The Reliability and Stability of an Inferred Phylogenetic Tree from Empirical Data.

PubMed

Katsura, Yukako; Stanley, Craig E; Kumar, Sudhir; Nei, Masatoshi

2017-03-01

The reliability of a phylogenetic tree obtained from empirical data is usually measured by the bootstrap probability (Pb) of interior branches of the tree. If the bootstrap probability is high for most branches, the tree is considered to be reliable. If some interior branches show relatively low bootstrap probabilities, we are not sure that the inferred tree is really reliable. Here, we propose another quantity measuring the reliability of the tree called the stability of a subtree. This quantity refers to the probability of obtaining a subtree (Ps) of an inferred tree obtained. We then show that if the tree is to be reliable, both Pb and Ps must be high. We also show that Ps is given by a bootstrap probability of the subtree with the closest outgroup sequence, and computer program RESTA for computing the Pb and Ps values will be presented. © The Author 2017. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.

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.

The impact of using informative priors in a Bayesian cost-effectiveness analysis: an application of endovascular versus open surgical repair for abdominal aortic aneurysms in high-risk patients.

PubMed

McCarron, C Elizabeth; Pullenayegum, Eleanor M; Thabane, Lehana; Goeree, Ron; Tarride, Jean-Eric

2013-04-01

Bayesian methods have been proposed as a way of synthesizing all available evidence to inform decision making. However, few practical applications of the use of Bayesian methods for combining patient-level data (i.e., trial) with additional evidence (e.g., literature) exist in the cost-effectiveness literature. The objective of this study was to compare a Bayesian cost-effectiveness analysis using informative priors to a standard non-Bayesian nonparametric method to assess the impact of incorporating additional information into a cost-effectiveness analysis. Patient-level data from a previously published nonrandomized study were analyzed using traditional nonparametric bootstrap techniques and bivariate normal Bayesian models with vague and informative priors. Two different types of informative priors were considered to reflect different valuations of the additional evidence relative to the patient-level data (i.e., "face value" and "skeptical"). The impact of using different distributions and valuations was assessed in a sensitivity analysis. Models were compared in terms of incremental net monetary benefit (INMB) and cost-effectiveness acceptability frontiers (CEAFs). The bootstrapping and Bayesian analyses using vague priors provided similar results. The most pronounced impact of incorporating the informative priors was the increase in estimated life years in the control arm relative to what was observed in the patient-level data alone. Consequently, the incremental difference in life years originally observed in the patient-level data was reduced, and the INMB and CEAF changed accordingly. The results of this study demonstrate the potential impact and importance of incorporating additional information into an analysis of patient-level data, suggesting this could alter decisions as to whether a treatment should be adopted and whether more information should be acquired.

A nonparametric method to generate synthetic populations to adjust for complex sampling design features.

PubMed

Dong, Qi; Elliott, Michael R; Raghunathan, Trivellore E

2014-06-01

Outside of the survey sampling literature, samples are often assumed to be generated by a simple random sampling process that produces independent and identically distributed (IID) samples. Many statistical methods are developed largely in this IID world. Application of these methods to data from complex sample surveys without making allowance for the survey design features can lead to erroneous inferences. Hence, much time and effort have been devoted to develop the statistical methods to analyze complex survey data and account for the sample design. This issue is particularly important when generating synthetic populations using finite population Bayesian inference, as is often done in missing data or disclosure risk settings, or when combining data from multiple surveys. By extending previous work in finite population Bayesian bootstrap literature, we propose a method to generate synthetic populations from a posterior predictive distribution in a fashion inverts the complex sampling design features and generates simple random samples from a superpopulation point of view, making adjustment on the complex data so that they can be analyzed as simple random samples. We consider a simulation study with a stratified, clustered unequal-probability of selection sample design, and use the proposed nonparametric method to generate synthetic populations for the 2006 National Health Interview Survey (NHIS), and the Medical Expenditure Panel Survey (MEPS), which are stratified, clustered unequal-probability of selection sample designs.

A nonparametric method to generate synthetic populations to adjust for complex sampling design features

PubMed Central

Dong, Qi; Elliott, Michael R.; Raghunathan, Trivellore E.

2017-01-01

Outside of the survey sampling literature, samples are often assumed to be generated by a simple random sampling process that produces independent and identically distributed (IID) samples. Many statistical methods are developed largely in this IID world. Application of these methods to data from complex sample surveys without making allowance for the survey design features can lead to erroneous inferences. Hence, much time and effort have been devoted to develop the statistical methods to analyze complex survey data and account for the sample design. This issue is particularly important when generating synthetic populations using finite population Bayesian inference, as is often done in missing data or disclosure risk settings, or when combining data from multiple surveys. By extending previous work in finite population Bayesian bootstrap literature, we propose a method to generate synthetic populations from a posterior predictive distribution in a fashion inverts the complex sampling design features and generates simple random samples from a superpopulation point of view, making adjustment on the complex data so that they can be analyzed as simple random samples. We consider a simulation study with a stratified, clustered unequal-probability of selection sample design, and use the proposed nonparametric method to generate synthetic populations for the 2006 National Health Interview Survey (NHIS), and the Medical Expenditure Panel Survey (MEPS), which are stratified, clustered unequal-probability of selection sample designs. PMID:29200608

Small sample mediation testing: misplaced confidence in bootstrapped confidence intervals.

PubMed

Koopman, Joel; Howe, Michael; Hollenbeck, John R; Sin, Hock-Peng

2015-01-01

Bootstrapping is an analytical tool commonly used in psychology to test the statistical significance of the indirect effect in mediation models. Bootstrapping proponents have particularly advocated for its use for samples of 20-80 cases. This advocacy has been heeded, especially in the Journal of Applied Psychology, as researchers are increasingly utilizing bootstrapping to test mediation with samples in this range. We discuss reasons to be concerned with this escalation, and in a simulation study focused specifically on this range of sample sizes, we demonstrate not only that bootstrapping has insufficient statistical power to provide a rigorous hypothesis test in most conditions but also that bootstrapping has a tendency to exhibit an inflated Type I error rate. We then extend our simulations to investigate an alternative empirical resampling method as well as a Bayesian approach and demonstrate that they exhibit comparable statistical power to bootstrapping in small samples without the associated inflated Type I error. Implications for researchers testing mediation hypotheses in small samples are presented. For researchers wishing to use these methods in their own research, we have provided R syntax in the online supplemental materials. (c) 2015 APA, all rights reserved.

Soft sensor modeling based on variable partition ensemble method for nonlinear batch processes

NASA Astrophysics Data System (ADS)

Wang, Li; Chen, Xiangguang; Yang, Kai; Jin, Huaiping

2017-01-01

Batch processes are always characterized by nonlinear and system uncertain properties, therefore, the conventional single model may be ill-suited. A local learning strategy soft sensor based on variable partition ensemble method is developed for the quality prediction of nonlinear and non-Gaussian batch processes. A set of input variable sets are obtained by bootstrapping and PMI criterion. Then, multiple local GPR models are developed based on each local input variable set. When a new test data is coming, the posterior probability of each best performance local model is estimated based on Bayesian inference and used to combine these local GPR models to get the final prediction result. The proposed soft sensor is demonstrated by applying to an industrial fed-batch chlortetracycline fermentation process.

On combination of strict Bayesian principles with model reduction technique or how stochastic model calibration can become feasible for large-scale applications

NASA Astrophysics Data System (ADS)

Oladyshkin, S.; Schroeder, P.; Class, H.; Nowak, W.

2013-12-01

Predicting underground carbon dioxide (CO2) storage represents a challenging problem in a complex dynamic system. Due to lacking information about reservoir parameters, quantification of uncertainties may become the dominant question in risk assessment. Calibration on past observed data from pilot-scale test injection can improve the predictive power of the involved geological, flow, and transport models. The current work performs history matching to pressure time series from a pilot storage site operated in Europe, maintained during an injection period. Simulation of compressible two-phase flow and transport (CO2/brine) in the considered site is computationally very demanding, requiring about 12 days of CPU time for an individual model run. For that reason, brute-force approaches for calibration are not feasible. In the current work, we explore an advanced framework for history matching based on the arbitrary polynomial chaos expansion (aPC) and strict Bayesian principles. The aPC [1] offers a drastic but accurate stochastic model reduction. Unlike many previous chaos expansions, it can handle arbitrary probability distribution shapes of uncertain parameters, and can therefore handle directly the statistical information appearing during the matching procedure. We capture the dependence of model output on these multipliers with the expansion-based reduced model. In our study we keep the spatial heterogeneity suggested by geophysical methods, but consider uncertainty in the magnitude of permeability trough zone-wise permeability multipliers. Next combined the aPC with Bootstrap filtering (a brute-force but fully accurate Bayesian updating mechanism) in order to perform the matching. In comparison to (Ensemble) Kalman Filters, our method accounts for higher-order statistical moments and for the non-linearity of both the forward model and the inversion, and thus allows a rigorous quantification of calibrated model uncertainty. The usually high computational costs of accurate filtering become very feasible for our suggested aPC-based calibration framework. However, the power of aPC-based Bayesian updating strongly depends on the accuracy of prior information. In the current study, the prior assumptions on the model parameters were not satisfactory and strongly underestimate the reservoir pressure. Thus, the aPC-based response surface used in Bootstrap filtering is fitted to a distant and poorly chosen region within the parameter space. Thanks to the iterative procedure suggested in [2] we overcome this drawback with small computational costs. The iteration successively improves the accuracy of the expansion around the current estimation of the posterior distribution. The final result is a calibrated model of the site that can be used for further studies, with an excellent match to the data. References [1] Oladyshkin S. and Nowak W. Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion. Reliability Engineering and System Safety, 106:179-190, 2012. [2] Oladyshkin S., Class H., Nowak W. Bayesian updating via Bootstrap filtering combined with data-driven polynomial chaos expansions: methodology and application to history matching for carbon dioxide storage in geological formations. Computational Geosciences, 17 (4), 671-687, 2013.

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.

Bootstrap imputation with a disease probability model minimized bias from misclassification due to administrative database codes.

PubMed

van Walraven, Carl

2017-04-01

Diagnostic codes used in administrative databases cause bias due to misclassification of patient disease status. It is unclear which methods minimize this bias. Serum creatinine measures were used to determine severe renal failure status in 50,074 hospitalized patients. The true prevalence of severe renal failure and its association with covariates were measured. These were compared to results for which renal failure status was determined using surrogate measures including the following: (1) diagnostic codes; (2) categorization of probability estimates of renal failure determined from a previously validated model; or (3) bootstrap methods imputation of disease status using model-derived probability estimates. Bias in estimates of severe renal failure prevalence and its association with covariates were minimal when bootstrap methods were used to impute renal failure status from model-based probability estimates. In contrast, biases were extensive when renal failure status was determined using codes or methods in which model-based condition probability was categorized. Bias due to misclassification from inaccurate diagnostic codes can be minimized using bootstrap methods to impute condition status using multivariable model-derived probability estimates. Copyright © 2017 Elsevier Inc. All rights reserved.

Hepatitis disease detection using Bayesian theory

NASA Astrophysics Data System (ADS)

Maseleno, Andino; Hidayati, Rohmah Zahroh

2017-02-01

This paper presents hepatitis disease diagnosis using a Bayesian theory for better understanding of the theory. In this research, we used a Bayesian theory for detecting hepatitis disease and displaying the result of diagnosis process. Bayesian algorithm theory is rediscovered and perfected by Laplace, the basic idea is using of the known prior probability and conditional probability density parameter, based on Bayes theorem to calculate the corresponding posterior probability, and then obtained the posterior probability to infer and make decisions. Bayesian methods combine existing knowledge, prior probabilities, with additional knowledge derived from new data, the likelihood function. The initial symptoms of hepatitis which include malaise, fever and headache. The probability of hepatitis given the presence of malaise, fever, and headache. The result revealed that a Bayesian theory has successfully identified the existence of hepatitis disease.

Defining Probability in Sex Offender Risk Assessment.

PubMed

Elwood, Richard W

2016-12-01

There is ongoing debate and confusion over using actuarial scales to predict individuals' risk of sexual recidivism. Much of the debate comes from not distinguishing Frequentist from Bayesian definitions of probability. Much of the confusion comes from applying Frequentist probability to individuals' risk. By definition, only Bayesian probability can be applied to the single case. The Bayesian concept of probability resolves most of the confusion and much of the debate in sex offender risk assessment. Although Bayesian probability is well accepted in risk assessment generally, it has not been widely used to assess the risk of sex offenders. I review the two concepts of probability and show how the Bayesian view alone provides a coherent scheme to conceptualize individuals' risk of sexual recidivism.

Bootstrap study of genome-enabled prediction reliabilities using haplotype blocks across Nordic Red cattle breeds.

PubMed

Cuyabano, B C D; Su, G; Rosa, G J M; Lund, M S; Gianola, D

2015-10-01

This study compared the accuracy of genome-enabled prediction models using individual single nucleotide polymorphisms (SNP) or haplotype blocks as covariates when using either a single breed or a combined population of Nordic Red cattle. The main objective was to compare predictions of breeding values of complex traits using a combined training population with haplotype blocks, with predictions using a single breed as training population and individual SNP as predictors. To compare the prediction reliabilities, bootstrap samples were taken from the test data set. With the bootstrapped samples of prediction reliabilities, we built and graphed confidence ellipses to allow comparisons. Finally, measures of statistical distances were used to calculate the gain in predictive ability. Our analyses are innovative in the context of assessment of predictive models, allowing a better understanding of prediction reliabilities and providing a statistical basis to effectively calibrate whether one prediction scenario is indeed more accurate than another. An ANOVA indicated that use of haplotype blocks produced significant gains mainly when Bayesian mixture models were used but not when Bayesian BLUP was fitted to the data. Furthermore, when haplotype blocks were used to train prediction models in a combined Nordic Red cattle population, we obtained up to a statistically significant 5.5% average gain in prediction accuracy, over predictions using individual SNP and training the model with a single breed. Copyright © 2015 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

The utility of Bayesian predictive probabilities for interim monitoring of clinical trials

PubMed Central

Connor, Jason T.; Ayers, Gregory D; Alvarez, JoAnn

2014-01-01

Background Bayesian predictive probabilities can be used for interim monitoring of clinical trials to estimate the probability of observing a statistically significant treatment effect if the trial were to continue to its predefined maximum sample size. Purpose We explore settings in which Bayesian predictive probabilities are advantageous for interim monitoring compared to Bayesian posterior probabilities, p-values, conditional power, or group sequential methods. Results For interim analyses that address prediction hypotheses, such as futility monitoring and efficacy monitoring with lagged outcomes, only predictive probabilities properly account for the amount of data remaining to be observed in a clinical trial and have the flexibility to incorporate additional information via auxiliary variables. Limitations Computational burdens limit the feasibility of predictive probabilities in many clinical trial settings. The specification of prior distributions brings additional challenges for regulatory approval. Conclusions The use of Bayesian predictive probabilities enables the choice of logical interim stopping rules that closely align with the clinical decision making process. PMID:24872363

A Multivariate and Probabilistic Assessment of Drought in the Pacific Northwest under Observed and Future Climate.

