclass correlation coefficient (ICC) and estimation method; maximum likelihood estimation with robust chi-squares and standard errors and Bayesian estimation, on the convergence rate are investigated. The other variables of interest were rate of inadmissible solutions and the relative parameter and standard error bias on the between level. The results showed that inadmissible solutions were obtained when there was between level collinearity and the estimation method was maximum likelihood. In the within level multicollinearity condition, all of the solutions were admissible but the bias values were higher compared with the between level collinearity condition. Bayesian estimation appeared to be robust in obtaining admissible parameters but the relative bias was higher than for maximum likelihood estimation. Finally, as expected, high ICC produced less biased results compared to medium ICC conditions. PMID:29795827

Estimation for coefficient of variation of an extension of the exponential distribution under type-II censoring scheme

NASA Astrophysics Data System (ADS)

Bakoban, Rana A.

2017-08-01

The coefficient of variation [CV] has several applications in applied statistics. So in this paper, we adopt Bayesian and non-Bayesian approaches for the estimation of CV under type-II censored data from extension exponential distribution [EED]. The point and interval estimate of the CV are obtained for each of the maximum likelihood and parametric bootstrap techniques. Also the Bayesian approach with the help of MCMC method is presented. A real data set is presented and analyzed, hence the obtained results are used to assess the obtained theoretical results.

Improving statistical inference on pathogen densities estimated by quantitative molecular methods: malaria gametocytaemia as a case study.

PubMed

Walker, Martin; Basáñez, María-Gloria; Ouédraogo, André Lin; Hermsen, Cornelus; Bousema, Teun; Churcher, Thomas S

2015-01-16

Quantitative molecular methods (QMMs) such as quantitative real-time polymerase chain reaction (q-PCR), reverse-transcriptase PCR (qRT-PCR) and quantitative nucleic acid sequence-based amplification (QT-NASBA) are increasingly used to estimate pathogen density in a variety of clinical and epidemiological contexts. These methods are often classified as semi-quantitative, yet estimates of reliability or sensitivity are seldom reported. Here, a statistical framework is developed for assessing the reliability (uncertainty) of pathogen densities estimated using QMMs and the associated diagnostic sensitivity. The method is illustrated with quantification of Plasmodium falciparum gametocytaemia by QT-NASBA. The reliability of pathogen (e.g. gametocyte) densities, and the accompanying diagnostic sensitivity, estimated by two contrasting statistical calibration techniques, are compared; a traditional method and a mixed model Bayesian approach. The latter accounts for statistical dependence of QMM assays run under identical laboratory protocols and permits structural modelling of experimental measurements, allowing precision to vary with pathogen density. Traditional calibration cannot account for inter-assay variability arising from imperfect QMMs and generates estimates of pathogen density that have poor reliability, are variable among assays and inaccurately reflect diagnostic sensitivity. The Bayesian mixed model approach assimilates information from replica QMM assays, improving reliability and inter-assay homogeneity, providing an accurate appraisal of quantitative and diagnostic performance. Bayesian mixed model statistical calibration supersedes traditional techniques in the context of QMM-derived estimates of pathogen density, offering the potential to improve substantially the depth and quality of clinical and epidemiological inference for a wide variety of pathogens.

A Bayesian evidence synthesis approach to estimate disease prevalence in hard-to-reach populations: hepatitis C in New York City.

PubMed

Tan, Sarah; Makela, Susanna; Heller, Daliah; Konty, Kevin; Balter, Sharon; Zheng, Tian; Stark, James H

2018-06-01

Existing methods to estimate the prevalence of chronic hepatitis C (HCV) in New York City (NYC) are limited in scope and fail to assess hard-to-reach subpopulations with highest risk such as injecting drug users (IDUs). To address these limitations, we employ a Bayesian multi-parameter evidence synthesis model to systematically combine multiple sources of data, account for bias in certain data sources, and provide unbiased HCV prevalence estimates with associated uncertainty. Our approach improves on previous estimates by explicitly accounting for injecting drug use and including data from high-risk subpopulations such as the incarcerated, and is more inclusive, utilizing ten NYC data sources. In addition, we derive two new equations to allow age at first injecting drug use data for former and current IDUs to be incorporated into the Bayesian evidence synthesis, a first for this type of model. Our estimated overall HCV prevalence as of 2012 among NYC adults aged 20-59 years is 2.78% (95% CI 2.61-2.94%), which represents between 124,900 and 140,000 chronic HCV cases. These estimates suggest that HCV prevalence in NYC is higher than previously indicated from household surveys (2.2%) and the surveillance system (2.37%), and that HCV transmission is increasing among young injecting adults in NYC. An ancillary benefit from our results is an estimate of current IDUs aged 20-59 in NYC: 0.58% or 27,600 individuals. Copyright © 2018 Elsevier B.V. All rights reserved.

A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology

NASA Astrophysics Data System (ADS)

Ait-El-Fquih, Boujemaa; El Gharamti, Mohamad; Hoteit, Ibrahim

2016-08-01

Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in subsurface groundwater models. The EnKF sequentially integrates field data into simulation models to obtain a better characterization of the model's state and parameters. These are generally estimated following joint and dual filtering strategies, in which, at each assimilation cycle, a forecast step by the model is followed by an update step with incoming observations. The joint EnKF directly updates the augmented state-parameter vector, whereas the dual EnKF empirically employs two separate filters, first estimating the parameters and then estimating the state based on the updated parameters. To develop a Bayesian consistent dual approach and improve the state-parameter estimates and their consistency, we propose in this paper a one-step-ahead (OSA) smoothing formulation of the state-parameter Bayesian filtering problem from which we derive a new dual-type EnKF, the dual EnKFOSA. Compared with the standard dual EnKF, it imposes a new update step to the state, which is shown to enhance the performance of the dual approach with almost no increase in the computational cost. Numerical experiments are conducted with a two-dimensional (2-D) synthetic groundwater aquifer model to investigate the performance and robustness of the proposed dual EnKFOSA, and to evaluate its results against those of the joint and dual EnKFs. The proposed scheme is able to successfully recover both the hydraulic head and the aquifer conductivity, providing further reliable estimates of their uncertainties. Furthermore, it is found to be more robust to different assimilation settings, such as the spatial and temporal distribution of the observations, and the level of noise in the data. Based on our experimental setups, it yields up to 25 % more accurate state and parameter estimations than the joint and dual approaches.

A Comparison of the β-Substitution Method and a Bayesian Method for Analyzing Left-Censored Data

PubMed Central

Huynh, Tran; Quick, Harrison; Ramachandran, Gurumurthy; Banerjee, Sudipto; Stenzel, Mark; Sandler, Dale P.; Engel, Lawrence S.; Kwok, Richard K.; Blair, Aaron; Stewart, Patricia A.

2016-01-01

Classical statistical methods for analyzing exposure data with values below the detection limits are well described in the occupational hygiene literature, but an evaluation of a Bayesian approach for handling such data is currently lacking. Here, we first describe a Bayesian framework for analyzing censored data. We then present the results of a simulation study conducted to compare the β-substitution method with a Bayesian method for exposure datasets drawn from lognormal distributions and mixed lognormal distributions with varying sample sizes, geometric standard deviations (GSDs), and censoring for single and multiple limits of detection. For each set of factors, estimates for the arithmetic mean (AM), geometric mean, GSD, and the 95th percentile (X0.95) of the exposure distribution were obtained. We evaluated the performance of each method using relative bias, the root mean squared error (rMSE), and coverage (the proportion of the computed 95% uncertainty intervals containing the true value). The Bayesian method using non-informative priors and the β-substitution method were generally comparable in bias and rMSE when estimating the AM and GM. For the GSD and the 95th percentile, the Bayesian method with non-informative priors was more biased and had a higher rMSE than the β-substitution method, but use of more informative priors generally improved the Bayesian method’s performance, making both the bias and the rMSE more comparable to the β-substitution method. An advantage of the Bayesian method is that it provided estimates of uncertainty for these parameters of interest and good coverage, whereas the β-substitution method only provided estimates of uncertainty for the AM, and coverage was not as consistent. Selection of one or the other method depends on the needs of the practitioner, the availability of prior information, and the distribution characteristics of the measurement data. We suggest the use of Bayesian methods if the practitioner has the computational resources and prior information, as the method would generally provide accurate estimates and also provides the distributions of all of the parameters, which could be useful for making decisions in some applications. PMID:26209598

A three-stage colonization model for the peopling of the Americas.

PubMed

Kitchen, Andrew; Miyamoto, Michael M; Mulligan, Connie J

2008-02-13

We evaluate the process by which the Americas were originally colonized and propose a three-stage model that integrates current genetic, archaeological, geological, and paleoecological data. Specifically, we analyze mitochondrial and nuclear genetic data by using complementary coalescent models of demographic history and incorporating non-genetic data to enhance the anthropological relevance of the analysis. Bayesian skyline plots, which provide dynamic representations of population size changes over time, indicate that Amerinds went through two stages of growth approximately 40,000 and approximately 15,000 years ago separated by a long period of population stability. Isolation-with-migration coalescent analyses, which utilize data from sister populations to estimate a divergence date and founder population sizes, suggest an Amerind population expansion starting approximately 15,000 years ago. These results support a model for the peopling of the New World in which Amerind ancestors diverged from the Asian gene pool prior to 40,000 years ago and experienced a gradual population expansion as they moved into Beringia. After a long period of little change in population size in greater Beringia, Amerinds rapidly expanded into the Americas approximately 15,000 years ago either through an interior ice-free corridor or along the coast. This rapid colonization of the New World was achieved by a founder group with an effective population size of approximately 1,000-5,400 individuals. Our model presents a detailed scenario for the timing and scale of the initial migration to the Americas, substantially refines the estimate of New World founders, and provides a unified theory for testing with future datasets and analytic methods.

Internal Medicine residents use heuristics to estimate disease probability.

PubMed

Phang, Sen Han; Ravani, Pietro; Schaefer, Jeffrey; Wright, Bruce; McLaughlin, Kevin

2015-01-01

Training in Bayesian reasoning may have limited impact on accuracy of probability estimates. In this study, our goal was to explore whether residents previously exposed to Bayesian reasoning use heuristics rather than Bayesian reasoning to estimate disease probabilities. We predicted that if residents use heuristics then post-test probability estimates would be increased by non-discriminating clinical features or a high anchor for a target condition. We randomized 55 Internal Medicine residents to different versions of four clinical vignettes and asked them to estimate probabilities of target conditions. We manipulated the clinical data for each vignette to be consistent with either 1) using a representative heuristic, by adding non-discriminating prototypical clinical features of the target condition, or 2) using anchoring with adjustment heuristic, by providing a high or low anchor for the target condition. When presented with additional non-discriminating data the odds of diagnosing the target condition were increased (odds ratio (OR) 2.83, 95% confidence interval [1.30, 6.15], p = 0.009). Similarly, the odds of diagnosing the target condition were increased when a high anchor preceded the vignette (OR 2.04, [1.09, 3.81], p = 0.025). Our findings suggest that despite previous exposure to the use of Bayesian reasoning, residents use heuristics, such as the representative heuristic and anchoring with adjustment, to estimate probabilities. Potential reasons for attribute substitution include the relative cognitive ease of heuristics vs. Bayesian reasoning or perhaps residents in their clinical practice use gist traces rather than precise probability estimates when diagnosing.

Robust Tracking of Small Displacements with a Bayesian Estimator

PubMed Central

Dumont, Douglas M.; Byram, Brett C.

2016-01-01

Radiation-force-based elasticity imaging describes a group of techniques that use acoustic radiation force (ARF) to displace tissue in order to obtain qualitative or quantitative measurements of tissue properties. Because ARF-induced displacements are on the order of micrometers, tracking these displacements in vivo can be challenging. Previously, it has been shown that Bayesian-based estimation can overcome some of the limitations of a traditional displacement estimator like normalized cross-correlation (NCC). In this work, we describe a Bayesian framework that combines a generalized Gaussian-Markov random field (GGMRF) prior with an automated method for selecting the prior’s width. We then evaluate its performance in the context of tracking the micrometer-order displacements encountered in an ARF-based method like acoustic radiation force impulse (ARFI) imaging. The results show that bias, variance, and mean-square error performance vary with prior shape and width, and that an almost one order-of-magnitude reduction in mean-square error can be achieved by the estimator at the automatically-selected prior width. Lesion simulations show that the proposed estimator has a higher contrast-to-noise ratio but lower contrast than NCC, median-filtered NCC, and the previous Bayesian estimator, with a non-Gaussian prior shape having better lesion-edge resolution than a Gaussian prior. In vivo results from a cardiac, radiofrequency ablation ARFI imaging dataset show quantitative improvements in lesion contrast-to-noise ratio over NCC as well as the previous Bayesian estimator. PMID:26529761

Fully Bayesian Estimation of Data from Single Case Designs

ERIC Educational Resources Information Center

Rindskopf, David

2013-01-01

Single case designs (SCDs) generally consist of a small number of short time series in two or more phases. The analysis of SCDs statistically fits in the framework of a multilevel model, or hierarchical model. The usual analysis does not take into account the uncertainty in the estimation of the random effects. This not only has an effect on the…

Spatial Distribution of the Coefficient of Variation and Bayesian Forecast for the Paleo-Earthquakes in Japan

NASA Astrophysics Data System (ADS)

Nomura, Shunichi; Ogata, Yosihiko

2016-04-01

We propose a Bayesian method of probability forecasting for recurrent earthquakes of inland active faults in Japan. Renewal processes with the Brownian Passage Time (BPT) distribution are applied for over a half of active faults in Japan by the Headquarters for Earthquake Research Promotion (HERP) of Japan. Long-term forecast with the BPT distribution needs two parameters; the mean and coefficient of variation (COV) for recurrence intervals. The HERP applies a common COV parameter for all of these faults because most of them have very few specified paleoseismic events, which is not enough to estimate reliable COV values for respective faults. However, different COV estimates are proposed for the same paleoseismic catalog by some related works. It can make critical difference in forecast to apply different COV estimates and so COV should be carefully selected for individual faults. Recurrence intervals on a fault are, on the average, determined by the long-term slip rate caused by the tectonic motion but fluctuated by nearby seismicities which influence surrounding stress field. The COVs of recurrence intervals depend on such stress perturbation and so have spatial trends due to the heterogeneity of tectonic motion and seismicity. Thus we introduce a spatial structure on its COV parameter by Bayesian modeling with a Gaussian process prior. The COVs on active faults are correlated and take similar values for closely located faults. It is found that the spatial trends in the estimated COV values coincide with the density of active faults in Japan. We also show Bayesian forecasts by the proposed model using Markov chain Monte Carlo method. Our forecasts are different from HERP's forecast especially on the active faults where HERP's forecasts are very high or low.

An improved Bayesian tensor regularization and sampling algorithm to track neuronal fiber pathways in the language circuit.

PubMed

Mishra, Arabinda; Anderson, Adam W; Wu, Xi; Gore, John C; Ding, Zhaohua

2010-08-01

The purpose of this work is to design a neuronal fiber tracking algorithm, which will be more suitable for reconstruction of fibers associated with functionally important regions in the human brain. The functional activations in the brain normally occur in the gray matter regions. Hence the fibers bordering these regions are weakly myelinated, resulting in poor performance of conventional tractography methods to trace the fiber links between them. A lower fractional anisotropy in this region makes it even difficult to track the fibers in the presence of noise. In this work, the authors focused on a stochastic approach to reconstruct these fiber pathways based on a Bayesian regularization framework. To estimate the true fiber direction (propagation vector), the a priori and conditional probability density functions are calculated in advance and are modeled as multivariate normal. The variance of the estimated tensor element vector is associated with the uncertainty due to noise and partial volume averaging (PVA). An adaptive and multiple sampling of the estimated tensor element vector, which is a function of the pre-estimated variance, overcomes the effect of noise and PVA in this work. The algorithm has been rigorously tested using a variety of synthetic data sets. The quantitative comparison of the results to standard algorithms motivated the authors to implement it for in vivo DTI data analysis. The algorithm has been implemented to delineate fibers in two major language pathways (Broca's to SMA and Broca's to Wernicke's) across 12 healthy subjects. Though the mean of standard deviation was marginally bigger than conventional (Euler's) approach [P. J. Basser et al., "In vivo fiber tractography using DT-MRI data," Magn. Reson. Med. 44(4), 625-632 (2000)], the number of extracted fibers in this approach was significantly higher. The authors also compared the performance of the proposed method to Lu's method [Y. Lu et al., "Improved fiber tractography with Bayesian tensor regularization," Neuroimage 31(3), 1061-1074 (2006)] and Friman's stochastic approach [O. Friman et al., "A Bayesian approach for stochastic white matter tractography," IEEE Trans. Med. Imaging 25(8), 965-978 (2006)]. Overall performance of the approach is found to be superior to above two methods, particularly when the signal-to-noise ratio was low. The authors observed that an adaptive sampling of the tensor element vectors, estimated as a function of the variance in a Bayesian framework, can effectively delineate neuronal fibers to analyze the structure-function relationship in human brain. The simulated and in vivo results are in good agreement with the theoretical aspects of the algorithm.

Applications of Bayesian spectrum representation in acoustics

NASA Astrophysics Data System (ADS)

Botts, Jonathan M.

This dissertation utilizes a Bayesian inference framework to enhance the solution of inverse problems where the forward model maps to acoustic spectra. A Bayesian solution to filter design inverts a acoustic spectra to pole-zero locations of a discrete-time filter model. Spatial sound field analysis with a spherical microphone array is a data analysis problem that requires inversion of spatio-temporal spectra to directions of arrival. As with many inverse problems, a probabilistic analysis results in richer solutions than can be achieved with ad-hoc methods. In the filter design problem, the Bayesian inversion results in globally optimal coefficient estimates as well as an estimate the most concise filter capable of representing the given spectrum, within a single framework. This approach is demonstrated on synthetic spectra, head-related transfer function spectra, and measured acoustic reflection spectra. The Bayesian model-based analysis of spatial room impulse responses is presented as an analogous problem with equally rich solution. The model selection mechanism provides an estimate of the number of arrivals, which is necessary to properly infer the directions of simultaneous arrivals. Although, spectrum inversion problems are fairly ubiquitous, the scope of this dissertation has been limited to these two and derivative problems. The Bayesian approach to filter design is demonstrated on an artificial spectrum to illustrate the model comparison mechanism and then on measured head-related transfer functions to show the potential range of application. Coupled with sampling methods, the Bayesian approach is shown to outperform least-squares filter design methods commonly used in commercial software, confirming the need for a global search of the parameter space. The resulting designs are shown to be comparable to those that result from global optimization methods, but the Bayesian approach has the added advantage of a filter length estimate within the same unified framework. The application to reflection data is useful for representing frequency-dependent impedance boundaries in finite difference acoustic simulations. Furthermore, since the filter transfer function is a parametric model, it can be modified to incorporate arbitrary frequency weighting and account for the band-limited nature of measured reflection spectra. Finally, the model is modified to compensate for dispersive error in the finite difference simulation, from the filter design process. Stemming from the filter boundary problem, the implementation of pressure sources in finite difference simulation is addressed in order to assure that schemes properly converge. A class of parameterized source functions is proposed and shown to offer straightforward control of residual error in the simulation. Guided by the notion that the solution to be approximated affects the approximation error, sources are designed which reduce residual dispersive error to the size of round-off errors. The early part of a room impulse response can be characterized by a series of isolated plane waves. Measured with an array of microphones, plane waves map to a directional response of the array or spatial intensity map. Probabilistic inversion of this response results in estimates of the number and directions of image source arrivals. The model-based inversion is shown to avoid ambiguities associated with peak-finding or inspection of the spatial intensity map. For this problem, determining the number of arrivals in a given frame is critical for properly inferring the state of the sound field. This analysis is effectively compression of the spatial room response, which is useful for analysis or encoding of the spatial sound field. Parametric, model-based formulations of these problems enhance the solution in all cases, and a Bayesian interpretation provides a principled approach to model comparison and parameter estimation. v

a Bayesian Synthesis of Predictions from Different Models for Setting Water Quality Criteria

NASA Astrophysics Data System (ADS)

Arhonditsis, G. B.; Ecological Modelling Laboratory

2011-12-01

Skeptical views of the scientific value of modelling argue that there is no true model of an ecological system, but rather several adequate descriptions of different conceptual basis and structure. In this regard, rather than picking the single "best-fit" model to predict future system responses, we can use Bayesian model averaging to synthesize the forecasts from different models. Hence, by acknowledging that models from different areas of the complexity spectrum have different strengths and weaknesses, the Bayesian model averaging is an appealing approach to improve the predictive capacity and to overcome the ambiguity surrounding the model selection or the risk of basing ecological forecasts on a single model. Our study addresses this question using a complex ecological model, developed by Ramin et al. (2011; Environ Modell Softw 26, 337-353) to guide the water quality criteria setting process in the Hamilton Harbour (Ontario, Canada), along with a simpler plankton model that considers the interplay among phosphate, detritus, and generic phytoplankton and zooplankton state variables. This simple approach is more easily subjected to detailed sensitivity analysis and also has the advantage of fewer unconstrained parameters. Using Markov Chain Monte Carlo simulations, we calculate the relative mean standard error to assess the posterior support of the two models from the existing data. Predictions from the two models are then combined using the respective standard error estimates as weights in a weighted model average. The model averaging approach is used to examine the robustness of predictive statements made from our earlier work regarding the response of Hamilton Harbour to the different nutrient loading reduction strategies. The two eutrophication models are then used in conjunction with the SPAtially Referenced Regressions On Watershed attributes (SPARROW) watershed model. The Bayesian nature of our work is used: (i) to alleviate problems of spatiotemporal resolution mismatch between watershed and receiving waterbody models; and (ii) to overcome the conceptual or scale misalignment between processes of interest and supporting information. The proposed Bayesian approach provides an effective means of empirically estimating the relation between in-stream measurements of nutrient fluxes and the sources/sinks of nutrients within the watershed, while explicitly accounting for the uncertainty associated with the existing knowledge from the system along with the different types of spatial correlation typically underlying the parameter estimation of watershed models. Our modelling exercise offers the first estimates of the export coefficients and the delivery rates from the different subcatchments and thus generates testable hypotheses regarding the nutrient export "hot spots" in the studied watershed. Finally, we conduct modeling experiments that evaluate the potential improvement of the model parameter estimates and the decrease of the predictive uncertainty, if the uncertainty associated with the contemporary nutrient loading estimates is reduced. The lessons learned from this study will contribute towards the development of integrated modelling frameworks.

Bayesian Mediation Analysis

ERIC Educational Resources Information Center

Yuan, Ying; MacKinnon, David P.

2009-01-01

In this article, we propose Bayesian analysis of mediation effects. Compared with conventional frequentist mediation analysis, the Bayesian approach has several advantages. First, it allows researchers to incorporate prior information into the mediation analysis, thus potentially improving the efficiency of estimates. Second, under the Bayesian…

Bayesian Monte Carlo and Maximum Likelihood Approach for ...

EPA Pesticide Factsheets

Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood estimation (BMCML) to calibrate a lake oxygen recovery model. We first derive an analytical solution of the differential equation governing lake-averaged oxygen dynamics as a function of time-variable wind speed. Statistical inferences on model parameters and predictive uncertainty are then drawn by Bayesian conditioning of the analytical solution on observed daily wind speed and oxygen concentration data obtained from an earlier study during two recovery periods on a eutrophic lake in upper state New York. The model is calibrated using oxygen recovery data for one year and statistical inferences were validated using recovery data for another year. Compared with essentially two-step, regression and optimization approach, the BMCML results are more comprehensive and performed relatively better in predicting the observed temporal dissolved oxygen levels (DO) in the lake. BMCML also produced comparable calibration and validation results with those obtained using popular Markov Chain Monte Carlo technique (MCMC) and is computationally simpler and easier to implement than the MCMC. Next, using the calibrated model, we derive an optimal relationship between liquid film-transfer coefficien

A Bayes linear Bayes method for estimation of correlated event rates.

PubMed

Quigley, John; Wilson, Kevin J; Walls, Lesley; Bedford, Tim

2013-12-01

Typically, full Bayesian estimation of correlated event rates can be computationally challenging since estimators are intractable. When estimation of event rates represents one activity within a larger modeling process, there is an incentive to develop more efficient inference than provided by a full Bayesian model. We develop a new subjective inference method for correlated event rates based on a Bayes linear Bayes model under the assumption that events are generated from a homogeneous Poisson process. To reduce the elicitation burden we introduce homogenization factors to the model and, as an alternative to a subjective prior, an empirical method using the method of moments is developed. Inference under the new method is compared against estimates obtained under a full Bayesian model, which takes a multivariate gamma prior, where the predictive and posterior distributions are derived in terms of well-known functions. The mathematical properties of both models are presented. A simulation study shows that the Bayes linear Bayes inference method and the full Bayesian model provide equally reliable estimates. An illustrative example, motivated by a problem of estimating correlated event rates across different users in a simple supply chain, shows how ignoring the correlation leads to biased estimation of event rates. © 2013 Society for Risk Analysis.

Sample Size for Tablet Compression and Capsule Filling Events During Process Validation.

PubMed

Charoo, Naseem Ahmad; Durivage, Mark; Rahman, Ziyaur; Ayad, Mohamad Haitham

2017-12-01

During solid dosage form manufacturing, the uniformity of dosage units (UDU) is ensured by testing samples at 2 stages, that is, blend stage and tablet compression or capsule/powder filling stage. The aim of this work is to propose a sample size selection approach based on quality risk management principles for process performance qualification (PPQ) and continued process verification (CPV) stages by linking UDU to potential formulation and process risk factors. Bayes success run theorem appeared to be the most appropriate approach among various methods considered in this work for computing sample size for PPQ. The sample sizes for high-risk (reliability level of 99%), medium-risk (reliability level of 95%), and low-risk factors (reliability level of 90%) were estimated to be 299, 59, and 29, respectively. Risk-based assignment of reliability levels was supported by the fact that at low defect rate, the confidence to detect out-of-specification units would decrease which must be supplemented with an increase in sample size to enhance the confidence in estimation. Based on level of knowledge acquired during PPQ and the level of knowledge further required to comprehend process, sample size for CPV was calculated using Bayesian statistics to accomplish reduced sampling design for CPV. Copyright © 2017 American Pharmacists Association®. Published by Elsevier Inc. All rights reserved.

Updated Three-Stage Model for the Peopling of the Americas

PubMed Central

Mulligan, Connie J.; Kitchen, Andrew; Miyamoto, Michael M.

2008-01-01

Background We re-assess support for our three stage model for the peopling of the Americas in light of a recent report that identified nine non-Native American mitochondrial genome sequences that should not have been included in our initial analysis. Removal of these sequences results in the elimination of an early (i.e. ∼40,000 years ago) expansion signal we had proposed for the proto-Amerind population. Methodology/Findings Bayesian skyline plot analysis of a new dataset of Native American mitochondrial coding genomes confirms the absence of an early expansion signal for the proto-Amerind population and allows us to reduce the variation around our estimate of the New World founder population size. In addition, genetic variants that define New World founder haplogroups are used to estimate the amount of time required between divergence of proto-Amerinds from the Asian gene pool and expansion into the New World. Conclusions/Significance The period of population isolation required for the generation of New World mitochondrial founder haplogroup-defining genetic variants makes the existence of three stages of colonization a logical conclusion. Thus, our three stage model remains an important and useful working hypothesis for researchers interested in the peopling of the Americas and the processes of colonization. PMID:18797500

Analysis of health trait data from on-farm computer systems in the U.S. II: Comparison of genomic analyses including two-stage and single-step methods

USDA-ARS?s Scientific Manuscript database

The development of genomic selection methodology, with accompanying substantial gains in reliability for low-heritability traits, may dramatically improve the feasibility of genetic improvement of dairy cow health. Many methods for genomic analysis have now been developed, including the “Bayesian Al...

Comparison of variance estimators for meta-analysis of instrumental variable estimates

PubMed Central

Schmidt, AF; Hingorani, AD; Jefferis, BJ; White, J; Groenwold, RHH; Dudbridge, F

2016-01-01

Abstract Background: Mendelian randomization studies perform instrumental variable (IV) analysis using genetic IVs. Results of individual Mendelian randomization studies can be pooled through meta-analysis. We explored how different variance estimators influence the meta-analysed IV estimate. Methods: Two versions of the delta method (IV before or after pooling), four bootstrap estimators, a jack-knife estimator and a heteroscedasticity-consistent (HC) variance estimator were compared using simulation. Two types of meta-analyses were compared, a two-stage meta-analysis pooling results, and a one-stage meta-analysis pooling datasets. Results: Using a two-stage meta-analysis, coverage of the point estimate using bootstrapped estimators deviated from nominal levels at weak instrument settings and/or outcome probabilities ≤ 0.10. The jack-knife estimator was the least biased resampling method, the HC estimator often failed at outcome probabilities ≤ 0.50 and overall the delta method estimators were the least biased. In the presence of between-study heterogeneity, the delta method before meta-analysis performed best. Using a one-stage meta-analysis all methods performed equally well and better than two-stage meta-analysis of greater or equal size. Conclusions: In the presence of between-study heterogeneity, two-stage meta-analyses should preferentially use the delta method before meta-analysis. Weak instrument bias can be reduced by performing a one-stage meta-analysis. PMID:27591262

SEMIPARAMETRIC ADDITIVE RISKS REGRESSION FOR TWO-STAGE DESIGN SURVIVAL STUDIES

PubMed Central

Li, Gang; Wu, Tong Tong

2011-01-01

In this article we study a semiparametric additive risks model (McKeague and Sasieni (1994)) for two-stage design survival data where accurate information is available only on second stage subjects, a subset of the first stage study. We derive two-stage estimators by combining data from both stages. Large sample inferences are developed. As a by-product, we also obtain asymptotic properties of the single stage estimators of McKeague and Sasieni (1994) when the semiparametric additive risks model is misspecified. The proposed two-stage estimators are shown to be asymptotically more efficient than the second stage estimators. They also demonstrate smaller bias and variance for finite samples. The developed methods are illustrated using small intestine cancer data from the SEER (Surveillance, Epidemiology, and End Results) Program. PMID:21931467

Efficient fuzzy Bayesian inference algorithms for incorporating expert knowledge in parameter estimation

NASA Astrophysics Data System (ADS)

Rajabi, Mohammad Mahdi; Ataie-Ashtiani, Behzad

2016-05-01

Bayesian inference has traditionally been conceived as the proper framework for the formal incorporation of expert knowledge in parameter estimation of groundwater models. However, conventional Bayesian inference is incapable of taking into account the imprecision essentially embedded in expert provided information. In order to solve this problem, a number of extensions to conventional Bayesian inference have been introduced in recent years. One of these extensions is 'fuzzy Bayesian inference' which is the result of integrating fuzzy techniques into Bayesian statistics. Fuzzy Bayesian inference has a number of desirable features which makes it an attractive approach for incorporating expert knowledge in the parameter estimation process of groundwater models: (1) it is well adapted to the nature of expert provided information, (2) it allows to distinguishably model both uncertainty and imprecision, and (3) it presents a framework for fusing expert provided information regarding the various inputs of the Bayesian inference algorithm. However an important obstacle in employing fuzzy Bayesian inference in groundwater numerical modeling applications is the computational burden, as the required number of numerical model simulations often becomes extremely exhaustive and often computationally infeasible. In this paper, a novel approach of accelerating the fuzzy Bayesian inference algorithm is proposed which is based on using approximate posterior distributions derived from surrogate modeling, as a screening tool in the computations. The proposed approach is first applied to a synthetic test case of seawater intrusion (SWI) in a coastal aquifer. It is shown that for this synthetic test case, the proposed approach decreases the number of required numerical simulations by an order of magnitude. Then the proposed approach is applied to a real-world test case involving three-dimensional numerical modeling of SWI in Kish Island, located in the Persian Gulf. An expert elicitation methodology is developed and applied to the real-world test case in order to provide a road map for the use of fuzzy Bayesian inference in groundwater modeling applications.