NASA Astrophysics Data System (ADS)

Mortuza, M. R.; Demissie, Y. K.

2015-12-01

In lieu with the recent and anticipated more server and frequently droughts incidences in Yakima River Basin (YRB), a reliable and comprehensive drought assessment is deemed necessary to avoid major crop production loss and better manage the water right issues in the region during low precipitation and/or snow accumulation years. In this study, we have conducted frequency analysis of hydrological droughts and quantified associated uncertainty in the YRB under both historical and changing climate. Streamflow drought index (SDI) was employed to identify mutually correlated drought characteristics (e.g., severity, duration and peak). The historical and future characteristics of drought were estimated by applying tri-variate copulas probability distribution, which effectively describe the joint distribution and dependence of drought severity, duration, and peak. The associated prediction uncertainty, related to parameters of the joint probability and climate projections, were evaluated using the Bayesian approach with bootstrap resampling. For the climate change scenarios, two future representative pathways (RCP4.5 and RCP8.5) from University of Idaho's Multivariate Adaptive Constructed Analogs (MACA) database were considered. The results from the study are expected to provide useful information towards drought risk management in YRB under anticipated climate changes.

Probabilistic Inference: Task Dependency and Individual Differences of Probability Weighting Revealed by Hierarchical Bayesian Modeling

PubMed Central

Boos, Moritz; Seer, Caroline; Lange, Florian; Kopp, Bruno

2016-01-01

Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modeling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities) by two (likelihoods) design. Five computational models of cognitive processes were compared with the observed behavior. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted) S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model's success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modeling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modeling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision. PMID:27303323

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.

A Bayesian pick-the-winner design in a randomized phase II clinical trial.

PubMed

Chen, Dung-Tsa; Huang, Po-Yu; Lin, Hui-Yi; Chiappori, Alberto A; Gabrilovich, Dmitry I; Haura, Eric B; Antonia, Scott J; Gray, Jhanelle E

2017-10-24

Many phase II clinical trials evaluate unique experimental drugs/combinations through multi-arm design to expedite the screening process (early termination of ineffective drugs) and to identify the most effective drug (pick the winner) to warrant a phase III trial. Various statistical approaches have been developed for the pick-the-winner design but have been criticized for lack of objective comparison among the drug agents. We developed a Bayesian pick-the-winner design by integrating a Bayesian posterior probability with Simon two-stage design in a randomized two-arm clinical trial. The Bayesian posterior probability, as the rule to pick the winner, is defined as probability of the response rate in one arm higher than in the other arm. The posterior probability aims to determine the winner when both arms pass the second stage of the Simon two-stage design. When both arms are competitive (i.e., both passing the second stage), the Bayesian posterior probability performs better to correctly identify the winner compared with the Fisher exact test in the simulation study. In comparison to a standard two-arm randomized design, the Bayesian pick-the-winner design has a higher power to determine a clear winner. In application to two studies, the approach is able to perform statistical comparison of two treatment arms and provides a winner probability (Bayesian posterior probability) to statistically justify the winning arm. We developed an integrated design that utilizes Bayesian posterior probability, Simon two-stage design, and randomization into a unique setting. It gives objective comparisons between the arms to determine the winner.

Application of the Bootstrap Statistical Method in Deriving Vibroacoustic Specifications

NASA Technical Reports Server (NTRS)

Hughes, William O.; Paez, Thomas L.

2006-01-01

This paper discusses the Bootstrap Method for specification of vibroacoustic test specifications. Vibroacoustic test specifications are necessary to properly accept or qualify a spacecraft and its components for the expected acoustic, random vibration and shock environments seen on an expendable launch vehicle. Traditionally, NASA and the U.S. Air Force have employed methods of Normal Tolerance Limits to derive these test levels based upon the amount of data available, and the probability and confidence levels desired. The Normal Tolerance Limit method contains inherent assumptions about the distribution of the data. The Bootstrap is a distribution-free statistical subsampling method which uses the measured data themselves to establish estimates of statistical measures of random sources. This is achieved through the computation of large numbers of Bootstrap replicates of a data measure of interest and the use of these replicates to derive test levels consistent with the probability and confidence desired. The comparison of the results of these two methods is illustrated via an example utilizing actual spacecraft vibroacoustic data.

Uncertainty Estimates of Psychoacoustic Thresholds Obtained from Group Tests

NASA Technical Reports Server (NTRS)

Rathsam, Jonathan; Christian, Andrew

2016-01-01

Adaptive psychoacoustic test methods, in which the next signal level depends on the response to the previous signal, are the most efficient for determining psychoacoustic thresholds of individual subjects. In many tests conducted in the NASA psychoacoustic labs, the goal is to determine thresholds representative of the general population. To do this economically, non-adaptive testing methods are used in which three or four subjects are tested at the same time with predetermined signal levels. This approach requires us to identify techniques for assessing the uncertainty in resulting group-average psychoacoustic thresholds. In this presentation we examine the Delta Method of frequentist statistics, the Generalized Linear Model (GLM), the Nonparametric Bootstrap, a frequentist method, and Markov Chain Monte Carlo Posterior Estimation and a Bayesian approach. Each technique is exercised on a manufactured, theoretical dataset and then on datasets from two psychoacoustics facilities at NASA. The Delta Method is the simplest to implement and accurate for the cases studied. The GLM is found to be the least robust, and the Bootstrap takes the longest to calculate. The Bayesian Posterior Estimate is the most versatile technique examined because it allows the inclusion of prior information.

Comparison of Bootstrapping and Markov Chain Monte Carlo for Copula Analysis of Hydrological Droughts

NASA Astrophysics Data System (ADS)

Yang, P.; Ng, T. L.; Yang, W.

2015-12-01

Effective water resources management depends on the reliable estimation of the uncertainty of drought events. Confidence intervals (CIs) are commonly applied to quantify this uncertainty. A CI seeks to be at the minimal length necessary to cover the true value of the estimated variable with the desired probability. In drought analysis where two or more variables (e.g., duration and severity) are often used to describe a drought, copulas have been found suitable for representing the joint probability behavior of these variables. However, the comprehensive assessment of the parameter uncertainties of copulas of droughts has been largely ignored, and the few studies that have recognized this issue have not explicitly compared the various methods to produce the best CIs. Thus, the objective of this study to compare the CIs generated using two widely applied uncertainty estimation methods, bootstrapping and Markov Chain Monte Carlo (MCMC). To achieve this objective, (1) the marginal distributions lognormal, Gamma, and Generalized Extreme Value, and the copula functions Clayton, Frank, and Plackett are selected to construct joint probability functions of two drought related variables. (2) The resulting joint functions are then fitted to 200 sets of simulated realizations of drought events with known distribution and extreme parameters and (3) from there, using bootstrapping and MCMC, CIs of the parameters are generated and compared. The effect of an informative prior on the CIs generated by MCMC is also evaluated. CIs are produced for different sample sizes (50, 100, and 200) of the simulated drought events for fitting the joint probability functions. Preliminary results assuming lognormal marginal distributions and the Clayton copula function suggest that for cases with small or medium sample sizes (~50-100), MCMC to be superior method if an informative prior exists. Where an informative prior is unavailable, for small sample sizes (~50), both bootstrapping and MCMC yield the same level of performance, and for medium sample sizes (~100), bootstrapping is better. For cases with a large sample size (~200), there is little difference between the CIs generated using bootstrapping and MCMC regardless of whether or not an informative prior exists.

Bayesian assessment of the expected data impact on prediction confidence in optimal sampling design

NASA Astrophysics Data System (ADS)

Leube, P. C.; Geiges, A.; Nowak, W.

2012-02-01

Incorporating hydro(geo)logical data, such as head and tracer data, into stochastic models of (subsurface) flow and transport helps to reduce prediction uncertainty. Because of financial limitations for investigation campaigns, information needs toward modeling or prediction goals should be satisfied efficiently and rationally. Optimal design techniques find the best one among a set of investigation strategies. They optimize the expected impact of data on prediction confidence or related objectives prior to data collection. We introduce a new optimal design method, called PreDIA(gnosis) (Preposterior Data Impact Assessor). PreDIA derives the relevant probability distributions and measures of data utility within a fully Bayesian, generalized, flexible, and accurate framework. It extends the bootstrap filter (BF) and related frameworks to optimal design by marginalizing utility measures over the yet unknown data values. PreDIA is a strictly formal information-processing scheme free of linearizations. It works with arbitrary simulation tools, provides full flexibility concerning measurement types (linear, nonlinear, direct, indirect), allows for any desired task-driven formulations, and can account for various sources of uncertainty (e.g., heterogeneity, geostatistical assumptions, boundary conditions, measurement values, model structure uncertainty, a large class of model errors) via Bayesian geostatistics and model averaging. Existing methods fail to simultaneously provide these crucial advantages, which our method buys at relatively higher-computational costs. We demonstrate the applicability and advantages of PreDIA over conventional linearized methods in a synthetic example of subsurface transport. In the example, we show that informative data is often invisible for linearized methods that confuse zero correlation with statistical independence. Hence, PreDIA will often lead to substantially better sampling designs. Finally, we extend our example to specifically highlight the consideration of conceptual model uncertainty.

Bootstrap Prediction Intervals in Non-Parametric Regression with Applications to Anomaly Detection

NASA Technical Reports Server (NTRS)

Kumar, Sricharan; Srivistava, Ashok N.

2012-01-01

Prediction intervals provide a measure of the probable interval in which the outputs of a regression model can be expected to occur. Subsequently, these prediction intervals can be used to determine if the observed output is anomalous or not, conditioned on the input. In this paper, a procedure for determining prediction intervals for outputs of nonparametric regression models using bootstrap methods is proposed. Bootstrap methods allow for a non-parametric approach to computing prediction intervals with no specific assumptions about the sampling distribution of the noise or the data. The asymptotic fidelity of the proposed prediction intervals is theoretically proved. Subsequently, the validity of the bootstrap based prediction intervals is illustrated via simulations. Finally, the bootstrap prediction intervals are applied to the problem of anomaly detection on aviation data.

Variations on Bayesian Prediction and Inference

DTIC Science & Technology

2016-05-09

inference 2.2.1 Background There are a number of statistical inference problems that are not generally formulated via a full probability model...problem of inference about an unknown parameter, the Bayesian approach requires a full probability 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...the problem of inference about an unknown parameter, the Bayesian approach requires a full probability model/likelihood which can be an obstacle

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.

Pig Data and Bayesian Inference on Multinomial Probabilities

ERIC Educational Resources Information Center

Kern, John C.

2006-01-01

Bayesian inference on multinomial probabilities is conducted based on data collected from the game Pass the Pigs[R]. Prior information on these probabilities is readily available from the instruction manual, and is easily incorporated in a Dirichlet prior. Posterior analysis of the scoring probabilities quantifies the discrepancy between empirical…

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.

Beginning Bayes

ERIC Educational Resources Information Center

Erickson, Tim

2017-01-01

Understanding a Bayesian perspective demands comfort with conditional probability and with probabilities that appear to change as we acquire additional information. This paper suggests a simple context in conditional probability that helps develop the understanding students would need for a successful introduction to Bayesian reasoning.

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…

Daniel Goodman’s empirical approach to Bayesian statistics

USGS Publications Warehouse

Gerrodette, Tim; Ward, Eric; Taylor, Rebecca L.; Schwarz, Lisa K.; Eguchi, Tomoharu; Wade, Paul; Himes Boor, Gina

2016-01-01

Bayesian statistics, in contrast to classical statistics, uses probability to represent uncertainty about the state of knowledge. Bayesian statistics has often been associated with the idea that knowledge is subjective and that a probability distribution represents a personal degree of belief. Dr. Daniel Goodman considered this viewpoint problematic for issues of public policy. He sought to ground his Bayesian approach in data, and advocated the construction of a prior as an empirical histogram of “similar” cases. In this way, the posterior distribution that results from a Bayesian analysis combined comparable previous data with case-specific current data, using Bayes’ formula. Goodman championed such a data-based approach, but he acknowledged that it was difficult in practice. If based on a true representation of our knowledge and uncertainty, Goodman argued that risk assessment and decision-making could be an exact science, despite the uncertainties. In his view, Bayesian statistics is a critical component of this science because a Bayesian analysis produces the probabilities of future outcomes. Indeed, Goodman maintained that the Bayesian machinery, following the rules of conditional probability, offered the best legitimate inference from available data. We give an example of an informative prior in a recent study of Steller sea lion spatial use patterns in Alaska.

Rapid and accurate taxonomic classification of insect (class Insecta) cytochrome c oxidase subunit 1 (COI) DNA barcode sequences using a naïve Bayesian classifier

PubMed Central

Porter, Teresita M; Gibson, Joel F; Shokralla, Shadi; Baird, Donald J; Golding, G Brian; Hajibabaei, Mehrdad

2014-01-01

Current methods to identify unknown insect (class Insecta) cytochrome c oxidase (COI barcode) sequences often rely on thresholds of distances that can be difficult to define, sequence similarity cut-offs, or monophyly. Some of the most commonly used metagenomic classification methods do not provide a measure of confidence for the taxonomic assignments they provide. The aim of this study was to use a naïve Bayesian classifier (Wang et al. Applied and Environmental Microbiology, 2007; 73: 5261) to automate taxonomic assignments for large batches of insect COI sequences such as data obtained from high-throughput environmental sequencing. This method provides rank-flexible taxonomic assignments with an associated bootstrap support value, and it is faster than the blast-based methods commonly used in environmental sequence surveys. We have developed and rigorously tested the performance of three different training sets using leave-one-out cross-validation, two field data sets, and targeted testing of Lepidoptera, Diptera and Mantodea sequences obtained from the Barcode of Life Data system. We found that type I error rates, incorrect taxonomic assignments with a high bootstrap support, were already relatively low but could be lowered further by ensuring that all query taxa are actually present in the reference database. Choosing bootstrap support cut-offs according to query length and summarizing taxonomic assignments to more inclusive ranks can also help to reduce error while retaining the maximum number of assignments. Additionally, we highlight gaps in the taxonomic and geographic representation of insects in public sequence databases that will require further work by taxonomists to improve the quality of assignments generated using any method.

From genus to phylum: large-subunit and internal transcribed spacer rRNA operon regions show similar classification accuracies influenced by database composition.

PubMed

Porras-Alfaro, Andrea; Liu, Kuan-Liang; Kuske, Cheryl R; Xie, Gary

2014-02-01

We compared the classification accuracy of two sections of the fungal internal transcribed spacer (ITS) region, individually and combined, and the 5' section (about 600 bp) of the large-subunit rRNA (LSU), using a naive Bayesian classifier and BLASTN. A hand-curated ITS-LSU training set of 1,091 sequences and a larger training set of 8,967 ITS region sequences were used. Of the factors evaluated, database composition and quality had the largest effect on classification accuracy, followed by fragment size and use of a bootstrap cutoff to improve classification confidence. The naive Bayesian classifier and BLASTN gave similar results at higher taxonomic levels, but the classifier was faster and more accurate at the genus level when a bootstrap cutoff was used. All of the ITS and LSU sections performed well (>97.7% accuracy) at higher taxonomic ranks from kingdom to family, and differences between them were small at the genus level (within 0.66 to 1.23%). When full-length sequence sections were used, the LSU outperformed the ITS1 and ITS2 fragments at the genus level, but the ITS1 and ITS2 showed higher accuracy when smaller fragment sizes of the same length and a 50% bootstrap cutoff were used. In a comparison using the larger ITS training set, ITS1 and ITS2 had very similar accuracy classification for fragments between 100 and 200 bp. Collectively, the results show that any of the ITS or LSU sections we tested provided comparable classification accuracy to the genus level and underscore the need for larger and more diverse classification training sets.

From Genus to Phylum: Large-Subunit and Internal Transcribed Spacer rRNA Operon Regions Show Similar Classification Accuracies Influenced by Database Composition

PubMed Central

Liu, Kuan-Liang; Kuske, Cheryl R.

2014-01-01

We compared the classification accuracy of two sections of the fungal internal transcribed spacer (ITS) region, individually and combined, and the 5′ section (about 600 bp) of the large-subunit rRNA (LSU), using a naive Bayesian classifier and BLASTN. A hand-curated ITS-LSU training set of 1,091 sequences and a larger training set of 8,967 ITS region sequences were used. Of the factors evaluated, database composition and quality had the largest effect on classification accuracy, followed by fragment size and use of a bootstrap cutoff to improve classification confidence. The naive Bayesian classifier and BLASTN gave similar results at higher taxonomic levels, but the classifier was faster and more accurate at the genus level when a bootstrap cutoff was used. All of the ITS and LSU sections performed well (>97.7% accuracy) at higher taxonomic ranks from kingdom to family, and differences between them were small at the genus level (within 0.66 to 1.23%). When full-length sequence sections were used, the LSU outperformed the ITS1 and ITS2 fragments at the genus level, but the ITS1 and ITS2 showed higher accuracy when smaller fragment sizes of the same length and a 50% bootstrap cutoff were used. In a comparison using the larger ITS training set, ITS1 and ITS2 had very similar accuracy classification for fragments between 100 and 200 bp. Collectively, the results show that any of the ITS or LSU sections we tested provided comparable classification accuracy to the genus level and underscore the need for larger and more diverse classification training sets. PMID:24242255

Assessing Mediational Models: Testing and Interval Estimation for Indirect Effects.

PubMed

Biesanz, Jeremy C; Falk, Carl F; Savalei, Victoria

2010-08-06

Theoretical models specifying indirect or mediated effects are common in the social sciences. An indirect effect exists when an independent variable's influence on the dependent variable is mediated through an intervening variable. Classic approaches to assessing such mediational hypotheses ( Baron & Kenny, 1986 ; Sobel, 1982 ) have in recent years been supplemented by computationally intensive methods such as bootstrapping, the distribution of the product methods, and hierarchical Bayesian Markov chain Monte Carlo (MCMC) methods. These different approaches for assessing mediation are illustrated using data from Dunn, Biesanz, Human, and Finn (2007). However, little is known about how these methods perform relative to each other, particularly in more challenging situations, such as with data that are incomplete and/or nonnormal. This article presents an extensive Monte Carlo simulation evaluating a host of approaches for assessing mediation. We examine Type I error rates, power, and coverage. We study normal and nonnormal data as well as complete and incomplete data. In addition, we adapt a method, recently proposed in statistical literature, that does not rely on confidence intervals (CIs) to test the null hypothesis of no indirect effect. The results suggest that the new inferential method-the partial posterior p value-slightly outperforms existing ones in terms of maintaining Type I error rates while maximizing power, especially with incomplete data. Among confidence interval approaches, the bias-corrected accelerated (BC a ) bootstrapping approach often has inflated Type I error rates and inconsistent coverage and is not recommended; In contrast, the bootstrapped percentile confidence interval and the hierarchical Bayesian MCMC method perform best overall, maintaining Type I error rates, exhibiting reasonable power, and producing stable and accurate coverage rates.

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.

Sparse Logistic Regression for Diagnosis of Liver Fibrosis in Rat by Using SCAD-Penalized Likelihood

PubMed Central

Yan, Fang-Rong; Lin, Jin-Guan; Liu, Yu

2011-01-01

The objective of the present study is to find out the quantitative relationship between progression of liver fibrosis and the levels of certain serum markers using mathematic model. We provide the sparse logistic regression by using smoothly clipped absolute deviation (SCAD) penalized function to diagnose the liver fibrosis in rats. Not only does it give a sparse solution with high accuracy, it also provides the users with the precise probabilities of classification with the class information. In the simulative case and the experiment case, the proposed method is comparable to the stepwise linear discriminant analysis (SLDA) and the sparse logistic regression with least absolute shrinkage and selection operator (LASSO) penalty, by using receiver operating characteristic (ROC) with bayesian bootstrap estimating area under the curve (AUC) diagnostic sensitivity for selected variable. Results show that the new approach provides a good correlation between the serum marker levels and the liver fibrosis induced by thioacetamide (TAA) in rats. Meanwhile, this approach might also be used in predicting the development of liver cirrhosis. PMID:21716672

Bayesian analyses of time-interval data for environmental radiation monitoring.

PubMed

Luo, Peng; Sharp, Julia L; DeVol, Timothy A

2013-01-01

Time-interval (time difference between two consecutive pulses) analysis based on the principles of Bayesian inference was investigated for online radiation monitoring. Using experimental and simulated data, Bayesian analysis of time-interval data [Bayesian (ti)] was compared with Bayesian and a conventional frequentist analysis of counts in a fixed count time [Bayesian (cnt) and single interval test (SIT), respectively]. The performances of the three methods were compared in terms of average run length (ARL) and detection probability for several simulated detection scenarios. Experimental data were acquired with a DGF-4C system in list mode. Simulated data were obtained using Monte Carlo techniques to obtain a random sampling of the Poisson distribution. All statistical algorithms were developed using the R Project for statistical computing. Bayesian analysis of time-interval information provided a similar detection probability as Bayesian analysis of count information, but the authors were able to make a decision with fewer pulses at relatively higher radiation levels. In addition, for the cases with very short presence of the source (< count time), time-interval information is more sensitive to detect a change than count information since the source data is averaged by the background data over the entire count time. The relationships of the source time, change points, and modifications to the Bayesian approach for increasing detection probability are presented.

Bayesian statistical inference enhances the interpretation of contemporary randomized controlled trials.

PubMed

Wijeysundera, Duminda N; Austin, Peter C; Hux, Janet E; Beattie, W Scott; Laupacis, Andreas

2009-01-01

Randomized trials generally use "frequentist" statistics based on P-values and 95% confidence intervals. Frequentist methods have limitations that might be overcome, in part, by Bayesian inference. To illustrate these advantages, we re-analyzed randomized trials published in four general medical journals during 2004. We used Medline to identify randomized superiority trials with two parallel arms, individual-level randomization and dichotomous or time-to-event primary outcomes. Studies with P<0.05 in favor of the intervention were deemed "positive"; otherwise, they were "negative." We used several prior distributions and exact conjugate analyses to calculate Bayesian posterior probabilities for clinically relevant effects. Of 88 included studies, 39 were positive using a frequentist analysis. Although the Bayesian posterior probabilities of any benefit (relative risk or hazard ratio<1) were high in positive studies, these probabilities were lower and variable for larger benefits. The positive studies had only moderate probabilities for exceeding the effects that were assumed for calculating the sample size. By comparison, there were moderate probabilities of any benefit in negative studies. Bayesian and frequentist analyses complement each other when interpreting the results of randomized trials. Future reports of randomized trials should include both.

BootGraph: probabilistic fiber tractography using bootstrap algorithms and graph theory.

PubMed

Vorburger, Robert S; Reischauer, Carolin; Boesiger, Peter

2013-02-01

Bootstrap methods have recently been introduced to diffusion-weighted magnetic resonance imaging to estimate the measurement uncertainty of ensuing diffusion parameters directly from the acquired data without the necessity to assume a noise model. These methods have been previously combined with deterministic streamline tractography algorithms to allow for the assessment of connection probabilities in the human brain. Thereby, the local noise induced disturbance in the diffusion data is accumulated additively due to the incremental progression of streamline tractography algorithms. Graph based approaches have been proposed to overcome this drawback of streamline techniques. For this reason, the bootstrap method is in the present work incorporated into a graph setup to derive a new probabilistic fiber tractography method, called BootGraph. The acquired data set is thereby converted into a weighted, undirected graph by defining a vertex in each voxel and edges between adjacent vertices. By means of the cone of uncertainty, which is derived using the wild bootstrap, a weight is thereafter assigned to each edge. Two path finding algorithms are subsequently applied to derive connection probabilities. While the first algorithm is based on the shortest path approach, the second algorithm takes all existing paths between two vertices into consideration. Tracking results are compared to an established algorithm based on the bootstrap method in combination with streamline fiber tractography and to another graph based algorithm. The BootGraph shows a very good performance in crossing situations with respect to false negatives and permits incorporating additional constraints, such as a curvature threshold. By inheriting the advantages of the bootstrap method and graph theory, the BootGraph method provides a computationally efficient and flexible probabilistic tractography setup to compute connection probability maps and virtual fiber pathways without the drawbacks of streamline tractography algorithms or the assumption of a noise distribution. Moreover, the BootGraph can be applied to common DTI data sets without further modifications and shows a high repeatability. Thus, it is very well suited for longitudinal studies and meta-studies based on DTI. Copyright © 2012 Elsevier Inc. All rights reserved.

Method for Automatic Selection of Parameters in Normal Tissue Complication Probability Modeling.

PubMed

Christophides, Damianos; Appelt, Ane L; Gusnanto, Arief; Lilley, John; Sebag-Montefiore, David

2018-07-01

To present a fully automatic method to generate multiparameter normal tissue complication probability (NTCP) models and compare its results with those of a published model, using the same patient cohort. Data were analyzed from 345 rectal cancer patients treated with external radiation therapy to predict the risk of patients developing grade 1 or ≥2 cystitis. In total, 23 clinical factors were included in the analysis as candidate predictors of cystitis. Principal component analysis was used to decompose the bladder dose-volume histogram into 8 principal components, explaining more than 95% of the variance. The data set of clinical factors and principal components was divided into training (70%) and test (30%) data sets, with the training data set used by the algorithm to compute an NTCP model. The first step of the algorithm was to obtain a bootstrap sample, followed by multicollinearity reduction using the variance inflation factor and genetic algorithm optimization to determine an ordinal logistic regression model that minimizes the Bayesian information criterion. The process was repeated 100 times, and the model with the minimum Bayesian information criterion was recorded on each iteration. The most frequent model was selected as the final "automatically generated model" (AGM). The published model and AGM were fitted on the training data sets, and the risk of cystitis was calculated. The 2 models had no significant differences in predictive performance, both for the training and test data sets (P value > .05) and found similar clinical and dosimetric factors as predictors. Both models exhibited good explanatory performance on the training data set (P values > .44), which was reduced on the test data sets (P values < .05). The predictive value of the AGM is equivalent to that of the expert-derived published model. It demonstrates potential in saving time, tackling problems with a large number of parameters, and standardizing variable selection in NTCP modeling. Crown Copyright © 2018. Published by Elsevier Inc. All rights reserved.

Ockham's razor and Bayesian analysis. [statistical theory for systems evaluation

NASA Technical Reports Server (NTRS)

Jefferys, William H.; Berger, James O.

1992-01-01

'Ockham's razor', the ad hoc principle enjoining the greatest possible simplicity in theoretical explanations, is presently shown to be justifiable as a consequence of Bayesian inference; Bayesian analysis can, moreover, clarify the nature of the 'simplest' hypothesis consistent with the given data. By choosing the prior probabilities of hypotheses, it becomes possible to quantify the scientific judgment that simpler hypotheses are more likely to be correct. Bayesian analysis also shows that a hypothesis with fewer adjustable parameters intrinsically possesses an enhanced posterior probability, due to the clarity of its predictions.

The PIT-trap-A "model-free" bootstrap procedure for inference about regression models with discrete, multivariate responses.