Branch length estimation and divergence dating: estimates of error in Bayesian and maximum likelihood frameworks.

PubMed

Schwartz, Rachel S; Mueller, Rachel L

2010-01-11

Estimates of divergence dates between species improve our understanding of processes ranging from nucleotide substitution to speciation. Such estimates are frequently based on molecular genetic differences between species; therefore, they rely on accurate estimates of the number of such differences (i.e. substitutions per site, measured as branch length on phylogenies). We used simulations to determine the effects of dataset size, branch length heterogeneity, branch depth, and analytical framework on branch length estimation across a range of branch lengths. We then reanalyzed an empirical dataset for plethodontid salamanders to determine how inaccurate branch length estimation can affect estimates of divergence dates. The accuracy of branch length estimation varied with branch length, dataset size (both number of taxa and sites), branch length heterogeneity, branch depth, dataset complexity, and analytical framework. For simple phylogenies analyzed in a Bayesian framework, branches were increasingly underestimated as branch length increased; in a maximum likelihood framework, longer branch lengths were somewhat overestimated. Longer datasets improved estimates in both frameworks; however, when the number of taxa was increased, estimation accuracy for deeper branches was less than for tip branches. Increasing the complexity of the dataset produced more misestimated branches in a Bayesian framework; however, in an ML framework, more branches were estimated more accurately. Using ML branch length estimates to re-estimate plethodontid salamander divergence dates generally resulted in an increase in the estimated age of older nodes and a decrease in the estimated age of younger nodes. Branch lengths are misestimated in both statistical frameworks for simulations of simple datasets. However, for complex datasets, length estimates are quite accurate in ML (even for short datasets), whereas few branches are estimated accurately in a Bayesian framework. Our reanalysis of empirical data demonstrates the magnitude of effects of Bayesian branch length misestimation on divergence date estimates. Because the length of branches for empirical datasets can be estimated most reliably in an ML framework when branches are <1 substitution/site and datasets are > or =1 kb, we suggest that divergence date estimates using datasets, branch lengths, and/or analytical techniques that fall outside of these parameters should be interpreted with caution.

Bayesian Mass Estimates of the Milky Way: Including Measurement Uncertainties with Hierarchical Bayes

NASA Astrophysics Data System (ADS)

Eadie, Gwendolyn M.; Springford, Aaron; Harris, William E.

2017-02-01

We present a hierarchical Bayesian method for estimating the total mass and mass profile of the Milky Way Galaxy. The new hierarchical Bayesian approach further improves the framework presented by Eadie et al. and Eadie and Harris and builds upon the preliminary reports by Eadie et al. The method uses a distribution function f({ E },L) to model the Galaxy and kinematic data from satellite objects, such as globular clusters (GCs), to trace the Galaxy’s gravitational potential. A major advantage of the method is that it not only includes complete and incomplete data simultaneously in the analysis, but also incorporates measurement uncertainties in a coherent and meaningful way. We first test the hierarchical Bayesian framework, which includes measurement uncertainties, using the same data and power-law model assumed in Eadie and Harris and find the results are similar but more strongly constrained. Next, we take advantage of the new statistical framework and incorporate all possible GC data, finding a cumulative mass profile with Bayesian credible regions. This profile implies a mass within 125 kpc of 4.8× {10}11{M}⊙ with a 95% Bayesian credible region of (4.0{--}5.8)× {10}11{M}⊙ . Our results also provide estimates of the true specific energies of all the GCs. By comparing these estimated energies to the measured energies of GCs with complete velocity measurements, we observe that (the few) remote tracers with complete measurements may play a large role in determining a total mass estimate of the Galaxy. Thus, our study stresses the need for more remote tracers with complete velocity measurements.

Basics of Bayesian methods.

PubMed

Ghosh, Sujit K

2010-01-01

Bayesian methods are rapidly becoming popular tools for making statistical inference in various fields of science including biology, engineering, finance, and genetics. One of the key aspects of Bayesian inferential method is its logical foundation that provides a coherent framework to utilize not only empirical but also scientific information available to a researcher. Prior knowledge arising from scientific background, expert judgment, or previously collected data is used to build a prior distribution which is then combined with current data via the likelihood function to characterize the current state of knowledge using the so-called posterior distribution. Bayesian methods allow the use of models of complex physical phenomena that were previously too difficult to estimate (e.g., using asymptotic approximations). Bayesian methods offer a means of more fully understanding issues that are central to many practical problems by allowing researchers to build integrated models based on hierarchical conditional distributions that can be estimated even with limited amounts of data. Furthermore, advances in numerical integration methods, particularly those based on Monte Carlo methods, have made it possible to compute the optimal Bayes estimators. However, there is a reasonably wide gap between the background of the empirically trained scientists and the full weight of Bayesian statistical inference. Hence, one of the goals of this chapter is to bridge the gap by offering elementary to advanced concepts that emphasize linkages between standard approaches and full probability modeling via Bayesian methods.

Cost and economic burden of illness over 15 years in Nepal: A comparative analysis.

PubMed

Swe, Khin Thet; Rahman, Md Mizanur; Rahman, Md Shafiur; Saito, Eiko; Abe, Sarah K; Gilmour, Stuart; Shibuya, Kenji

2018-01-01

With an increasing burden of non-communicable disease in Nepal and limited progress towards universal health coverage, country- and disease-specific estimates of financial hardship related to healthcare costs need to be evaluated to protect the population effectively from healthcare-related financial burden. To estimate the cost and economic burden of illness and to assess the inequality in the financial burden due to catastrophic health expenditure from 1995 to 2010 in Nepal. This study used nationally representative Nepal Living Standards Surveys conducted in 1995 and 2010. A Bayesian two-stage hurdle model was used to estimate average cost of illness and Bayesian logistic regression models were used to estimate the disease-specific incidence of catastrophic health payment and impoverishment. The concentration curve and index were estimated by disease category to examine inequality in healthcare-related financial hardship. Inflation-adjusted mean out-of-pocket (OOP) payments for chronic illness and injury increased by 4.6% and 7.3%, respectively, while the cost of recent acute illness declined by 1.5% between 1995 and 2010. Injury showed the highest incidence of catastrophic expenditure (30.7% in 1995 and 22.4% in 2010) followed by chronic illness (12.0% in 1995 and 9.6% in 2010) and recent acute illness (21.1% in 1995 and 7.8% in 2010). Asthma, diabetes, heart conditions, malaria, jaundice and parasitic illnesses showed increased catastrophic health expenditure over time. Impoverishment due to injury declined most (by 12% change in average annual rate) followed by recent acute illness (9.7%) and chronic illness (9.6%) in 15 years. Inequality analysis indicated that poorer populations with recent acute illness suffered more catastrophic health expenditure in both sample years, while wealthier households with injury and chronic illnesses suffered more catastrophic health expenditure in 2010. To minimize the economic burden of illness, several approaches need to be adopted, including social health insurance complemented with an upgraded community-based health insurance system, subsidy program expansion for diseases with high economic burden and third party liability motor insurance to reduce the economic burden of injury.

Cost and economic burden of illness over 15 years in Nepal: A comparative analysis

PubMed Central

Rahman, Md. Mizanur; Rahman, Md. Shafiur; Saito, Eiko; Abe, Sarah K.; Gilmour, Stuart; Shibuya, Kenji

2018-01-01

Background With an increasing burden of non-communicable disease in Nepal and limited progress towards universal health coverage, country- and disease-specific estimates of financial hardship related to healthcare costs need to be evaluated to protect the population effectively from healthcare-related financial burden. Objectives To estimate the cost and economic burden of illness and to assess the inequality in the financial burden due to catastrophic health expenditure from 1995 to 2010 in Nepal. Methods This study used nationally representative Nepal Living Standards Surveys conducted in 1995 and 2010. A Bayesian two-stage hurdle model was used to estimate average cost of illness and Bayesian logistic regression models were used to estimate the disease-specific incidence of catastrophic health payment and impoverishment. The concentration curve and index were estimated by disease category to examine inequality in healthcare-related financial hardship. Findings Inflation-adjusted mean out-of-pocket (OOP) payments for chronic illness and injury increased by 4.6% and 7.3%, respectively, while the cost of recent acute illness declined by 1.5% between 1995 and 2010. Injury showed the highest incidence of catastrophic expenditure (30.7% in 1995 and 22.4% in 2010) followed by chronic illness (12.0% in 1995 and 9.6% in 2010) and recent acute illness (21.1% in 1995 and 7.8% in 2010). Asthma, diabetes, heart conditions, malaria, jaundice and parasitic illnesses showed increased catastrophic health expenditure over time. Impoverishment due to injury declined most (by 12% change in average annual rate) followed by recent acute illness (9.7%) and chronic illness (9.6%) in 15 years. Inequality analysis indicated that poorer populations with recent acute illness suffered more catastrophic health expenditure in both sample years, while wealthier households with injury and chronic illnesses suffered more catastrophic health expenditure in 2010. Conclusion To minimize the economic burden of illness, several approaches need to be adopted, including social health insurance complemented with an upgraded community-based health insurance system, subsidy program expansion for diseases with high economic burden and third party liability motor insurance to reduce the economic burden of injury. PMID:29617393

Consider the alternative: The effects of causal knowledge on representing and using alternative hypotheses in judgments under uncertainty.

PubMed

Hayes, Brett K; Hawkins, Guy E; Newell, Ben R

2016-05-01

Four experiments examined the locus of impact of causal knowledge on consideration of alternative hypotheses in judgments under uncertainty. Two possible loci were examined; overcoming neglect of the alternative when developing a representation of a judgment problem and improving utilization of statistics associated with the alternative hypothesis. In Experiment 1, participants could search for information about the various components of Bayes's rule in a diagnostic problem. A majority failed to spontaneously search for information about an alternative hypothesis, but this bias was reduced when a specific alternative hypothesis was mentioned before search. No change in search patterns was found when a generic alternative cause was mentioned. Experiments 2a and 2b broadly replicated these patterns when participants rated or made binary judgments about the relevance of each of the Bayesian components. In contrast, Experiment 3 showed that when participants were given the likelihood of the data given a focal hypothesis p(D|H) and an alternative hypothesis p(D|¬H), they gave estimates of p(H|D) that were consistent with Bayesian principles. Additional causal knowledge had relatively little impact on such judgments. These results show that causal knowledge primarily affects neglect of the alternative hypothesis at the initial stage of problem representation. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond.

PubMed

Perdikaris, Paris; Karniadakis, George Em

2016-05-01

We present a computational framework for model inversion based on multi-fidelity information fusion and Bayesian optimization. The proposed methodology targets the accurate construction of response surfaces in parameter space, and the efficient pursuit to identify global optima while keeping the number of expensive function evaluations at a minimum. We train families of correlated surrogates on available data using Gaussian processes and auto-regressive stochastic schemes, and exploit the resulting predictive posterior distributions within a Bayesian optimization setting. This enables a smart adaptive sampling procedure that uses the predictive posterior variance to balance the exploration versus exploitation trade-off, and is a key enabler for practical computations under limited budgets. The effectiveness of the proposed framework is tested on three parameter estimation problems. The first two involve the calibration of outflow boundary conditions of blood flow simulations in arterial bifurcations using multi-fidelity realizations of one- and three-dimensional models, whereas the last one aims to identify the forcing term that generated a particular solution to an elliptic partial differential equation. © 2016 The Author(s).

Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond

PubMed Central

Perdikaris, Paris; Karniadakis, George Em

2016-01-01

We present a computational framework for model inversion based on multi-fidelity information fusion and Bayesian optimization. The proposed methodology targets the accurate construction of response surfaces in parameter space, and the efficient pursuit to identify global optima while keeping the number of expensive function evaluations at a minimum. We train families of correlated surrogates on available data using Gaussian processes and auto-regressive stochastic schemes, and exploit the resulting predictive posterior distributions within a Bayesian optimization setting. This enables a smart adaptive sampling procedure that uses the predictive posterior variance to balance the exploration versus exploitation trade-off, and is a key enabler for practical computations under limited budgets. The effectiveness of the proposed framework is tested on three parameter estimation problems. The first two involve the calibration of outflow boundary conditions of blood flow simulations in arterial bifurcations using multi-fidelity realizations of one- and three-dimensional models, whereas the last one aims to identify the forcing term that generated a particular solution to an elliptic partial differential equation. PMID:27194481

Comparison of Classifiers for Decoding Sensory and Cognitive Information from Prefrontal Neuronal Populations

PubMed Central

Astrand, Elaine; Enel, Pierre; Ibos, Guilhem; Dominey, Peter Ford; Baraduc, Pierre; Ben Hamed, Suliann

2014-01-01

Decoding neuronal information is important in neuroscience, both as a basic means to understand how neuronal activity is related to cerebral function and as a processing stage in driving neuroprosthetic effectors. Here, we compare the readout performance of six commonly used classifiers at decoding two different variables encoded by the spiking activity of the non-human primate frontal eye fields (FEF): the spatial position of a visual cue, and the instructed orientation of the animal's attention. While the first variable is exogenously driven by the environment, the second variable corresponds to the interpretation of the instruction conveyed by the cue; it is endogenously driven and corresponds to the output of internal cognitive operations performed on the visual attributes of the cue. These two variables were decoded using either a regularized optimal linear estimator in its explicit formulation, an optimal linear artificial neural network estimator, a non-linear artificial neural network estimator, a non-linear naïve Bayesian estimator, a non-linear Reservoir recurrent network classifier or a non-linear Support Vector Machine classifier. Our results suggest that endogenous information such as the orientation of attention can be decoded from the FEF with the same accuracy as exogenous visual information. All classifiers did not behave equally in the face of population size and heterogeneity, the available training and testing trials, the subject's behavior and the temporal structure of the variable of interest. In most situations, the regularized optimal linear estimator and the non-linear Support Vector Machine classifiers outperformed the other tested decoders. PMID:24466019

A Bayesian framework for infrasound location

NASA Astrophysics Data System (ADS)

Modrak, Ryan T.; Arrowsmith, Stephen J.; Anderson, Dale N.

2010-04-01

We develop a framework for location of infrasound events using backazimuth and infrasonic arrival times from multiple arrays. Bayesian infrasonic source location (BISL) developed here estimates event location and associated credibility regions. BISL accounts for unknown source-to-array path or phase by formulating infrasonic group velocity as random. Differences between observed and predicted source-to-array traveltimes are partitioned into two additive Gaussian sources, measurement error and model error, the second of which accounts for the unknown influence of wind and temperature on path. By applying the technique to both synthetic tests and ground-truth events, we highlight the complementary nature of back azimuths and arrival times for estimating well-constrained event locations. BISL is an extension to methods developed earlier by Arrowsmith et al. that provided simple bounds on location using a grid-search technique.

Inference on cancer screening exam accuracy using population-level administrative data.

PubMed

Jiang, H; Brown, P E; Walter, S D

2016-01-15

This paper develops a model for cancer screening and cancer incidence data, accommodating the partially unobserved disease status, clustered data structures, general covariate effects, and dependence between exams. The true unobserved cancer and detection status of screening participants are treated as latent variables, and a Markov Chain Monte Carlo algorithm is used to estimate the Bayesian posterior distributions of the diagnostic error rates and disease prevalence. We show how the Bayesian approach can be used to draw inferences about screening exam properties and disease prevalence while allowing for the possibility of conditional dependence between two exams. The techniques are applied to the estimation of the diagnostic accuracy of mammography and clinical breast examination using data from the Ontario Breast Screening Program in Canada. Copyright © 2015 John Wiley & Sons, Ltd.

Sequential recruitment of study participants may inflate genetic heritability estimates.

PubMed

Noce, Damia; Gögele, Martin; Schwienbacher, Christine; Caprioli, Giulia; De Grandi, Alessandro; Foco, Luisa; Platzgummer, Stefan; Pramstaller, Peter P; Pattaro, Cristian

2017-06-01

After the success of genome-wide association studies to uncover complex trait loci, attempts to explain the remaining genetic heritability (h 2 ) are mainly focused on unraveling rare variant associations and gene-gene or gene-environment interactions. Little attention is paid to the possibility that h 2 estimates are inflated as a consequence of the epidemiological study design. We studied the time series of 54 biochemical traits in 4373 individuals from the Cooperative Health Research In South Tyrol (CHRIS) study, a pedigree-based study enrolling ten participants/day over several years, with close relatives preferentially invited within the same day. We observed distributional changes of measured traits over time. We hypothesized that the combination of such changes with the pedigree structure might generate a shared-environment component with consequent h 2 inflation. We performed variance components (VC) h 2 estimation for all traits after accounting for the enrollment period in a linear mixed model (two-stage approach). Accounting for the enrollment period caused a median h 2 reduction of 4%. For 9 traits, the reduction was of >20%. Results were confirmed by a Bayesian Markov chain Monte Carlo analysis with all VCs included at the same time (one-stage approach). The electrolytes were the traits most affected by the enrollment period. The h 2 inflation was independent of the h 2 magnitude, laboratory protocol changes, and length of the enrollment period. The enrollment process may induce shared-environment effects even under very stringent and standardized operating procedures, causing h 2 inflation. Including the day of participation as a random effect is a sensitive way to avoid overestimation.

Nonlinear finite element model updating for damage identification of civil structures using batch Bayesian estimation

NASA Astrophysics Data System (ADS)

Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.; de Callafon, Raymond A.

2017-02-01

This paper presents a framework for structural health monitoring (SHM) and damage identification of civil structures. This framework integrates advanced mechanics-based nonlinear finite element (FE) modeling and analysis techniques with a batch Bayesian estimation approach to estimate time-invariant model parameters used in the FE model of the structure of interest. The framework uses input excitation and dynamic response of the structure and updates a nonlinear FE model of the structure to minimize the discrepancies between predicted and measured response time histories. The updated FE model can then be interrogated to detect, localize, classify, and quantify the state of damage and predict the remaining useful life of the structure. As opposed to recursive estimation methods, in the batch Bayesian estimation approach, the entire time history of the input excitation and output response of the structure are used as a batch of data to estimate the FE model parameters through a number of iterations. In the case of non-informative prior, the batch Bayesian method leads to an extended maximum likelihood (ML) estimation method to estimate jointly time-invariant model parameters and the measurement noise amplitude. The extended ML estimation problem is solved efficiently using a gradient-based interior-point optimization algorithm. Gradient-based optimization algorithms require the FE response sensitivities with respect to the model parameters to be identified. The FE response sensitivities are computed accurately and efficiently using the direct differentiation method (DDM). The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem by computing the exact Fisher Information matrix using the FE response sensitivities with respect to the model parameters. The accuracy of the proposed uncertainty quantification approach is verified using a sampling approach based on the unscented transformation. Two validation studies, based on realistic structural FE models of a bridge pier and a moment resisting steel frame, are performed to validate the performance and accuracy of the presented nonlinear FE model updating approach and demonstrate its application to SHM. These validation studies show the excellent performance of the proposed framework for SHM and damage identification even in the presence of high measurement noise and/or way-out initial estimates of the model parameters. Furthermore, the detrimental effects of the input measurement noise on the performance of the proposed framework are illustrated and quantified through one of the validation studies.

A two-stage method of quantitative flood risk analysis for reservoir real-time operation using ensemble-based hydrologic forecasts

NASA Astrophysics Data System (ADS)

Liu, P.

2013-12-01

Quantitative analysis of the risk for reservoir real-time operation is a hard task owing to the difficulty of accurate description of inflow uncertainties. The ensemble-based hydrologic forecasts directly depict the inflows not only the marginal distributions but also their persistence via scenarios. This motivates us to analyze the reservoir real-time operating risk with ensemble-based hydrologic forecasts as inputs. A method is developed by using the forecast horizon point to divide the future time into two stages, the forecast lead-time and the unpredicted time. The risk within the forecast lead-time is computed based on counting the failure number of forecast scenarios, and the risk in the unpredicted time is estimated using reservoir routing with the design floods and the reservoir water levels of forecast horizon point. As a result, a two-stage risk analysis method is set up to quantify the entire flood risks by defining the ratio of the number of scenarios that excessive the critical value to the total number of scenarios. The China's Three Gorges Reservoir (TGR) is selected as a case study, where the parameter and precipitation uncertainties are implemented to produce ensemble-based hydrologic forecasts. The Bayesian inference, Markov Chain Monte Carlo, is used to account for the parameter uncertainty. Two reservoir operation schemes, the real operated and scenario optimization, are evaluated for the flood risks and hydropower profits analysis. With the 2010 flood, it is found that the improvement of the hydrologic forecast accuracy is unnecessary to decrease the reservoir real-time operation risk, and most risks are from the forecast lead-time. It is therefore valuable to decrease the avarice of ensemble-based hydrologic forecasts with less bias for a reservoir operational purpose.

Development and comparison of Bayesian modularization method in uncertainty assessment of hydrological models

NASA Astrophysics Data System (ADS)

Li, L.; Xu, C.-Y.; Engeland, K.

2012-04-01

With respect to model calibration, parameter estimation and analysis of uncertainty sources, different approaches have been used in hydrological models. Bayesian method is one of the most widely used methods for uncertainty assessment of hydrological models, which incorporates different sources of information into a single analysis through Bayesian theorem. However, none of these applications can well treat the uncertainty in extreme flows of hydrological models' simulations. This study proposes a Bayesian modularization method approach in uncertainty assessment of conceptual hydrological models by considering the extreme flows. It includes a comprehensive comparison and evaluation of uncertainty assessments by a new Bayesian modularization method approach and traditional Bayesian models using the Metropolis Hasting (MH) algorithm with the daily hydrological model WASMOD. Three likelihood functions are used in combination with traditional Bayesian: the AR (1) plus Normal and time period independent model (Model 1), the AR (1) plus Normal and time period dependent model (Model 2) and the AR (1) plus multi-normal model (Model 3). The results reveal that (1) the simulations derived from Bayesian modularization method are more accurate with the highest Nash-Sutcliffe efficiency value, and (2) the Bayesian modularization method performs best in uncertainty estimates of entire flows and in terms of the application and computational efficiency. The study thus introduces a new approach for reducing the extreme flow's effect on the discharge uncertainty assessment of hydrological models via Bayesian. Keywords: extreme flow, uncertainty assessment, Bayesian modularization, hydrological model, WASMOD

Hierarchical Bayesian Model (HBM) - Derived Estimates of Air Quality for 2007: Annual Report

EPA Science Inventory

This report describes EPA's Hierarchical Bayesian model generated (HBM) estimates of ozone (O₃) and fine particulate matter (PM_2.5 particles with aerodynamic diameter < 2.5 microns)concentrations throughout the continental United States during the 2007 calen...

Continuous event monitoring via a Bayesian predictive approach.

PubMed

Di, Jianing; Wang, Daniel; Brashear, H Robert; Dragalin, Vladimir; Krams, Michael

2016-01-01

In clinical trials, continuous monitoring of event incidence rate plays a critical role in making timely decisions affecting trial outcome. For example, continuous monitoring of adverse events protects the safety of trial participants, while continuous monitoring of efficacy events helps identify early signals of efficacy or futility. Because the endpoint of interest is often the event incidence associated with a given length of treatment duration (e.g., incidence proportion of an adverse event with 2 years of dosing), assessing the event proportion before reaching the intended treatment duration becomes challenging, especially when the event onset profile evolves over time with accumulated exposure. In particular, in the earlier part of the study, ignoring censored subjects may result in significant bias in estimating the cumulative event incidence rate. Such a problem is addressed using a predictive approach in the Bayesian framework. In the proposed approach, experts' prior knowledge about both the frequency and timing of the event occurrence is combined with observed data. More specifically, during any interim look, each event-free subject will be counted with a probability that is derived using prior knowledge. The proposed approach is particularly useful in early stage studies for signal detection based on limited information. But it can also be used as a tool for safety monitoring (e.g., data monitoring committee) during later stage trials. Application of the approach is illustrated using a case study where the incidence rate of an adverse event is continuously monitored during an Alzheimer's disease clinical trial. The performance of the proposed approach is also assessed and compared with other Bayesian and frequentist methods via simulation. Copyright © 2015 John Wiley & Sons, Ltd.

Bayesian accrual prediction for interim review of clinical studies: open source R package and smartphone application.

PubMed

Jiang, Yu; Guarino, Peter; Ma, Shuangge; Simon, Steve; Mayo, Matthew S; Raghavan, Rama; Gajewski, Byron J

2016-07-22

Subject recruitment for medical research is challenging. Slow patient accrual leads to increased costs and delays in treatment advances. Researchers need reliable tools to manage and predict the accrual rate. The previously developed Bayesian method integrates researchers' experience on former trials and data from an ongoing study, providing a reliable prediction of accrual rate for clinical studies. In this paper, we present a user-friendly graphical user interface program developed in R. A closed-form solution for the total subjects that can be recruited within a fixed time is derived. We also present a built-in Android system using Java for web browsers and mobile devices. Using the accrual software, we re-evaluated the Veteran Affairs Cooperative Studies Program 558- ROBOTICS study. The application of the software in monitoring and management of recruitment is illustrated for different stages of the trial. This developed accrual software provides a more convenient platform for estimation and prediction of the accrual process.

Temporal Trends and Future Prediction of Breast Cancer Incidence Across Age Groups in Trivandrum, South India.

PubMed

Mathew, Aleyamma; George, Preethi Sara; Arjunan, Asha; Augustine, Paul; Kalavathy, Mc; Padmakumari, G; Mathew, Beela Sarah

2016-01-01

Increasing breast cancer (BC) incidence rates have been reported from India; causal factors for this increased incidence are not understood and diagnosis is mostly in advanced stages. Trivandrum exhibits the highest BC incidence rates in India. This study aimed to estimate trends in incidence by age from 2005- 2014, to predict rates through 2020 and to assess the stage at diagnosis of BC in Trivandrum. BC cases were obtained from the Population Based Cancer Registry, Trivandrum. Distribution of stage at diagnosis and incidence rates of BC [Age-specific (ASpR), crude (CR) and age-standardized (ASR)] are described and employed with a joinpoint regression model to estimate average annual percent changes (AAPC) and a Bayesian model to estimate predictive rates. BC accounts for 31% (2681/8737) of all female cancers in Trivandrum. Thirty-five percent (944/2681) are <50 years of age and only 9% present with stage I disease. Average age increased from 53 to 56.4 years (p=0.0001), CR (per 105 women) increased from 39 (ASR: 35.2) to 55.4 (ASR: 43.4), AAPC for CR was 5.0 (p=0.001) and ASR was 3.1 (p=0.001). Rates increased from 50 years. Predicted ASpR is 174 in 50-59 years, 231 in > 60 years and overall CR is 80 (ASR: 57) for 2019- 20. BC, mostly diagnosed in advanced stages, is rising rapidly in South India with large increases likely in the future; particularly among post-menopausal women. This increase might be due to aging and/or changes in lifestyle factors. Reasons for the increased incidence and late stage diagnosis need to be studied.

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

NASA Astrophysics Data System (ADS)

Sandhu, Rimple; Poirel, Dominique; Pettit, Chris; Khalil, Mohammad; Sarkar, Abhijit

2016-07-01

A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid-structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib-Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sandhu, Rimple; Poirel, Dominique; Pettit, Chris

2016-07-01

A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic systemmore » leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.« less

Exploring the Specifications of Spatial Adjacencies and Weights in Bayesian Spatial Modeling with Intrinsic Conditional Autoregressive Priors in a Small-area Study of Fall Injuries

PubMed Central

Law, Jane

2016-01-01

Intrinsic conditional autoregressive modeling in a Bayeisan hierarchical framework has been increasingly applied in small-area ecological studies. This study explores the specifications of spatial structure in this Bayesian framework in two aspects: adjacency, i.e., the set of neighbor(s) for each area; and (spatial) weight for each pair of neighbors. Our analysis was based on a small-area study of falling injuries among people age 65 and older in Ontario, Canada, that was aimed to estimate risks and identify risk factors of such falls. In the case study, we observed incorrect adjacencies information caused by deficiencies in the digital map itself. Further, when equal weights was replaced by weights based on a variable of expected count, the range of estimated risks increased, the number of areas with probability of estimated risk greater than one at different probability thresholds increased, and model fit improved. More importantly, significance of a risk factor diminished. Further research to thoroughly investigate different methods of variable weights; quantify the influence of specifications of spatial weights; and develop strategies for better defining spatial structure of a map in small-area analysis in Bayesian hierarchical spatial modeling is recommended. PMID:29546147

Internal Medicine residents use heuristics to estimate disease probability

PubMed Central

Phang, Sen Han; Ravani, Pietro; Schaefer, Jeffrey; Wright, Bruce; McLaughlin, Kevin

2015-01-01

Background Training in Bayesian reasoning may have limited impact on accuracy of probability estimates. In this study, our goal was to explore whether residents previously exposed to Bayesian reasoning use heuristics rather than Bayesian reasoning to estimate disease probabilities. We predicted that if residents use heuristics then post-test probability estimates would be increased by non-discriminating clinical features or a high anchor for a target condition. Method We randomized 55 Internal Medicine residents to different versions of four clinical vignettes and asked them to estimate probabilities of target conditions. We manipulated the clinical data for each vignette to be consistent with either 1) using a representative heuristic, by adding non-discriminating prototypical clinical features of the target condition, or 2) using anchoring with adjustment heuristic, by providing a high or low anchor for the target condition. Results When presented with additional non-discriminating data the odds of diagnosing the target condition were increased (odds ratio (OR) 2.83, 95% confidence interval [1.30, 6.15], p = 0.009). Similarly, the odds of diagnosing the target condition were increased when a high anchor preceded the vignette (OR 2.04, [1.09, 3.81], p = 0.025). Conclusions Our findings suggest that despite previous exposure to the use of Bayesian reasoning, residents use heuristics, such as the representative heuristic and anchoring with adjustment, to estimate probabilities. Potential reasons for attribute substitution include the relative cognitive ease of heuristics vs. Bayesian reasoning or perhaps residents in their clinical practice use gist traces rather than precise probability estimates when diagnosing. PMID:27004080

Comparison of age estimation between 15-25 years using a modified form of Demirjian’s ten stage method and two teeth regression formula

NASA Astrophysics Data System (ADS)

Amiroh; Priaminiarti, M.; Syahraini, S. I.