PubMed

Warton, David I; Thibaut, Loïc; Wang, Yi Alice

2017-01-01

Bootstrap methods are widely used in statistics, and bootstrapping of residuals can be especially useful in the regression context. However, difficulties are encountered extending residual resampling to regression settings where residuals are not identically distributed (thus not amenable to bootstrapping)-common examples including logistic or Poisson regression and generalizations to handle clustered or multivariate data, such as generalised estimating equations. We propose a bootstrap method based on probability integral transform (PIT-) residuals, which we call the PIT-trap, which assumes data come from some marginal distribution F of known parametric form. This method can be understood as a type of "model-free bootstrap", adapted to the problem of discrete and highly multivariate data. PIT-residuals have the key property that they are (asymptotically) pivotal. The PIT-trap thus inherits the key property, not afforded by any other residual resampling approach, that the marginal distribution of data can be preserved under PIT-trapping. This in turn enables the derivation of some standard bootstrap properties, including second-order correctness of pivotal PIT-trap test statistics. In multivariate data, bootstrapping rows of PIT-residuals affords the property that it preserves correlation in data without the need for it to be modelled, a key point of difference as compared to a parametric bootstrap. The proposed method is illustrated on an example involving multivariate abundance data in ecology, and demonstrated via simulation to have improved properties as compared to competing resampling methods.

Bootstrap Percolation on Homogeneous Trees Has 2 Phase Transitions

NASA Astrophysics Data System (ADS)

Fontes, L. R. G.; Schonmann, R. H.

2008-09-01

We study the threshold θ bootstrap percolation model on the homogeneous tree with degree b+1, 2≤ θ≤ b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call p f , such that a) for p> p f , the final bootstrapped configuration is fully occupied for almost every initial configuration, and b) if p< p f , then for almost every initial configuration, the final bootstrapped configuration has density of occupied vertices less than 1. In this paper, we establish the existence of a distinct critical value for p, p c , such that 0< p c < p f , with the following properties: 1) if p≤ p c , then for almost every initial configuration there is no infinite cluster of occupied vertices in the final bootstrapped configuration; 2) if p> p c , then for almost every initial configuration there are infinite clusters of occupied vertices in the final bootstrapped configuration. Moreover, we show that 3) for p< p c , the distribution of the occupied cluster size in the final bootstrapped configuration has an exponential tail; 4) at p= p c , the expected occupied cluster size in the final bootstrapped configuration is infinite; 5) the probability of percolation of occupied vertices in the final bootstrapped configuration is continuous on [0, p f ] and analytic on ( p c , p f ), admitting an analytic continuation from the right at p c and, only in the case θ= b, also from the left at p f .

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.

Randomized path optimization for thevMitigated counter detection of UAVS

DTIC Science & Technology

2017-06-01

using Bayesian filtering . The KL divergence is used to compare the probability density of aircraft termination to a normal distribution around the...Bayesian filtering . The KL divergence is used to compare the probability density of aircraft termination to a normal distribution around the true terminal...algorithm’s success. A recursive Bayesian filtering scheme is used to assimilate noisy measurements of the UAVs position to predict its terminal location. We

Bayesian selection of misspecified models is overconfident and may cause spurious posterior probabilities for phylogenetic trees.

PubMed

Yang, Ziheng; Zhu, Tianqi

2018-02-20

The Bayesian method is noted to produce spuriously high posterior probabilities for phylogenetic trees in analysis of large datasets, but the precise reasons for this overconfidence are unknown. In general, the performance of Bayesian selection of misspecified models is poorly understood, even though this is of great scientific interest since models are never true in real data analysis. Here we characterize the asymptotic behavior of Bayesian model selection and show that when the competing models are equally wrong, Bayesian model selection exhibits surprising and polarized behaviors in large datasets, supporting one model with full force while rejecting the others. If one model is slightly less wrong than the other, the less wrong model will eventually win when the amount of data increases, but the method may become overconfident before it becomes reliable. We suggest that this extreme behavior may be a major factor for the spuriously high posterior probabilities for evolutionary trees. The philosophical implications of our results to the application of Bayesian model selection to evaluate opposing scientific hypotheses are yet to be explored, as are the behaviors of non-Bayesian methods in similar situations.

Bootstrap investigation of the stability of a Cox regression model.

PubMed

Altman, D G; Andersen, P K

1989-07-01

We describe a bootstrap investigation of the stability of a Cox proportional hazards regression model resulting from the analysis of a clinical trial of azathioprine versus placebo in patients with primary biliary cirrhosis. We have considered stability to refer both to the choice of variables included in the model and, more importantly, to the predictive ability of the model. In stepwise Cox regression analyses of 100 bootstrap samples using 17 candidate variables, the most frequently selected variables were those selected in the original analysis, and no other important variable was identified. Thus there was no reason to doubt the model obtained in the original analysis. For each patient in the trial, bootstrap confidence intervals were constructed for the estimated probability of surviving two years. It is shown graphically that these intervals are markedly wider than those obtained from the original model.

Improved dynamical scaling analysis using the kernel method for nonequilibrium relaxation.

PubMed

Echinaka, Yuki; Ozeki, Yukiyasu

2016-10-01

The dynamical scaling analysis for the Kosterlitz-Thouless transition in the nonequilibrium relaxation method is improved by the use of Bayesian statistics and the kernel method. This allows data to be fitted to a scaling function without using any parametric model function, which makes the results more reliable and reproducible and enables automatic and faster parameter estimation. Applying this method, the bootstrap method is introduced and a numerical discrimination for the transition type is proposed.

Sequential Probability Ratio Test for Collision Avoidance Maneuver Decisions

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell; Markley, F. Landis

2010-01-01

When facing a conjunction between space objects, decision makers must chose whether to maneuver for collision avoidance or not. We apply a well-known decision procedure, the sequential probability ratio test, to this problem. We propose two approaches to the problem solution, one based on a frequentist method, and the other on a Bayesian method. The frequentist method does not require any prior knowledge concerning the conjunction, while the Bayesian method assumes knowledge of prior probability densities. Our results show that both methods achieve desired missed detection rates, but the frequentist method's false alarm performance is inferior to the Bayesian method's

A Bayesian method for using simulator data to enhance human error probabilities assigned by existing HRA methods

DOE PAGES

Groth, Katrina M.; Smith, Curtis L.; Swiler, Laura P.

2014-04-05

In the past several years, several international agencies have begun to collect data on human performance in nuclear power plant simulators [1]. This data provides a valuable opportunity to improve human reliability analysis (HRA), but there improvements will not be realized without implementation of Bayesian methods. Bayesian methods are widely used in to incorporate sparse data into models in many parts of probabilistic risk assessment (PRA), but Bayesian methods have not been adopted by the HRA community. In this article, we provide a Bayesian methodology to formally use simulator data to refine the human error probabilities (HEPs) assigned by existingmore » HRA methods. We demonstrate the methodology with a case study, wherein we use simulator data from the Halden Reactor Project to update the probability assignments from the SPAR-H method. The case study demonstrates the ability to use performance data, even sparse data, to improve existing HRA methods. Furthermore, this paper also serves as a demonstration of the value of Bayesian methods to improve the technical basis of HRA.« less

A Bayesian-frequentist two-stage single-arm phase II clinical trial design.

PubMed

Dong, Gaohong; Shih, Weichung Joe; Moore, Dirk; Quan, Hui; Marcella, Stephen

2012-08-30

It is well-known that both frequentist and Bayesian clinical trial designs have their own advantages and disadvantages. To have better properties inherited from these two types of designs, we developed a Bayesian-frequentist two-stage single-arm phase II clinical trial design. This design allows both early acceptance and rejection of the null hypothesis ( H(0) ). The measures (for example probability of trial early termination, expected sample size, etc.) of the design properties under both frequentist and Bayesian settings are derived. Moreover, under the Bayesian setting, the upper and lower boundaries are determined with predictive probability of trial success outcome. Given a beta prior and a sample size for stage I, based on the marginal distribution of the responses at stage I, we derived Bayesian Type I and Type II error rates. By controlling both frequentist and Bayesian error rates, the Bayesian-frequentist two-stage design has special features compared with other two-stage designs. Copyright © 2012 John Wiley & Sons, Ltd.

Uncertainty plus prior equals rational bias: an intuitive Bayesian probability weighting function.

PubMed

Fennell, John; Baddeley, Roland

2012-10-01

Empirical research has shown that when making choices based on probabilistic options, people behave as if they overestimate small probabilities, underestimate large probabilities, and treat positive and negative outcomes differently. These distortions have been modeled using a nonlinear probability weighting function, which is found in several nonexpected utility theories, including rank-dependent models and prospect theory; here, we propose a Bayesian approach to the probability weighting function and, with it, a psychological rationale. In the real world, uncertainty is ubiquitous and, accordingly, the optimal strategy is to combine probability statements with prior information using Bayes' rule. First, we show that any reasonable prior on probabilities leads to 2 of the observed effects; overweighting of low probabilities and underweighting of high probabilities. We then investigate 2 plausible kinds of priors: informative priors based on previous experience and uninformative priors of ignorance. Individually, these priors potentially lead to large problems of bias and inefficiency, respectively; however, when combined using Bayesian model comparison methods, both forms of prior can be applied adaptively, gaining the efficiency of empirical priors and the robustness of ignorance priors. We illustrate this for the simple case of generic good and bad options, using Internet blogs to estimate the relevant priors of inference. Given this combined ignorant/informative prior, the Bayesian probability weighting function is not only robust and efficient but also matches all of the major characteristics of the distortions found in empirical research. PsycINFO Database Record (c) 2012 APA, all rights reserved.

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.

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

Finding Useful Questions: On Bayesian Diagnosticity, Probability, Impact, and Information Gain

ERIC Educational Resources Information Center

Nelson, Jonathan D.

2005-01-01

Several norms for how people should assess a question's usefulness have been proposed, notably Bayesian diagnosticity, information gain (mutual information), Kullback-Liebler distance, probability gain (error minimization), and impact (absolute change). Several probabilistic models of previous experiments on categorization, covariation assessment,…

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.

Reasoning and choice in the Monty Hall Dilemma (MHD): implications for improving Bayesian reasoning

PubMed Central

Tubau, Elisabet; Aguilar-Lleyda, David; Johnson, Eric D.

2015-01-01

The Monty Hall Dilemma (MHD) is a two-step decision problem involving counterintuitive conditional probabilities. The first choice is made among three equally probable options, whereas the second choice takes place after the elimination of one of the non-selected options which does not hide the prize. Differing from most Bayesian problems, statistical information in the MHD has to be inferred, either by learning outcome probabilities or by reasoning from the presented sequence of events. This often leads to suboptimal decisions and erroneous probability judgments. Specifically, decision makers commonly develop a wrong intuition that final probabilities are equally distributed, together with a preference for their first choice. Several studies have shown that repeated practice enhances sensitivity to the different reward probabilities, but does not facilitate correct Bayesian reasoning. However, modest improvements in probability judgments have been observed after guided explanations. To explain these dissociations, the present review focuses on two types of causes producing the observed biases: Emotional-based choice biases and cognitive limitations in understanding probabilistic information. Among the latter, we identify a crucial cause for the universal difficulty in overcoming the equiprobability illusion: Incomplete representation of prior and conditional probabilities. We conclude that repeated practice and/or high incentives can be effective for overcoming choice biases, but promoting an adequate partitioning of possibilities seems to be necessary for overcoming cognitive illusions and improving Bayesian reasoning. PMID:25873906

CytoBayesJ: software tools for Bayesian analysis of cytogenetic radiation dosimetry data.

PubMed

Ainsbury, Elizabeth A; Vinnikov, Volodymyr; Puig, Pedro; Maznyk, Nataliya; Rothkamm, Kai; Lloyd, David C

2013-08-30

A number of authors have suggested that a Bayesian approach may be most appropriate for analysis of cytogenetic radiation dosimetry data. In the Bayesian framework, probability of an event is described in terms of previous expectations and uncertainty. Previously existing, or prior, information is used in combination with experimental results to infer probabilities or the likelihood that a hypothesis is true. It has been shown that the Bayesian approach increases both the accuracy and quality assurance of radiation dose estimates. New software entitled CytoBayesJ has been developed with the aim of bringing Bayesian analysis to cytogenetic biodosimetry laboratory practice. CytoBayesJ takes a number of Bayesian or 'Bayesian like' methods that have been proposed in the literature and presents them to the user in the form of simple user-friendly tools, including testing for the most appropriate model for distribution of chromosome aberrations and calculations of posterior probability distributions. The individual tools are described in detail and relevant examples of the use of the methods and the corresponding CytoBayesJ software tools are given. In this way, the suitability of the Bayesian approach to biological radiation dosimetry is highlighted and its wider application encouraged by providing a user-friendly software interface and manual in English and Russian. Copyright © 2013 Elsevier B.V. All rights reserved.

Quantum mechanics: The Bayesian theory generalized to the space of Hermitian matrices

NASA Astrophysics Data System (ADS)

Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco

2016-10-01

We consider the problem of gambling on a quantum experiment and enforce rational behavior by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield the Bayesian theory generalized to the space of Hermitian matrices. This very theory is quantum mechanics: in fact, we derive all its four postulates from the generalized Bayesian theory. This implies that quantum mechanics is self-consistent. It also leads us to reinterpret the main operations in quantum mechanics as probability rules: Bayes' rule (measurement), marginalization (partial tracing), independence (tensor product). To say it with a slogan, we obtain that quantum mechanics is the Bayesian theory in the complex numbers.

The PIT-trap—A “model-free” bootstrap procedure for inference about regression models with discrete, multivariate responses

PubMed Central

Thibaut, Loïc; Wang, Yi Alice

2017-01-01

Bootstrap methods are widely used in statistics, and bootstrapping of residuals can be especially useful in the regression context. However, difficulties are encountered extending residual resampling to regression settings where residuals are not identically distributed (thus not amenable to bootstrapping)—common examples including logistic or Poisson regression and generalizations to handle clustered or multivariate data, such as generalised estimating equations. We propose a bootstrap method based on probability integral transform (PIT-) residuals, which we call the PIT-trap, which assumes data come from some marginal distribution F of known parametric form. This method can be understood as a type of “model-free bootstrap”, adapted to the problem of discrete and highly multivariate data. PIT-residuals have the key property that they are (asymptotically) pivotal. The PIT-trap thus inherits the key property, not afforded by any other residual resampling approach, that the marginal distribution of data can be preserved under PIT-trapping. This in turn enables the derivation of some standard bootstrap properties, including second-order correctness of pivotal PIT-trap test statistics. In multivariate data, bootstrapping rows of PIT-residuals affords the property that it preserves correlation in data without the need for it to be modelled, a key point of difference as compared to a parametric bootstrap. The proposed method is illustrated on an example involving multivariate abundance data in ecology, and demonstrated via simulation to have improved properties as compared to competing resampling methods. PMID:28738071

Bayesian performance metrics of binary sensors in homeland security applications

NASA Astrophysics Data System (ADS)

Jannson, Tomasz P.; Forrester, Thomas C.

2008-04-01

Bayesian performance metrics, based on such parameters, as: prior probability, probability of detection (or, accuracy), false alarm rate, and positive predictive value, characterizes the performance of binary sensors; i.e., sensors that have only binary response: true target/false target. Such binary sensors, very common in Homeland Security, produce an alarm that can be true, or false. They include: X-ray airport inspection, IED inspections, product quality control, cancer medical diagnosis, part of ATR, and many others. In this paper, we analyze direct and inverse conditional probabilities in the context of Bayesian inference and binary sensors, using X-ray luggage inspection statistical results as a guideline.

Evidence reasoning method for constructing conditional probability tables in a Bayesian network of multimorbidity.

PubMed

Du, Yuanwei; Guo, Yubin

2015-01-01

The intrinsic mechanism of multimorbidity is difficult to recognize and prediction and diagnosis are difficult to carry out accordingly. Bayesian networks can help to diagnose multimorbidity in health care, but it is difficult to obtain the conditional probability table (CPT) because of the lack of clinically statistical data. Today, expert knowledge and experience are increasingly used in training Bayesian networks in order to help predict or diagnose diseases, but the CPT in Bayesian networks is usually irrational or ineffective for ignoring realistic constraints especially in multimorbidity. In order to solve these problems, an evidence reasoning (ER) approach is employed to extract and fuse inference data from experts using a belief distribution and recursive ER algorithm, based on which evidence reasoning method for constructing conditional probability tables in Bayesian network of multimorbidity is presented step by step. A multimorbidity numerical example is used to demonstrate the method and prove its feasibility and application. Bayesian network can be determined as long as the inference assessment is inferred by each expert according to his/her knowledge or experience. Our method is more effective than existing methods for extracting expert inference data accurately and is fused effectively for constructing CPTs in a Bayesian network of multimorbidity.

Using the Bootstrap Method for a Statistical Significance Test of Differences between Summary Histograms

NASA Technical Reports Server (NTRS)

Xu, Kuan-Man

2006-01-01

A new method is proposed to compare statistical differences between summary histograms, which are the histograms summed over a large ensemble of individual histograms. It consists of choosing a distance statistic for measuring the difference between summary histograms and using a bootstrap procedure to calculate the statistical significance level. Bootstrapping is an approach to statistical inference that makes few assumptions about the underlying probability distribution that describes the data. Three distance statistics are compared in this study. They are the Euclidean distance, the Jeffries-Matusita distance and the Kuiper distance. The data used in testing the bootstrap method are satellite measurements of cloud systems called cloud objects. Each cloud object is defined as a contiguous region/patch composed of individual footprints or fields of view. A histogram of measured values over footprints is generated for each parameter of each cloud object and then summary histograms are accumulated over all individual histograms in a given cloud-object size category. The results of statistical hypothesis tests using all three distances as test statistics are generally similar, indicating the validity of the proposed method. The Euclidean distance is determined to be most suitable after comparing the statistical tests of several parameters with distinct probability distributions among three cloud-object size categories. Impacts on the statistical significance levels resulting from differences in the total lengths of satellite footprint data between two size categories are also discussed.

A new prior for bayesian anomaly detection: application to biosurveillance.

PubMed

Shen, Y; Cooper, G F

2010-01-01

Bayesian anomaly detection computes posterior probabilities of anomalous events by combining prior beliefs and evidence from data. However, the specification of prior probabilities can be challenging. This paper describes a Bayesian prior in the context of disease outbreak detection. The goal is to provide a meaningful, easy-to-use prior that yields a posterior probability of an outbreak that performs at least as well as a standard frequentist approach. If this goal is achieved, the resulting posterior could be usefully incorporated into a decision analysis about how to act in light of a possible disease outbreak. This paper describes a Bayesian method for anomaly detection that combines learning from data with a semi-informative prior probability over patterns of anomalous events. A univariate version of the algorithm is presented here for ease of illustration of the essential ideas. The paper describes the algorithm in the context of disease-outbreak detection, but it is general and can be used in other anomaly detection applications. For this application, the semi-informative prior specifies that an increased count over baseline is expected for the variable being monitored, such as the number of respiratory chief complaints per day at a given emergency department. The semi-informative prior is derived based on the baseline prior, which is estimated from using historical data. The evaluation reported here used semi-synthetic data to evaluate the detection performance of the proposed Bayesian method and a control chart method, which is a standard frequentist algorithm that is closest to the Bayesian method in terms of the type of data it uses. The disease-outbreak detection performance of the Bayesian method was statistically significantly better than that of the control chart method when proper baseline periods were used to estimate the baseline behavior to avoid seasonal effects. When using longer baseline periods, the Bayesian method performed as well as the control chart method. The time complexity of the Bayesian algorithm is linear in the number of the observed events being monitored, due to a novel, closed-form derivation that is introduced in the paper. This paper introduces a novel prior probability for Bayesian outbreak detection that is expressive, easy-to-apply, computationally efficient, and performs as well or better than a standard frequentist method.

An evaluation of the Bayesian approach to fitting the N-mixture model for use with pseudo-replicated count data

USGS Publications Warehouse

Toribo, S.G.; Gray, B.R.; Liang, S.

2011-01-01

The N-mixture model proposed by Royle in 2004 may be used to approximate the abundance and detection probability of animal species in a given region. In 2006, Royle and Dorazio discussed the advantages of using a Bayesian approach in modelling animal abundance and occurrence using a hierarchical N-mixture model. N-mixture models assume replication on sampling sites, an assumption that may be violated when the site is not closed to changes in abundance during the survey period or when nominal replicates are defined spatially. In this paper, we studied the robustness of a Bayesian approach to fitting the N-mixture model for pseudo-replicated count data. Our simulation results showed that the Bayesian estimates for abundance and detection probability are slightly biased when the actual detection probability is small and are sensitive to the presence of extra variability within local sites.

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 Dynamic Bayesian Network Model for the Production and Inventory Control

NASA Astrophysics Data System (ADS)

Shin, Ji-Sun; Takazaki, Noriyuki; Lee, Tae-Hong; Kim, Jin-Il; Lee, Hee-Hyol

In general, the production quantities and delivered goods are changed randomly and then the total stock is also changed randomly. This paper deals with the production and inventory control using the Dynamic Bayesian Network. Bayesian Network is a probabilistic model which represents the qualitative dependence between two or more random variables by the graph structure, and indicates the quantitative relations between individual variables by the conditional probability. The probabilistic distribution of the total stock is calculated through the propagation of the probability on the network. Moreover, an adjusting rule of the production quantities to maintain the probability of a lower limit and a ceiling of the total stock to certain values is shown.

The Psychology of Bayesian Reasoning

DTIC Science & Technology

2014-10-21

The psychology of Bayesian reasoning David R. Mandel* Socio-Cognitive Systems Section, Defence Research and Development Canada and Department...belief revision, subjective probability, human judgment, psychological methods. Most psychological research on Bayesian reasoning since the 1970s has...attention to some important problems with the conventional approach to studying Bayesian reasoning in psychology that has been dominant since the

A Gibbs sampler for Bayesian analysis of site-occupancy data

USGS Publications Warehouse

Dorazio, Robert M.; Rodriguez, Daniel Taylor

2012-01-01

1. A Bayesian analysis of site-occupancy data containing covariates of species occurrence and species detection probabilities is usually completed using Markov chain Monte Carlo methods in conjunction with software programs that can implement those methods for any statistical model, not just site-occupancy models. Although these software programs are quite flexible, considerable experience is often required to specify a model and to initialize the Markov chain so that summaries of the posterior distribution can be estimated efficiently and accurately. 2. As an alternative to these programs, we develop a Gibbs sampler for Bayesian analysis of site-occupancy data that include covariates of species occurrence and species detection probabilities. This Gibbs sampler is based on a class of site-occupancy models in which probabilities of species occurrence and detection are specified as probit-regression functions of site- and survey-specific covariate measurements. 3. To illustrate the Gibbs sampler, we analyse site-occupancy data of the blue hawker, Aeshna cyanea (Odonata, Aeshnidae), a common dragonfly species in Switzerland. Our analysis includes a comparison of results based on Bayesian and classical (non-Bayesian) methods of inference. We also provide code (based on the R software program) for conducting Bayesian and classical analyses of site-occupancy data.

Bayesian analysis of the astrobiological implications of life’s early emergence on Earth

PubMed Central

Spiegel, David S.; Turner, Edwin L.

2012-01-01

Life arose on Earth sometime in the first few hundred million years after the young planet had cooled to the point that it could support water-based organisms on its surface. The early emergence of life on Earth has been taken as evidence that the probability of abiogenesis is high, if starting from young Earth-like conditions. We revisit this argument quantitatively in a Bayesian statistical framework. By constructing a simple model of the probability of abiogenesis, we calculate a Bayesian estimate of its posterior probability, given the data that life emerged fairly early in Earth’s history and that, billions of years later, curious creatures noted this fact and considered its implications. We find that, given only this very limited empirical information, the choice of Bayesian prior for the abiogenesis probability parameter has a dominant influence on the computed posterior probability. Although terrestrial life's early emergence provides evidence that life might be abundant in the universe if early-Earth-like conditions are common, the evidence is inconclusive and indeed is consistent with an arbitrarily low intrinsic probability of abiogenesis for plausible uninformative priors. Finding a single case of life arising independently of our lineage (on Earth, elsewhere in the solar system, or on an extrasolar planet) would provide much stronger evidence that abiogenesis is not extremely rare in the universe. PMID:22198766

Bayesian analysis of the astrobiological implications of life's early emergence on Earth.

PubMed

Spiegel, David S; Turner, Edwin L

2012-01-10

Life arose on Earth sometime in the first few hundred million years after the young planet had cooled to the point that it could support water-based organisms on its surface. The early emergence of life on Earth has been taken as evidence that the probability of abiogenesis is high, if starting from young Earth-like conditions. We revisit this argument quantitatively in a bayesian statistical framework. By constructing a simple model of the probability of abiogenesis, we calculate a bayesian estimate of its posterior probability, given the data that life emerged fairly early in Earth's history and that, billions of years later, curious creatures noted this fact and considered its implications. We find that, given only this very limited empirical information, the choice of bayesian prior for the abiogenesis probability parameter has a dominant influence on the computed posterior probability. Although terrestrial life's early emergence provides evidence that life might be abundant in the universe if early-Earth-like conditions are common, the evidence is inconclusive and indeed is consistent with an arbitrarily low intrinsic probability of abiogenesis for plausible uninformative priors. Finding a single case of life arising independently of our lineage (on Earth, elsewhere in the solar system, or on an extrasolar planet) would provide much stronger evidence that abiogenesis is not extremely rare in the universe.

Little Bayesians or Little Einsteins? Probability and Explanatory Virtue in Children's Inferences

ERIC Educational Resources Information Center

Johnston, Angie M.; Johnson, Samuel G. B.; Koven, Marissa L.; Keil, Frank C.

2017-01-01

Like scientists, children seek ways to explain causal systems in the world. But are children scientists in the strict Bayesian tradition of maximizing posterior probability? Or do they attend to other explanatory considerations, as laypeople and scientists--such as Einstein--do? Four experiments support the latter possibility. In particular, we…

BANYAN_Sigma: Bayesian classifier for members of young stellar associations

NASA Astrophysics Data System (ADS)

Gagné, Jonathan; Mamajek, Eric E.; Malo, Lison; Riedel, Adric; Rodriguez, David; Lafrenière, David; Faherty, Jacqueline K.; Roy-Loubier, Olivier; Pueyo, Laurent; Robin, Annie C.; Doyon, René

2018-01-01

BANYAN_Sigma calculates the membership probability that a given astrophysical object belongs to one of the currently known 27 young associations within 150 pc of the Sun, using Bayesian inference. This tool uses the sky position and proper motion measurements of an object, with optional radial velocity (RV) and distance (D) measurements, to derive a Bayesian membership probability. By default, the priors are adjusted such that a probability threshold of 90% will recover 50%, 68%, 82% or 90% of true association members depending on what observables are input (only sky position and proper motion, with RV, with D, with both RV and D, respectively). The algorithm is implemented in a Python package, in IDL, and is also implemented as an interactive web page.

Bayesian learning

NASA Technical Reports Server (NTRS)

Denning, Peter J.

1989-01-01

In 1983 and 1984, the Infrared Astronomical Satellite (IRAS) detected 5,425 stellar objects and measured their infrared spectra. In 1987 a program called AUTOCLASS used Bayesian inference methods to discover the classes present in these data and determine the most probable class of each object, revealing unknown phenomena in astronomy. AUTOCLASS has rekindled the old debate on the suitability of Bayesian methods, which are computationally intensive, interpret probabilities as plausibility measures rather than frequencies, and appear to depend on a subjective assessment of the probability of a hypothesis before the data were collected. Modern statistical methods have, however, recently been shown to also depend on subjective elements. These debates bring into question the whole tradition of scientific objectivity and offer scientists a new way to take responsibility for their findings and conclusions.

Quantum-Bayesian coherence

NASA Astrophysics Data System (ADS)

Fuchs, Christopher A.; Schack, Rüdiger

2013-10-01

In the quantum-Bayesian interpretation of quantum theory (or QBism), the Born rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In this paper, the argument is given that it should be seen as an empirical addition to Bayesian reasoning itself. Particularly, it is shown how to view the Born rule as a normative rule in addition to usual Dutch-book coherence. It is a rule that takes into account how one should assign probabilities to the consequences of various intended measurements on a physical system, but explicitly in terms of prior probabilities for and conditional probabilities consequent upon the imagined outcomes of a special counterfactual reference measurement. This interpretation is exemplified by representing quantum states in terms of probabilities for the outcomes of a fixed, fiducial symmetric informationally complete measurement. The extent to which the general form of the new normative rule implies the full state-space structure of quantum mechanics is explored.