2017-08-01

Age estimation of individuals, both dead and living, is important for victim identification and legal certainty. The Demirjian method uses the third molar for age estimation of individuals above 15 years old. The aim is to compare age estimation between 15-25 years using two Demirjian methods. Development stage of third molars in panoramic radiographs of 50 male and female samples were assessed by two observers using Demirjian’s ten stages and two teeth regression formula. Reliability was calculated using Cohen’s kappa coefficient and the significance of the observations was obtained from Wilcoxon tests. Deviations of age estimation were calculated using various methods. The deviation of age estimation with the two teeth regression formula was ±1.090 years; with ten stages, it was ±1.191 years. The deviation of age estimation using the two teeth regression formula was less than with the ten stages method. The age estimations using the two teeth regression formula or the ten stages method are significantly different until the age of 25, but they can be applied up to the age of 22.

A comparison of Hong Kong and United Kingdom SF-6D health states valuations using a nonparametric Bayesian method.

PubMed

Kharroubi, Samer A; Brazier, John E; McGhee, Sarah

2014-06-01

There is interest in the extent to which valuations of health may differ between different countries and cultures, but few studies have compared preference values of health states obtained in different countries. The present study applies a nonparametric model to estimate and compare two HK and UK standard gamble values for six-dimensional health state short form (derived from short-form 36 health survey) (SF-6D) health states using Bayesian methods. The data set is the HK and UK SF-6D valuation studies in which two samples of 197 and 249 states defined by the SF-6D were valued by representative samples of the HK and UK general populations, respectively, both using the standard gamble technique. We estimated a function applicable across both countries that explicitly accounts for the differences between them, and is estimated using the data from both countries. The results suggest that differences in SF-6D health state valuations between the UK and HK general populations are potentially important. In particular, the valuations of Hong Kong were meaningfully higher than those of the United Kingdom for most of the selected SF-6D health states. The magnitude of these country-specific differences in health state valuation depended, however, in a complex way on the levels of individual dimensions. The new Bayesian nonparametric method is a powerful approach for analyzing data from multiple nationalities or ethnic groups to understand the differences between them and potentially to estimate the underlying utility functions more efficiently. Copyright © 2014 International Society for Pharmacoeconomics and Outcomes Research (ISPOR). Published by Elsevier Inc. All rights reserved.

Bayesian updating in a fault tree model for shipwreck risk assessment.

PubMed

Landquist, H; Rosén, L; Lindhe, A; Norberg, T; Hassellöv, I-M

2017-07-15

Shipwrecks containing oil and other hazardous substances have been deteriorating on the seabeds of the world for many years and are threatening to pollute the marine environment. The status of the wrecks and the potential volume of harmful substances present in the wrecks are affected by a multitude of uncertainties. Each shipwreck poses a unique threat, the nature of which is determined by the structural status of the wreck and possible damage resulting from hazardous activities that could potentially cause a discharge. Decision support is required to ensure the efficiency of the prioritisation process and the allocation of resources required to carry out risk mitigation measures. Whilst risk assessments can provide the requisite decision support, comprehensive methods that take into account key uncertainties related to shipwrecks are limited. The aim of this paper was to develop a method for estimating the probability of discharge of hazardous substances from shipwrecks. The method is based on Bayesian updating of generic information on the hazards posed by different activities in the surroundings of the wreck, with information on site-specific and wreck-specific conditions in a fault tree model. Bayesian updating is performed using Monte Carlo simulations for estimating the probability of a discharge of hazardous substances and formal handling of intrinsic uncertainties. An example application involving two wrecks located off the Swedish coast is presented. Results show the estimated probability of opening, discharge and volume of the discharge for the two wrecks and illustrate the capability of the model to provide decision support. Together with consequence estimations of a discharge of hazardous substances, the suggested model enables comprehensive and probabilistic risk assessments of shipwrecks to be made. Copyright © 2017 Elsevier B.V. All rights reserved.

BAYESIAN ESTIMATION OF THERMONUCLEAR REACTION RATES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iliadis, C.; Anderson, K. S.; Coc, A.

The problem of estimating non-resonant astrophysical S -factors and thermonuclear reaction rates, based on measured nuclear cross sections, is of major interest for nuclear energy generation, neutrino physics, and element synthesis. Many different methods have been applied to this problem in the past, almost all of them based on traditional statistics. Bayesian methods, on the other hand, are now in widespread use in the physical sciences. In astronomy, for example, Bayesian statistics is applied to the observation of extrasolar planets, gravitational waves, and Type Ia supernovae. However, nuclear physics, in particular, has been slow to adopt Bayesian methods. We presentmore » astrophysical S -factors and reaction rates based on Bayesian statistics. We develop a framework that incorporates robust parameter estimation, systematic effects, and non-Gaussian uncertainties in a consistent manner. The method is applied to the reactions d(p, γ ){sup 3}He, {sup 3}He({sup 3}He,2p){sup 4}He, and {sup 3}He( α , γ ){sup 7}Be, important for deuterium burning, solar neutrinos, and Big Bang nucleosynthesis.« less

Hierarchical Bayesian sparse image reconstruction with application to MRFM.

PubMed

Dobigeon, Nicolas; Hero, Alfred O; Tourneret, Jean-Yves

2009-09-01

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument.

Bayesian inference based on stationary Fokker-Planck sampling.

PubMed

Berrones, Arturo

2010-06-01

A novel formalism for bayesian learning in the context of complex inference models is proposed. The method is based on the use of the stationary Fokker-Planck (SFP) approach to sample from the posterior density. Stationary Fokker-Planck sampling generalizes the Gibbs sampler algorithm for arbitrary and unknown conditional densities. By the SFP procedure, approximate analytical expressions for the conditionals and marginals of the posterior can be constructed. At each stage of SFP, the approximate conditionals are used to define a Gibbs sampling process, which is convergent to the full joint posterior. By the analytical marginals efficient learning methods in the context of artificial neural networks are outlined. Offline and incremental bayesian inference and maximum likelihood estimation from the posterior are performed in classification and regression examples. A comparison of SFP with other Monte Carlo strategies in the general problem of sampling from arbitrary densities is also presented. It is shown that SFP is able to jump large low-probability regions without the need of a careful tuning of any step-size parameter. In fact, the SFP method requires only a small set of meaningful parameters that can be selected following clear, problem-independent guidelines. The computation cost of SFP, measured in terms of loss function evaluations, grows linearly with the given model's dimension.

Uncertainty Management for Diagnostics and Prognostics of Batteries using Bayesian Techniques

NASA Technical Reports Server (NTRS)

Saha, Bhaskar; Goebel, kai

2007-01-01

Uncertainty management has always been the key hurdle faced by diagnostics and prognostics algorithms. A Bayesian treatment of this problem provides an elegant and theoretically sound approach to the modern Condition- Based Maintenance (CBM)/Prognostic Health Management (PHM) paradigm. The application of the Bayesian techniques to regression and classification in the form of Relevance Vector Machine (RVM), and to state estimation as in Particle Filters (PF), provides a powerful tool to integrate the diagnosis and prognosis of battery health. The RVM, which is a Bayesian treatment of the Support Vector Machine (SVM), is used for model identification, while the PF framework uses the learnt model, statistical estimates of noise and anticipated operational conditions to provide estimates of remaining useful life (RUL) in the form of a probability density function (PDF). This type of prognostics generates a significant value addition to the management of any operation involving electrical systems.

Clinical judgment to estimate pretest probability in the diagnosis of Cushing's syndrome under a Bayesian perspective.

PubMed

Cipoli, Daniel E; Martinez, Edson Z; Castro, Margaret de; Moreira, Ayrton C

2012-12-01

To estimate the pretest probability of Cushing's syndrome (CS) diagnosis by a Bayesian approach using intuitive clinical judgment. Physicians were requested, in seven endocrinology meetings, to answer three questions: "Based on your personal expertise, after obtaining clinical history and physical examination, without using laboratorial tests, what is your probability of diagnosing Cushing's Syndrome?"; "For how long have you been practicing Endocrinology?"; and "Where do you work?". A Bayesian beta regression, using the WinBugs software was employed. We obtained 294 questionnaires. The mean pretest probability of CS diagnosis was 51.6% (95%CI: 48.7-54.3). The probability was directly related to experience in endocrinology, but not with the place of work. Pretest probability of CS diagnosis was estimated using a Bayesian methodology. Although pretest likelihood can be context-dependent, experience based on years of practice may help the practitioner to diagnosis CS.

Novel non-parametric models to estimate evolutionary rates and divergence times from heterochronous sequence data.

PubMed

Fourment, Mathieu; Holmes, Edward C

2014-07-24

Early methods for estimating divergence times from gene sequence data relied on the assumption of a molecular clock. More sophisticated methods were created to model rate variation and used auto-correlation of rates, local clocks, or the so called "uncorrelated relaxed clock" where substitution rates are assumed to be drawn from a parametric distribution. In the case of Bayesian inference methods the impact of the prior on branching times is not clearly understood, and if the amount of data is limited the posterior could be strongly influenced by the prior. We develop a maximum likelihood method--Physher--that uses local or discrete clocks to estimate evolutionary rates and divergence times from heterochronous sequence data. Using two empirical data sets we show that our discrete clock estimates are similar to those obtained by other methods, and that Physher outperformed some methods in the estimation of the root age of an influenza virus data set. A simulation analysis suggests that Physher can outperform a Bayesian method when the real topology contains two long branches below the root node, even when evolution is strongly clock-like. These results suggest it is advisable to use a variety of methods to estimate evolutionary rates and divergence times from heterochronous sequence data. Physher and the associated data sets used here are available online at http://code.google.com/p/physher/.

Development of a Bayesian Estimator for Audio-Visual Integration: A Neurocomputational Study

PubMed Central

Ursino, Mauro; Crisafulli, Andrea; di Pellegrino, Giuseppe; Magosso, Elisa; Cuppini, Cristiano

2017-01-01

The brain integrates information from different sensory modalities to generate a coherent and accurate percept of external events. Several experimental studies suggest that this integration follows the principle of Bayesian estimate. However, the neural mechanisms responsible for this behavior, and its development in a multisensory environment, are still insufficiently understood. We recently presented a neural network model of audio-visual integration (Neural Computation, 2017) to investigate how a Bayesian estimator can spontaneously develop from the statistics of external stimuli. Model assumes the presence of two unimodal areas (auditory and visual) topologically organized. Neurons in each area receive an input from the external environment, computed as the inner product of the sensory-specific stimulus and the receptive field synapses, and a cross-modal input from neurons of the other modality. Based on sensory experience, synapses were trained via Hebbian potentiation and a decay term. Aim of this work is to improve the previous model, including a more realistic distribution of visual stimuli: visual stimuli have a higher spatial accuracy at the central azimuthal coordinate and a lower accuracy at the periphery. Moreover, their prior probability is higher at the center, and decreases toward the periphery. Simulations show that, after training, the receptive fields of visual and auditory neurons shrink to reproduce the accuracy of the input (both at the center and at the periphery in the visual case), thus realizing the likelihood estimate of unimodal spatial position. Moreover, the preferred positions of visual neurons contract toward the center, thus encoding the prior probability of the visual input. Finally, a prior probability of the co-occurrence of audio-visual stimuli is encoded in the cross-modal synapses. The model is able to simulate the main properties of a Bayesian estimator and to reproduce behavioral data in all conditions examined. In particular, in unisensory conditions the visual estimates exhibit a bias toward the fovea, which increases with the level of noise. In cross modal conditions, the SD of the estimates decreases when using congruent audio-visual stimuli, and a ventriloquism effect becomes evident in case of spatially disparate stimuli. Moreover, the ventriloquism decreases with the eccentricity. PMID:29046631

Prediction and assimilation of surf-zone processes using a Bayesian network: Part II: Inverse models

USGS Publications Warehouse

Plant, Nathaniel G.; Holland, K. Todd

2011-01-01

A Bayesian network model has been developed to simulate a relatively simple problem of wave propagation in the surf zone (detailed in Part I). Here, we demonstrate that this Bayesian model can provide both inverse modeling and data-assimilation solutions for predicting offshore wave heights and depth estimates given limited wave-height and depth information from an onshore location. The inverse method is extended to allow data assimilation using observational inputs that are not compatible with deterministic solutions of the problem. These inputs include sand bar positions (instead of bathymetry) and estimates of the intensity of wave breaking (instead of wave-height observations). Our results indicate that wave breaking information is essential to reduce prediction errors. In many practical situations, this information could be provided from a shore-based observer or from remote-sensing systems. We show that various combinations of the assimilated inputs significantly reduce the uncertainty in the estimates of water depths and wave heights in the model domain. Application of the Bayesian network model to new field data demonstrated significant predictive skill (R2 = 0.7) for the inverse estimate of a month-long time series of offshore wave heights. The Bayesian inverse results include uncertainty estimates that were shown to be most accurate when given uncertainty in the inputs (e.g., depth and tuning parameters). Furthermore, the inverse modeling was extended to directly estimate tuning parameters associated with the underlying wave-process model. The inverse estimates of the model parameters not only showed an offshore wave height dependence consistent with results of previous studies but the uncertainty estimates of the tuning parameters also explain previously reported variations in the model parameters.

Bayesian Monte Carlo and Maximum Likelihood Approach for Uncertainty Estimation and Risk Management: Application to Lake Oxygen Recovery Model

EPA Science Inventory

Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood e...

Hierarchical Bayesian Model (HBM) - Derived Estimates of Air Quality for 2008: Annual Report

EPA Science Inventory

This report describes EPA’s Hierarchical Bayesian model generated (HBM) estimates of ozone (O₃) and fine particulate matter (PM_2.5, particles with aerodynamic diameter < 2.5 microns) concentrations throughout the continental United States during the 2007 ca...

Comparison of the Performance of the TPTest, Tubex, Typhidot and Widal Immunodiagnostic Assays and Blood Cultures in Detecting Patients with Typhoid Fever in Bangladesh, Including Using a Bayesian Latent Class Modeling Approach.

PubMed

Islam, Kamrul; Sayeed, Md Abu; Hossen, Emran; Khanam, Farhana; Charles, Richelle C; Andrews, Jason; Ryan, Edward T; Qadri, Firdausi

2016-04-01

There is an urgent need for an improved diagnostic assay for typhoid fever. In this current study, we compared the recently developed TPTest (Typhoid and Paratyphoid Test) with the Widal test, blood culture, and two commonly used commercially available kits, Tubex and Typhidot. For analysis, we categorized 92 Bangladeshi patients with suspected enteric fever into four groups: S. Typhi bacteremic patients (n = 28); patients with a fourfold change in Widal test from day 0 to convalescent period (n = 7); patients with Widal titer ≥1:320 (n = 13) at either acute or convalescent stage of disease; and patients suspected with enteric fever, but with a negative blood culture and Widal titer (n = 44). We also tested healthy endemic zone controls (n = 20) and Bangladeshi patients with other febrile illnesses (n = 15). Sample size was based on convenience to facilitate preliminary analysis. Of 28 S. Typhi bacteremic patients, 28 (100%), 21 (75%) and 18 (64%) patients were positive by TPTest, Tubex and Typhidot, respectively. In healthy endemic zone controls, the TPTest method was negative in all, whereas Tubex and Typhidot were positive in 3 (15%) and 5 (25%), respectively. We then estimated sensitivity and specificity of all diagnostic tests using Bayesian latent class modeling. The sensitivity of TPTest, Tubex and Typhidot were estimated at 96.0% (95% CI: 87.1%-99.8%), 60.2% (95% CI: 49.3%-71.2%), and 59.6% (95% CI: 50.1%-69.3%), respectively. Specificity was estimated at 96.6% (90.7%-99.2%) for TPTest, 89.9% (79.6%-96.8%) for Tubex, and 80.0% (67.7%-89.7%) for Typhidot. These results suggest that the TPTest is highly sensitive and specific in diagnosing individuals with typhoid fever in a typhoid endemic setting, outperforming currently available and commonly used alternatives.

Nowcasting Cloud Fields for U.S. Air Force Special Operations

DTIC Science & Technology

2017-03-01

application of Bayes’ Rule offers many advantages over Kernel Density Estimation (KDE) and other commonly used statistical post-processing methods...reflectance and probability of cloud. A statistical post-processing technique is applied using Bayesian estimation to train the system from a set of past...nowcasting, low cloud forecasting, cloud reflectance, ISR, Bayesian estimation, statistical post-processing, machine learning 15. NUMBER OF PAGES

Bayesian hierarchical model for large-scale covariance matrix estimation.

PubMed

Zhu, Dongxiao; Hero, Alfred O

2007-12-01

Many bioinformatics problems implicitly depend on estimating large-scale covariance matrix. The traditional approaches tend to give rise to high variance and low accuracy due to "overfitting." We cast the large-scale covariance matrix estimation problem into the Bayesian hierarchical model framework, and introduce dependency between covariance parameters. We demonstrate the advantages of our approaches over the traditional approaches using simulations and OMICS data analysis.

Modelling the initial phase of an epidemic using incidence and infection network data: 2009 H1N1 pandemic in Israel as a case study

PubMed Central

Katriel, G.; Yaari, R.; Huppert, A.; Roll, U.; Stone, L.

2011-01-01

This paper presents new computational and modelling tools for studying the dynamics of an epidemic in its initial stages that use both available incidence time series and data describing the population's infection network structure. The work is motivated by data collected at the beginning of the H1N1 pandemic outbreak in Israel in the summer of 2009. We formulated a new discrete-time stochastic epidemic SIR (susceptible-infected-recovered) model that explicitly takes into account the disease's specific generation-time distribution and the intrinsic demographic stochasticity inherent to the infection process. Moreover, in contrast with many other modelling approaches, the model allows direct analytical derivation of estimates for the effective reproductive number (Re) and of their credible intervals, by maximum likelihood and Bayesian methods. The basic model can be extended to include age–class structure, and a maximum likelihood methodology allows us to estimate the model's next-generation matrix by combining two types of data: (i) the incidence series of each age group, and (ii) infection network data that provide partial information of ‘who-infected-who’. Unlike other approaches for estimating the next-generation matrix, the method developed here does not require making a priori assumptions about the structure of the next-generation matrix. We show, using a simulation study, that even a relatively small amount of information about the infection network greatly improves the accuracy of estimation of the next-generation matrix. The method is applied in practice to estimate the next-generation matrix from the Israeli H1N1 pandemic data. The tools developed here should be of practical importance for future investigations of epidemics during their initial stages. However, they require the availability of data which represent a random sample of the real epidemic process. We discuss the conditions under which reporting rates may or may not influence our estimated quantities and the effects of bias. PMID:21247949

Bayesian Inference on Malignant Breast Cancer in Nigeria: A Diagnosis of MCMC Convergence

PubMed Central

Ogunsakin, Ropo Ebenezer; Siaka, Lougue

2017-01-01

Background: There has been no previous study to classify malignant breast tumor in details based on Markov Chain Monte Carlo (MCMC) convergence in Western, Nigeria. This study therefore aims to profile patients living with benign and malignant breast tumor in two different hospitals among women of Western Nigeria, with a focus on prognostic factors and MCMC convergence. Materials and Methods: A hospital-based record was used to identify prognostic factors for malignant breast cancer among women of Western Nigeria. This paper describes Bayesian inference and demonstrates its usage to estimation of parameters of the logistic regression via Markov Chain Monte Carlo (MCMC) algorithm. The result of the Bayesian approach is compared with the classical statistics. Results: The mean age of the respondents was 42.2 ±16.6 years with 52% of the women aged between 35-49 years. The results of both techniques suggest that age and women with at least high school education have a significantly higher risk of being diagnosed with malignant breast tumors than benign breast tumors. The results also indicate a reduction of standard errors is associated with the coefficients obtained from the Bayesian approach. In addition, simulation result reveal that women with at least high school are 1.3 times more at risk of having malignant breast lesion in western Nigeria compared to benign breast lesion. Conclusion: We concluded that more efforts are required towards creating awareness and advocacy campaigns on how the prevalence of malignant breast lesions can be reduced, especially among women. The application of Bayesian produces precise estimates for modeling malignant breast cancer. PMID:29072396

Using Bayesian neural networks to classify forest scenes

NASA Astrophysics Data System (ADS)

Vehtari, Aki; Heikkonen, Jukka; Lampinen, Jouko; Juujarvi, Jouni

1998-10-01

We present results that compare the performance of Bayesian learning methods for neural networks on the task of classifying forest scenes into trees and background. Classification task is demanding due to the texture richness of the trees, occlusions of the forest scene objects and diverse lighting conditions under operation. This makes it difficult to determine which are optimal image features for the classification. A natural way to proceed is to extract many different types of potentially suitable features, and to evaluate their usefulness in later processing stages. One approach to cope with large number of features is to use Bayesian methods to control the model complexity. Bayesian learning uses a prior on model parameters, combines this with evidence from a training data, and the integrates over the resulting posterior to make predictions. With this method, we can use large networks and many features without fear of overfitting. For this classification task we compare two Bayesian learning methods for multi-layer perceptron (MLP) neural networks: (1) The evidence framework of MacKay uses a Gaussian approximation to the posterior weight distribution and maximizes with respect to hyperparameters. (2) In a Markov Chain Monte Carlo (MCMC) method due to Neal, the posterior distribution of the network parameters is numerically integrated using the MCMC method. As baseline classifiers for comparison we use (3) MLP early stop committee, (4) K-nearest-neighbor and (5) Classification And Regression Tree.

A Comparison of the β-Substitution Method and a Bayesian Method for Analyzing Left-Censored Data.

PubMed

Huynh, Tran; Quick, Harrison; Ramachandran, Gurumurthy; Banerjee, Sudipto; Stenzel, Mark; Sandler, Dale P; Engel, Lawrence S; Kwok, Richard K; Blair, Aaron; Stewart, Patricia A

2016-01-01

Classical statistical methods for analyzing exposure data with values below the detection limits are well described in the occupational hygiene literature, but an evaluation of a Bayesian approach for handling such data is currently lacking. Here, we first describe a Bayesian framework for analyzing censored data. We then present the results of a simulation study conducted to compare the β-substitution method with a Bayesian method for exposure datasets drawn from lognormal distributions and mixed lognormal distributions with varying sample sizes, geometric standard deviations (GSDs), and censoring for single and multiple limits of detection. For each set of factors, estimates for the arithmetic mean (AM), geometric mean, GSD, and the 95th percentile (X0.95) of the exposure distribution were obtained. We evaluated the performance of each method using relative bias, the root mean squared error (rMSE), and coverage (the proportion of the computed 95% uncertainty intervals containing the true value). The Bayesian method using non-informative priors and the β-substitution method were generally comparable in bias and rMSE when estimating the AM and GM. For the GSD and the 95th percentile, the Bayesian method with non-informative priors was more biased and had a higher rMSE than the β-substitution method, but use of more informative priors generally improved the Bayesian method's performance, making both the bias and the rMSE more comparable to the β-substitution method. An advantage of the Bayesian method is that it provided estimates of uncertainty for these parameters of interest and good coverage, whereas the β-substitution method only provided estimates of uncertainty for the AM, and coverage was not as consistent. Selection of one or the other method depends on the needs of the practitioner, the availability of prior information, and the distribution characteristics of the measurement data. We suggest the use of Bayesian methods if the practitioner has the computational resources and prior information, as the method would generally provide accurate estimates and also provides the distributions of all of the parameters, which could be useful for making decisions in some applications. © The Author 2015. Published by Oxford University Press on behalf of the British Occupational Hygiene Society.

A product Pearson-type VII density distribution

NASA Astrophysics Data System (ADS)

Nadarajah, Saralees; Kotz, Samuel

2008-01-01

The Pearson-type VII distributions (containing the Student's t distributions) are becoming increasing prominent and are being considered as competitors to the normal distribution. Motivated by real examples in decision sciences, Bayesian statistics, probability theory and Physics, a new Pearson-type VII distribution is introduced by taking the product of two Pearson-type VII pdfs. Various structural properties of this distribution are derived, including its cdf, moments, mean deviation about the mean, mean deviation about the median, entropy, asymptotic distribution of the extreme order statistics, maximum likelihood estimates and the Fisher information matrix. Finally, an application to a Bayesian testing problem is illustrated.

Detection of mastitis in dairy cattle by use of mixture models for repeated somatic cell scores: a Bayesian approach via Gibbs sampling.

PubMed

Odegård, J; Jensen, J; Madsen, P; Gianola, D; Klemetsdal, G; Heringstad, B

2003-11-01

The distribution of somatic cell scores could be regarded as a mixture of at least two components depending on a cow's udder health status. A heteroscedastic two-component Bayesian normal mixture model with random effects was developed and implemented via Gibbs sampling. The model was evaluated using datasets consisting of simulated somatic cell score records. Somatic cell score was simulated as a mixture representing two alternative udder health statuses ("healthy" or "diseased"). Animals were assigned randomly to the two components according to the probability of group membership (Pm). Random effects (additive genetic and permanent environment), when included, had identical distributions across mixture components. Posterior probabilities of putative mastitis were estimated for all observations, and model adequacy was evaluated using measures of sensitivity, specificity, and posterior probability of misclassification. Fitting different residual variances in the two mixture components caused some bias in estimation of parameters. When the components were difficult to disentangle, so were their residual variances, causing bias in estimation of Pm and of location parameters of the two underlying distributions. When all variance components were identical across mixture components, the mixture model analyses returned parameter estimates essentially without bias and with a high degree of precision. Including random effects in the model increased the probability of correct classification substantially. No sizable differences in probability of correct classification were found between models in which a single cow effect (ignoring relationships) was fitted and models where this effect was split into genetic and permanent environmental components, utilizing relationship information. When genetic and permanent environmental effects were fitted, the between-replicate variance of estimates of posterior means was smaller because the model accounted for random genetic drift.

A Bayesian Approach for Summarizing and Modeling Time-Series Exposure Data with Left Censoring.

PubMed

Houseman, E Andres; Virji, M Abbas

2017-08-01

Direct reading instruments are valuable tools for measuring exposure as they provide real-time measurements for rapid decision making. However, their use is limited to general survey applications in part due to issues related to their performance. Moreover, statistical analysis of real-time data is complicated by autocorrelation among successive measurements, non-stationary time series, and the presence of left-censoring due to limit-of-detection (LOD). A Bayesian framework is proposed that accounts for non-stationary autocorrelation and LOD issues in exposure time-series data in order to model workplace factors that affect exposure and estimate summary statistics for tasks or other covariates of interest. A spline-based approach is used to model non-stationary autocorrelation with relatively few assumptions about autocorrelation structure. Left-censoring is addressed by integrating over the left tail of the distribution. The model is fit using Markov-Chain Monte Carlo within a Bayesian paradigm. The method can flexibly account for hierarchical relationships, random effects and fixed effects of covariates. The method is implemented using the rjags package in R, and is illustrated by applying it to real-time exposure data. Estimates for task means and covariates from the Bayesian model are compared to those from conventional frequentist models including linear regression, mixed-effects, and time-series models with different autocorrelation structures. Simulations studies are also conducted to evaluate method performance. Simulation studies with percent of measurements below the LOD ranging from 0 to 50% showed lowest root mean squared errors for task means and the least biased standard deviations from the Bayesian model compared to the frequentist models across all levels of LOD. In the application, task means from the Bayesian model were similar to means from the frequentist models, while the standard deviations were different. Parameter estimates for covariates were significant in some frequentist models, but in the Bayesian model their credible intervals contained zero; such discrepancies were observed in multiple datasets. Variance components from the Bayesian model reflected substantial autocorrelation, consistent with the frequentist models, except for the auto-regressive moving average model. Plots of means from the Bayesian model showed good fit to the observed data. The proposed Bayesian model provides an approach for modeling non-stationary autocorrelation in a hierarchical modeling framework to estimate task means, standard deviations, quantiles, and parameter estimates for covariates that are less biased and have better performance characteristics than some of the contemporary methods. Published by Oxford University Press on behalf of the British Occupational Hygiene Society 2017.

A Gentle Introduction to Bayesian Analysis: Applications to Developmental Research

PubMed Central

van de Schoot, Rens; Kaplan, David; Denissen, Jaap; Asendorpf, Jens B; Neyer, Franz J; van Aken, Marcel AG

2014-01-01

Bayesian statistical methods are becoming ever more popular in applied and fundamental research. In this study a gentle introduction to Bayesian analysis is provided. It is shown under what circumstances it is attractive to use Bayesian estimation, and how to interpret properly the results. First, the ingredients underlying Bayesian methods are introduced using a simplified example. Thereafter, the advantages and pitfalls of the specification of prior knowledge are discussed. To illustrate Bayesian methods explained in this study, in a second example a series of studies that examine the theoretical framework of dynamic interactionism are considered. In the Discussion the advantages and disadvantages of using Bayesian statistics are reviewed, and guidelines on how to report on Bayesian statistics are provided. PMID:24116396

Methods for fitting a parametric probability distribution to most probable number data.

PubMed

Williams, Michael S; Ebel, Eric D

2012-07-02

Every year hundreds of thousands, if not millions, of samples are collected and analyzed to assess microbial contamination in food and water. The concentration of pathogenic organisms at the end of the production process is low for most commodities, so a highly sensitive screening test is used to determine whether the organism of interest is present in a sample. In some applications, samples that test positive are subjected to quantitation. The most probable number (MPN) technique is a common method to quantify the level of contamination in a sample because it is able to provide estimates at low concentrations. This technique uses a series of dilution count experiments to derive estimates of the concentration of the microorganism of interest. An application for these data is food-safety risk assessment, where the MPN concentration estimates can be fitted to a parametric distribution to summarize the range of potential exposures to the contaminant. Many different methods (e.g., substitution methods, maximum likelihood and regression on order statistics) have been proposed to fit microbial contamination data to a distribution, but the development of these methods rarely considers how the MPN technique influences the choice of distribution function and fitting method. An often overlooked aspect when applying these methods is whether the data represent actual measurements of the average concentration of microorganism per milliliter or the data are real-valued estimates of the average concentration, as is the case with MPN data. In this study, we propose two methods for fitting MPN data to a probability distribution. The first method uses a maximum likelihood estimator that takes average concentration values as the data inputs. The second is a Bayesian latent variable method that uses the counts of the number of positive tubes at each dilution to estimate the parameters of the contamination distribution. The performance of the two fitting methods is compared for two data sets that represent Salmonella and Campylobacter concentrations on chicken carcasses. The results demonstrate a bias in the maximum likelihood estimator that increases with reductions in average concentration. The Bayesian method provided unbiased estimates of the concentration distribution parameters for all data sets. We provide computer code for the Bayesian fitting method. Published by Elsevier B.V.