Bayesian Statistics for Biological Data: Pedigree Analysis

ERIC Educational Resources Information Center

Stanfield, William D.; Carlton, Matthew A.

2004-01-01

The use of Bayes' formula is applied to the biological problem of pedigree analysis to show that the Bayes' formula and non-Bayesian or "classical" methods of probability calculation give different answers. First year college students of biology can be introduced to the Bayesian statistics.

To P or Not to P: Backing Bayesian Statistics.

PubMed

Buchinsky, Farrel J; Chadha, Neil K

2017-12-01

In biomedical research, it is imperative to differentiate chance variation from truth before we generalize what we see in a sample of subjects to the wider population. For decades, we have relied on null hypothesis significance testing, where we calculate P values for our data to decide whether to reject a null hypothesis. This methodology is subject to substantial misinterpretation and errant conclusions. Instead of working backward by calculating the probability of our data if the null hypothesis were true, Bayesian statistics allow us instead to work forward, calculating the probability of our hypothesis given the available data. This methodology gives us a mathematical means of incorporating our "prior probabilities" from previous study data (if any) to produce new "posterior probabilities." Bayesian statistics tell us how confidently we should believe what we believe. It is time to embrace and encourage their use in our otolaryngology research.

Bayesian analysis of rare events

NASA Astrophysics Data System (ADS)

Straub, Daniel; Papaioannou, Iason; Betz, Wolfgang

2016-06-01

In many areas of engineering and science there is an interest in predicting the probability of rare events, in particular in applications related to safety and security. Increasingly, such predictions are made through computer models of physical systems in an uncertainty quantification framework. Additionally, with advances in IT, monitoring and sensor technology, an increasing amount of data on the performance of the systems is collected. This data can be used to reduce uncertainty, improve the probability estimates and consequently enhance the management of rare events and associated risks. Bayesian analysis is the ideal method to include the data into the probabilistic model. It ensures a consistent probabilistic treatment of uncertainty, which is central in the prediction of rare events, where extrapolation from the domain of observation is common. We present a framework for performing Bayesian updating of rare event probabilities, termed BUS. It is based on a reinterpretation of the classical rejection-sampling approach to Bayesian analysis, which enables the use of established methods for estimating probabilities of rare events. By drawing upon these methods, the framework makes use of their computational efficiency. These methods include the First-Order Reliability Method (FORM), tailored importance sampling (IS) methods and Subset Simulation (SuS). In this contribution, we briefly review these methods in the context of the BUS framework and investigate their applicability to Bayesian analysis of rare events in different settings. We find that, for some applications, FORM can be highly efficient and is surprisingly accurate, enabling Bayesian analysis of rare events with just a few model evaluations. In a general setting, BUS implemented through IS and SuS is more robust and flexible.

Bayesian statistics in radionuclide metrology: measurement of a decaying source

NASA Astrophysics Data System (ADS)

Bochud, François O.; Bailat, Claude J.; Laedermann, Jean-Pascal

2007-08-01

The most intuitive way of defining a probability is perhaps through the frequency at which it appears when a large number of trials are realized in identical conditions. The probability derived from the obtained histogram characterizes the so-called frequentist or conventional statistical approach. In this sense, probability is defined as a physical property of the observed system. By contrast, in Bayesian statistics, a probability is not a physical property or a directly observable quantity, but a degree of belief or an element of inference. The goal of this paper is to show how Bayesian statistics can be used in radionuclide metrology and what its advantages and disadvantages are compared with conventional statistics. This is performed through the example of an yttrium-90 source typically encountered in environmental surveillance measurement. Because of the very low activity of this kind of source and the small half-life of the radionuclide, this measurement takes several days, during which the source decays significantly. Several methods are proposed to compute simultaneously the number of unstable nuclei at a given reference time, the decay constant and the background. Asymptotically, all approaches give the same result. However, Bayesian statistics produces coherent estimates and confidence intervals in a much smaller number of measurements. Apart from the conceptual understanding of statistics, the main difficulty that could deter radionuclide metrologists from using Bayesian statistics is the complexity of the computation.

The relationship between the number of loci and the statistical support for the topology of UPGMA trees obtained from genetic distance data.

PubMed

Highton, R

1993-12-01

An analysis of the relationship between the number of loci utilized in an electrophoretic study of genetic relationships and the statistical support for the topology of UPGMA trees is reported for two published data sets. These are Highton and Larson (Syst. Zool.28:579-599, 1979), an analysis of the relationships of 28 species of plethodonine salamanders, and Hedges (Syst. Zool., 35:1-21, 1986), a similar study of 30 taxa of Holarctic hylid frogs. As the number of loci increases, the statistical support for the topology at each node in UPGMA trees was determined by both the bootstrap and jackknife methods. The results show that the bootstrap and jackknife probabilities supporting the topology at some nodes of UPGMA trees increase as the number of loci utilized in a study is increased, as expected for nodes that have groupings that reflect phylogenetic relationships. The pattern of increase varies and is especially rapid in the case of groups with no close relatives. At nodes that likely do not represent correct phylogenetic relationships, the bootstrap probabilities do not increase and often decline with the addition of more loci.

Inference of emission rates from multiple sources using Bayesian probability theory.

PubMed

Yee, Eugene; Flesch, Thomas K

2010-03-01

The determination of atmospheric emission rates from multiple sources using inversion (regularized least-squares or best-fit technique) is known to be very susceptible to measurement and model errors in the problem, rendering the solution unusable. In this paper, a new perspective is offered for this problem: namely, it is argued that the problem should be addressed as one of inference rather than inversion. Towards this objective, Bayesian probability theory is used to estimate the emission rates from multiple sources. The posterior probability distribution for the emission rates is derived, accounting fully for the measurement errors in the concentration data and the model errors in the dispersion model used to interpret the data. The Bayesian inferential methodology for emission rate recovery is validated against real dispersion data, obtained from a field experiment involving various source-sensor geometries (scenarios) consisting of four synthetic area sources and eight concentration sensors. The recovery of discrete emission rates from three different scenarios obtained using Bayesian inference and singular value decomposition inversion are compared and contrasted.

Probabilistic Model for Untargeted Peak Detection in LC-MS Using Bayesian Statistics.

PubMed

Woldegebriel, Michael; Vivó-Truyols, Gabriel

2015-07-21

We introduce a novel Bayesian probabilistic peak detection algorithm for liquid chromatography-mass spectroscopy (LC-MS). The final probabilistic result allows the user to make a final decision about which points in a chromatogram are affected by a chromatographic peak and which ones are only affected by noise. The use of probabilities contrasts with the traditional method in which a binary answer is given, relying on a threshold. By contrast, with the Bayesian peak detection presented here, the values of probability can be further propagated into other preprocessing steps, which will increase (or decrease) the importance of chromatographic regions into the final results. The present work is based on the use of the statistical overlap theory of component overlap from Davis and Giddings (Davis, J. M.; Giddings, J. Anal. Chem. 1983, 55, 418-424) as prior probability in the Bayesian formulation. The algorithm was tested on LC-MS Orbitrap data and was able to successfully distinguish chemical noise from actual peaks without any data preprocessing.

Analysis of small sample size studies using nonparametric bootstrap test with pooled resampling method.

PubMed

Dwivedi, Alok Kumar; Mallawaarachchi, Indika; Alvarado, Luis A

2017-06-30

Experimental studies in biomedical research frequently pose analytical problems related to small sample size. In such studies, there are conflicting findings regarding the choice of parametric and nonparametric analysis, especially with non-normal data. In such instances, some methodologists questioned the validity of parametric tests and suggested nonparametric tests. In contrast, other methodologists found nonparametric tests to be too conservative and less powerful and thus preferred using parametric tests. Some researchers have recommended using a bootstrap test; however, this method also has small sample size limitation. We used a pooled method in nonparametric bootstrap test that may overcome the problem related with small samples in hypothesis testing. The present study compared nonparametric bootstrap test with pooled resampling method corresponding to parametric, nonparametric, and permutation tests through extensive simulations under various conditions and using real data examples. The nonparametric pooled bootstrap t-test provided equal or greater power for comparing two means as compared with unpaired t-test, Welch t-test, Wilcoxon rank sum test, and permutation test while maintaining type I error probability for any conditions except for Cauchy and extreme variable lognormal distributions. In such cases, we suggest using an exact Wilcoxon rank sum test. Nonparametric bootstrap paired t-test also provided better performance than other alternatives. Nonparametric bootstrap test provided benefit over exact Kruskal-Wallis test. We suggest using nonparametric bootstrap test with pooled resampling method for comparing paired or unpaired means and for validating the one way analysis of variance test results for non-normal data in small sample size studies. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

A Tutorial in Bayesian Potential Outcomes Mediation Analysis.

PubMed

Miočević, Milica; Gonzalez, Oscar; Valente, Matthew J; MacKinnon, David P

2018-01-01

Statistical mediation analysis is used to investigate intermediate variables in the relation between independent and dependent variables. Causal interpretation of mediation analyses is challenging because randomization of subjects to levels of the independent variable does not rule out the possibility of unmeasured confounders of the mediator to outcome relation. Furthermore, commonly used frequentist methods for mediation analysis compute the probability of the data given the null hypothesis, which is not the probability of a hypothesis given the data as in Bayesian analysis. Under certain assumptions, applying the potential outcomes framework to mediation analysis allows for the computation of causal effects, and statistical mediation in the Bayesian framework gives indirect effects probabilistic interpretations. This tutorial combines causal inference and Bayesian methods for mediation analysis so the indirect and direct effects have both causal and probabilistic interpretations. Steps in Bayesian causal mediation analysis are shown in the application to an empirical example.

Traffic Video Image Segmentation Model Based on Bayesian and Spatio-Temporal Markov Random Field

NASA Astrophysics Data System (ADS)

Zhou, Jun; Bao, Xu; Li, Dawei; Yin, Yongwen

2017-10-01

Traffic video image is a kind of dynamic image and its background and foreground is changed at any time, which results in the occlusion. In this case, using the general method is more difficult to get accurate image segmentation. A segmentation algorithm based on Bayesian and Spatio-Temporal Markov Random Field is put forward, which respectively build the energy function model of observation field and label field to motion sequence image with Markov property, then according to Bayesian' rule, use the interaction of label field and observation field, that is the relationship of label field’s prior probability and observation field’s likelihood probability, get the maximum posterior probability of label field’s estimation parameter, use the ICM model to extract the motion object, consequently the process of segmentation is finished. Finally, the segmentation methods of ST - MRF and the Bayesian combined with ST - MRF were analyzed. Experimental results: the segmentation time in Bayesian combined with ST-MRF algorithm is shorter than in ST-MRF, and the computing workload is small, especially in the heavy traffic dynamic scenes the method also can achieve better segmentation effect.

A local approach for focussed Bayesian fusion

NASA Astrophysics Data System (ADS)

Sander, Jennifer; Heizmann, Michael; Goussev, Igor; Beyerer, Jürgen

2009-04-01

Local Bayesian fusion approaches aim to reduce high storage and computational costs of Bayesian fusion which is separated from fixed modeling assumptions. Using the small world formalism, we argue why this proceeding is conform with Bayesian theory. Then, we concentrate on the realization of local Bayesian fusion by focussing the fusion process solely on local regions that are task relevant with a high probability. The resulting local models correspond then to restricted versions of the original one. In a previous publication, we used bounds for the probability of misleading evidence to show the validity of the pre-evaluation of task specific knowledge and prior information which we perform to build local models. In this paper, we prove the validity of this proceeding using information theoretic arguments. For additional efficiency, local Bayesian fusion can be realized in a distributed manner. Here, several local Bayesian fusion tasks are evaluated and unified after the actual fusion process. For the practical realization of distributed local Bayesian fusion, software agents are predestinated. There is a natural analogy between the resulting agent based architecture and criminal investigations in real life. We show how this analogy can be used to improve the efficiency of distributed local Bayesian fusion additionally. Using a landscape model, we present an experimental study of distributed local Bayesian fusion in the field of reconnaissance, which highlights its high potential.

Reweighting Data in the Spirit of Tukey: Using Bayesian Posterior Probabilities as Rasch Residuals for Studying Misfit

ERIC Educational Resources Information Center

Dardick, William R.; Mislevy, Robert J.

2016-01-01

A new variant of the iterative "data = fit + residual" data-analytical approach described by Mosteller and Tukey is proposed and implemented in the context of item response theory psychometric models. Posterior probabilities from a Bayesian mixture model of a Rasch item response theory model and an unscalable latent class are expressed…

"Finding Useful Questions: On Bayesian Diagnosticity, Probability, Impact, and Information Gain": Correction to Nelson (2005)

ERIC Educational Resources Information Center

Nelson, Jonathan D.

2007-01-01

Reports an error in "Finding Useful Questions: On Bayesian Diagnosticity, Probability, Impact, and Information Gain" by Jonathan D. Nelson (Psychological Review, 2005[Oct], Vol 112[4], 979-999). In Table 13, the data should indicate that 7% of females had short hair and 93% of females had long hair. The calculations and discussion in the article…

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 Posterior Odds Ratios: Statistical Tools for Collaborative Evaluations

ERIC Educational Resources Information Center

Hicks, Tyler; Rodríguez-Campos, Liliana; Choi, Jeong Hoon

2018-01-01

To begin statistical analysis, Bayesians quantify their confidence in modeling hypotheses with priors. A prior describes the probability of a certain modeling hypothesis apart from the data. Bayesians should be able to defend their choice of prior to a skeptical audience. Collaboration between evaluators and stakeholders could make their choices…

Metrics for More than Two Points at Once

NASA Technical Reports Server (NTRS)

Wolpert, David H.