A comparison of two worlds: How does Bayes hold up to the status quo for the analysis of clinical trials?

PubMed

Pressman, Alice R; Avins, Andrew L; Hubbard, Alan; Satariano, William A

2011-07-01

There is a paucity of literature comparing Bayesian analytic techniques with traditional approaches for analyzing clinical trials using real trial data. We compared Bayesian and frequentist group sequential methods using data from two published clinical trials. We chose two widely accepted frequentist rules, O'Brien-Fleming and Lan-DeMets, and conjugate Bayesian priors. Using the nonparametric bootstrap, we estimated a sampling distribution of stopping times for each method. Because current practice dictates the preservation of an experiment-wise false positive rate (Type I error), we approximated these error rates for our Bayesian and frequentist analyses with the posterior probability of detecting an effect in a simulated null sample. Thus for the data-generated distribution represented by these trials, we were able to compare the relative performance of these techniques. No final outcomes differed from those of the original trials. However, the timing of trial termination differed substantially by method and varied by trial. For one trial, group sequential designs of either type dictated early stopping of the study. In the other, stopping times were dependent upon the choice of spending function and prior distribution. Results indicate that trialists ought to consider Bayesian methods in addition to traditional approaches for analysis of clinical trials. Though findings from this small sample did not demonstrate either method to consistently outperform the other, they did suggest the need to replicate these comparisons using data from varied clinical trials in order to determine the conditions under which the different methods would be most efficient. Copyright © 2011 Elsevier Inc. All rights reserved.

A comparison of two worlds: How does Bayes hold up to the status quo for the analysis of clinical trials?

PubMed Central

Pressman, Alice R.; Avins, Andrew L.; Hubbard, Alan; Satariano, William A.

2014-01-01

Background There is a paucity of literature comparing Bayesian analytic techniques with traditional approaches for analyzing clinical trials using real trial data. Methods We compared Bayesian and frequentist group sequential methods using data from two published clinical trials. We chose two widely accepted frequentist rules, O'Brien–Fleming and Lan–DeMets, and conjugate Bayesian priors. Using the nonparametric bootstrap, we estimated a sampling distribution of stopping times for each method. Because current practice dictates the preservation of an experiment-wise false positive rate (Type I error), we approximated these error rates for our Bayesian and frequentist analyses with the posterior probability of detecting an effect in a simulated null sample. Thus for the data-generated distribution represented by these trials, we were able to compare the relative performance of these techniques. Results No final outcomes differed from those of the original trials. However, the timing of trial termination differed substantially by method and varied by trial. For one trial, group sequential designs of either type dictated early stopping of the study. In the other, stopping times were dependent upon the choice of spending function and prior distribution. Conclusions Results indicate that trialists ought to consider Bayesian methods in addition to traditional approaches for analysis of clinical trials. Though findings from this small sample did not demonstrate either method to consistently outperform the other, they did suggest the need to replicate these comparisons using data from varied clinical trials in order to determine the conditions under which the different methods would be most efficient. PMID:21453792

A Sparse Bayesian Learning Algorithm for White Matter Parameter Estimation from Compressed Multi-shell Diffusion MRI.

PubMed

Pisharady, Pramod Kumar; Sotiropoulos, Stamatios N; Sapiro, Guillermo; Lenglet, Christophe

2017-09-01

We propose a sparse Bayesian learning algorithm for improved estimation of white matter fiber parameters from compressed (under-sampled q-space) multi-shell diffusion MRI data. The multi-shell data is represented in a dictionary form using a non-monoexponential decay model of diffusion, based on continuous gamma distribution of diffusivities. The fiber volume fractions with predefined orientations, which are the unknown parameters, form the dictionary weights. These unknown parameters are estimated with a linear un-mixing framework, using a sparse Bayesian learning algorithm. A localized learning of hyperparameters at each voxel and for each possible fiber orientations improves the parameter estimation. Our experiments using synthetic data from the ISBI 2012 HARDI reconstruction challenge and in-vivo data from the Human Connectome Project demonstrate the improvements.

Estimating micro area behavioural risk factor prevalence from large population-based surveys: a full Bayesian approach.

PubMed

Seliske, L; Norwood, T A; McLaughlin, J R; Wang, S; Palleschi, C; Holowaty, E

2016-06-07

An important public health goal is to decrease the prevalence of key behavioural risk factors, such as tobacco use and obesity. Survey information is often available at the regional level, but heterogeneity within large geographic regions cannot be assessed. Advanced spatial analysis techniques are demonstrated to produce sensible micro area estimates of behavioural risk factors that enable identification of areas with high prevalence. A spatial Bayesian hierarchical model was used to estimate the micro area prevalence of current smoking and excess bodyweight for the Erie-St. Clair region in southwestern Ontario. Estimates were mapped for male and female respondents of five cycles of the Canadian Community Health Survey (CCHS). The micro areas were 2006 Census Dissemination Areas, with an average population of 400-700 people. Two individual-level models were specified: one controlled for survey cycle and age group (model 1), and one controlled for survey cycle, age group and micro area median household income (model 2). Post-stratification was used to derive micro area behavioural risk factor estimates weighted to the population structure. SaTScan analyses were conducted on the granular, postal-code level CCHS data to corroborate findings of elevated prevalence. Current smoking was elevated in two urban areas for both sexes (Sarnia and Windsor), and an additional small community (Chatham) for males only. Areas of excess bodyweight were prevalent in an urban core (Windsor) among males, but not females. Precision of the posterior post-stratified current smoking estimates was improved in model 2, as indicated by narrower credible intervals and a lower coefficient of variation. For excess bodyweight, both models had similar precision. Aggregation of the micro area estimates to CCHS design-based estimates validated the findings. This is among the first studies to apply a full Bayesian model to complex sample survey data to identify micro areas with variation in risk factor prevalence, accounting for spatial correlation and other covariates. Application of micro area analysis techniques helps define areas for public health planning, and may be informative to surveillance and research modeling of relevant chronic disease outcomes.

Conventional, Bayesian, and Modified Prony's methods for characterizing fast and slow waves in equine cancellous bone

PubMed Central

Groopman, Amber M.; Katz, Jonathan I.; Holland, Mark R.; Fujita, Fuminori; Matsukawa, Mami; Mizuno, Katsunori; Wear, Keith A.; Miller, James G.

2015-01-01

Conventional, Bayesian, and the modified least-squares Prony's plus curve-fitting (MLSP + CF) methods were applied to data acquired using 1 MHz center frequency, broadband transducers on a single equine cancellous bone specimen that was systematically shortened from 11.8 mm down to 0.5 mm for a total of 24 sample thicknesses. Due to overlapping fast and slow waves, conventional analysis methods were restricted to data from sample thicknesses ranging from 11.8 mm to 6.0 mm. In contrast, Bayesian and MLSP + CF methods successfully separated fast and slow waves and provided reliable estimates of the ultrasonic properties of fast and slow waves for sample thicknesses ranging from 11.8 mm down to 3.5 mm. Comparisons of the three methods were carried out for phase velocity at the center frequency and the slope of the attenuation coefficient for the fast and slow waves. Good agreement among the three methods was also observed for average signal loss at the center frequency. The Bayesian and MLSP + CF approaches were able to separate the fast and slow waves and provide good estimates of the fast and slow wave properties even when the two wave modes overlapped in both time and frequency domains making conventional analysis methods unreliable. PMID:26328678

Valence-Dependent Belief Updating: Computational Validation

PubMed Central

Kuzmanovic, Bojana; Rigoux, Lionel

2017-01-01

People tend to update beliefs about their future outcomes in a valence-dependent way: they are likely to incorporate good news and to neglect bad news. However, belief formation is a complex process which depends not only on motivational factors such as the desire for favorable conclusions, but also on multiple cognitive variables such as prior beliefs, knowledge about personal vulnerabilities and resources, and the size of the probabilities and estimation errors. Thus, we applied computational modeling in order to test for valence-induced biases in updating while formally controlling for relevant cognitive factors. We compared biased and unbiased Bayesian models of belief updating, and specified alternative models based on reinforcement learning. The experiment consisted of 80 trials with 80 different adverse future life events. In each trial, participants estimated the base rate of one of these events and estimated their own risk of experiencing the event before and after being confronted with the actual base rate. Belief updates corresponded to the difference between the two self-risk estimates. Valence-dependent updating was assessed by comparing trials with good news (better-than-expected base rates) with trials with bad news (worse-than-expected base rates). After receiving bad relative to good news, participants' updates were smaller and deviated more strongly from rational Bayesian predictions, indicating a valence-induced bias. Model comparison revealed that the biased (i.e., optimistic) Bayesian model of belief updating better accounted for data than the unbiased (i.e., rational) Bayesian model, confirming that the valence of the new information influenced the amount of updating. Moreover, alternative computational modeling based on reinforcement learning demonstrated higher learning rates for good than for bad news, as well as a moderating role of personal knowledge. Finally, in this specific experimental context, the approach based on reinforcement learning was superior to the Bayesian approach. The computational validation of valence-dependent belief updating represents a novel support for a genuine optimism bias in human belief formation. Moreover, the precise control of relevant cognitive variables justifies the conclusion that the motivation to adopt the most favorable self-referential conclusions biases human judgments. PMID:28706499

Valence-Dependent Belief Updating: Computational Validation.

PubMed

Kuzmanovic, Bojana; Rigoux, Lionel

2017-01-01

People tend to update beliefs about their future outcomes in a valence-dependent way: they are likely to incorporate good news and to neglect bad news. However, belief formation is a complex process which depends not only on motivational factors such as the desire for favorable conclusions, but also on multiple cognitive variables such as prior beliefs, knowledge about personal vulnerabilities and resources, and the size of the probabilities and estimation errors. Thus, we applied computational modeling in order to test for valence-induced biases in updating while formally controlling for relevant cognitive factors. We compared biased and unbiased Bayesian models of belief updating, and specified alternative models based on reinforcement learning. The experiment consisted of 80 trials with 80 different adverse future life events. In each trial, participants estimated the base rate of one of these events and estimated their own risk of experiencing the event before and after being confronted with the actual base rate. Belief updates corresponded to the difference between the two self-risk estimates. Valence-dependent updating was assessed by comparing trials with good news (better-than-expected base rates) with trials with bad news (worse-than-expected base rates). After receiving bad relative to good news, participants' updates were smaller and deviated more strongly from rational Bayesian predictions, indicating a valence-induced bias. Model comparison revealed that the biased (i.e., optimistic) Bayesian model of belief updating better accounted for data than the unbiased (i.e., rational) Bayesian model, confirming that the valence of the new information influenced the amount of updating. Moreover, alternative computational modeling based on reinforcement learning demonstrated higher learning rates for good than for bad news, as well as a moderating role of personal knowledge. Finally, in this specific experimental context, the approach based on reinforcement learning was superior to the Bayesian approach. The computational validation of valence-dependent belief updating represents a novel support for a genuine optimism bias in human belief formation. Moreover, the precise control of relevant cognitive variables justifies the conclusion that the motivation to adopt the most favorable self-referential conclusions biases human judgments.

Practical Bayesian tomography

NASA Astrophysics Data System (ADS)

Granade, Christopher; Combes, Joshua; Cory, D. G.

2016-03-01

In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of-the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a lack of informative prior distributions, and an inability to track time-dependent processes. Here, we address all three problems. First, we use modern statistical methods, as pioneered by Huszár and Houlsby (2012 Phys. Rev. A 85 052120) and by Ferrie (2014 New J. Phys. 16 093035), to make Bayesian tomography numerically tractable. Our approach allows for practical computation of Bayesian point and region estimators for quantum states and channels. Second, we propose the first priors on quantum states and channels that allow for including useful experimental insight. Finally, we develop a method that allows tracking of time-dependent states and estimates the drift and diffusion processes affecting a state. We provide source code and animated visual examples for our methods.

Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes.

PubMed

Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon

2017-12-01

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. © 2017, The International Biometric Society.

Epistemic-based investigation of the probability of hazard scenarios using Bayesian network for the lifting operation of floating objects

NASA Astrophysics Data System (ADS)

Toroody, Ahmad Bahoo; Abaiee, Mohammad Mahdi; Gholamnia, Reza; Ketabdari, Mohammad Javad

2016-09-01

Owing to the increase in unprecedented accidents with new root causes in almost all operational areas, the importance of risk management has dramatically risen. Risk assessment, one of the most significant aspects of risk management, has a substantial impact on the system-safety level of organizations, industries, and operations. If the causes of all kinds of failure and the interactions between them are considered, effective risk assessment can be highly accurate. A combination of traditional risk assessment approaches and modern scientific probability methods can help in realizing better quantitative risk assessment methods. Most researchers face the problem of minimal field data with respect to the probability and frequency of each failure. Because of this limitation in the availability of epistemic knowledge, it is important to conduct epistemic estimations by applying the Bayesian theory for identifying plausible outcomes. In this paper, we propose an algorithm and demonstrate its application in a case study for a light-weight lifting operation in the Persian Gulf of Iran. First, we identify potential accident scenarios and present them in an event tree format. Next, excluding human error, we use the event tree to roughly estimate the prior probability of other hazard-promoting factors using a minimal amount of field data. We then use the Success Likelihood Index Method (SLIM) to calculate the probability of human error. On the basis of the proposed event tree, we use the Bayesian network of the provided scenarios to compensate for the lack of data. Finally, we determine the resulting probability of each event based on its evidence in the epistemic estimation format by building on two Bayesian network types: the probability of hazard promotion factors and the Bayesian theory. The study results indicate that despite the lack of available information on the operation of floating objects, a satisfactory result can be achieved using epistemic data.

Bayesian models for comparative analysis integrating phylogenetic uncertainty.

PubMed

de Villemereuil, Pierre; Wells, Jessie A; Edwards, Robert D; Blomberg, Simon P

2012-06-28

Uncertainty in comparative analyses can come from at least two sources: a) phylogenetic uncertainty in the tree topology or branch lengths, and b) uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow) and inflated significance in hypothesis testing (e.g. p-values will be too small). Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable. We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses. We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS. Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible general purpose tool for phylogenetic comparative analyses, particularly for modelling in the face of phylogenetic uncertainty and accounting for measurement error or individual variation in explanatory variables. Code for all models is provided in the BUGS model description language.

Bayesian models for comparative analysis integrating phylogenetic uncertainty

PubMed Central

2012-01-01

Background Uncertainty in comparative analyses can come from at least two sources: a) phylogenetic uncertainty in the tree topology or branch lengths, and b) uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow) and inflated significance in hypothesis testing (e.g. p-values will be too small). Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable. Methods We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses. Results We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS. Conclusions Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible general purpose tool for phylogenetic comparative analyses, particularly for modelling in the face of phylogenetic uncertainty and accounting for measurement error or individual variation in explanatory variables. Code for all models is provided in the BUGS model description language. PMID:22741602

Bayesian switching factor analysis for estimating time-varying functional connectivity in fMRI.

PubMed

Taghia, Jalil; Ryali, Srikanth; Chen, Tianwen; Supekar, Kaustubh; Cai, Weidong; Menon, Vinod

2017-07-15

There is growing interest in understanding the dynamical properties of functional interactions between distributed brain regions. However, robust estimation of temporal dynamics from functional magnetic resonance imaging (fMRI) data remains challenging due to limitations in extant multivariate methods for modeling time-varying functional interactions between multiple brain areas. Here, we develop a Bayesian generative model for fMRI time-series within the framework of hidden Markov models (HMMs). The model is a dynamic variant of the static factor analysis model (Ghahramani and Beal, 2000). We refer to this model as Bayesian switching factor analysis (BSFA) as it integrates factor analysis into a generative HMM in a unified Bayesian framework. In BSFA, brain dynamic functional networks are represented by latent states which are learnt from the data. Crucially, BSFA is a generative model which estimates the temporal evolution of brain states and transition probabilities between states as a function of time. An attractive feature of BSFA is the automatic determination of the number of latent states via Bayesian model selection arising from penalization of excessively complex models. Key features of BSFA are validated using extensive simulations on carefully designed synthetic data. We further validate BSFA using fingerprint analysis of multisession resting-state fMRI data from the Human Connectome Project (HCP). Our results show that modeling temporal dependencies in the generative model of BSFA results in improved fingerprinting of individual participants. Finally, we apply BSFA to elucidate the dynamic functional organization of the salience, central-executive, and default mode networks-three core neurocognitive systems with central role in cognitive and affective information processing (Menon, 2011). Across two HCP sessions, we demonstrate a high level of dynamic interactions between these networks and determine that the salience network has the highest temporal flexibility among the three networks. Our proposed methods provide a novel and powerful generative model for investigating dynamic brain connectivity. Copyright © 2017 Elsevier Inc. All rights reserved.

Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data

ERIC Educational Resources Information Center

Lee, Sik-Yum

2006-01-01

A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm is used to produce the joint Bayesian estimates of…

Bayesian Data-Model Fit Assessment for Structural Equation Modeling

ERIC Educational Resources Information Center

Levy, Roy

2011-01-01

Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes…

Estimating the Term Structure With a Semiparametric Bayesian Hierarchical Model: An Application to Corporate Bonds.

PubMed

Cruz-Marcelo, Alejandro; Ensor, Katherine B; Rosner, Gary L

2011-06-01

The term structure of interest rates is used to price defaultable bonds and credit derivatives, as well as to infer the quality of bonds for risk management purposes. We introduce a model that jointly estimates term structures by means of a Bayesian hierarchical model with a prior probability model based on Dirichlet process mixtures. The modeling methodology borrows strength across term structures for purposes of estimation. The main advantage of our framework is its ability to produce reliable estimators at the company level even when there are only a few bonds per company. After describing the proposed model, we discuss an empirical application in which the term structure of 197 individual companies is estimated. The sample of 197 consists of 143 companies with only one or two bonds. In-sample and out-of-sample tests are used to quantify the improvement in accuracy that results from approximating the term structure of corporate bonds with estimators by company rather than by credit rating, the latter being a popular choice in the financial literature. A complete description of a Markov chain Monte Carlo (MCMC) scheme for the proposed model is available as Supplementary Material.

Estimating the Term Structure With a Semiparametric Bayesian Hierarchical Model: An Application to Corporate Bonds1

PubMed Central

Cruz-Marcelo, Alejandro; Ensor, Katherine B.; Rosner, Gary L.

2011-01-01

The term structure of interest rates is used to price defaultable bonds and credit derivatives, as well as to infer the quality of bonds for risk management purposes. We introduce a model that jointly estimates term structures by means of a Bayesian hierarchical model with a prior probability model based on Dirichlet process mixtures. The modeling methodology borrows strength across term structures for purposes of estimation. The main advantage of our framework is its ability to produce reliable estimators at the company level even when there are only a few bonds per company. After describing the proposed model, we discuss an empirical application in which the term structure of 197 individual companies is estimated. The sample of 197 consists of 143 companies with only one or two bonds. In-sample and out-of-sample tests are used to quantify the improvement in accuracy that results from approximating the term structure of corporate bonds with estimators by company rather than by credit rating, the latter being a popular choice in the financial literature. A complete description of a Markov chain Monte Carlo (MCMC) scheme for the proposed model is available as Supplementary Material. PMID:21765566

Bayesian Inference on the Radio-quietness of Gamma-ray Pulsars

NASA Astrophysics Data System (ADS)

Yu, Hoi-Fung; Hui, Chung Yue; Kong, Albert K. H.; Takata, Jumpei

2018-04-01

For the first time we demonstrate using a robust Bayesian approach to analyze the populations of radio-quiet (RQ) and radio-loud (RL) gamma-ray pulsars. We quantify their differences and obtain their distributions of the radio-cone opening half-angle δ and the magnetic inclination angle α by Bayesian inference. In contrast to the conventional frequentist point estimations that might be non-representative when the distribution is highly skewed or multi-modal, which is often the case when data points are scarce, Bayesian statistics displays the complete posterior distribution that the uncertainties can be readily obtained regardless of the skewness and modality. We found that the spin period, the magnetic field strength at the light cylinder, the spin-down power, the gamma-ray-to-X-ray flux ratio, and the spectral curvature significance of the two groups of pulsars exhibit significant differences at the 99% level. Using Bayesian inference, we are able to infer the values and uncertainties of δ and α from the distribution of RQ and RL pulsars. We found that δ is between 10° and 35° and the distribution of α is skewed toward large values.

Retrodiction for Bayesian multiple-hypothesis/multiple-target tracking in densely cluttered environment

NASA Astrophysics Data System (ADS)

Koch, Wolfgang

1996-05-01

Sensor data processing in a dense target/dense clutter environment is inevitably confronted with data association conflicts which correspond with the multiple hypothesis character of many modern approaches (MHT: multiple hypothesis tracking). In this paper we analyze the efficiency of retrodictive techniques that generalize standard fixed interval smoothing to MHT applications. 'Delayed estimation' based on retrodiction provides uniquely interpretable and accurate trajectories from ambiguous MHT output if a certain time delay is tolerated. In a Bayesian framework the theoretical background of retrodiction and its intimate relation to Bayesian MHT is sketched. By a simulated example with two closely-spaced targets, relatively low detection probabilities, and rather high false return densities, we demonstrate the benefits of retrodiction and quantitatively discuss the achievable track accuracies and the time delays involved for typical radar parameters.

A simulation study on Bayesian Ridge regression models for several collinearity levels

NASA Astrophysics Data System (ADS)

Efendi, Achmad; Effrihan

2017-12-01

When analyzing data with multiple regression model if there are collinearities, then one or several predictor variables are usually omitted from the model. However, there sometimes some reasons, for instance medical or economic reasons, the predictors are all important and should be included in the model. Ridge regression model is not uncommon in some researches to use to cope with collinearity. Through this modeling, weights for predictor variables are used for estimating parameters. The next estimation process could follow the concept of likelihood. Furthermore, for the estimation nowadays the Bayesian version could be an alternative. This estimation method does not match likelihood one in terms of popularity due to some difficulties; computation and so forth. Nevertheless, with the growing improvement of computational methodology recently, this caveat should not at the moment become a problem. This paper discusses about simulation process for evaluating the characteristic of Bayesian Ridge regression parameter estimates. There are several simulation settings based on variety of collinearity levels and sample sizes. The results show that Bayesian method gives better performance for relatively small sample sizes, and for other settings the method does perform relatively similar to the likelihood method.

Detection of obstacles on runway using Ego-Motion compensation and tracking of significant features

NASA Technical Reports Server (NTRS)

Kasturi, Rangachar (Principal Investigator); Camps, Octavia (Principal Investigator); Gandhi, Tarak; Devadiga, Sadashiva

1996-01-01

This report describes a method for obstacle detection on a runway for autonomous navigation and landing of an aircraft. Detection is done in the presence of extraneous features such as tiremarks. Suitable features are extracted from the image and warping using approximately known camera and plane parameters is performed in order to compensate ego-motion as far as possible. Residual disparity after warping is estimated using an optical flow algorithm. Features are tracked from frame to frame so as to obtain more reliable estimates of their motion. Corrections are made to motion parameters with the residual disparities using a robust method, and features having large residual disparities are signaled as obstacles. Sensitivity analysis of the procedure is also studied. Nelson's optical flow constraint is proposed to separate moving obstacles from stationary ones. A Bayesian framework is used at every stage so that the confidence in the estimates can be determined.

Bayesian analysis of the kinetics of quantal transmitter secretion at the neuromuscular junction.

PubMed

Saveliev, Anatoly; Khuzakhmetova, Venera; Samigullin, Dmitry; Skorinkin, Andrey; Kovyazina, Irina; Nikolsky, Eugeny; Bukharaeva, Ellya

2015-10-01

The timing of transmitter release from nerve endings is considered nowadays as one of the factors determining the plasticity and efficacy of synaptic transmission. In the neuromuscular junction, the moments of release of individual acetylcholine quanta are related to the synaptic delays of uniquantal endplate currents recorded under conditions of lowered extracellular calcium. Using Bayesian modelling, we performed a statistical analysis of synaptic delays in mouse neuromuscular junction with different patterns of rhythmic nerve stimulation and when the entry of calcium ions into the nerve terminal was modified. We have obtained a statistical model of the release timing which is represented as the summation of two independent statistical distributions. The first of these is the exponentially modified Gaussian distribution. The mixture of normal and exponential components in this distribution can be interpreted as a two-stage mechanism of early and late periods of phasic synchronous secretion. The parameters of this distribution depend on both the stimulation frequency of the motor nerve and the calcium ions' entry conditions. The second distribution was modelled as quasi-uniform, with parameters independent of nerve stimulation frequency and calcium entry. Two different probability density functions for the distribution of synaptic delays suggest at least two independent processes controlling the time course of secretion, one of them potentially involving two stages. The relative contribution of these processes to the total number of mediator quanta released depends differently on the motor nerve stimulation pattern and on calcium ion entry into nerve endings.

Bayesian methods in reliability

NASA Astrophysics Data System (ADS)

Sander, P.; Badoux, R.

1991-11-01

The present proceedings from a course on Bayesian methods in reliability encompasses Bayesian statistical methods and their computational implementation, models for analyzing censored data from nonrepairable systems, the traits of repairable systems and growth models, the use of expert judgment, and a review of the problem of forecasting software reliability. Specific issues addressed include the use of Bayesian methods to estimate the leak rate of a gas pipeline, approximate analyses under great prior uncertainty, reliability estimation techniques, and a nonhomogeneous Poisson process. Also addressed are the calibration sets and seed variables of expert judgment systems for risk assessment, experimental illustrations of the use of expert judgment for reliability testing, and analyses of the predictive quality of software-reliability growth models such as the Weibull order statistics.

Logistic random effects regression models: a comparison of statistical packages for binary and ordinal outcomes.

PubMed

Li, Baoyue; Lingsma, Hester F; Steyerberg, Ewout W; Lesaffre, Emmanuel

2011-05-23

Logistic random effects models are a popular tool to analyze multilevel also called hierarchical data with a binary or ordinal outcome. Here, we aim to compare different statistical software implementations of these models. We used individual patient data from 8509 patients in 231 centers with moderate and severe Traumatic Brain Injury (TBI) enrolled in eight Randomized Controlled Trials (RCTs) and three observational studies. We fitted logistic random effects regression models with the 5-point Glasgow Outcome Scale (GOS) as outcome, both dichotomized as well as ordinal, with center and/or trial as random effects, and as covariates age, motor score, pupil reactivity or trial. We then compared the implementations of frequentist and Bayesian methods to estimate the fixed and random effects. Frequentist approaches included R (lme4), Stata (GLLAMM), SAS (GLIMMIX and NLMIXED), MLwiN ([R]IGLS) and MIXOR, Bayesian approaches included WinBUGS, MLwiN (MCMC), R package MCMCglmm and SAS experimental procedure MCMC.Three data sets (the full data set and two sub-datasets) were analysed using basically two logistic random effects models with either one random effect for the center or two random effects for center and trial. For the ordinal outcome in the full data set also a proportional odds model with a random center effect was fitted. The packages gave similar parameter estimates for both the fixed and random effects and for the binary (and ordinal) models for the main study and when based on a relatively large number of level-1 (patient level) data compared to the number of level-2 (hospital level) data. However, when based on relatively sparse data set, i.e. when the numbers of level-1 and level-2 data units were about the same, the frequentist and Bayesian approaches showed somewhat different results. The software implementations differ considerably in flexibility, computation time, and usability. There are also differences in the availability of additional tools for model evaluation, such as diagnostic plots. The experimental SAS (version 9.2) procedure MCMC appeared to be inefficient. On relatively large data sets, the different software implementations of logistic random effects regression models produced similar results. Thus, for a large data set there seems to be no explicit preference (of course if there is no preference from a philosophical point of view) for either a frequentist or Bayesian approach (if based on vague priors). The choice for a particular implementation may largely depend on the desired flexibility, and the usability of the package. For small data sets the random effects variances are difficult to estimate. In the frequentist approaches the MLE of this variance was often estimated zero with a standard error that is either zero or could not be determined, while for Bayesian methods the estimates could depend on the chosen "non-informative" prior of the variance parameter. The starting value for the variance parameter may be also critical for the convergence of the Markov chain.

Audio-visual speech cue combination.

PubMed

Arnold, Derek H; Tear, Morgan; Schindel, Ryan; Roseboom, Warrick

2010-04-16

Different sources of sensory information can interact, often shaping what we think we have seen or heard. This can enhance the precision of perceptual decisions relative to those made on the basis of a single source of information. From a computational perspective, there are multiple reasons why this might happen, and each predicts a different degree of enhanced precision. Relatively slight improvements can arise when perceptual decisions are made on the basis of multiple independent sensory estimates, as opposed to just one. These improvements can arise as a consequence of probability summation. Greater improvements can occur if two initially independent estimates are summated to form a single integrated code, especially if the summation is weighted in accordance with the variance associated with each independent estimate. This form of combination is often described as a Bayesian maximum likelihood estimate. Still greater improvements are possible if the two sources of information are encoded via a common physiological process. Here we show that the provision of simultaneous audio and visual speech cues can result in substantial sensitivity improvements, relative to single sensory modality based decisions. The magnitude of the improvements is greater than can be predicted on the basis of either a Bayesian maximum likelihood estimate or a probability summation. Our data suggest that primary estimates of speech content are determined by a physiological process that takes input from both visual and auditory processing, resulting in greater sensitivity than would be possible if initially independent audio and visual estimates were formed and then subsequently combined.

Ensemble Bayesian forecasting system Part I: Theory and algorithms

NASA Astrophysics Data System (ADS)

Herr, Henry D.; Krzysztofowicz, Roman

2015-05-01

The ensemble Bayesian forecasting system (EBFS), whose theory was published in 2001, is developed for the purpose of quantifying the total uncertainty about a discrete-time, continuous-state, non-stationary stochastic process such as a time series of stages, discharges, or volumes at a river gauge. The EBFS is built of three components: an input ensemble forecaster (IEF), which simulates the uncertainty associated with random inputs; a deterministic hydrologic model (of any complexity), which simulates physical processes within a river basin; and a hydrologic uncertainty processor (HUP), which simulates the hydrologic uncertainty (an aggregate of all uncertainties except input). It works as a Monte Carlo simulator: an ensemble of time series of inputs (e.g., precipitation amounts) generated by the IEF is transformed deterministically through a hydrologic model into an ensemble of time series of outputs, which is next transformed stochastically by the HUP into an ensemble of time series of predictands (e.g., river stages). Previous research indicated that in order to attain an acceptable sampling error, the ensemble size must be on the order of hundreds (for probabilistic river stage forecasts and probabilistic flood forecasts) or even thousands (for probabilistic stage transition forecasts). The computing time needed to run the hydrologic model this many times renders the straightforward simulations operationally infeasible. This motivates the development of the ensemble Bayesian forecasting system with randomization (EBFSR), which takes full advantage of the analytic meta-Gaussian HUP and generates multiple ensemble members after each run of the hydrologic model; this auxiliary randomization reduces the required size of the meteorological input ensemble and makes it operationally feasible to generate a Bayesian ensemble forecast of large size. Such a forecast quantifies the total uncertainty, is well calibrated against the prior (climatic) distribution of predictand, possesses a Bayesian coherence property, constitutes a random sample of the predictand, and has an acceptable sampling error-which makes it suitable for rational decision making under uncertainty.