2005-01-01

The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of "how separated" two points in that space are. Here it is shown how to extend that definition, and in particular the triangle inequality, to concern arbitrary numbers of points. Such a measure of how separated the points within a collection are can be bootstrapped, to measure "how separated" from each other are two (or more) collections. The measure presented here also allows fractional membership of an element in a collection. This means it directly concerns measures of "how spread out" a probability distribution over a space is. When such a measure is bootstrapped to compare two collections, it allows us to measure how separated two probability distributions are, or more generally, how separated a distribution of distributions is.

Practical differences among probabilities, possibilities, and credibilities

NASA Astrophysics Data System (ADS)

Grandin, Jean-Francois; Moulin, Caroline

2002-03-01

This paper presents some important differences that exist between theories, which allow the uncertainty management in data fusion. The main comparative results illustrated in this paper are the followings: Incompatibility between decisions got from probabilities and credibilities is highlighted. In the dynamic frame, as remarked in [19] or [17], belief and plausibility of Dempster-Shafer model do not frame the Bayesian probability. This framing can however be obtained by the Modified Dempster-Shafer approach. It also can be obtained in the Bayesian framework either by simulation techniques, or with a studentization. The uncommitted in the Dempster-Shafer way, e.g. the mass accorded to the ignorance, gives a mechanism similar to the reliability in the Bayesian model. Uncommitted mass in Dempster-Shafer theory or reliability in Bayes theory act like a filter that weakens extracted information, and improves robustness to outliners. So, it is logical to observe on examples like the one presented particularly by D.M. Buede, a faster convergence of a Bayesian method that doesn't take into account the reliability, in front of Dempster-Shafer method which uses uncommitted mass. But, on Bayesian masses, if reliability is taken into account, at the same level that the uncommited, e.g. F=1-m, we observe an equivalent rate for convergence. When Dempster-Shafer and Bayes operator are informed by uncertainty, faster or lower convergence can be exhibited on non Bayesian masses. This is due to positive or negative synergy between information delivered by sensors. This effect is a direct consequence of non additivity when considering non Bayesian masses. Unknowledge of the prior in bayesian techniques can be quickly compensated by information accumulated as time goes on by a set of sensors. All these results are presented on simple examples, and developed when necessary.

Bayesian network ensemble as a multivariate strategy to predict radiation pneumonitis risk

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

Lee, Sangkyu, E-mail: sangkyu.lee@mail.mcgill.ca; Ybarra, Norma; Jeyaseelan, Krishinima

2015-05-15

Purpose: Prediction of radiation pneumonitis (RP) has been shown to be challenging due to the involvement of a variety of factors including dose–volume metrics and radiosensitivity biomarkers. Some of these factors are highly correlated and might affect prediction results when combined. Bayesian network (BN) provides a probabilistic framework to represent variable dependencies in a directed acyclic graph. The aim of this study is to integrate the BN framework and a systems’ biology approach to detect possible interactions among RP risk factors and exploit these relationships to enhance both the understanding and prediction of RP. Methods: The authors studied 54 nonsmall-cellmore » lung cancer patients who received curative 3D-conformal radiotherapy. Nineteen RP events were observed (common toxicity criteria for adverse events grade 2 or higher). Serum concentration of the following four candidate biomarkers were measured at baseline and midtreatment: alpha-2-macroglobulin, angiotensin converting enzyme (ACE), transforming growth factor, interleukin-6. Dose-volumetric and clinical parameters were also included as covariates. Feature selection was performed using a Markov blanket approach based on the Koller–Sahami filter. The Markov chain Monte Carlo technique estimated the posterior distribution of BN graphs built from the observed data of the selected variables and causality constraints. RP probability was estimated using a limited number of high posterior graphs (ensemble) and was averaged for the final RP estimate using Bayes’ rule. A resampling method based on bootstrapping was applied to model training and validation in order to control under- and overfit pitfalls. Results: RP prediction power of the BN ensemble approach reached its optimum at a size of 200. The optimized performance of the BN model recorded an area under the receiver operating characteristic curve (AUC) of 0.83, which was significantly higher than multivariate logistic regression (0.77), mean heart dose (0.69), and a pre-to-midtreatment change in ACE (0.66). When RP prediction was made only with pretreatment information, the AUC ranged from 0.76 to 0.81 depending on the ensemble size. Bootstrap validation of graph features in the ensemble quantified confidence of association between variables in the graphs where ten interactions were statistically significant. Conclusions: The presented BN methodology provides the flexibility to model hierarchical interactions between RP covariates, which is applied to probabilistic inference on RP. The authors’ preliminary results demonstrate that such framework combined with an ensemble method can possibly improve prediction of RP under real-life clinical circumstances such as missing data or treatment plan adaptation.« less

Bayesian analysis of rare events

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

Straub, Daniel, E-mail: straub@tum.de; Papaioannou, Iason; Betz, Wolfgang

2016-06-01

In many areas of engineering and science there is an interest in predicting the probability of rare events, in particular in applications related to safety and security. Increasingly, such predictions are made through computer models of physical systems in an uncertainty quantification framework. Additionally, with advances in IT, monitoring and sensor technology, an increasing amount of data on the performance of the systems is collected. This data can be used to reduce uncertainty, improve the probability estimates and consequently enhance the management of rare events and associated risks. Bayesian analysis is the ideal method to include the data into themore » probabilistic model. It ensures a consistent probabilistic treatment of uncertainty, which is central in the prediction of rare events, where extrapolation from the domain of observation is common. We present a framework for performing Bayesian updating of rare event probabilities, termed BUS. It is based on a reinterpretation of the classical rejection-sampling approach to Bayesian analysis, which enables the use of established methods for estimating probabilities of rare events. By drawing upon these methods, the framework makes use of their computational efficiency. These methods include the First-Order Reliability Method (FORM), tailored importance sampling (IS) methods and Subset Simulation (SuS). In this contribution, we briefly review these methods in the context of the BUS framework and investigate their applicability to Bayesian analysis of rare events in different settings. We find that, for some applications, FORM can be highly efficient and is surprisingly accurate, enabling Bayesian analysis of rare events with just a few model evaluations. In a general setting, BUS implemented through IS and SuS is more robust and flexible.« less

Information-Based Analysis of Data Assimilation (Invited)

NASA Astrophysics Data System (ADS)

Nearing, G. S.; Gupta, H. V.; Crow, W. T.; Gong, W.

2013-12-01

Data assimilation is defined as the Bayesian conditioning of uncertain model simulations on observations for the purpose of reducing uncertainty about model states. Practical data assimilation methods make the application of Bayes' law tractable either by employing assumptions about the prior, posterior and likelihood distributions (e.g., the Kalman family of filters) or by using resampling methods (e.g., bootstrap filter). We propose to quantify the efficiency of these approximations in an OSSE setting using information theory and, in an OSSE or real-world validation setting, to measure the amount - and more importantly, the quality - of information extracted from observations during data assimilation. To analyze DA assumptions, uncertainty is quantified as the Shannon-type entropy of a discretized probability distribution. The maximum amount of information that can be extracted from observations about model states is the mutual information between states and observations, which is equal to the reduction in entropy in our estimate of the state due to Bayesian filtering. The difference between this potential and the actual reduction in entropy due to Kalman (or other type of) filtering measures the inefficiency of the filter assumptions. Residual uncertainty in DA posterior state estimates can be attributed to three sources: (i) non-injectivity of the observation operator, (ii) noise in the observations, and (iii) filter approximations. The contribution of each of these sources is measurable in an OSSE setting. The amount of information extracted from observations by data assimilation (or system identification, including parameter estimation) can also be measured by Shannon's theory. Since practical filters are approximations of Bayes' law, it is important to know whether the information that is extracted form observations by a filter is reliable. We define information as either good or bad, and propose to measure these two types of information using partial Kullback-Leibler divergences. Defined this way, good and bad information sum to total information. This segregation of information into good and bad components requires a validation target distribution; in a DA OSSE setting, this can be the true Bayesian posterior, but in a real-world setting the validation target might be determined by a set of in situ observations.

CGBayesNets: Conditional Gaussian Bayesian Network Learning and Inference with Mixed Discrete and Continuous Data

PubMed Central

Weiss, Scott T.

2014-01-01

Bayesian Networks (BN) have been a popular predictive modeling formalism in bioinformatics, but their application in modern genomics has been slowed by an inability to cleanly handle domains with mixed discrete and continuous variables. Existing free BN software packages either discretize continuous variables, which can lead to information loss, or do not include inference routines, which makes prediction with the BN impossible. We present CGBayesNets, a BN package focused around prediction of a clinical phenotype from mixed discrete and continuous variables, which fills these gaps. CGBayesNets implements Bayesian likelihood and inference algorithms for the conditional Gaussian Bayesian network (CGBNs) formalism, one appropriate for predicting an outcome of interest from, e.g., multimodal genomic data. We provide four different network learning algorithms, each making a different tradeoff between computational cost and network likelihood. CGBayesNets provides a full suite of functions for model exploration and verification, including cross validation, bootstrapping, and AUC manipulation. We highlight several results obtained previously with CGBayesNets, including predictive models of wood properties from tree genomics, leukemia subtype classification from mixed genomic data, and robust prediction of intensive care unit mortality outcomes from metabolomic profiles. We also provide detailed example analysis on public metabolomic and gene expression datasets. CGBayesNets is implemented in MATLAB and available as MATLAB source code, under an Open Source license and anonymous download at http://www.cgbayesnets.com. PMID:24922310

CGBayesNets: conditional Gaussian Bayesian network learning and inference with mixed discrete and continuous data.

PubMed

McGeachie, Michael J; Chang, Hsun-Hsien; Weiss, Scott T

2014-06-01

Bayesian Networks (BN) have been a popular predictive modeling formalism in bioinformatics, but their application in modern genomics has been slowed by an inability to cleanly handle domains with mixed discrete and continuous variables. Existing free BN software packages either discretize continuous variables, which can lead to information loss, or do not include inference routines, which makes prediction with the BN impossible. We present CGBayesNets, a BN package focused around prediction of a clinical phenotype from mixed discrete and continuous variables, which fills these gaps. CGBayesNets implements Bayesian likelihood and inference algorithms for the conditional Gaussian Bayesian network (CGBNs) formalism, one appropriate for predicting an outcome of interest from, e.g., multimodal genomic data. We provide four different network learning algorithms, each making a different tradeoff between computational cost and network likelihood. CGBayesNets provides a full suite of functions for model exploration and verification, including cross validation, bootstrapping, and AUC manipulation. We highlight several results obtained previously with CGBayesNets, including predictive models of wood properties from tree genomics, leukemia subtype classification from mixed genomic data, and robust prediction of intensive care unit mortality outcomes from metabolomic profiles. We also provide detailed example analysis on public metabolomic and gene expression datasets. CGBayesNets is implemented in MATLAB and available as MATLAB source code, under an Open Source license and anonymous download at http://www.cgbayesnets.com.

Bootstrap-after-bootstrap model averaging for reducing model uncertainty in model selection for air pollution mortality studies.

PubMed

Roberts, Steven; Martin, Michael A

2010-01-01

Concerns have been raised about findings of associations between particulate matter (PM) air pollution and mortality that have been based on a single "best" model arising from a model selection procedure, because such a strategy may ignore model uncertainty inherently involved in searching through a set of candidate models to find the best model. Model averaging has been proposed as a method of allowing for model uncertainty in this context. To propose an extension (double BOOT) to a previously described bootstrap model-averaging procedure (BOOT) for use in time series studies of the association between PM and mortality. We compared double BOOT and BOOT with Bayesian model averaging (BMA) and a standard method of model selection [standard Akaike's information criterion (AIC)]. Actual time series data from the United States are used to conduct a simulation study to compare and contrast the performance of double BOOT, BOOT, BMA, and standard AIC. Double BOOT produced estimates of the effect of PM on mortality that have had smaller root mean squared error than did those produced by BOOT, BMA, and standard AIC. This performance boost resulted from estimates produced by double BOOT having smaller variance than those produced by BOOT and BMA. Double BOOT is a viable alternative to BOOT and BMA for producing estimates of the mortality effect of PM.

Properties of the Bayesian Knowledge Tracing Model

ERIC Educational Resources Information Center

van de Sande, Brett

2013-01-01

Bayesian Knowledge Tracing is used very widely to model student learning. It comes in two different forms: The first form is the Bayesian Knowledge Tracing "hidden Markov model" which predicts the probability of correct application of a skill as a function of the number of previous opportunities to apply that skill and the model…

Bayesian data analysis tools for atomic physics

NASA Astrophysics Data System (ADS)

Trassinelli, Martino

2017-10-01

We present an introduction to some concepts of Bayesian data analysis in the context of atomic physics. Starting from basic rules of probability, we present the Bayes' theorem and its applications. In particular we discuss about how to calculate simple and joint probability distributions and the Bayesian evidence, a model dependent quantity that allows to assign probabilities to different hypotheses from the analysis of a same data set. To give some practical examples, these methods are applied to two concrete cases. In the first example, the presence or not of a satellite line in an atomic spectrum is investigated. In the second example, we determine the most probable model among a set of possible profiles from the analysis of a statistically poor spectrum. We show also how to calculate the probability distribution of the main spectral component without having to determine uniquely the spectrum modeling. For these two studies, we implement the program Nested_fit to calculate the different probability distributions and other related quantities. Nested_fit is a Fortran90/Python code developed during the last years for analysis of atomic spectra. As indicated by the name, it is based on the nested algorithm, which is presented in details together with the program itself.

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 predictive power: choice of prior and some recommendations for its use as probability of success in drug development.

PubMed

Rufibach, Kaspar; Burger, Hans Ulrich; Abt, Markus

2016-09-01

Bayesian predictive power, the expectation of the power function with respect to a prior distribution for the true underlying effect size, is routinely used in drug development to quantify the probability of success of a clinical trial. Choosing the prior is crucial for the properties and interpretability of Bayesian predictive power. We review recommendations on the choice of prior for Bayesian predictive power and explore its features as a function of the prior. The density of power values induced by a given prior is derived analytically and its shape characterized. We find that for a typical clinical trial scenario, this density has a u-shape very similar, but not equal, to a β-distribution. Alternative priors are discussed, and practical recommendations to assess the sensitivity of Bayesian predictive power to its input parameters are provided. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Detecting temporal trends in species assemblages with bootstrapping procedures and hierarchical models

USGS Publications Warehouse

Gotelli, Nicholas J.; Dorazio, Robert M.; Ellison, Aaron M.; Grossman, Gary D.