The Role of Parametric Assumptions in Adaptive Bayesian Estimation

ERIC Educational Resources Information Center

Alcala-Quintana, Rocio; Garcia-Perez, Miguel A.

2004-01-01

Variants of adaptive Bayesian procedures for estimating the 5% point on a psychometric function were studied by simulation. Bias and standard error were the criteria to evaluate performance. The results indicated a superiority of (a) uniform priors, (b) model likelihood functions that are odd symmetric about threshold and that have parameter…

Bayesian Estimation of Fugitive Methane Point Source Emission Rates from a SingleDownwind High-Frequency Gas Sensor

EPA Science Inventory

Bayesian Estimation of Fugitive Methane Point Source Emission Rates from a Single Downwind High-Frequency Gas Sensor With the tremendous advances in onshore oil and gas exploration and production (E&P) capability comes the realization that new tools are needed to support env...

Bayesian Threshold Estimation

ERIC Educational Resources Information Center

Gustafson, S. C.; Costello, C. S.; Like, E. C.; Pierce, S. J.; Shenoy, K. N.

2009-01-01

Bayesian estimation of a threshold time (hereafter simply threshold) for the receipt of impulse signals is accomplished given the following: 1) data, consisting of the number of impulses received in a time interval from zero to one and the time of the largest time impulse; 2) a model, consisting of a uniform probability density of impulse time…

Mixture class recovery in GMM under varying degrees of class separation: frequentist versus Bayesian estimation.

PubMed

Depaoli, Sarah

2013-06-01

Growth mixture modeling (GMM) represents a technique that is designed to capture change over time for unobserved subgroups (or latent classes) that exhibit qualitatively different patterns of growth. The aim of the current article was to explore the impact of latent class separation (i.e., how similar growth trajectories are across latent classes) on GMM performance. Several estimation conditions were compared: maximum likelihood via the expectation maximization (EM) algorithm and the Bayesian framework implementing diffuse priors, "accurate" informative priors, weakly informative priors, data-driven informative priors, priors reflecting partial-knowledge of parameters, and "inaccurate" (but informative) priors. The main goal was to provide insight about the optimal estimation condition under different degrees of latent class separation for GMM. Results indicated that optimal parameter recovery was obtained though the Bayesian approach using "accurate" informative priors, and partial-knowledge priors showed promise for the recovery of the growth trajectory parameters. Maximum likelihood and the remaining Bayesian estimation conditions yielded poor parameter recovery for the latent class proportions and the growth trajectories. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

Cross-Cultural Invariance of the Mental Toughness Inventory Among Australian, Chinese, and Malaysian Athletes: A Bayesian Estimation Approach.

PubMed

Gucciardi, Daniel F; Zhang, Chun-Qing; Ponnusamy, Vellapandian; Si, Gangyan; Stenling, Andreas

2016-04-01

The aims of this study were to assess the cross-cultural invariance of athletes' self-reports of mental toughness and to introduce and illustrate the application of approximate measurement invariance using Bayesian estimation for sport and exercise psychology scholars. Athletes from Australia (n = 353, Mage = 19.13, SD = 3.27, men = 161), China (n = 254, Mage = 17.82, SD = 2.28, men = 138), and Malaysia (n = 341, Mage = 19.13, SD = 3.27, men = 200) provided a cross-sectional snapshot of their mental toughness. The cross-cultural invariance of the mental toughness inventory in terms of (a) the factor structure (configural invariance), (b) factor loadings (metric invariance), and (c) item intercepts (scalar invariance) was tested using an approximate measurement framework with Bayesian estimation. Results indicated that approximate metric and scalar invariance was established. From a methodological standpoint, this study demonstrated the usefulness and flexibility of Bayesian estimation for single-sample and multigroup analyses of measurement instruments. Substantively, the current findings suggest that the measurement of mental toughness requires cultural adjustments to better capture the contextually salient (emic) aspects of this concept.

K-ε Turbulence Model Parameter Estimates Using an Approximate Self-similar Jet-in-Crossflow Solution

DOE PAGES

DeChant, Lawrence; Ray, Jaideep; Lefantzi, Sophia; ...

2017-06-09

The k-ε turbulence model has been described as perhaps “the most widely used complete turbulence model.” This family of heuristic Reynolds Averaged Navier-Stokes (RANS) turbulence closures is supported by a suite of model parameters that have been estimated by demanding the satisfaction of well-established canonical flows such as homogeneous shear flow, log-law behavior, etc. While this procedure does yield a set of so-called nominal parameters, it is abundantly clear that they do not provide a universally satisfactory turbulence model that is capable of simulating complex flows. Recent work on the Bayesian calibration of the k-ε model using jet-in-crossflow wind tunnelmore » data has yielded parameter estimates that are far more predictive than nominal parameter values. In this paper, we develop a self-similar asymptotic solution for axisymmetric jet-in-crossflow interactions and derive analytical estimates of the parameters that were inferred using Bayesian calibration. The self-similar method utilizes a near field approach to estimate the turbulence model parameters while retaining the classical far-field scaling to model flow field quantities. Our parameter values are seen to be far more predictive than the nominal values, as checked using RANS simulations and experimental measurements. They are also closer to the Bayesian estimates than the nominal parameters. A traditional simplified jet trajectory model is explicitly related to the turbulence model parameters and is shown to yield good agreement with measurement when utilizing the analytical derived turbulence model coefficients. Finally, the close agreement between the turbulence model coefficients obtained via Bayesian calibration and the analytically estimated coefficients derived in this paper is consistent with the contention that the Bayesian calibration approach is firmly rooted in the underlying physical description.« less

Moments and Root-Mean-Square Error of the Bayesian MMSE Estimator of Classification Error in the Gaussian Model.

PubMed

Zollanvari, Amin; Dougherty, Edward R

2014-06-01

The most important aspect of any classifier is its error rate, because this quantifies its predictive capacity. Thus, the accuracy of error estimation is critical. Error estimation is problematic in small-sample classifier design because the error must be estimated using the same data from which the classifier has been designed. Use of prior knowledge, in the form of a prior distribution on an uncertainty class of feature-label distributions to which the true, but unknown, feature-distribution belongs, can facilitate accurate error estimation (in the mean-square sense) in circumstances where accurate completely model-free error estimation is impossible. This paper provides analytic asymptotically exact finite-sample approximations for various performance metrics of the resulting Bayesian Minimum Mean-Square-Error (MMSE) error estimator in the case of linear discriminant analysis (LDA) in the multivariate Gaussian model. These performance metrics include the first, second, and cross moments of the Bayesian MMSE error estimator with the true error of LDA, and therefore, the Root-Mean-Square (RMS) error of the estimator. We lay down the theoretical groundwork for Kolmogorov double-asymptotics in a Bayesian setting, which enables us to derive asymptotic expressions of the desired performance metrics. From these we produce analytic finite-sample approximations and demonstrate their accuracy via numerical examples. Various examples illustrate the behavior of these approximations and their use in determining the necessary sample size to achieve a desired RMS. The Supplementary Material contains derivations for some equations and added figures.

A Three-Stage Colonization Model for the Peopling of the Americas

PubMed Central

Kitchen, Andrew; Miyamoto, Michael M.; Mulligan, Connie J.

2008-01-01

Background We evaluate the process by which the Americas were originally colonized and propose a three-stage model that integrates current genetic, archaeological, geological, and paleoecological data. Specifically, we analyze mitochondrial and nuclear genetic data by using complementary coalescent models of demographic history and incorporating non-genetic data to enhance the anthropological relevance of the analysis. Methodology/Findings Bayesian skyline plots, which provide dynamic representations of population size changes over time, indicate that Amerinds went through two stages of growth ≈40,000 and ≈15,000 years ago separated by a long period of population stability. Isolation-with-migration coalescent analyses, which utilize data from sister populations to estimate a divergence date and founder population sizes, suggest an Amerind population expansion starting ≈15,000 years ago. Conclusions/Significance These results support a model for the peopling of the New World in which Amerind ancestors diverged from the Asian gene pool prior to 40,000 years ago and experienced a gradual population expansion as they moved into Beringia. After a long period of little change in population size in greater Beringia, Amerinds rapidly expanded into the Americas ≈15,000 years ago either through an interior ice-free corridor or along the coast. This rapid colonization of the New World was achieved by a founder group with an effective population size of ≈1,000–5,400 individuals. Our model presents a detailed scenario for the timing and scale of the initial migration to the Americas, substantially refines the estimate of New World founders, and provides a unified theory for testing with future datasets and analytic methods. PMID:18270583

Bayesian networks of age estimation and classification based on dental evidence: A study on the third molar mineralization.

PubMed

Sironi, Emanuele; Pinchi, Vilma; Pradella, Francesco; Focardi, Martina; Bozza, Silvia; Taroni, Franco

2018-04-01

Not only does the Bayesian approach offer a rational and logical environment for evidence evaluation in a forensic framework, but it also allows scientists to coherently deal with uncertainty related to a collection of multiple items of evidence, due to its flexible nature. Such flexibility might come at the expense of elevated computational complexity, which can be handled by using specific probabilistic graphical tools, namely Bayesian networks. In the current work, such probabilistic tools are used for evaluating dental evidence related to the development of third molars. A set of relevant properties characterizing the graphical models are discussed and Bayesian networks are implemented to deal with the inferential process laying beyond the estimation procedure, as well as to provide age estimates. Such properties include operationality, flexibility, coherence, transparence and sensitivity. A data sample composed of Italian subjects was employed for the analysis; results were in agreement with previous studies in terms of point estimate and age classification. The influence of the prior probability elicitation in terms of Bayesian estimate and classifies was also analyzed. Findings also supported the opportunity to take into consideration multiple teeth in the evaluative procedure, since it can be shown this results in an increased robustness towards the prior probability elicitation process, as well as in more favorable outcomes from a forensic perspective. Copyright © 2018 Elsevier Ltd and Faculty of Forensic and Legal Medicine. All rights reserved.

An efficient Bayesian data-worth analysis using a multilevel Monte Carlo method

NASA Astrophysics Data System (ADS)

Lu, Dan; Ricciuto, Daniel; Evans, Katherine

2018-03-01

Improving the understanding of subsurface systems and thus reducing prediction uncertainty requires collection of data. As the collection of subsurface data is costly, it is important that the data collection scheme is cost-effective. Design of a cost-effective data collection scheme, i.e., data-worth analysis, requires quantifying model parameter, prediction, and both current and potential data uncertainties. Assessment of these uncertainties in large-scale stochastic subsurface hydrological model simulations using standard Monte Carlo (MC) sampling or surrogate modeling is extremely computationally intensive, sometimes even infeasible. In this work, we propose an efficient Bayesian data-worth analysis using a multilevel Monte Carlo (MLMC) method. Compared to the standard MC that requires a significantly large number of high-fidelity model executions to achieve a prescribed accuracy in estimating expectations, the MLMC can substantially reduce computational costs using multifidelity approximations. Since the Bayesian data-worth analysis involves a great deal of expectation estimation, the cost saving of the MLMC in the assessment can be outstanding. While the proposed MLMC-based data-worth analysis is broadly applicable, we use it for a highly heterogeneous two-phase subsurface flow simulation to select an optimal candidate data set that gives the largest uncertainty reduction in predicting mass flow rates at four production wells. The choices made by the MLMC estimation are validated by the actual measurements of the potential data, and consistent with the standard MC estimation. But compared to the standard MC, the MLMC greatly reduces the computational costs.

Efficient, adaptive estimation of two-dimensional firing rate surfaces via Gaussian process methods.

PubMed

Rad, Kamiar Rahnama; Paninski, Liam

2010-01-01

Estimating two-dimensional firing rate maps is a common problem, arising in a number of contexts: the estimation of place fields in hippocampus, the analysis of temporally nonstationary tuning curves in sensory and motor areas, the estimation of firing rates following spike-triggered covariance analyses, etc. Here we introduce methods based on Gaussian process nonparametric Bayesian techniques for estimating these two-dimensional rate maps. These techniques offer a number of advantages: the estimates may be computed efficiently, come equipped with natural errorbars, adapt their smoothness automatically to the local density and informativeness of the observed data, and permit direct fitting of the model hyperparameters (e.g., the prior smoothness of the rate map) via maximum marginal likelihood. We illustrate the method's flexibility and performance on a variety of simulated and real data.

Number of pins in two-stage stratified sampling for estimating herbage yield

Treesearch

William G. O' Regan; C. Eugene Conrad

1975-01-01

In a two-stage stratified procedure for sampling herbage yield, plots are stratified by a pin frame in stage one, and clipped. In stage two, clippings from selected plots are sorted, dried, and weighed. Sample size and distribution of plots between the two stages are determined by equations. A way to compute the effect of number of pins on the variance of estimated...

Integrating health economics modeling in the product development cycle of medical devices: a Bayesian approach.

PubMed

Vallejo-Torres, Laura; Steuten, Lotte M G; Buxton, Martin J; Girling, Alan J; Lilford, Richard J; Young, Terry

2008-01-01

Medical device companies are under growing pressure to provide health-economic evaluations of their products. Cost-effectiveness analyses are commonly undertaken as a one-off exercise at the late stage of development of new technologies; however, the benefits of an iterative use of economic evaluation during the development process of new products have been acknowledged in the literature. Furthermore, the use of Bayesian methods within health technology assessment has been shown to be of particular value in the dynamic framework of technology appraisal when new information becomes available in the life cycle of technologies. In this study, we set out a methodology to adapt these methods for their application to directly support investment decisions in a commercial setting from early stages of the development of new medical devices. Starting with relatively simple analysis from the very early development phase and proceeding to greater depth of analysis at later stages, a Bayesian approach facilitates the incorporation of all available evidence and would help companies to make better informed choices at each decision point.

A Bayesian procedure for evaluating the frequency of calibration factor updates in highway safety manual (HSM) applications.

PubMed

Saha, Dibakar; Alluri, Priyanka; Gan, Albert

2017-01-01

The Highway Safety Manual (HSM) presents statistical models to quantitatively estimate an agency's safety performance. The models were developed using data from only a few U.S. states. To account for the effects of the local attributes and temporal factors on crash occurrence, agencies are required to calibrate the HSM-default models for crash predictions. The manual suggests updating calibration factors every two to three years, or preferably on an annual basis. Given that the calibration process involves substantial time, effort, and resources, a comprehensive analysis of the required calibration factor update frequency is valuable to the agencies. Accordingly, the objective of this study is to evaluate the HSM's recommendation and determine the required frequency of calibration factor updates. A robust Bayesian estimation procedure is used to assess the variation between calibration factors computed annually, biennially, and triennially using data collected from over 2400 miles of segments and over 700 intersections on urban and suburban facilities in Florida. Bayesian model yields a posterior distribution of the model parameters that give credible information to infer whether the difference between calibration factors computed at specified intervals is credibly different from the null value which represents unaltered calibration factors between the comparison years or in other words, zero difference. The concept of the null value is extended to include the range of values that are practically equivalent to zero. Bayesian inference shows that calibration factors based on total crash frequency are required to be updated every two years in cases where the variations between calibration factors are not greater than 0.01. When the variations are between 0.01 and 0.05, calibration factors based on total crash frequency could be updated every three years. Copyright © 2016 Elsevier Ltd. All rights reserved.

An objective Bayesian analysis of a crossover design via model selection and model averaging.

PubMed

Li, Dandan; Sivaganesan, Siva

2016-11-10

Inference about the treatment effect in a crossover design has received much attention over time owing to the uncertainty in the existence of the carryover effect and its impact on the estimation of the treatment effect. Adding to this uncertainty is that the existence of the carryover effect and its size may depend on the presence of the treatment effect and its size. We consider estimation and testing hypothesis about the treatment effect in a two-period crossover design, assuming normally distributed response variable, and use an objective Bayesian approach to test the hypothesis about the treatment effect and to estimate its size when it exists while accounting for the uncertainty about the presence of the carryover effect as well as the treatment and period effects. We evaluate and compare the performance of the proposed approach with a standard frequentist approach using simulated data, and real data. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

A Bayesian model for estimating population means using a link-tracing sampling design.

PubMed

St Clair, Katherine; O'Connell, Daniel

2012-03-01

Link-tracing sampling designs can be used to study human populations that contain "hidden" groups who tend to be linked together by a common social trait. These links can be used to increase the sampling intensity of a hidden domain by tracing links from individuals selected in an initial wave of sampling to additional domain members. Chow and Thompson (2003, Survey Methodology 29, 197-205) derived a Bayesian model to estimate the size or proportion of individuals in the hidden population for certain link-tracing designs. We propose an addition to their model that will allow for the modeling of a quantitative response. We assess properties of our model using a constructed population and a real population of at-risk individuals, both of which contain two domains of hidden and nonhidden individuals. Our results show that our model can produce good point and interval estimates of the population mean and domain means when our population assumptions are satisfied. © 2011, The International Biometric Society.

Evaluating the Impact of Genomic Data and Priors on Bayesian Estimates of the Angiosperm Evolutionary Timescale.

PubMed

Foster, Charles S P; Sauquet, Hervê; van der Merwe, Marlien; McPherson, Hannah; Rossetto, Maurizio; Ho, Simon Y W

2017-05-01

The evolutionary timescale of angiosperms has long been a key question in biology. Molecular estimates of this timescale have shown considerable variation, being influenced by differences in taxon sampling, gene sampling, fossil calibrations, evolutionary models, and choices of priors. Here, we analyze a data set comprising 76 protein-coding genes from the chloroplast genomes of 195 taxa spanning 86 families, including novel genome sequences for 11 taxa, to evaluate the impact of models, priors, and gene sampling on Bayesian estimates of the angiosperm evolutionary timescale. Using a Bayesian relaxed molecular-clock method, with a core set of 35 minimum and two maximum fossil constraints, we estimated that crown angiosperms arose 221 (251-192) Ma during the Triassic. Based on a range of additional sensitivity and subsampling analyses, we found that our date estimates were generally robust to large changes in the parameters of the birth-death tree prior and of the model of rate variation across branches. We found an exception to this when we implemented fossil calibrations in the form of highly informative gamma priors rather than as uniform priors on node ages. Under all other calibration schemes, including trials of seven maximum age constraints, we consistently found that the earliest divergences of angiosperm clades substantially predate the oldest fossils that can be assigned unequivocally to their crown group. Overall, our results and experiments with genome-scale data suggest that reliable estimates of the angiosperm crown age will require increased taxon sampling, significant methodological changes, and new information from the fossil record. [Angiospermae, chloroplast, genome, molecular dating, Triassic.]. © The Author(s) 2016. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Robust Bayesian hypocentre and uncertainty region estimation: the effect of heavy-tailed distributions and prior information in cases with poor, inconsistent and insufficient arrival times

NASA Astrophysics Data System (ADS)

Martinsson, J.

2013-03-01

We propose methods for robust Bayesian inference of the hypocentre in presence of poor, inconsistent and insufficient phase arrival times. The objectives are to increase the robustness, the accuracy and the precision by introducing heavy-tailed distributions and an informative prior distribution of the seismicity. The effects of the proposed distributions are studied under real measurement conditions in two underground mine networks and validated using 53 blasts with known hypocentres. To increase the robustness against poor, inconsistent or insufficient arrivals, a Gaussian Mixture Model is used as a hypocentre prior distribution to describe the seismically active areas, where the parameters are estimated based on previously located events in the region. The prior is truncated to constrain the solution to valid geometries, for example below the ground surface, excluding known cavities, voids and fractured zones. To reduce the sensitivity to outliers, different heavy-tailed distributions are evaluated to model the likelihood distribution of the arrivals given the hypocentre and the origin time. Among these distributions, the multivariate t-distribution is shown to produce the overall best performance, where the tail-mass adapts to the observed data. Hypocentre and uncertainty region estimates are based on simulations from the posterior distribution using Markov Chain Monte Carlo techniques. Velocity graphs (equivalent to traveltime graphs) are estimated using blasts from known locations, and applied to reduce the main uncertainties and thereby the final estimation error. To focus on the behaviour and the performance of the proposed distributions, a basic single-event Bayesian procedure is considered in this study for clarity. Estimation results are shown with different distributions, with and without prior distribution of seismicity, with wrong prior distribution, with and without error compensation, with and without error description, with insufficient arrival times and in presence of significant outliers. A particular focus is on visual results and comparisons to give a better understanding of the Bayesian advantage and to show the effects of heavy-tailed distributions and informative prior information on real data.

The estimation of lower refractivity uncertainty from radar sea clutter using the Bayesian—MCMC method

NASA Astrophysics Data System (ADS)

Sheng, Zheng

2013-02-01

The estimation of lower atmospheric refractivity from radar sea clutter (RFC) is a complicated nonlinear optimization problem. This paper deals with the RFC problem in a Bayesian framework. It uses the unbiased Markov Chain Monte Carlo (MCMC) sampling technique, which can provide accurate posterior probability distributions of the estimated refractivity parameters by using an electromagnetic split-step fast Fourier transform terrain parabolic equation propagation model within a Bayesian inversion framework. In contrast to the global optimization algorithm, the Bayesian—MCMC can obtain not only the approximate solutions, but also the probability distributions of the solutions, that is, uncertainty analyses of solutions. The Bayesian—MCMC algorithm is implemented on the simulation radar sea-clutter data and the real radar sea-clutter data. Reference data are assumed to be simulation data and refractivity profiles are obtained using a helicopter. The inversion algorithm is assessed (i) by comparing the estimated refractivity profiles from the assumed simulation and the helicopter sounding data; (ii) the one-dimensional (1D) and two-dimensional (2D) posterior probability distribution of solutions.

Bayesian modelling to estimate the test characteristics of coprology, coproantigen ELISA and a novel real-time PCR for the diagnosis of taeniasis.

PubMed

Praet, Nicolas; Verweij, Jaco J; Mwape, Kabemba E; Phiri, Isaac K; Muma, John B; Zulu, Gideon; van Lieshout, Lisette; Rodriguez-Hidalgo, Richar; Benitez-Ortiz, Washington; Dorny, Pierre; Gabriël, Sarah

2013-05-01

To estimate and compare the performances of coprology, copro-Ag ELISA and real-time polymerase chain reaction assay (copro-PCR) for detection of Taenia solium tapeworm carriers. The three diagnostic tests were applied on 817 stool samples collected in two Zambian communities where taeniasis is endemic. A Bayesian approach was used to allow estimation of the test characteristics. Two (0.2%; 95% Confidence Interval (CI): 0-0.8), 67 (8.2%; 95% CI: 6.4-10.3) and 10 (1.2%; 95% CI: 0.5-2.2) samples were positive using coprology, copro-Ag ELISA and copro-PCR, respectively. Specificities of 99.9%, 92.0% and 99.0% were determined for coprology, copro-Ag ELISA and copro-PCR, respectively. Sensitivities of 52.5%, 84.5% and 82.7% were determined for coprology, copro-Ag ELISA and copro-PCR, respectively. We urge for additional studies exploring possible cross-reactions of the copro-Ag ELISA and for the use of more sensitive tests, such as copro-PCR, for the detection of tapeworm carriers, which is a key factor in controlling the parasite in endemic areas. © 2013 Blackwell Publishing Ltd.

A multi-source precipitation approach to fill gaps over a radar precipitation field

NASA Astrophysics Data System (ADS)

Tesfagiorgis, K. B.; Mahani, S. E.; Khanbilvardi, R.

2012-12-01

Satellite Precipitation Estimates (SPEs) may be the only available source of information for operational hydrologic and flash flood prediction due to spatial limitations of radar and gauge products. The present work develops an approach to seamlessly blend satellite, radar, climatological and gauge precipitation products to fill gaps over ground-based radar precipitation fields. To mix different precipitation products, the bias of any of the products relative to each other should be removed. For bias correction, the study used an ensemble-based method which aims to estimate spatially varying multiplicative biases in SPEs using a radar rainfall product. Bias factors were calculated for a randomly selected sample of rainy pixels in the study area. Spatial fields of estimated bias were generated taking into account spatial variation and random errors in the sampled values. A weighted Successive Correction Method (SCM) is proposed to make the merging between error corrected satellite and radar rainfall estimates. In addition to SCM, we use a Bayesian spatial method for merging the gap free radar with rain gauges, climatological rainfall sources and SPEs. We demonstrate the method using SPE Hydro-Estimator (HE), radar- based Stage-II, a climatological product PRISM and rain gauge dataset for several rain events from 2006 to 2008 over three different geographical locations of the United States. Results show that: the SCM method in combination with the Bayesian spatial model produced a precipitation product in good agreement with independent measurements. The study implies that using the available radar pixels surrounding the gap area, rain gauge, PRISM and satellite products, a radar like product is achievable over radar gap areas that benefits the scientific community.

Approaches in highly parameterized inversion: bgaPEST, a Bayesian geostatistical approach implementation with PEST: documentation and instructions

USGS Publications Warehouse

Fienen, Michael N.; D'Oria, Marco; Doherty, John E.; Hunt, Randall J.

2013-01-01

The application bgaPEST is a highly parameterized inversion software package implementing the Bayesian Geostatistical Approach in a framework compatible with the parameter estimation suite PEST. Highly parameterized inversion refers to cases in which parameters are distributed in space or time and are correlated with one another. The Bayesian aspect of bgaPEST is related to Bayesian probability theory in which prior information about parameters is formally revised on the basis of the calibration dataset used for the inversion. Conceptually, this approach formalizes the conditionality of estimated parameters on the specific data and model available. The geostatistical component of the method refers to the way in which prior information about the parameters is used. A geostatistical autocorrelation function is used to enforce structure on the parameters to avoid overfitting and unrealistic results. Bayesian Geostatistical Approach is designed to provide the smoothest solution that is consistent with the data. Optionally, users can specify a level of fit or estimate a balance between fit and model complexity informed by the data. Groundwater and surface-water applications are used as examples in this text, but the possible uses of bgaPEST extend to any distributed parameter applications.

Bayesian logistic regression approaches to predict incorrect DRG assignment.

PubMed

Suleiman, Mani; Demirhan, Haydar; Boyd, Leanne; Girosi, Federico; Aksakalli, Vural

2018-05-07

Episodes of care involving similar diagnoses and treatments and requiring similar levels of resource utilisation are grouped to the same Diagnosis-Related Group (DRG). In jurisdictions which implement DRG based payment systems, DRGs are a major determinant of funding for inpatient care. Hence, service providers often dedicate auditing staff to the task of checking that episodes have been coded to the correct DRG. The use of statistical models to estimate an episode's probability of DRG error can significantly improve the efficiency of clinical coding audits. This study implements Bayesian logistic regression models with weakly informative prior distributions to estimate the likelihood that episodes require a DRG revision, comparing these models with each other and to classical maximum likelihood estimates. All Bayesian approaches had more stable model parameters than maximum likelihood. The best performing Bayesian model improved overall classification per- formance by 6% compared to maximum likelihood, with a 34% gain compared to random classification, respectively. We found that the original DRG, coder and the day of coding all have a significant effect on the likelihood of DRG error. Use of Bayesian approaches has improved model parameter stability and classification accuracy. This method has already lead to improved audit efficiency in an operational capacity.

Bayesian Item Selection in Constrained Adaptive Testing Using Shadow Tests

ERIC Educational Resources Information Center

Veldkamp, Bernard P.

2010-01-01

Application of Bayesian item selection criteria in computerized adaptive testing might result in improvement of bias and MSE of the ability estimates. The question remains how to apply Bayesian item selection criteria in the context of constrained adaptive testing, where large numbers of specifications have to be taken into account in the item…

Bayesian Analysis of Longitudinal Data Using Growth Curve Models

ERIC Educational Resources Information Center

Zhang, Zhiyong; Hamagami, Fumiaki; Wang, Lijuan Lijuan; Nesselroade, John R.; Grimm, Kevin J.

2007-01-01

Bayesian methods for analyzing longitudinal data in social and behavioral research are recommended for their ability to incorporate prior information in estimating simple and complex models. We first summarize the basics of Bayesian methods before presenting an empirical example in which we fit a latent basis growth curve model to achievement data…

Bayesian Asymmetric Regression as a Means to Estimate and Evaluate Oral Reading Fluency Slopes

ERIC Educational Resources Information Center

Solomon, Benjamin G.; Forsberg, Ole J.

2017-01-01

Bayesian techniques have become increasingly present in the social sciences, fueled by advances in computer speed and the development of user-friendly software. In this paper, we forward the use of Bayesian Asymmetric Regression (BAR) to monitor intervention responsiveness when using Curriculum-Based Measurement (CBM) to assess oral reading…

Bayesian Approaches to Imputation, Hypothesis Testing, and Parameter Estimation

ERIC Educational Resources Information Center

Ross, Steven J.; Mackey, Beth

2015-01-01

This chapter introduces three applications of Bayesian inference to common and novel issues in second language research. After a review of the critiques of conventional hypothesis testing, our focus centers on ways Bayesian inference can be used for dealing with missing data, for testing theory-driven substantive hypotheses without a default null…

Influence of gene flow on divergence dating - implications for the speciation history of Takydromus grass lizards.

PubMed

Tseng, Shu-Ping; Li, Shou-Hsien; Hsieh, Chia-Hung; Wang, Hurng-Yi; Lin, Si-Min

2014-10-01

Dating the time of divergence and understanding speciation processes are central to the study of the evolutionary history of organisms but are notoriously difficult. The difficulty is largely rooted in variations in the ancestral population size or in the genealogy variation across loci. To depict the speciation processes and divergence histories of three monophyletic Takydromus species endemic to Taiwan, we sequenced 20 nuclear loci and combined with one mitochondrial locus published in GenBank. They were analysed by a multispecies coalescent approach within a Bayesian framework. Divergence dating based on the gene tree approach showed high variation among loci, and the divergence was estimated at an earlier date than when derived by the species-tree approach. To test whether variations in the ancestral population size accounted for the majority of this variation, we conducted computer inferences using isolation-with-migration (IM) and approximate Bayesian computation (ABC) frameworks. The results revealed that gene flow during the early stage of speciation was strongly favoured over the isolation model, and the initiation of the speciation process was far earlier than the dates estimated by gene- and species-based divergence dating. Due to their limited dispersal ability, it is suggested that geographical isolation may have played a major role in the divergence of these Takydromus species. Nevertheless, this study reveals a more complex situation and demonstrates that gene flow during the speciation process cannot be overlooked and may have a great impact on divergence dating. By using multilocus data and incorporating Bayesian coalescence approaches, we provide a more biologically realistic framework for delineating the divergence history of Takydromus. © 2014 John Wiley & Sons Ltd.

A Bayesian Framework for Analysis of Pseudo-Spatial Models of Comparable Engineered Systems with Application to Spacecraft Anomaly Prediction Based on Precedent Data

NASA Astrophysics Data System (ADS)

Ndu, Obibobi Kamtochukwu

To ensure that estimates of risk and reliability inform design and resource allocation decisions in the development of complex engineering systems, early engagement in the design life cycle is necessary. An unfortunate constraint on the accuracy of such estimates at this stage of concept development is the limited amount of high fidelity design and failure information available on the actual system under development. Applying the human ability to learn from experience and augment our state of knowledge to evolve better solutions mitigates this limitation. However, the challenge lies in formalizing a methodology that takes this highly abstract, but fundamentally human cognitive, ability and extending it to the field of risk analysis while maintaining the tenets of generalization, Bayesian inference, and probabilistic risk analysis. We introduce an integrated framework for inferring the reliability, or other probabilistic measures of interest, of a new system or a conceptual variant of an existing system. Abstractly, our framework is based on learning from the performance of precedent designs and then applying the acquired knowledge, appropriately adjusted based on degree of relevance, to the inference process. This dissertation presents a method for inferring properties of the conceptual variant using a pseudo-spatial model that describes the spatial configuration of the family of systems to which the concept belongs. Through non-metric multidimensional scaling, we formulate the pseudo-spatial model based on rank-ordered subjective expert perception of design similarity between systems that elucidate the psychological space of the family. By a novel extension of Kriging methods for analysis of geospatial data to our "pseudo-space of comparable engineered systems", we develop a Bayesian inference model that allows prediction of the probabilistic measure of interest.

Modelling maximum river flow by using Bayesian Markov Chain Monte Carlo

NASA Astrophysics Data System (ADS)

Cheong, R. Y.; Gabda, D.

2017-09-01

Analysis of flood trends is vital since flooding threatens human living in terms of financial, environment and security. The data of annual maximum river flows in Sabah were fitted into generalized extreme value (GEV) distribution. Maximum likelihood estimator (MLE) raised naturally when working with GEV distribution. However, previous researches showed that MLE provide unstable results especially in small sample size. In this study, we used different Bayesian Markov Chain Monte Carlo (MCMC) based on Metropolis-Hastings algorithm to estimate GEV parameters. Bayesian MCMC method is a statistical inference which studies the parameter estimation by using posterior distribution based on Bayes’ theorem. Metropolis-Hastings algorithm is used to overcome the high dimensional state space faced in Monte Carlo method. This approach also considers more uncertainty in parameter estimation which then presents a better prediction on maximum river flow in Sabah.

Bayesian estimation of dynamic matching function for U-V analysis in Japan

NASA Astrophysics Data System (ADS)

Kyo, Koki; Noda, Hideo; Kitagawa, Genshiro

2012-05-01

In this paper we propose a Bayesian method for analyzing unemployment dynamics. We derive a Beveridge curve for unemployment and vacancy (U-V) analysis from a Bayesian model based on a labor market matching function. In our framework, the efficiency of matching and the elasticities of new hiring with respect to unemployment and vacancy are regarded as time varying parameters. To construct a flexible model and obtain reasonable estimates in an underdetermined estimation problem, we treat the time varying parameters as random variables and introduce smoothness priors. The model is then described in a state space representation, enabling the parameter estimation to be carried out using Kalman filter and fixed interval smoothing. In such a representation, dynamic features of the cyclic unemployment rate and the structural-frictional unemployment rate can be accurately captured.

Density dependence governs when population responses to multiple stressors are magnified or mitigated.

PubMed

Hodgson, Emma E; Essington, Timothy E; Halpern, Benjamin S

2017-10-01

Population endangerment typically arises from multiple, potentially interacting anthropogenic stressors. Extensive research has investigated the consequences of multiple stressors on organisms, frequently focusing on individual life stages. Less is known about population-level consequences of exposure to multiple stressors, especially when exposure varies through life. We provide the first theoretical basis for identifying species at risk of magnified effects from multiple stressors across life history. By applying a population modeling framework, we reveal conditions under which population responses from stressors applied to distinct life stages are either magnified (synergistic) or mitigated. We find that magnification or mitigation critically depends on the shape of density dependence, but not the life stage in which it occurs. Stressors are always magnified when density dependence is linear or concave, and magnified or mitigated when it is convex. Using Bayesian numerical methods, we estimated the shape of density dependence for eight species across diverse taxa, finding support for all three shapes. © 2017 by the Ecological Society of America.

Bayesian Modeling of Exposure and Airflow Using Two-Zone Models

PubMed Central

Zhang, Yufen; Banerjee, Sudipto; Yang, Rui; Lungu, Claudiu; Ramachandran, Gurumurthy

2009-01-01

Mathematical modeling is being increasingly used as a means for assessing occupational exposures. However, predicting exposure in real settings is constrained by lack of quantitative knowledge of exposure determinants. Validation of models in occupational settings is, therefore, a challenge. Not only do the model parameters need to be known, the models also need to predict the output with some degree of accuracy. In this paper, a Bayesian statistical framework is used for estimating model parameters and exposure concentrations for a two-zone model. The model predicts concentrations in a zone near the source and far away from the source as functions of the toluene generation rate, air ventilation rate through the chamber, and the airflow between near and far fields. The framework combines prior or expert information on the physical model along with the observed data. The framework is applied to simulated data as well as data obtained from the experiments conducted in a chamber. Toluene vapors are generated from a source under different conditions of airflow direction, the presence of a mannequin, and simulated body heat of the mannequin. The Bayesian framework accounts for uncertainty in measurement as well as in the unknown rate of airflow between the near and far fields. The results show that estimates of the interzonal airflow are always close to the estimated equilibrium solutions, which implies that the method works efficiently. The predictions of near-field concentration for both the simulated and real data show nice concordance with the true values, indicating that the two-zone model assumptions agree with the reality to a large extent and the model is suitable for predicting the contaminant concentration. Comparison of the estimated model and its margin of error with the experimental data thus enables validation of the physical model assumptions. The approach illustrates how exposure models and information on model parameters together with the knowledge of uncertainty and variability in these quantities can be used to not only provide better estimates of model outputs but also model parameters. PMID:19403840

Evaluation of the procedure 1A component of the 1980 US/Canada wheat and barley exploratory experiment

NASA Technical Reports Server (NTRS)

Chapman, G. M. (Principal Investigator); Carnes, J. G.

1981-01-01

Several techniques which use clusters generated by a new clustering algorithm, CLASSY, are proposed as alternatives to random sampling to obtain greater precision in crop proportion estimation: (1) Proportional Allocation/relative count estimator (PA/RCE) uses proportional allocation of dots to clusters on the basis of cluster size and a relative count cluster level estimate; (2) Proportional Allocation/Bayes Estimator (PA/BE) uses proportional allocation of dots to clusters and a Bayesian cluster-level estimate; and (3) Bayes Sequential Allocation/Bayesian Estimator (BSA/BE) uses sequential allocation of dots to clusters and a Bayesian cluster level estimate. Clustering in an effective method in making proportion estimates. It is estimated that, to obtain the same precision with random sampling as obtained by the proportional sampling of 50 dots with an unbiased estimator, samples of 85 or 166 would need to be taken if dot sets with AI labels (integrated procedure) or ground truth labels, respectively were input. Dot reallocation provides dot sets that are unbiased. It is recommended that these proportion estimation techniques are maintained, particularly the PA/BE because it provides the greatest precision.

Parameter estimation for an immortal model of colonic stem cell division using approximate Bayesian computation.

PubMed

Walters, Kevin

2012-08-07

In this paper we use approximate Bayesian computation to estimate the parameters in an immortal model of colonic stem cell division. We base the inferences on the observed DNA methylation patterns of cells sampled from the human colon. Utilising DNA methylation patterns as a form of molecular clock is an emerging area of research and has been used in several studies investigating colonic stem cell turnover. There is much debate concerning the two competing models of stem cell turnover: the symmetric (immortal) and asymmetric models. Early simulation studies concluded that the observed methylation data were not consistent with the immortal model. A later modified version of the immortal model that included preferential strand segregation was subsequently shown to be consistent with the same methylation data. Most of this earlier work assumes site independent methylation models that do not take account of the known processivity of methyltransferases whilst other work does not take into account the methylation errors that occur in differentiated cells. This paper addresses both of these issues for the immortal model and demonstrates that approximate Bayesian computation provides accurate estimates of the parameters in this neighbour-dependent model of methylation error rates. The results indicate that if colonic stem cells divide asymmetrically then colon stem cell niches are maintained by more than 8 stem cells. Results also indicate the possibility of preferential strand segregation and provide clear evidence against a site-independent model for methylation errors. In addition, algebraic expressions for some of the summary statistics used in the approximate Bayesian computation (that allow for the additional variation arising from cell division in differentiated cells) are derived and their utility discussed. Copyright © 2012 Elsevier Ltd. All rights reserved.

Bayesian inference and assessment for rare-event bycatch in marine fisheries: a drift gillnet fishery case study.

PubMed

Martin, Summer L; Stohs, Stephen M; Moore, Jeffrey E

2015-03-01

Fisheries bycatch is a global threat to marine megafauna. Environmental laws require bycatch assessment for protected species, but this is difficult when bycatch is rare. Low bycatch rates, combined with low observer coverage, may lead to biased, imprecise estimates when using standard ratio estimators. Bayesian model-based approaches incorporate uncertainty, produce less volatile estimates, and enable probabilistic evaluation of estimates relative to management thresholds. Here, we demonstrate a pragmatic decision-making process that uses Bayesian model-based inferences to estimate the probability of exceeding management thresholds for bycatch in fisheries with < 100% observer coverage. Using the California drift gillnet fishery as a case study, we (1) model rates of rare-event bycatch and mortality using Bayesian Markov chain Monte Carlo estimation methods and 20 years of observer data; (2) predict unobserved counts of bycatch and mortality; (3) infer expected annual mortality; (4) determine probabilities of mortality exceeding regulatory thresholds; and (5) classify the fishery as having low, medium, or high bycatch impact using those probabilities. We focused on leatherback sea turtles (Dermochelys coriacea) and humpback whales (Megaptera novaeangliae). Candidate models included Poisson or zero-inflated Poisson likelihood, fishing effort, and a bycatch rate that varied with area, time, or regulatory regime. Regulatory regime had the strongest effect on leatherback bycatch, with the highest levels occurring prior to a regulatory change. Area had the strongest effect on humpback bycatch. Cumulative bycatch estimates for the 20-year period were 104-242 leatherbacks (52-153 deaths) and 6-50 humpbacks (0-21 deaths). The probability of exceeding a regulatory threshold under the U.S. Marine Mammal Protection Act (Potential Biological Removal, PBR) of 0.113 humpback deaths was 0.58, warranting a "medium bycatch impact" classification of the fishery. No PBR thresholds exist for leatherbacks, but the probability of exceeding an anticipated level of two deaths per year, stated as part of a U.S. Endangered Species Act assessment process, was 0.0007. The approach demonstrated here would allow managers to objectively and probabilistically classify fisheries with respect to bycatch impacts on species that have population-relevant mortality reference points, and declare with a stipulated level of certainty that bycatch did or did not exceed estimated upper bounds.

An Improved Estimation Using Polya-Gamma Augmentation for Bayesian Structural Equation Models with Dichotomous Variables

ERIC Educational Resources Information Center

Kim, Seohyun; Lu, Zhenqiu; Cohen, Allan S.

2018-01-01

Bayesian algorithms have been used successfully in the social and behavioral sciences to analyze dichotomous data particularly with complex structural equation models. In this study, we investigate the use of the Polya-Gamma data augmentation method with Gibbs sampling to improve estimation of structural equation models with dichotomous variables.…

A BAYESIAN METHOD OF ESTIMATING KINETIC PARAMETERS FOR THE INACTIVATION OF CRYPTOSPORIDIUM PARVUM OOCYSTS WITH CHLORINE DIOXIDE AND OZONE

EPA Science Inventory

The main objective of this paper is to use Bayesian methods to estimate the kinetic parameters for the inactivation kinetics of Cryptosporidium parvum oocysts with chlorine dioxide or ozone which are characterized by the delayed Chick-Watson model, i.e., a lag phase or shoulder f...

A General and Flexible Approach to Estimating the Social Relations Model Using Bayesian Methods

ERIC Educational Resources Information Center

Ludtke, Oliver; Robitzsch, Alexander; Kenny, David A.; Trautwein, Ulrich

2013-01-01

The social relations model (SRM) is a conceptual, methodological, and analytical approach that is widely used to examine dyadic behaviors and interpersonal perception within groups. This article introduces a general and flexible approach to estimating the parameters of the SRM that is based on Bayesian methods using Markov chain Monte Carlo…

Using SAS PROC MCMC for Item Response Theory Models

ERIC Educational Resources Information Center

Ames, Allison J.; Samonte, Kelli

2015-01-01

Interest in using Bayesian methods for estimating item response theory models has grown at a remarkable rate in recent years. This attentiveness to Bayesian estimation has also inspired a growth in available software such as WinBUGS, R packages, BMIRT, MPLUS, and SAS PROC MCMC. This article intends to provide an accessible overview of Bayesian…

Technical note: Bayesian calibration of dynamic ruminant nutrition models.

PubMed

Reed, K F; Arhonditsis, G B; France, J; Kebreab, E

2016-08-01

Mechanistic models of ruminant digestion and metabolism have advanced our understanding of the processes underlying ruminant animal physiology. Deterministic modeling practices ignore the inherent variation within and among individual animals and thus have no way to assess how sources of error influence model outputs. We introduce Bayesian calibration of mathematical models to address the need for robust mechanistic modeling tools that can accommodate error analysis by remaining within the bounds of data-based parameter estimation. For the purpose of prediction, the Bayesian approach generates a posterior predictive distribution that represents the current estimate of the value of the response variable, taking into account both the uncertainty about the parameters and model residual variability. Predictions are expressed as probability distributions, thereby conveying significantly more information than point estimates in regard to uncertainty. Our study illustrates some of the technical advantages of Bayesian calibration and discusses the future perspectives in the context of animal nutrition modeling. Copyright © 2016 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Bayesian hierarchical model of ceftriaxone resistance proportions among Salmonella serotype Heidelberg infections.

PubMed

Gu, Weidong; Medalla, Felicita; Hoekstra, Robert M

2018-02-01

The National Antimicrobial Resistance Monitoring System (NARMS) at the Centers for Disease Control and Prevention tracks resistance among Salmonella infections. The annual number of Salmonella isolates of a particular serotype from states may be small, making direct estimation of resistance proportions unreliable. We developed a Bayesian hierarchical model to improve estimation by borrowing strength from relevant sampling units. We illustrate the models with different specifications of spatio-temporal interaction using 2004-2013 NARMS data for ceftriaxone-resistant Salmonella serotype Heidelberg. Our results show that Bayesian estimates of resistance proportions were smoother than observed values, and the difference between predicted and observed proportions was inversely related to the number of submitted isolates. The model with interaction allowed for tracking of annual changes in resistance proportions at the state level. We demonstrated that Bayesian hierarchical models provide a useful tool to examine spatio-temporal patterns of small sample size such as those found in NARMS. Published by Elsevier Ltd.

Bayesian Model Averaging of Artificial Intelligence Models for Hydraulic Conductivity Estimation

NASA Astrophysics Data System (ADS)

Nadiri, A.; Chitsazan, N.; Tsai, F. T.; Asghari Moghaddam, A.

2012-12-01

This research presents a Bayesian artificial intelligence model averaging (BAIMA) method that incorporates multiple artificial intelligence (AI) models to estimate hydraulic conductivity and evaluate estimation uncertainties. Uncertainty in the AI model outputs stems from error in model input as well as non-uniqueness in selecting different AI methods. Using one single AI model tends to bias the estimation and underestimate uncertainty. BAIMA employs Bayesian model averaging (BMA) technique to address the issue of using one single AI model for estimation. BAIMA estimates hydraulic conductivity by averaging the outputs of AI models according to their model weights. In this study, the model weights were determined using the Bayesian information criterion (BIC) that follows the parsimony principle. BAIMA calculates the within-model variances to account for uncertainty propagation from input data to AI model output. Between-model variances are evaluated to account for uncertainty due to model non-uniqueness. We employed Takagi-Sugeno fuzzy logic (TS-FL), artificial neural network (ANN) and neurofuzzy (NF) to estimate hydraulic conductivity for the Tasuj plain aquifer, Iran. BAIMA combined three AI models and produced better fitting than individual models. While NF was expected to be the best AI model owing to its utilization of both TS-FL and ANN models, the NF model is nearly discarded by the parsimony principle. The TS-FL model and the ANN model showed equal importance although their hydraulic conductivity estimates were quite different. This resulted in significant between-model variances that are normally ignored by using one AI model.

Mobile sensing of point-source fugitive methane emissions using Bayesian inference: the determination of the likelihood function

NASA Astrophysics Data System (ADS)

Zhou, X.; Albertson, J. D.

2016-12-01

Natural gas is considered as a bridge fuel towards clean energy due to its potential lower greenhouse gas emission comparing with other fossil fuels. Despite numerous efforts, an efficient and cost-effective approach to monitor fugitive methane emissions along the natural gas production-supply chain has not been developed yet. Recently, mobile methane measurement has been introduced which applies a Bayesian approach to probabilistically infer methane emission rates and update estimates recursively when new measurements become available. However, the likelihood function, especially the error term which determines the shape of the estimate uncertainty, is not rigorously defined and evaluated with field data. To address this issue, we performed a series of near-source (< 30 m) controlled methane release experiments using a specialized vehicle mounted with fast response methane analyzers and a GPS unit. Methane concentrations were measured at two different heights along mobile traversals downwind of the sources, and concurrent wind and temperature data are recorded by nearby 3-D sonic anemometers. With known methane release rates, the measurements were used to determine the functional form and the parameterization of the likelihood function in the Bayesian inference scheme under different meteorological conditions.

Uncertainty analysis of depth predictions from seismic reflection data using Bayesian statistics

NASA Astrophysics Data System (ADS)

Michelioudakis, Dimitrios G.; Hobbs, Richard W.; Caiado, Camila C. S.

2018-03-01

Estimating the depths of target horizons from seismic reflection data is an important task in exploration geophysics. To constrain these depths we need a reliable and accurate velocity model. Here, we build an optimum 2D seismic reflection data processing flow focused on pre - stack deghosting filters and velocity model building and apply Bayesian methods, including Gaussian process emulation and Bayesian History Matching (BHM), to estimate the uncertainties of the depths of key horizons near the borehole DSDP-258 located in the Mentelle Basin, south west of Australia, and compare the results with the drilled core from that well. Following this strategy, the tie between the modelled and observed depths from DSDP-258 core was in accordance with the ± 2σ posterior credibility intervals and predictions for depths to key horizons were made for the two new drill sites, adjacent the existing borehole of the area. The probabilistic analysis allowed us to generate multiple realizations of pre-stack depth migrated images, these can be directly used to better constrain interpretation and identify potential risk at drill sites. The method will be applied to constrain the drilling targets for the upcoming International Ocean Discovery Program (IODP), leg 369.

Uncertainty analysis of depth predictions from seismic reflection data using Bayesian statistics

NASA Astrophysics Data System (ADS)

Michelioudakis, Dimitrios G.; Hobbs, Richard W.; Caiado, Camila C. S.

2018-06-01

Estimating the depths of target horizons from seismic reflection data is an important task in exploration geophysics. To constrain these depths we need a reliable and accurate velocity model. Here, we build an optimum 2-D seismic reflection data processing flow focused on pre-stack deghosting filters and velocity model building and apply Bayesian methods, including Gaussian process emulation and Bayesian History Matching, to estimate the uncertainties of the depths of key horizons near the Deep Sea Drilling Project (DSDP) borehole 258 (DSDP-258) located in the Mentelle Basin, southwest of Australia, and compare the results with the drilled core from that well. Following this strategy, the tie between the modelled and observed depths from DSDP-258 core was in accordance with the ±2σ posterior credibility intervals and predictions for depths to key horizons were made for the two new drill sites, adjacent to the existing borehole of the area. The probabilistic analysis allowed us to generate multiple realizations of pre-stack depth migrated images, these can be directly used to better constrain interpretation and identify potential risk at drill sites. The method will be applied to constrain the drilling targets for the upcoming International Ocean Discovery Program, leg 369.

Bayesian structural equation modeling: a more flexible representation of substantive theory.

PubMed

Muthén, Bengt; Asparouhov, Tihomir

2012-09-01

This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed Bayesian approach is particularly beneficial in applications where parameters are added to a conventional model such that a nonidentified model is obtained if maximum-likelihood estimation is applied. This approach is useful for measurement aspects of latent variable modeling, such as with confirmatory factor analysis, and the measurement part of structural equation modeling. Two application areas are studied, cross-loadings and residual correlations in confirmatory factor analysis. An example using a full structural equation model is also presented, showing an efficient way to find model misspecification. The approach encompasses 3 elements: model testing using posterior predictive checking, model estimation, and model modification. Monte Carlo simulations and real data are analyzed using Mplus. The real-data analyses use data from Holzinger and Swineford's (1939) classic mental abilities study, Big Five personality factor data from a British survey, and science achievement data from the National Educational Longitudinal Study of 1988.

Confident difference criterion: a new Bayesian differentially expressed gene selection algorithm with applications.

PubMed

Yu, Fang; Chen, Ming-Hui; Kuo, Lynn; Talbott, Heather; Davis, John S

2015-08-07

Recently, the Bayesian method becomes more popular for analyzing high dimensional gene expression data as it allows us to borrow information across different genes and provides powerful estimators for evaluating gene expression levels. It is crucial to develop a simple but efficient gene selection algorithm for detecting differentially expressed (DE) genes based on the Bayesian estimators. In this paper, by extending the two-criterion idea of Chen et al. (Chen M-H, Ibrahim JG, Chi Y-Y. A new class of mixture models for differential gene expression in DNA microarray data. J Stat Plan Inference. 2008;138:387-404), we propose two new gene selection algorithms for general Bayesian models and name these new methods as the confident difference criterion methods. One is based on the standardized differences between two mean expression values among genes; the other adds the differences between two variances to it. The proposed confident difference criterion methods first evaluate the posterior probability of a gene having different gene expressions between competitive samples and then declare a gene to be DE if the posterior probability is large. The theoretical connection between the proposed first method based on the means and the Bayes factor approach proposed by Yu et al. (Yu F, Chen M-H, Kuo L. Detecting differentially expressed genes using alibrated Bayes factors. Statistica Sinica. 2008;18:783-802) is established under the normal-normal-model with equal variances between two samples. The empirical performance of the proposed methods is examined and compared to those of several existing methods via several simulations. The results from these simulation studies show that the proposed confident difference criterion methods outperform the existing methods when comparing gene expressions across different conditions for both microarray studies and sequence-based high-throughput studies. A real dataset is used to further demonstrate the proposed methodology. In the real data application, the confident difference criterion methods successfully identified more clinically important DE genes than the other methods. The confident difference criterion method proposed in this paper provides a new efficient approach for both microarray studies and sequence-based high-throughput studies to identify differentially expressed genes.

Population pharmacokinetics and maximum a posteriori probability Bayesian estimator of abacavir: application of individualized therapy in HIV-infected infants and toddlers.

PubMed

Zhao, Wei; Cella, Massimo; Della Pasqua, Oscar; Burger, David; Jacqz-Aigrain, Evelyne

2012-04-01

Abacavir is used to treat HIV infection in both adults and children. The recommended paediatric dose is 8 mg kg(-1) twice daily up to a maximum of 300 mg twice daily. Weight was identified as the central covariate influencing pharmacokinetics of abacavir in children. A population pharmacokinetic model was developed to describe both once and twice daily pharmacokinetic profiles of abacavir in infants and toddlers. Standard dosage regimen is associated with large interindividual variability in abacavir concentrations. A maximum a posteriori probability Bayesian estimator of AUC(0-) (t) based on three time points (0, 1 or 2, and 3 h) is proposed to support area under the concentration-time curve (AUC) targeted individualized therapy in infants and toddlers. To develop a population pharmacokinetic model for abacavir in HIV-infected infants and toddlers, which will be used to describe both once and twice daily pharmacokinetic profiles, identify covariates that explain variability and propose optimal time points to optimize the area under the concentration-time curve (AUC) targeted dosage and individualize therapy. The pharmacokinetics of abacavir was described with plasma concentrations from 23 patients using nonlinear mixed-effects modelling (NONMEM) software. A two-compartment model with first-order absorption and elimination was developed. The final model was validated using bootstrap, visual predictive check and normalized prediction distribution errors. The Bayesian estimator was validated using the cross-validation and simulation-estimation method. The typical population pharmacokinetic parameters and relative standard errors (RSE) were apparent systemic clearance (CL) 13.4 () h−1 (RSE 6.3%), apparent central volume of distribution 4.94 () (RSE 28.7%), apparent peripheral volume of distribution 8.12 () (RSE14.2%), apparent intercompartment clearance 1.25 () h−1 (RSE 16.9%) and absorption rate constant 0.758 h−1 (RSE 5.8%). The covariate analysis identified weight as the individual factor influencing the apparent oral clearance: CL = 13.4 × (weight/12)1.14. The maximum a posteriori probability Bayesian estimator, based on three concentrations measured at 0, 1 or 2, and 3 h after drug intake allowed predicting individual AUC0–t. The population pharmacokinetic model developed for abacavir in HIV-infected infants and toddlers accurately described both once and twice daily pharmacokinetic profiles. The maximum a posteriori probability Bayesian estimator of AUC(0-) (t) was developed from the final model and can be used routinely to optimize individual dosing. © 2011 The Authors. British Journal of Clinical Pharmacology © 2011 The British Pharmacological Society.

Multi-subject hierarchical inverse covariance modelling improves estimation of functional brain networks.

PubMed

Colclough, Giles L; Woolrich, Mark W; Harrison, Samuel J; Rojas López, Pedro A; Valdes-Sosa, Pedro A; Smith, Stephen M

2018-05-07

A Bayesian model for sparse, hierarchical, inver-covariance estimation is presented, and applied to multi-subject functional connectivity estimation in the human brain. It enables simultaneous inference of the strength of connectivity between brain regions at both subject and population level, and is applicable to fMRI, MEG and EEG data. Two versions of the model can encourage sparse connectivity, either using continuous priors to suppress irrelevant connections, or using an explicit description of the network structure to estimate the connection probability between each pair of regions. A large evaluation of this model, and thirteen methods that represent the state of the art of inverse covariance modelling, is conducted using both simulated and resting-state functional imaging datasets. Our novel Bayesian approach has similar performance to the best extant alternative, Ng et al.'s Sparse Group Gaussian Graphical Model algorithm, which also is based on a hierarchical structure. Using data from the Human Connectome Project, we show that these hierarchical models are able to reduce the measurement error in MEG beta-band functional networks by 10%, producing concomitant increases in estimates of the genetic influence on functional connectivity. Copyright © 2018. Published by Elsevier Inc.

Bayesian estimation of the sensitivity and specificity of individual fecal culture and Paralisa to detect Mycobacterium avium subspecies paratuberculosis infection in young farmed deer.

PubMed

Stringer, Lesley A; Jones, Geoff; Jewell, Chris P; Noble, Alasdair D; Heuer, Cord; Wilson, Peter R; Johnson, Wesley O

2013-11-01

A Bayesian latent class model was used to estimate the sensitivity and specificity of an immunoglobulin G1 serum enzyme-linked immunosorbent assay (Paralisa) and individual fecal culture to detect young deer infected with Mycobacterium avium subsp. paratuberculosis. Paired fecal and serum samples were collected, between July 2009 and April 2010, from 20 individual yearling (12-24-month-old) deer in each of 20 South Island and 18 North Island herds in New Zealand and subjected to culture and Paralisa, respectively. Two fecal samples and 16 serum samples from 356 North Island deer, and 55 fecal and 37 serum samples from 401 South Island deer, were positive. The estimate of individual fecal culture sensitivity was 77% (95% credible interval [CI] = 61-92%) with specificity of 99% (95% CI = 98-99.7%). The Paralisa sensitivity estimate was 19% (95% CI = 10-30%), with specificity of 94% (95% CI = 93-96%). All estimates were robust to variation of priors and assumptions tested in a sensitivity analysis. The data informs the use of the tests in determining infection status at the individual and herd level.

Bayesian LASSO, scale space and decision making in association genetics.

PubMed

Pasanen, Leena; Holmström, Lasse; Sillanpää, Mikko J

2015-01-01

LASSO is a penalized regression method that facilitates model fitting in situations where there are as many, or even more explanatory variables than observations, and only a few variables are relevant in explaining the data. We focus on the Bayesian version of LASSO and consider four problems that need special attention: (i) controlling false positives, (ii) multiple comparisons, (iii) collinearity among explanatory variables, and (iv) the choice of the tuning parameter that controls the amount of shrinkage and the sparsity of the estimates. The particular application considered is association genetics, where LASSO regression can be used to find links between chromosome locations and phenotypic traits in a biological organism. However, the proposed techniques are relevant also in other contexts where LASSO is used for variable selection. We separate the true associations from false positives using the posterior distribution of the effects (regression coefficients) provided by Bayesian LASSO. We propose to solve the multiple comparisons problem by using simultaneous inference based on the joint posterior distribution of the effects. Bayesian LASSO also tends to distribute an effect among collinear variables, making detection of an association difficult. We propose to solve this problem by considering not only individual effects but also their functionals (i.e. sums and differences). Finally, whereas in Bayesian LASSO the tuning parameter is often regarded as a random variable, we adopt a scale space view and consider a whole range of fixed tuning parameters, instead. The effect estimates and the associated inference are considered for all tuning parameters in the selected range and the results are visualized with color maps that provide useful insights into data and the association problem considered. The methods are illustrated using two sets of artificial data and one real data set, all representing typical settings in association genetics.

Evaluation of a Partial Genome Screening of Two Asthma Susceptibility Regions Using Bayesian Network Based Bayesian Multilevel Analysis of Relevance

PubMed Central

Antal, Péter; Kiszel, Petra Sz.; Gézsi, András; Hadadi, Éva; Virág, Viktor; Hajós, Gergely; Millinghoffer, András; Nagy, Adrienne; Kiss, András; Semsei, Ágnes F.; Temesi, Gergely; Melegh, Béla; Kisfali, Péter; Széll, Márta; Bikov, András; Gálffy, Gabriella; Tamási, Lilla; Falus, András; Szalai, Csaba

2012-01-01

Genetic studies indicate high number of potential factors related to asthma. Based on earlier linkage analyses we selected the 11q13 and 14q22 asthma susceptibility regions, for which we designed a partial genome screening study using 145 SNPs in 1201 individuals (436 asthmatic children and 765 controls). The results were evaluated with traditional frequentist methods and we applied a new statistical method, called Bayesian network based Bayesian multilevel analysis of relevance (BN-BMLA). This method uses Bayesian network representation to provide detailed characterization of the relevance of factors, such as joint significance, the type of dependency, and multi-target aspects. We estimated posteriors for these relations within the Bayesian statistical framework, in order to estimate the posteriors whether a variable is directly relevant or its association is only mediated. With frequentist methods one SNP (rs3751464 in the FRMD6 gene) provided evidence for an association with asthma (OR = 1.43(1.2–1.8); p = 3×10−4). The possible role of the FRMD6 gene in asthma was also confirmed in an animal model and human asthmatics. In the BN-BMLA analysis altogether 5 SNPs in 4 genes were found relevant in connection with asthma phenotype: PRPF19 on chromosome 11, and FRMD6, PTGER2 and PTGDR on chromosome 14. In a subsequent step a partial dataset containing rhinitis and further clinical parameters was used, which allowed the analysis of relevance of SNPs for asthma and multiple targets. These analyses suggested that SNPs in the AHNAK and MS4A2 genes were indirectly associated with asthma. This paper indicates that BN-BMLA explores the relevant factors more comprehensively than traditional statistical methods and extends the scope of strong relevance based methods to include partial relevance, global characterization of relevance and multi-target relevance. PMID:22432035

Improved Determination of the Myelin Water Fraction in Human Brain using Magnetic Resonance Imaging through Bayesian Analysis of mcDESPOT

PubMed Central

Bouhrara, Mustapha; Spencer, Richard G.

2015-01-01

Myelin water fraction (MWF) mapping with magnetic resonance imaging has led to the ability to directly observe myelination and demyelination in both the developing brain and in disease. Multicomponent driven equilibrium single pulse observation of T1 and T2 (mcDESPOT) has been proposed as a rapid approach for multicomponent relaxometry and has been applied to map MWF in human brain. However, even for the simplest two-pool signal model consisting of MWF and non-myelin-associated water, the dimensionality of the parameter space for obtaining MWF estimates remains high. This renders parameter estimation difficult, especially at low-to-moderate signal-to-noise ratios (SNR), due to the presence of local minima and the flatness of the fit residual energy surface used for parameter determination using conventional nonlinear least squares (NLLS)-based algorithms. In this study, we introduce three Bayesian approaches for analysis of the mcDESPOT signal model to determine MWF. Given the high dimensional nature of mcDESPOT signal model, and, thereby, the high dimensional marginalizations over nuisance parameters needed to derive the posterior probability distribution of MWF parameter, the introduced Bayesian analyses use different approaches to reduce the dimensionality of the parameter space. The first approach uses normalization by average signal amplitude, and assumes that noise can be accurately estimated from signal-free regions of the image. The second approach likewise uses average amplitude normalization, but incorporates a full treatment of noise as an unknown variable through marginalization. The third approach does not use amplitude normalization and incorporates marginalization over both noise and signal amplitude. Through extensive Monte Carlo numerical simulations and analysis of in-vivo human brain datasets exhibiting a range of SNR and spatial resolution, we demonstrated the markedly improved accuracy and precision in the estimation of MWF using these Bayesian methods as compared to the stochastic region contraction (SRC) implementation of NLLS. PMID:26499810

Empirical Bayes estimation of proportions with application to cowbird parasitism rates

USGS Publications Warehouse

Link, W.A.; Hahn, D.C.

1996-01-01

Bayesian models provide a structure for studying collections of parameters such as are considered in the investigation of communities, ecosystems, and landscapes. This structure allows for improved estimation of individual parameters, by considering them in the context of a group of related parameters. Individual estimates are differentially adjusted toward an overall mean, with the magnitude of their adjustment based on their precision. Consequently, Bayesian estimation allows for a more credible identification of extreme values in a collection of estimates. Bayesian models regard individual parameters as values sampled from a specified probability distribution, called a prior. The requirement that the prior be known is often regarded as an unattractive feature of Bayesian analysis and may be the reason why Bayesian analyses are not frequently applied in ecological studies. Empirical Bayes methods provide an alternative approach that incorporates the structural advantages of Bayesian models while requiring a less stringent specification of prior knowledge. Rather than requiring that the prior distribution be known, empirical Bayes methods require only that it be in a certain family of distributions, indexed by hyperparameters that can be estimated from the available data. This structure is of interest per se, in addition to its value in allowing for improved estimation of individual parameters; for example, hypotheses regarding the existence of distinct subgroups in a collection of parameters can be considered under the empirical Bayes framework by allowing the hyperparameters to vary among subgroups. Though empirical Bayes methods have been applied in a variety of contexts, they have received little attention in the ecological literature. We describe the empirical Bayes approach in application to estimation of proportions, using data obtained in a community-wide study of cowbird parasitism rates for illustration. Since observed proportions based on small sample sizes are heavily adjusted toward the mean, extreme values among empirical Bayes estimates identify those species for which there is the greatest evidence of extreme parasitism rates. Applying a subgroup analysis to our data on cowbird parasitism rates, we conclude that parasitism rates for Neotropical Migrants as a group are no greater than those of Resident/Short-distance Migrant species in this forest community. Our data and analyses demonstrate that the parasitism rates for certain Neotropical Migrant species are remarkably low (Wood Thrush and Rose-breasted Grosbeak) while those for others are remarkably high (Ovenbird and Red-eyed Vireo).

Adaptive statistical pattern classifiers for remotely sensed data

NASA Technical Reports Server (NTRS)

Gonzalez, R. C.; Pace, M. O.; Raulston, H. S.

1975-01-01

A technique for the adaptive estimation of nonstationary statistics necessary for Bayesian classification is developed. The basic approach to the adaptive estimation procedure consists of two steps: (1) an optimal stochastic approximation of the parameters of interest and (2) a projection of the parameters in time or position. A divergence criterion is developed to monitor algorithm performance. Comparative results of adaptive and nonadaptive classifier tests are presented for simulated four dimensional spectral scan data.

Inference of Gene Regulatory Networks Using Bayesian Nonparametric Regression and Topology Information.

PubMed

Fan, Yue; Wang, Xiao; Peng, Qinke

2017-01-01

Gene regulatory networks (GRNs) play an important role in cellular systems and are important for understanding biological processes. Many algorithms have been developed to infer the GRNs. However, most algorithms only pay attention to the gene expression data but do not consider the topology information in their inference process, while incorporating this information can partially compensate for the lack of reliable expression data. Here we develop a Bayesian group lasso with spike and slab priors to perform gene selection and estimation for nonparametric models. B-spline basis functions are used to capture the nonlinear relationships flexibly and penalties are used to avoid overfitting. Further, we incorporate the topology information into the Bayesian method as a prior. We present the application of our method on DREAM3 and DREAM4 datasets and two real biological datasets. The results show that our method performs better than existing methods and the topology information prior can improve the result.

Bayesian Computation for Log-Gaussian Cox Processes: A Comparative Analysis of Methods

PubMed Central

Teng, Ming; Nathoo, Farouk S.; Johnson, Timothy D.

2017-01-01

The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point pattern data. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Various methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulation studies as well as through two applications, the first examining ecological data and the second involving neuroimaging data. PMID:29200537

Bayesian median regression for temporal gene expression data

NASA Astrophysics Data System (ADS)

Yu, Keming; Vinciotti, Veronica; Liu, Xiaohui; 't Hoen, Peter A. C.

2007-09-01

Most of the existing methods for the identification of biologically interesting genes in a temporal expression profiling dataset do not fully exploit the temporal ordering in the dataset and are based on normality assumptions for the gene expression. In this paper, we introduce a Bayesian median regression model to detect genes whose temporal profile is significantly different across a number of biological conditions. The regression model is defined by a polynomial function where both time and condition effects as well as interactions between the two are included. MCMC-based inference returns the posterior distribution of the polynomial coefficients. From this a simple Bayes factor test is proposed to test for significance. The estimation of the median rather than the mean, and within a Bayesian framework, increases the robustness of the method compared to a Hotelling T2-test previously suggested. This is shown on simulated data and on muscular dystrophy gene expression data.

Robust point matching via vector field consensus.

PubMed

Jiayi Ma; Ji Zhao; Jinwen Tian; Yuille, Alan L; Zhuowen Tu

2014-04-01

In this paper, we propose an efficient algorithm, called vector field consensus, for establishing robust point correspondences between two sets of points. Our algorithm starts by creating a set of putative correspondences which can contain a very large number of false correspondences, or outliers, in addition to a limited number of true correspondences (inliers). Next, we solve for correspondence by interpolating a vector field between the two point sets, which involves estimating a consensus of inlier points whose matching follows a nonparametric geometrical constraint. We formulate this a maximum a posteriori (MAP) estimation of a Bayesian model with hidden/latent variables indicating whether matches in the putative set are outliers or inliers. We impose nonparametric geometrical constraints on the correspondence, as a prior distribution, using Tikhonov regularizers in a reproducing kernel Hilbert space. MAP estimation is performed by the EM algorithm which by also estimating the variance of the prior model (initialized to a large value) is able to obtain good estimates very quickly (e.g., avoiding many of the local minima inherent in this formulation). We illustrate this method on data sets in 2D and 3D and demonstrate that it is robust to a very large number of outliers (even up to 90%). We also show that in the special case where there is an underlying parametric geometrical model (e.g., the epipolar line constraint) that we obtain better results than standard alternatives like RANSAC if a large number of outliers are present. This suggests a two-stage strategy, where we use our nonparametric model to reduce the size of the putative set and then apply a parametric variant of our approach to estimate the geometric parameters. Our algorithm is computationally efficient and we provide code for others to use it. In addition, our approach is general and can be applied to other problems, such as learning with a badly corrupted training data set.

A novel Pareto-based Bayesian approach on extension of the infogram for extracting repetitive transients

NASA Astrophysics Data System (ADS)

Gu, Xiaohui; Yang, Shaopu; Liu, Yongqiang; Hao, Rujiang

2018-06-01

Two most important signatures of repetitive transients in the vibration signals of a faulty rotating machine are impulsiveness and cyclostationarity. In the newly proposed infogram, the time-domain and frequency-domain spectral negentropy were put forward to characterize these two aspects, respectively. However, in extension of the infogram to Bayesian inference based optimal wavelet filtering, only one spectral negentropy was employed in identifying the informative frequency band. To overcome its drawback, a novel Pareto-based Bayesian approach was proposed in this paper. The Pareto optimal solutions which can simultaneously maximize the time-domain and frequency-domain spectral negentropy were utilized in estimating the posterior wavelet parameters distributions. Moreover, the relationship between the impulsive and cyclostationary signatures was established by the domination. It can help balance the contributions due to these two aspects other than simply synthesize by the average weight in the infogram. Three instance studies including simulated and experimental signals were investigated to illustrate the effectiveness of the proposed method by challenging different noises and interferences. In addition, some comparisons with the aforementioned peer methods were also conducted to show its superiority and robustness in extracting the repetitive transients.

Estimation of Post-Test Probabilities by Residents: Bayesian Reasoning versus Heuristics?

ERIC Educational Resources Information Center

Hall, Stacey; Phang, Sen Han; Schaefer, Jeffrey P.; Ghali, William; Wright, Bruce; McLaughlin, Kevin

2014-01-01

Although the process of diagnosing invariably begins with a heuristic, we encourage our learners to support their diagnoses by analytical cognitive processes, such as Bayesian reasoning, in an attempt to mitigate the effects of heuristics on diagnosing. There are, however, limited data on the use ± impact of Bayesian reasoning on the accuracy of…

A comparison of Monte Carlo-based Bayesian parameter estimation methods for stochastic models of genetic networks

PubMed Central

Zaikin, Alexey; Míguez, Joaquín

2017-01-01

We compare three state-of-the-art Bayesian inference methods for the estimation of the unknown parameters in a stochastic model of a genetic network. In particular, we introduce a stochastic version of the paradigmatic synthetic multicellular clock model proposed by Ullner et al., 2007. By introducing dynamical noise in the model and assuming that the partial observations of the system are contaminated by additive noise, we enable a principled mechanism to represent experimental uncertainties in the synthesis of the multicellular system and pave the way for the design of probabilistic methods for the estimation of any unknowns in the model. Within this setup, we tackle the Bayesian estimation of a subset of the model parameters. Specifically, we compare three Monte Carlo based numerical methods for the approximation of the posterior probability density function of the unknown parameters given a set of partial and noisy observations of the system. The schemes we assess are the particle Metropolis-Hastings (PMH) algorithm, the nonlinear population Monte Carlo (NPMC) method and the approximate Bayesian computation sequential Monte Carlo (ABC-SMC) scheme. We present an extensive numerical simulation study, which shows that while the three techniques can effectively solve the problem there are significant differences both in estimation accuracy and computational efficiency. PMID:28797087

Receptive Field Inference with Localized Priors

PubMed Central

Park, Mijung; Pillow, Jonathan W.

2011-01-01

The linear receptive field describes a mapping from sensory stimuli to a one-dimensional variable governing a neuron's spike response. However, traditional receptive field estimators such as the spike-triggered average converge slowly and often require large amounts of data. Bayesian methods seek to overcome this problem by biasing estimates towards solutions that are more likely a priori, typically those with small, smooth, or sparse coefficients. Here we introduce a novel Bayesian receptive field estimator designed to incorporate locality, a powerful form of prior information about receptive field structure. The key to our approach is a hierarchical receptive field model that flexibly adapts to localized structure in both spacetime and spatiotemporal frequency, using an inference method known as empirical Bayes. We refer to our method as automatic locality determination (ALD), and show that it can accurately recover various types of smooth, sparse, and localized receptive fields. We apply ALD to neural data from retinal ganglion cells and V1 simple cells, and find it achieves error rates several times lower than standard estimators. Thus, estimates of comparable accuracy can be achieved with substantially less data. Finally, we introduce a computationally efficient Markov Chain Monte Carlo (MCMC) algorithm for fully Bayesian inference under the ALD prior, yielding accurate Bayesian confidence intervals for small or noisy datasets. PMID:22046110

A Bayesian Approach to Determination of F, D, and Z Values Used in Steam Sterilization Validation.

PubMed

Faya, Paul; Stamey, James D; Seaman, John W

2017-01-01

For manufacturers of sterile drug products, steam sterilization is a common method used to provide assurance of the sterility of manufacturing equipment and products. The validation of sterilization processes is a regulatory requirement and relies upon the estimation of key resistance parameters of microorganisms. Traditional methods have relied upon point estimates for the resistance parameters. In this paper, we propose a Bayesian method for estimation of the well-known D T , z , and F o values that are used in the development and validation of sterilization processes. A Bayesian approach allows the uncertainty about these values to be modeled using probability distributions, thereby providing a fully risk-based approach to measures of sterility assurance. An example is given using the survivor curve and fraction negative methods for estimation of resistance parameters, and we present a means by which a probabilistic conclusion can be made regarding the ability of a process to achieve a specified sterility criterion. LAY ABSTRACT: For manufacturers of sterile drug products, steam sterilization is a common method used to provide assurance of the sterility of manufacturing equipment and products. The validation of sterilization processes is a regulatory requirement and relies upon the estimation of key resistance parameters of microorganisms. Traditional methods have relied upon point estimates for the resistance parameters. In this paper, we propose a Bayesian method for estimation of the critical process parameters that are evaluated in the development and validation of sterilization processes. A Bayesian approach allows the uncertainty about these parameters to be modeled using probability distributions, thereby providing a fully risk-based approach to measures of sterility assurance. An example is given using the survivor curve and fraction negative methods for estimation of resistance parameters, and we present a means by which a probabilistic conclusion can be made regarding the ability of a process to achieve a specified sterility criterion. © PDA, Inc. 2017.

Artificial Intelligence (AI) Center of Excellence at the University of Pennsylvania

DTIC Science & Technology

1995-07-01

that controls impact forces. Robust Location Estimation for MLR and Non-MLR Distributions (Dissertation Proposal) Gerda L. Kamberova MS-CIS-92-28...Bayesian Approach To Computer Vision Problems Gerda L. Kamberova MS-CIS-92-29 GRASP LAB 310 The object of our study is the Bayesian approach in...Estimation for MLR and Non-MLR Distributions (Dissertation) Gerda L. Kamberova MS-CIS-92-93 GRASP LAB 340 We study the problem of estimating an unknown

Improved inference in Bayesian segmentation using Monte Carlo sampling: application to hippocampal subfield volumetry.

PubMed

Iglesias, Juan Eugenio; Sabuncu, Mert Rory; Van Leemput, Koen

2013-10-01

Many segmentation algorithms in medical image analysis use Bayesian modeling to augment local image appearance with prior anatomical knowledge. Such methods often contain a large number of free parameters that are first estimated and then kept fixed during the actual segmentation process. However, a faithful Bayesian analysis would marginalize over such parameters, accounting for their uncertainty by considering all possible values they may take. Here we propose to incorporate this uncertainty into Bayesian segmentation methods in order to improve the inference process. In particular, we approximate the required marginalization over model parameters using computationally efficient Markov chain Monte Carlo techniques. We illustrate the proposed approach using a recently developed Bayesian method for the segmentation of hippocampal subfields in brain MRI scans, showing a significant improvement in an Alzheimer's disease classification task. As an additional benefit, the technique also allows one to compute informative "error bars" on the volume estimates of individual structures. Copyright © 2013 Elsevier B.V. All rights reserved.

Improved Inference in Bayesian Segmentation Using Monte Carlo Sampling: Application to Hippocampal Subfield Volumetry

PubMed Central

Iglesias, Juan Eugenio; Sabuncu, Mert Rory; Leemput, Koen Van

2013-01-01

Many segmentation algorithms in medical image analysis use Bayesian modeling to augment local image appearance with prior anatomical knowledge. Such methods often contain a large number of free parameters that are first estimated and then kept fixed during the actual segmentation process. However, a faithful Bayesian analysis would marginalize over such parameters, accounting for their uncertainty by considering all possible values they may take. Here we propose to incorporate this uncertainty into Bayesian segmentation methods in order to improve the inference process. In particular, we approximate the required marginalization over model parameters using computationally efficient Markov chain Monte Carlo techniques. We illustrate the proposed approach using a recently developed Bayesian method for the segmentation of hippocampal subfields in brain MRI scans, showing a significant improvement in an Alzheimer’s disease classification task. As an additional benefit, the technique also allows one to compute informative “error bars” on the volume estimates of individual structures. PMID:23773521

Quantifying Uncertainty in Near Surface Electromagnetic Imaging Using Bayesian Methods

NASA Astrophysics Data System (ADS)

Blatter, D. B.; Ray, A.; Key, K.

2017-12-01

Geoscientists commonly use electromagnetic methods to image the Earth's near surface. Field measurements of EM fields are made (often with the aid an artificial EM source) and then used to infer near surface electrical conductivity via a process known as inversion. In geophysics, the standard inversion tool kit is robust and can provide an estimate of the Earth's near surface conductivity that is both geologically reasonable and compatible with the measured field data. However, standard inverse methods struggle to provide a sense of the uncertainty in the estimate they provide. This is because the task of finding an Earth model that explains the data to within measurement error is non-unique - that is, there are many, many such models; but the standard methods provide only one "answer." An alternative method, known as Bayesian inversion, seeks to explore the full range of Earth model parameters that can adequately explain the measured data, rather than attempting to find a single, "ideal" model. Bayesian inverse methods can therefore provide a quantitative assessment of the uncertainty inherent in trying to infer near surface conductivity from noisy, measured field data. This study applies a Bayesian inverse method (called trans-dimensional Markov chain Monte Carlo) to transient airborne EM data previously collected over Taylor Valley - one of the McMurdo Dry Valleys in Antarctica. Our results confirm the reasonableness of previous estimates (made using standard methods) of near surface conductivity beneath Taylor Valley. In addition, we demonstrate quantitatively the uncertainty associated with those estimates. We demonstrate that Bayesian inverse methods can provide quantitative uncertainty to estimates of near surface conductivity.

A fully Bayesian method for jointly fitting instrumental calibration and X-ray spectral models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Jin; Yu, Yaming; Van Dyk, David A.

2014-10-20

Owing to a lack of robust principled methods, systematic instrumental uncertainties have generally been ignored in astrophysical data analysis despite wide recognition of the importance of including them. Ignoring calibration uncertainty can cause bias in the estimation of source model parameters and can lead to underestimation of the variance of these estimates. We previously introduced a pragmatic Bayesian method to address this problem. The method is 'pragmatic' in that it introduced an ad hoc technique that simplified computation by neglecting the potential information in the data for narrowing the uncertainty for the calibration product. Following that work, we use amore » principal component analysis to efficiently represent the uncertainty of the effective area of an X-ray (or γ-ray) telescope. Here, however, we leverage this representation to enable a principled, fully Bayesian method that coherently accounts for the calibration uncertainty in high-energy spectral analysis. In this setting, the method is compared with standard analysis techniques and the pragmatic Bayesian method. The advantage of the fully Bayesian method is that it allows the data to provide information not only for estimation of the source parameters but also for the calibration product—here the effective area, conditional on the adopted spectral model. In this way, it can yield more accurate and efficient estimates of the source parameters along with valid estimates of their uncertainty. Provided that the source spectrum can be accurately described by a parameterized model, this method allows rigorous inference about the effective area by quantifying which possible curves are most consistent with the data.« less

Comparison of 3 estimation methods of mycophenolic acid AUC based on a limited sampling strategy in renal transplant patients.

PubMed

Hulin, Anne; Blanchet, Benoît; Audard, Vincent; Barau, Caroline; Furlan, Valérie; Durrbach, Antoine; Taïeb, Fabrice; Lang, Philippe; Grimbert, Philippe; Tod, Michel

2009-04-01

A significant relationship between mycophenolic acid (MPA) area under the plasma concentration-time curve (AUC) and the risk for rejection has been reported. Based on 3 concentration measurements, 3 approaches have been proposed for the estimation of MPA AUC, involving either a multilinear regression approach model (MLRA) or a Bayesian estimation using either gamma absorption or zero-order absorption population models. The aim of the study was to compare the 3 approaches for the estimation of MPA AUC in 150 renal transplant patients treated with mycophenolate mofetil and tacrolimus. The population parameters were determined in 77 patients (learning study). The AUC estimation methods were compared in the learning population and in 73 patients from another center (validation study). In the latter study, the reference AUCs were estimated by the trapezoidal rule on 8 measurements. MPA concentrations were measured by liquid chromatography. The gamma absorption model gave the best fit. In the learning study, the AUCs estimated by both Bayesian methods were very similar, whereas the multilinear approach was highly correlated but yielded estimates about 20% lower than Bayesian methods. This resulted in dosing recommendations differing by 250 mg/12 h or more in 27% of cases. In the validation study, AUC estimates based on the Bayesian method with gamma absorption model and multilinear regression approach model were, respectively, 12% higher and 7% lower than the reference values. To conclude, the bicompartmental model with gamma absorption rate gave the best fit. The 3 AUC estimation methods are highly correlated but not concordant. For a given patient, the same estimation method should always be used.

A Fatigue Crack Size Evaluation Method Based on Lamb Wave Simulation and Limited Experimental Data

PubMed Central

He, Jingjing; Ran, Yunmeng; Liu, Bin; Yang, Jinsong; Guan, Xuefei

2017-01-01

This paper presents a systematic and general method for Lamb wave-based crack size quantification using finite element simulations and Bayesian updating. The method consists of construction of a baseline quantification model using finite element simulation data and Bayesian updating with limited Lamb wave data from target structure. The baseline model correlates two proposed damage sensitive features, namely the normalized amplitude and phase change, with the crack length through a response surface model. The two damage sensitive features are extracted from the first received S0 mode wave package. The model parameters of the baseline model are estimated using finite element simulation data. To account for uncertainties from numerical modeling, geometry, material and manufacturing between the baseline model and the target model, Bayesian method is employed to update the baseline model with a few measurements acquired from the actual target structure. A rigorous validation is made using in-situ fatigue testing and Lamb wave data from coupon specimens and realistic lap-joint components. The effectiveness and accuracy of the proposed method is demonstrated under different loading and damage conditions. PMID:28902148

Adaptive control of theophylline therapy: importance of blood sampling times.

PubMed

D'Argenio, D Z; Khakmahd, K

1983-10-01

A two-observation protocol for estimating theophylline clearance during a constant-rate intravenous infusion is used to examine the importance of blood sampling schedules with regard to the information content of resulting concentration data. Guided by a theory for calculating maximally informative sample times, population simulations are used to assess the effect of specific sampling times on the precision of resulting clearance estimates and subsequent predictions of theophylline plasma concentrations. The simulations incorporated noise terms for intersubject variability, dosing errors, sample collection errors, and assay error. Clearance was estimated using Chiou's method, least squares, and a Bayesian estimation procedure. The results of these simulations suggest that clinically significant estimation and prediction errors may result when using the above two-point protocol for estimating theophylline clearance if the time separating the two blood samples is less than one population mean elimination half-life.

A Bayesian Model for the Estimation of Latent Interaction and Quadratic Effects When Latent Variables Are Non-Normally Distributed

ERIC Educational Resources Information Center

Kelava, Augustin; Nagengast, Benjamin

2012-01-01

Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we present a Bayesian model for the estimation of latent nonlinear effects when the latent…

Time-varying Concurrent Risk of Extreme Droughts and Heatwaves in California

NASA Astrophysics Data System (ADS)

Sarhadi, A.; Diffenbaugh, N. S.; Ausin, M. C.

2016-12-01

Anthropogenic global warming has changed the nature and the risk of extreme climate phenomena such as droughts and heatwaves. The concurrent of these nature-changing climatic extremes may result in intensifying undesirable consequences in terms of human health and destructive effects in water resources. The present study assesses the risk of concurrent extreme droughts and heatwaves under dynamic nonstationary conditions arising from climate change in California. For doing so, a generalized fully Bayesian time-varying multivariate risk framework is proposed evolving through time under dynamic human-induced environment. In this methodology, an extreme, Bayesian, dynamic copula (Gumbel) is developed to model the time-varying dependence structure between the two different climate extremes. The time-varying extreme marginals are previously modeled using a Generalized Extreme Value (GEV) distribution. Bayesian Markov Chain Monte Carlo (MCMC) inference is integrated to estimate parameters of the nonstationary marginals and copula using a Gibbs sampling method. Modelled marginals and copula are then used to develop a fully Bayesian, time-varying joint return period concept for the estimation of concurrent risk. Here we argue that climate change has increased the chance of concurrent droughts and heatwaves over decades in California. It is also demonstrated that a time-varying multivariate perspective should be incorporated to assess realistic concurrent risk of the extremes for water resources planning and management in a changing climate in this area. The proposed generalized methodology can be applied for other stochastic nature-changing compound climate extremes that are under the influence of climate change.

Implementing informative priors for heterogeneity in meta-analysis using meta-regression and pseudo data.

PubMed

Rhodes, Kirsty M; Turner, Rebecca M; White, Ian R; Jackson, Dan; Spiegelhalter, David J; Higgins, Julian P T

2016-12-20

Many meta-analyses combine results from only a small number of studies, a situation in which the between-study variance is imprecisely estimated when standard methods are applied. Bayesian meta-analysis allows incorporation of external evidence on heterogeneity, providing the potential for more robust inference on the effect size of interest. We present a method for performing Bayesian meta-analysis using data augmentation, in which we represent an informative conjugate prior for between-study variance by pseudo data and use meta-regression for estimation. To assist in this, we derive predictive inverse-gamma distributions for the between-study variance expected in future meta-analyses. These may serve as priors for heterogeneity in new meta-analyses. In a simulation study, we compare approximate Bayesian methods using meta-regression and pseudo data against fully Bayesian approaches based on importance sampling techniques and Markov chain Monte Carlo (MCMC). We compare the frequentist properties of these Bayesian methods with those of the commonly used frequentist DerSimonian and Laird procedure. The method is implemented in standard statistical software and provides a less complex alternative to standard MCMC approaches. An importance sampling approach produces almost identical results to standard MCMC approaches, and results obtained through meta-regression and pseudo data are very similar. On average, data augmentation provides closer results to MCMC, if implemented using restricted maximum likelihood estimation rather than DerSimonian and Laird or maximum likelihood estimation. The methods are applied to real datasets, and an extension to network meta-analysis is described. The proposed method facilitates Bayesian meta-analysis in a way that is accessible to applied researchers. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Hierarchical animal movement models for population-level inference

USGS Publications Warehouse

Hooten, Mevin B.; Buderman, Frances E.; Brost, Brian M.; Hanks, Ephraim M.; Ivans, Jacob S.

2016-01-01

New methods for modeling animal movement based on telemetry data are developed regularly. With advances in telemetry capabilities, animal movement models are becoming increasingly sophisticated. Despite a need for population-level inference, animal movement models are still predominantly developed for individual-level inference. Most efforts to upscale the inference to the population level are either post hoc or complicated enough that only the developer can implement the model. Hierarchical Bayesian models provide an ideal platform for the development of population-level animal movement models but can be challenging to fit due to computational limitations or extensive tuning required. We propose a two-stage procedure for fitting hierarchical animal movement models to telemetry data. The two-stage approach is statistically rigorous and allows one to fit individual-level movement models separately, then resample them using a secondary MCMC algorithm. The primary advantages of the two-stage approach are that the first stage is easily parallelizable and the second stage is completely unsupervised, allowing for an automated fitting procedure in many cases. We demonstrate the two-stage procedure with two applications of animal movement models. The first application involves a spatial point process approach to modeling telemetry data, and the second involves a more complicated continuous-time discrete-space animal movement model. We fit these models to simulated data and real telemetry data arising from a population of monitored Canada lynx in Colorado, USA.

Exploiting neurovascular coupling: a Bayesian sequential Monte Carlo approach applied to simulated EEG fNIRS data

NASA Astrophysics Data System (ADS)

Croce, Pierpaolo; Zappasodi, Filippo; Merla, Arcangelo; Chiarelli, Antonio Maria

2017-08-01

Objective. Electrical and hemodynamic brain activity are linked through the neurovascular coupling process and they can be simultaneously measured through integration of electroencephalography (EEG) and functional near-infrared spectroscopy (fNIRS). Thanks to the lack of electro-optical interference, the two procedures can be easily combined and, whereas EEG provides electrophysiological information, fNIRS can provide measurements of two hemodynamic variables, such as oxygenated and deoxygenated hemoglobin. A Bayesian sequential Monte Carlo approach (particle filter, PF) was applied to simulated recordings of electrical and neurovascular mediated hemodynamic activity, and the advantages of a unified framework were shown. Approach. Multiple neural activities and hemodynamic responses were simulated in the primary motor cortex of a subject brain. EEG and fNIRS recordings were obtained by means of forward models of volume conduction and light propagation through the head. A state space model of combined EEG and fNIRS data was built and its dynamic evolution was estimated through a Bayesian sequential Monte Carlo approach (PF). Main results. We showed the feasibility of the procedure and the improvements in both electrical and hemodynamic brain activity reconstruction when using the PF on combined EEG and fNIRS measurements. Significance. The investigated procedure allows one to combine the information provided by the two methodologies, and, by taking advantage of a physical model of the coupling between electrical and hemodynamic response, to obtain a better estimate of brain activity evolution. Despite the high computational demand, application of such an approach to in vivo recordings could fully exploit the advantages of this combined brain imaging technology.

Bayesian inference in an item response theory model with a generalized student t link function

NASA Astrophysics Data System (ADS)

Azevedo, Caio L. N.; Migon, Helio S.

2012-10-01

In this paper we introduce a new item response theory (IRT) model with a generalized Student t-link function with unknown degrees of freedom (df), named generalized t-link (GtL) IRT model. In this model we consider only the difficulty parameter in the item response function. GtL is an alternative to the two parameter logit and probit models, since the degrees of freedom (df) play a similar role to the discrimination parameter. However, the behavior of the curves of the GtL is different from those of the two parameter models and the usual Student t link, since in GtL the curve obtained from different df's can cross the probit curves in more than one latent trait level. The GtL model has similar proprieties to the generalized linear mixed models, such as the existence of sufficient statistics and easy parameter interpretation. Also, many techniques of parameter estimation, model fit assessment and residual analysis developed for that models can be used for the GtL model. We develop fully Bayesian estimation and model fit assessment tools through a Metropolis-Hastings step within Gibbs sampling algorithm. We consider a prior sensitivity choice concerning the degrees of freedom. The simulation study indicates that the algorithm recovers all parameters properly. In addition, some Bayesian model fit assessment tools are considered. Finally, a real data set is analyzed using our approach and other usual models. The results indicate that our model fits the data better than the two parameter models.

Probabilistic segmentation and intensity estimation for microarray images.

PubMed

Gottardo, Raphael; Besag, Julian; Stephens, Matthew; Murua, Alejandro

2006-01-01

We describe a probabilistic approach to simultaneous image segmentation and intensity estimation for complementary DNA microarray experiments. The approach overcomes several limitations of existing methods. In particular, it (a) uses a flexible Markov random field approach to segmentation that allows for a wider range of spot shapes than existing methods, including relatively common 'doughnut-shaped' spots; (b) models the image directly as background plus hybridization intensity, and estimates the two quantities simultaneously, avoiding the common logical error that estimates of foreground may be less than those of the corresponding background if the two are estimated separately; and (c) uses a probabilistic modeling approach to simultaneously perform segmentation and intensity estimation, and to compute spot quality measures. We describe two approaches to parameter estimation: a fast algorithm, based on the expectation-maximization and the iterated conditional modes algorithms, and a fully Bayesian framework. These approaches produce comparable results, and both appear to offer some advantages over other methods. We use an HIV experiment to compare our approach to two commercial software products: Spot and Arrayvision.

Quantity Competition in a Differentiated Duopoly

NASA Astrophysics Data System (ADS)

Ferreira, Fernanda A.; Ferreira, Flávio; Ferreira, Miguel; Pinto, Alberto A.

In this paper, we consider a Stackelberg duopoly competition with differentiated goods, linear and symmetric demand and with unknown costs. In our model, the two firms play a non-cooperative game with two stages: in a first stage, firm F 1 chooses the quantity, q 1, that is going to produce; in the second stage, firm F 2 observes the quantity q 1 produced by firm F 1 and chooses its own quantity q 2. Firms choose their output levels in order to maximise their profits. We suppose that each firm has two different technologies, and uses one of them following a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We show that there is exactly one perfect Bayesian equilibrium for this game. We analyse the variations of the expected profits with the parameters of the model, namely with the parameters of the probability distributions, and with the parameters of the demand and differentiation.

Estimation of Lithological Classification in Taipei Basin: A Bayesian Maximum Entropy Method

NASA Astrophysics Data System (ADS)

Wu, Meng-Ting; Lin, Yuan-Chien; Yu, Hwa-Lung

2015-04-01

In environmental or other scientific applications, we must have a certain understanding of geological lithological composition. Because of restrictions of real conditions, only limited amount of data can be acquired. To find out the lithological distribution in the study area, many spatial statistical methods used to estimate the lithological composition on unsampled points or grids. This study applied the Bayesian Maximum Entropy (BME method), which is an emerging method of the geological spatiotemporal statistics field. The BME method can identify the spatiotemporal correlation of the data, and combine not only the hard data but the soft data to improve estimation. The data of lithological classification is discrete categorical data. Therefore, this research applied Categorical BME to establish a complete three-dimensional Lithological estimation model. Apply the limited hard data from the cores and the soft data generated from the geological dating data and the virtual wells to estimate the three-dimensional lithological classification in Taipei Basin. Keywords: Categorical Bayesian Maximum Entropy method, Lithological Classification, Hydrogeological Setting

Inference on the Genetic Basis of Eye and Skin Color in an Admixed Population via Bayesian Linear Mixed Models.

PubMed

Lloyd-Jones, Luke R; Robinson, Matthew R; Moser, Gerhard; Zeng, Jian; Beleza, Sandra; Barsh, Gregory S; Tang, Hua; Visscher, Peter M

2017-06-01

Genetic association studies in admixed populations are underrepresented in the genomics literature, with a key concern for researchers being the adequate control of spurious associations due to population structure. Linear mixed models (LMMs) are well suited for genome-wide association studies (GWAS) because they account for both population stratification and cryptic relatedness and achieve increased statistical power by jointly modeling all genotyped markers. Additionally, Bayesian LMMs allow for more flexible assumptions about the underlying distribution of genetic effects, and can concurrently estimate the proportion of phenotypic variance explained by genetic markers. Using three recently published Bayesian LMMs, Bayes R, BSLMM, and BOLT-LMM, we investigate an existing data set on eye ( n = 625) and skin ( n = 684) color from Cape Verde, an island nation off West Africa that is home to individuals with a broad range of phenotypic values for eye and skin color due to the mix of West African and European ancestry. We use simulations to demonstrate the utility of Bayesian LMMs for mapping loci and studying the genetic architecture of quantitative traits in admixed populations. The Bayesian LMMs provide evidence for two new pigmentation loci: one for eye color ( AHRR ) and one for skin color ( DDB1 ). Copyright © 2017 by the Genetics Society of America.

A full-spectral Bayesian reconstruction approach based on the material decomposition model applied in dual-energy computed tomography.

PubMed

Cai, C; Rodet, T; Legoupil, S; Mohammad-Djafari, A

2013-11-01

Dual-energy computed tomography (DECT) makes it possible to get two fractions of basis materials without segmentation. One is the soft-tissue equivalent water fraction and the other is the hard-matter equivalent bone fraction. Practical DECT measurements are usually obtained with polychromatic x-ray beams. Existing reconstruction approaches based on linear forward models without counting the beam polychromaticity fail to estimate the correct decomposition fractions and result in beam-hardening artifacts (BHA). The existing BHA correction approaches either need to refer to calibration measurements or suffer from the noise amplification caused by the negative-log preprocessing and the ill-conditioned water and bone separation problem. To overcome these problems, statistical DECT reconstruction approaches based on nonlinear forward models counting the beam polychromaticity show great potential for giving accurate fraction images. This work proposes a full-spectral Bayesian reconstruction approach which allows the reconstruction of high quality fraction images from ordinary polychromatic measurements. This approach is based on a Gaussian noise model with unknown variance assigned directly to the projections without taking negative-log. Referring to Bayesian inferences, the decomposition fractions and observation variance are estimated by using the joint maximum a posteriori (MAP) estimation method. Subject to an adaptive prior model assigned to the variance, the joint estimation problem is then simplified into a single estimation problem. It transforms the joint MAP estimation problem into a minimization problem with a nonquadratic cost function. To solve it, the use of a monotone conjugate gradient algorithm with suboptimal descent steps is proposed. The performance of the proposed approach is analyzed with both simulated and experimental data. The results show that the proposed Bayesian approach is robust to noise and materials. It is also necessary to have the accurate spectrum information about the source-detector system. When dealing with experimental data, the spectrum can be predicted by a Monte Carlo simulator. For the materials between water and bone, less than 5% separation errors are observed on the estimated decomposition fractions. The proposed approach is a statistical reconstruction approach based on a nonlinear forward model counting the full beam polychromaticity and applied directly to the projections without taking negative-log. Compared to the approaches based on linear forward models and the BHA correction approaches, it has advantages in noise robustness and reconstruction accuracy.

Results of Bayesian methods depend on details of implementation: An example of estimating salmon escapement goals

USGS Publications Warehouse

Adkison, Milo D.; Peterman, R.M.

1996-01-01

Bayesian methods have been proposed to estimate optimal escapement goals, using both knowledge about physical determinants of salmon productivity and stock-recruitment data. The Bayesian approach has several advantages over many traditional methods for estimating stock productivity: it allows integration of information from diverse sources and provides a framework for decision-making that takes into account uncertainty reflected in the data. However, results can be critically dependent on details of implementation of this approach. For instance, unintended and unwarranted confidence about stock-recruitment relationships can arise if the range of relationships examined is too narrow, if too few discrete alternatives are considered, or if data are contradictory. This unfounded confidence can result in a suboptimal choice of a spawning escapement goal.

Bayesian probability estimates are not necessary to make choices satisfying Bayes' rule in elementary situations.

PubMed

Domurat, Artur; Kowalczuk, Olga; Idzikowska, Katarzyna; Borzymowska, Zuzanna; Nowak-Przygodzka, Marta

2015-01-01

This paper has two aims. First, we investigate how often people make choices conforming to Bayes' rule when natural sampling is applied. Second, we show that using Bayes' rule is not necessary to make choices satisfying Bayes' rule. Simpler methods, even fallacious heuristics, might prescribe correct choices reasonably often under specific circumstances. We considered elementary situations with binary sets of hypotheses and data. We adopted an ecological approach and prepared two-stage computer tasks resembling natural sampling. Probabilistic relations were inferred from a set of pictures, followed by a choice which was made to maximize the chance of a preferred outcome. Use of Bayes' rule was deduced indirectly from choices. Study 1 used a stratified sample of N = 60 participants equally distributed with regard to gender and type of education (humanities vs. pure sciences). Choices satisfying Bayes' rule were dominant. To investigate ways of making choices more directly, we replicated Study 1, adding a task with a verbal report. In Study 2 (N = 76) choices conforming to Bayes' rule dominated again. However, the verbal reports revealed use of a new, non-inverse rule, which always renders correct choices, but is easier than Bayes' rule to apply. It does not require inversion of conditions [transforming P(H) and P(D|H) into P(H|D)] when computing chances. Study 3 examined the efficiency of three fallacious heuristics (pre-Bayesian, representativeness, and evidence-only) in producing choices concordant with Bayes' rule. Computer-simulated scenarios revealed that the heuristics produced correct choices reasonably often under specific base rates and likelihood ratios. Summing up we conclude that natural sampling results in most choices conforming to Bayes' rule. However, people tend to replace Bayes' rule with simpler methods, and even use of fallacious heuristics may be satisfactorily efficient.

Bayesian probability estimates are not necessary to make choices satisfying Bayes’ rule in elementary situations

PubMed Central

Domurat, Artur; Kowalczuk, Olga; Idzikowska, Katarzyna; Borzymowska, Zuzanna; Nowak-Przygodzka, Marta

2015-01-01

This paper has two aims. First, we investigate how often people make choices conforming to Bayes’ rule when natural sampling is applied. Second, we show that using Bayes’ rule is not necessary to make choices satisfying Bayes’ rule. Simpler methods, even fallacious heuristics, might prescribe correct choices reasonably often under specific circumstances. We considered elementary situations with binary sets of hypotheses and data. We adopted an ecological approach and prepared two-stage computer tasks resembling natural sampling. Probabilistic relations were inferred from a set of pictures, followed by a choice which was made to maximize the chance of a preferred outcome. Use of Bayes’ rule was deduced indirectly from choices. Study 1 used a stratified sample of N = 60 participants equally distributed with regard to gender and type of education (humanities vs. pure sciences). Choices satisfying Bayes’ rule were dominant. To investigate ways of making choices more directly, we replicated Study 1, adding a task with a verbal report. In Study 2 (N = 76) choices conforming to Bayes’ rule dominated again. However, the verbal reports revealed use of a new, non-inverse rule, which always renders correct choices, but is easier than Bayes’ rule to apply. It does not require inversion of conditions [transforming P(H) and P(D|H) into P(H|D)] when computing chances. Study 3 examined the efficiency of three fallacious heuristics (pre-Bayesian, representativeness, and evidence-only) in producing choices concordant with Bayes’ rule. Computer-simulated scenarios revealed that the heuristics produced correct choices reasonably often under specific base rates and likelihood ratios. Summing up we conclude that natural sampling results in most choices conforming to Bayes’ rule. However, people tend to replace Bayes’ rule with simpler methods, and even use of fallacious heuristics may be satisfactorily efficient. PMID:26347676

Hierarchical Bayesian analysis to incorporate age uncertainty in growth curve analysis and estimates of age from length: Florida manatee (Trichechus manatus) carcasses

USGS Publications Warehouse

Schwarz, L.K.; Runge, M.C.

2009-01-01

Age estimation of individuals is often an integral part of species management research, and a number of ageestimation techniques are commonly employed. Often, the error in these techniques is not quantified or accounted for in other analyses, particularly in growth curve models used to describe physiological responses to environment and human impacts. Also, noninvasive, quick, and inexpensive methods to estimate age are needed. This research aims to provide two Bayesian methods to (i) incorporate age uncertainty into an age-length Schnute growth model and (ii) produce a method from the growth model to estimate age from length. The methods are then employed for Florida manatee (Trichechus manatus) carcasses. After quantifying the uncertainty in the aging technique (counts of ear bone growth layers), we fit age-length data to the Schnute growth model separately by sex and season. Independent prior information about population age structure and the results of the Schnute model are then combined to estimate age from length. Results describing the age-length relationship agree with our understanding of manatee biology. The new methods allow us to estimate age, with quantified uncertainty, for 98% of collected carcasses: 36% from ear bones, 62% from length.

A hierarchical Bayesian approach to adaptive vision testing: A case study with the contrast sensitivity function.

PubMed

Gu, Hairong; Kim, Woojae; Hou, Fang; Lesmes, Luis Andres; Pitt, Mark A; Lu, Zhong-Lin; Myung, Jay I

2016-01-01

Measurement efficiency is of concern when a large number of observations are required to obtain reliable estimates for parametric models of vision. The standard entropy-based Bayesian adaptive testing procedures addressed the issue by selecting the most informative stimulus in sequential experimental trials. Noninformative, diffuse priors were commonly used in those tests. Hierarchical adaptive design optimization (HADO; Kim, Pitt, Lu, Steyvers, & Myung, 2014) further improves the efficiency of the standard Bayesian adaptive testing procedures by constructing an informative prior using data from observers who have already participated in the experiment. The present study represents an empirical validation of HADO in estimating the human contrast sensitivity function. The results show that HADO significantly improves the accuracy and precision of parameter estimates, and therefore requires many fewer observations to obtain reliable inference about contrast sensitivity, compared to the method of quick contrast sensitivity function (Lesmes, Lu, Baek, & Albright, 2010), which uses the standard Bayesian procedure. The improvement with HADO was maintained even when the prior was constructed from heterogeneous populations or a relatively small number of observers. These results of this case study support the conclusion that HADO can be used in Bayesian adaptive testing by replacing noninformative, diffuse priors with statistically justified informative priors without introducing unwanted bias.

Tracking composite material damage evolution using Bayesian filtering and flash thermography data

NASA Astrophysics Data System (ADS)

Gregory, Elizabeth D.; Holland, Steve D.

2016-05-01

We propose a method for tracking the condition of a composite part using Bayesian filtering of ash thermography data over the lifetime of the part. In this demonstration, composite panels were fabricated; impacted to induce subsurface delaminations; and loaded in compression over multiple time steps, causing the delaminations to grow in size. Flash thermography data was collected between each damage event to serve as a time history of the part. The ash thermography indicated some areas of damage but provided little additional information as to the exact nature or depth of the damage. Computed tomography (CT) data was also collected after each damage event and provided a high resolution volume model of damage that acted as truth. After each cycle, the condition estimate, from the ash thermography data and the Bayesian filter, was compared to 'ground truth'. The Bayesian process builds on the lifetime history of ash thermography scans and can give better estimates of material condition as compared to the most recent scan alone, which is common practice in the aerospace industry. Bayesian inference provides probabilistic estimates of damage condition that are updated as each new set of data becomes available. The method was tested on simulated data and then on an experimental data set.

Approximate Bayesian evaluations of measurement uncertainty

NASA Astrophysics Data System (ADS)

Possolo, Antonio; Bodnar, Olha

2018-04-01

The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

A hierarchical Bayesian approach to adaptive vision testing: A case study with the contrast sensitivity function

PubMed Central

Gu, Hairong; Kim, Woojae; Hou, Fang; Lesmes, Luis Andres; Pitt, Mark A.; Lu, Zhong-Lin; Myung, Jay I.

2016-01-01

Measurement efficiency is of concern when a large number of observations are required to obtain reliable estimates for parametric models of vision. The standard entropy-based Bayesian adaptive testing procedures addressed the issue by selecting the most informative stimulus in sequential experimental trials. Noninformative, diffuse priors were commonly used in those tests. Hierarchical adaptive design optimization (HADO; Kim, Pitt, Lu, Steyvers, & Myung, 2014) further improves the efficiency of the standard Bayesian adaptive testing procedures by constructing an informative prior using data from observers who have already participated in the experiment. The present study represents an empirical validation of HADO in estimating the human contrast sensitivity function. The results show that HADO significantly improves the accuracy and precision of parameter estimates, and therefore requires many fewer observations to obtain reliable inference about contrast sensitivity, compared to the method of quick contrast sensitivity function (Lesmes, Lu, Baek, & Albright, 2010), which uses the standard Bayesian procedure. The improvement with HADO was maintained even when the prior was constructed from heterogeneous populations or a relatively small number of observers. These results of this case study support the conclusion that HADO can be used in Bayesian adaptive testing by replacing noninformative, diffuse priors with statistically justified informative priors without introducing unwanted bias. PMID:27105061

Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach

NASA Technical Reports Server (NTRS)

Warner, James E.; Hochhalter, Jacob D.

2016-01-01

This work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches.

A hierarchical Bayesian GEV model for improving local and regional flood quantile estimates

NASA Astrophysics Data System (ADS)

Lima, Carlos H. R.; Lall, Upmanu; Troy, Tara; Devineni, Naresh

2016-10-01

We estimate local and regional Generalized Extreme Value (GEV) distribution parameters for flood frequency analysis in a multilevel, hierarchical Bayesian framework, to explicitly model and reduce uncertainties. As prior information for the model, we assume that the GEV location and scale parameters for each site come from independent log-normal distributions, whose mean parameter scales with the drainage area. From empirical and theoretical arguments, the shape parameter for each site is shrunk towards a common mean. Non-informative prior distributions are assumed for the hyperparameters and the MCMC method is used to sample from the joint posterior distribution. The model is tested using annual maximum series from 20 streamflow gauges located in an 83,000 km2 flood prone basin in Southeast Brazil. The results show a significant reduction of uncertainty estimates of flood quantile estimates over the traditional GEV model, particularly for sites with shorter records. For return periods within the range of the data (around 50 years), the Bayesian credible intervals for the flood quantiles tend to be narrower than the classical confidence limits based on the delta method. As the return period increases beyond the range of the data, the confidence limits from the delta method become unreliable and the Bayesian credible intervals provide a way to estimate satisfactory confidence bands for the flood quantiles considering parameter uncertainties and regional information. In order to evaluate the applicability of the proposed hierarchical Bayesian model for regional flood frequency analysis, we estimate flood quantiles for three randomly chosen out-of-sample sites and compare with classical estimates using the index flood method. The posterior distributions of the scaling law coefficients are used to define the predictive distributions of the GEV location and scale parameters for the out-of-sample sites given only their drainage areas and the posterior distribution of the average shape parameter is taken as the regional predictive distribution for this parameter. While the index flood method does not provide a straightforward way to consider the uncertainties in the index flood and in the regional parameters, the results obtained here show that the proposed Bayesian method is able to produce adequate credible intervals for flood quantiles that are in accordance with empirical estimates.

HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python.

PubMed

Wiecki, Thomas V; Sofer, Imri; Frank, Michael J

2013-01-01

The diffusion model is a commonly used tool to infer latent psychological processes underlying decision-making, and to link them to neural mechanisms based on response times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of response time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model), which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject/condition than non-hierarchical methods, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g., fMRI) influence decision-making parameters. This paper will first describe the theoretical background of the drift diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the χ(2)-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs/

Point estimation following two-stage adaptive threshold enrichment clinical trials.

PubMed

Kimani, Peter K; Todd, Susan; Renfro, Lindsay A; Stallard, Nigel

2018-05-31

Recently, several study designs incorporating treatment effect assessment in biomarker-based subpopulations have been proposed. Most statistical methodologies for such designs focus on the control of type I error rate and power. In this paper, we have developed point estimators for clinical trials that use the two-stage adaptive enrichment threshold design. The design consists of two stages, where in stage 1, patients are recruited in the full population. Stage 1 outcome data are then used to perform interim analysis to decide whether the trial continues to stage 2 with the full population or a subpopulation. The subpopulation is defined based on one of the candidate threshold values of a numerical predictive biomarker. To estimate treatment effect in the selected subpopulation, we have derived unbiased estimators, shrinkage estimators, and estimators that estimate bias and subtract it from the naive estimate. We have recommended one of the unbiased estimators. However, since none of the estimators dominated in all simulation scenarios based on both bias and mean squared error, an alternative strategy would be to use a hybrid estimator where the estimator used depends on the subpopulation selected. This would require a simulation study of plausible scenarios before the trial. © 2018 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Estimation from incomplete multinomial data. Ph.D. Thesis - Harvard Univ.

NASA Technical Reports Server (NTRS)

Credeur, K. R.

1978-01-01

The vector of multinomial cell probabilities was estimated from incomplete data, incomplete in that it contains partially classified observations. Each such partially classified observation was observed to fall in one of two or more selected categories but was not classified further into a single category. The data were assumed to be incomplete at random. The estimation criterion was minimization of risk for quadratic loss. The estimators were the classical maximum likelihood estimate, the Bayesian posterior mode, and the posterior mean. An approximation was developed for the posterior mean. The Dirichlet, the conjugate prior for the multinomial distribution, was assumed for the prior distribution.

A Massively Parallel Bayesian Approach to Planetary Protection Trajectory Analysis and Design

NASA Technical Reports Server (NTRS)

Wallace, Mark S.

2015-01-01

The NASA Planetary Protection Office has levied a requirement that the upper stage of future planetary launches have a less than 10(exp -4) chance of impacting Mars within 50 years after launch. A brute-force approach requires a decade of computer time to demonstrate compliance. By using a Bayesian approach and taking advantage of the demonstrated reliability of the upper stage, the required number of fifty-year propagations can be massively reduced. By spreading the remaining embarrassingly parallel Monte Carlo simulations across multiple computers, compliance can be demonstrated in a reasonable time frame. The method used is described here.

Logistic random effects regression models: a comparison of statistical packages for binary and ordinal outcomes

PubMed Central

2011-01-01

Background Logistic random effects models are a popular tool to analyze multilevel also called hierarchical data with a binary or ordinal outcome. Here, we aim to compare different statistical software implementations of these models. Methods We used individual patient data from 8509 patients in 231 centers with moderate and severe Traumatic Brain Injury (TBI) enrolled in eight Randomized Controlled Trials (RCTs) and three observational studies. We fitted logistic random effects regression models with the 5-point Glasgow Outcome Scale (GOS) as outcome, both dichotomized as well as ordinal, with center and/or trial as random effects, and as covariates age, motor score, pupil reactivity or trial. We then compared the implementations of frequentist and Bayesian methods to estimate the fixed and random effects. Frequentist approaches included R (lme4), Stata (GLLAMM), SAS (GLIMMIX and NLMIXED), MLwiN ([R]IGLS) and MIXOR, Bayesian approaches included WinBUGS, MLwiN (MCMC), R package MCMCglmm and SAS experimental procedure MCMC. Three data sets (the full data set and two sub-datasets) were analysed using basically two logistic random effects models with either one random effect for the center or two random effects for center and trial. For the ordinal outcome in the full data set also a proportional odds model with a random center effect was fitted. Results The packages gave similar parameter estimates for both the fixed and random effects and for the binary (and ordinal) models for the main study and when based on a relatively large number of level-1 (patient level) data compared to the number of level-2 (hospital level) data. However, when based on relatively sparse data set, i.e. when the numbers of level-1 and level-2 data units were about the same, the frequentist and Bayesian approaches showed somewhat different results. The software implementations differ considerably in flexibility, computation time, and usability. There are also differences in the availability of additional tools for model evaluation, such as diagnostic plots. The experimental SAS (version 9.2) procedure MCMC appeared to be inefficient. Conclusions On relatively large data sets, the different software implementations of logistic random effects regression models produced similar results. Thus, for a large data set there seems to be no explicit preference (of course if there is no preference from a philosophical point of view) for either a frequentist or Bayesian approach (if based on vague priors). The choice for a particular implementation may largely depend on the desired flexibility, and the usability of the package. For small data sets the random effects variances are difficult to estimate. In the frequentist approaches the MLE of this variance was often estimated zero with a standard error that is either zero or could not be determined, while for Bayesian methods the estimates could depend on the chosen "non-informative" prior of the variance parameter. The starting value for the variance parameter may be also critical for the convergence of the Markov chain. PMID:21605357

Application of Bayesian Approach in Cancer Clinical Trial

PubMed Central

Bhattacharjee, Atanu

2014-01-01

The application of Bayesian approach in clinical trials becomes more useful over classical method. It is beneficial from design to analysis phase. The straight forward statement is possible to obtain through Bayesian about the drug treatment effect. Complex computational problems are simple to handle with Bayesian techniques. The technique is only feasible to performing presence of prior information of the data. The inference is possible to establish through posterior estimates. However, some limitations are present in this method. The objective of this work was to explore the several merits and demerits of Bayesian approach in cancer research. The review of the technique will be helpful for the clinical researcher involved in the oncology to explore the limitation and power of Bayesian techniques. PMID:29147387

Bayesian alternative to the ISO-GUM's use of the Welch Satterthwaite formula

NASA Astrophysics Data System (ADS)

Kacker, Raghu N.

2006-02-01

In certain disciplines, uncertainty is traditionally expressed as an interval about an estimate for the value of the measurand. Development of such uncertainty intervals with a stated coverage probability based on the International Organization for Standardization (ISO) Guide to the Expression of Uncertainty in Measurement (GUM) requires a description of the probability distribution for the value of the measurand. The ISO-GUM propagates the estimates and their associated standard uncertainties for various input quantities through a linear approximation of the measurement equation to determine an estimate and its associated standard uncertainty for the value of the measurand. This procedure does not yield a probability distribution for the value of the measurand. The ISO-GUM suggests that under certain conditions motivated by the central limit theorem the distribution for the value of the measurand may be approximated by a scaled-and-shifted t-distribution with effective degrees of freedom obtained from the Welch-Satterthwaite (W-S) formula. The approximate t-distribution may then be used to develop an uncertainty interval with a stated coverage probability for the value of the measurand. We propose an approximate normal distribution based on a Bayesian uncertainty as an alternative to the t-distribution based on the W-S formula. A benefit of the approximate normal distribution based on a Bayesian uncertainty is that it greatly simplifies the expression of uncertainty by eliminating altogether the need for calculating effective degrees of freedom from the W-S formula. In the special case where the measurand is the difference between two means, each evaluated from statistical analyses of independent normally distributed measurements with unknown and possibly unequal variances, the probability distribution for the value of the measurand is known to be a Behrens-Fisher distribution. We compare the performance of the approximate normal distribution based on a Bayesian uncertainty and the approximate t-distribution based on the W-S formula with respect to the Behrens-Fisher distribution. The approximate normal distribution is simpler and better in this case. A thorough investigation of the relative performance of the two approximate distributions would require comparison for a range of measurement equations by numerical methods.

Improved prediction of tacrolimus concentrations early after kidney transplantation using theory-based pharmacokinetic modelling.

PubMed

Størset, Elisabet; Holford, Nick; Hennig, Stefanie; Bergmann, Troels K; Bergan, Stein; Bremer, Sara; Åsberg, Anders; Midtvedt, Karsten; Staatz, Christine E

2014-09-01

The aim was to develop a theory-based population pharmacokinetic model of tacrolimus in adult kidney transplant recipients and to externally evaluate this model and two previous empirical models. Data were obtained from 242 patients with 3100 tacrolimus whole blood concentrations. External evaluation was performed by examining model predictive performance using Bayesian forecasting. Pharmacokinetic disposition parameters were estimated based on tacrolimus plasma concentrations, predicted from whole blood concentrations, haematocrit and literature values for tacrolimus binding to red blood cells. Disposition parameters were allometrically scaled to fat free mass. Tacrolimus whole blood clearance/bioavailability standardized to haematocrit of 45% and fat free mass of 60 kg was estimated to be 16.1 l h−1 [95% CI 12.6, 18.0 l h−1]. Tacrolimus clearance was 30% higher (95% CI 13, 46%) and bioavailability 18% lower (95% CI 2, 29%) in CYP3A5 expressers compared with non-expressers. An Emax model described decreasing tacrolimus bioavailability with increasing prednisolone dose. The theory-based model was superior to the empirical models during external evaluation displaying a median prediction error of −1.2% (95% CI −3.0, 0.1%). Based on simulation, Bayesian forecasting led to 65% (95% CI 62, 68%) of patients achieving a tacrolimus average steady-state concentration within a suggested acceptable range. A theory-based population pharmacokinetic model was superior to two empirical models for prediction of tacrolimus concentrations and seemed suitable for Bayesian prediction of tacrolimus doses early after kidney transplantation.