2010-01-01

Quantifying patterns of temporal trends in species assemblages is an important analytical challenge in community ecology. We describe methods of analysis that can be applied to a matrix of counts of individuals that is organized by species (rows) and time-ordered sampling periods (columns). We first developed a bootstrapping procedure to test the null hypothesis of random sampling from a stationary species abundance distribution with temporally varying sampling probabilities. This procedure can be modified to account for undetected species. We next developed a hierarchical model to estimate species-specific trends in abundance while accounting for species-specific probabilities of detection. We analysed two long-term datasets on stream fishes and grassland insects to demonstrate these methods. For both assemblages, the bootstrap test indicated that temporal trends in abundance were more heterogeneous than expected under the null model. We used the hierarchical model to estimate trends in abundance and identified sets of species in each assemblage that were steadily increasing, decreasing or remaining constant in abundance over more than a decade of standardized annual surveys. Our methods of analysis are broadly applicable to other ecological datasets, and they represent an advance over most existing procedures, which do not incorporate effects of incomplete sampling and imperfect detection.

Pinworm diversity in free-ranging howler monkeys (Alouatta spp.) in Mexico: Morphological and molecular evidence for two new Trypanoxyuris species (Nematoda: Oxyuridae).

PubMed

Solórzano-García, Brenda; Nadler, Steven A; Pérez-Ponce de León, Gerardo

2016-10-01

Two new species of Trypanoxyuris are described from the intestine of free-ranging howler monkeys in Mexico, Trypanoxyuris multilabiatus n. sp. from the mantled howler Alouatta palliata, and Trypanoxyuris pigrae n. sp. from the black howler Alouatta pigra. An integrative taxonomic approach is followed, where conspicuous morphological traits and phylogenetic trees based on DNA sequences are used to test the validity of the two new species. The mitochondrial cytochrome oxidase subunit 1 gene, and the nuclear ribosomal 18S and 28S rRNA genes were used for evolutionary analyses, with the concatenated dataset of all three genes used for maximum likelihood and Bayesian phylogenetic analyses. The two new species of pinworms from howler monkeys were morphologically distinct and formed reciprocally monophyletic lineages in molecular phylogenetic trees. The three species from howler monkeys, T. multilabiatus n. sp., T. pigrae n. sp., and Trypanoxyuris minutus, formed a monophyletic group with high bootstrap and posterior probability support values. Phylogenetic patterns inferred from sequence data support the hypothesis of a close evolutionary association between these primate hosts and their pinworm parasites. The results suggest that the diversity of pinworm parasites from Neotropical primates might be underestimated. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Phylogenetic placement of an unusual coral mushroom challenges the classic hypothesis of strict coevolution in the apterostigma pilosum group ant-fungus mutualism.

PubMed

Dentinger, Bryn T M; Lodge, D Jean; Munkacsi, Andrew B; Desjardin, Dennis E; McLaughlin, David J

2009-08-01

The approximately 50 million-year-old fungus-farming ant mutualism is a classic example of coevolution, involving ants that subsist on asexual, fungal biomass, in turn propagating the fungus clonally through nest-to-nest transmission. Most mutualistic ants cultivate two closely related groups of gilled mushrooms, whereas one small group of ants in the genus Apterostigma cultivates a distantly related lineage comprised of the G2 and G4 groups. The G2 and G4 fungi were previously shown to form a monophyletic group sister to the thread-like coral mushroom family Pterulaceae. Here, we identify an enigmatic coral mushroom that produces both fertile and sterile fruiting structures as the closest free-living relative of the G4 fungi, challenging the monophyly of the Apterostigma-cultivated fungi for the first time. Both nonparametric bootstrap and Bayesian posterior probability support the node leading to the G4 cultivars and a free-living Pterula mushroom. These data suggest three scenarios that contradict the hypothesis of strict coevolution: (1) multiple domestications, (2) escape from domestication, (3) selection of single cultivar lineages from an ancestral mixed-fungus garden. These results illustrate how incomplete phylogenies for coevolved symbionts impede our understanding of the patterns and processes of coevolution.

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…

Evaluating impacts using a BACI design, ratios, and a Bayesian approach with a focus on restoration.

PubMed

Conner, Mary M; Saunders, W Carl; Bouwes, Nicolaas; Jordan, Chris

2015-10-01

Before-after-control-impact (BACI) designs are an effective method to evaluate natural and human-induced perturbations on ecological variables when treatment sites cannot be randomly chosen. While effect sizes of interest can be tested with frequentist methods, using Bayesian Markov chain Monte Carlo (MCMC) sampling methods, probabilities of effect sizes, such as a ≥20 % increase in density after restoration, can be directly estimated. Although BACI and Bayesian methods are used widely for assessing natural and human-induced impacts for field experiments, the application of hierarchal Bayesian modeling with MCMC sampling to BACI designs is less common. Here, we combine these approaches and extend the typical presentation of results with an easy to interpret ratio, which provides an answer to the main study question-"How much impact did a management action or natural perturbation have?" As an example of this approach, we evaluate the impact of a restoration project, which implemented beaver dam analogs, on survival and density of juvenile steelhead. Results indicated the probabilities of a ≥30 % increase were high for survival and density after the dams were installed, 0.88 and 0.99, respectively, while probabilities for a higher increase of ≥50 % were variable, 0.17 and 0.82, respectively. This approach demonstrates a useful extension of Bayesian methods that can easily be generalized to other study designs from simple (e.g., single factor ANOVA, paired t test) to more complicated block designs (e.g., crossover, split-plot). This approach is valuable for estimating the probabilities of restoration impacts or other management actions.

Assessing uncertainties in superficial water provision by different bootstrap-based techniques

NASA Astrophysics Data System (ADS)

Rodrigues, Dulce B. B.; Gupta, Hoshin V.; Mendiondo, Eduardo Mario

2014-05-01

An assessment of water security can incorporate several water-related concepts, characterizing the interactions between societal needs, ecosystem functioning, and hydro-climatic conditions. The superficial freshwater provision level depends on the methods chosen for 'Environmental Flow Requirement' estimations, which integrate the sources of uncertainty in the understanding of how water-related threats to aquatic ecosystem security arise. Here, we develop an uncertainty assessment of superficial freshwater provision based on different bootstrap techniques (non-parametric resampling with replacement). To illustrate this approach, we use an agricultural basin (291 km2) within the Cantareira water supply system in Brazil monitored by one daily streamflow gage (24-year period). The original streamflow time series has been randomly resampled for different times or sample sizes (N = 500; ...; 1000), then applied to the conventional bootstrap approach and variations of this method, such as: 'nearest neighbor bootstrap'; and 'moving blocks bootstrap'. We have analyzed the impact of the sampling uncertainty on five Environmental Flow Requirement methods, based on: flow duration curves or probability of exceedance (Q90%, Q75% and Q50%); 7-day 10-year low-flow statistic (Q7,10); and presumptive standard (80% of the natural monthly mean ?ow). The bootstrap technique has been also used to compare those 'Environmental Flow Requirement' (EFR) methods among themselves, considering the difference between the bootstrap estimates and the "true" EFR characteristic, which has been computed averaging the EFR values of the five methods and using the entire streamflow record at monitoring station. This study evaluates the bootstrapping strategies, the representativeness of streamflow series for EFR estimates and their confidence intervals, in addition to overview of the performance differences between the EFR methods. The uncertainties arisen during EFR methods assessment will be propagated through water security indicators referring to water scarcity and vulnerability, seeking to provide meaningful support to end-users and water managers facing the incorporation of uncertainties in the decision making process.

Using Playing Cards to Differentiate Probability Interpretations

ERIC Educational Resources Information Center

López Puga, Jorge

2014-01-01

The aprioristic (classical, naïve and symmetric) and frequentist interpretations of probability are commonly known. Bayesian or subjective interpretation of probability is receiving increasing attention. This paper describes an activity to help students differentiate between the three types of probability interpretations.

Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis

PubMed Central

Fancher, Chris M.; Han, Zhen; Levin, Igor; Page, Katharine; Reich, Brian J.; Smith, Ralph C.; Wilson, Alyson G.; Jones, Jacob L.

2016-01-01

A Bayesian inference method for refining crystallographic structures is presented. The distribution of model parameters is stochastically sampled using Markov chain Monte Carlo. Posterior probability distributions are constructed for all model parameters to properly quantify uncertainty by appropriately modeling the heteroskedasticity and correlation of the error structure. The proposed method is demonstrated by analyzing a National Institute of Standards and Technology silicon standard reference material. The results obtained by Bayesian inference are compared with those determined by Rietveld refinement. Posterior probability distributions of model parameters provide both estimates and uncertainties. The new method better estimates the true uncertainties in the model as compared to the Rietveld method. PMID:27550221

Bayesian demography 250 years after Bayes

PubMed Central

Bijak, Jakub; Bryant, John

2016-01-01

Bayesian statistics offers an alternative to classical (frequentist) statistics. It is distinguished by its use of probability distributions to describe uncertain quantities, which leads to elegant solutions to many difficult statistical problems. Although Bayesian demography, like Bayesian statistics more generally, is around 250 years old, only recently has it begun to flourish. The aim of this paper is to review the achievements of Bayesian demography, address some misconceptions, and make the case for wider use of Bayesian methods in population studies. We focus on three applications: demographic forecasts, limited data, and highly structured or complex models. The key advantages of Bayesian methods are the ability to integrate information from multiple sources and to describe uncertainty coherently. Bayesian methods also allow for including additional (prior) information next to the data sample. As such, Bayesian approaches are complementary to many traditional methods, which can be productively re-expressed in Bayesian terms. PMID:26902889

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.

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).

Multivariate Bayesian modeling of known and unknown causes of events--an application to biosurveillance.

PubMed

Shen, Yanna; Cooper, Gregory F

2012-09-01

This paper investigates Bayesian modeling of known and unknown causes of events in the context of disease-outbreak detection. We introduce a multivariate Bayesian approach that models multiple evidential features of every person in the population. This approach models and detects (1) known diseases (e.g., influenza and anthrax) by using informative prior probabilities and (2) unknown diseases (e.g., a new, highly contagious respiratory virus that has never been seen before) by using relatively non-informative prior probabilities. We report the results of simulation experiments which support that this modeling method can improve the detection of new disease outbreaks in a population. A contribution of this paper is that it introduces a multivariate Bayesian approach for jointly modeling both known and unknown causes of events. Such modeling has general applicability in domains where the space of known causes is incomplete. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.

Encoding dependence in Bayesian causal networks

USDA-ARS?s Scientific Manuscript database

Bayesian networks (BNs) represent complex, uncertain spatio-temporal dynamics by propagation of conditional probabilities between identifiable states with a testable causal interaction model. Typically, they assume random variables are discrete in time and space with a static network structure that ...

Quantum Inference on Bayesian Networks

NASA Astrophysics Data System (ADS)

Yoder, Theodore; Low, Guang Hao; Chuang, Isaac

2014-03-01

Because quantum physics is naturally probabilistic, it seems reasonable to expect physical systems to describe probabilities and their evolution in a natural fashion. Here, we use quantum computation to speedup sampling from a graphical probability model, the Bayesian network. A specialization of this sampling problem is approximate Bayesian inference, where the distribution on query variables is sampled given the values e of evidence variables. Inference is a key part of modern machine learning and artificial intelligence tasks, but is known to be NP-hard. Classically, a single unbiased sample is obtained from a Bayesian network on n variables with at most m parents per node in time (nmP(e) - 1 / 2) , depending critically on P(e) , the probability the evidence might occur in the first place. However, by implementing a quantum version of rejection sampling, we obtain a square-root speedup, taking (n2m P(e) -1/2) time per sample. The speedup is the result of amplitude amplification, which is proving to be broadly applicable in sampling and machine learning tasks. In particular, we provide an explicit and efficient circuit construction that implements the algorithm without the need for oracle access.

A Bootstrap Metropolis-Hastings Algorithm for Bayesian Analysis of Big Data.

PubMed

Liang, Faming; Kim, Jinsu; Song, Qifan

2016-01-01

Markov chain Monte Carlo (MCMC) methods have proven to be a very powerful tool for analyzing data of complex structures. However, their computer-intensive nature, which typically require a large number of iterations and a complete scan of the full dataset for each iteration, precludes their use for big data analysis. In this paper, we propose the so-called bootstrap Metropolis-Hastings (BMH) algorithm, which provides a general framework for how to tame powerful MCMC methods to be used for big data analysis; that is to replace the full data log-likelihood by a Monte Carlo average of the log-likelihoods that are calculated in parallel from multiple bootstrap samples. The BMH algorithm possesses an embarrassingly parallel structure and avoids repeated scans of the full dataset in iterations, and is thus feasible for big data problems. Compared to the popular divide-and-combine method, BMH can be generally more efficient as it can asymptotically integrate the whole data information into a single simulation run. The BMH algorithm is very flexible. Like the Metropolis-Hastings algorithm, it can serve as a basic building block for developing advanced MCMC algorithms that are feasible for big data problems. This is illustrated in the paper by the tempering BMH algorithm, which can be viewed as a combination of parallel tempering and the BMH algorithm. BMH can also be used for model selection and optimization by combining with reversible jump MCMC and simulated annealing, respectively.

A Bootstrap Metropolis–Hastings Algorithm for Bayesian Analysis of Big Data

PubMed Central

Kim, Jinsu; Song, Qifan

2016-01-01

Markov chain Monte Carlo (MCMC) methods have proven to be a very powerful tool for analyzing data of complex structures. However, their computer-intensive nature, which typically require a large number of iterations and a complete scan of the full dataset for each iteration, precludes their use for big data analysis. In this paper, we propose the so-called bootstrap Metropolis-Hastings (BMH) algorithm, which provides a general framework for how to tame powerful MCMC methods to be used for big data analysis; that is to replace the full data log-likelihood by a Monte Carlo average of the log-likelihoods that are calculated in parallel from multiple bootstrap samples. The BMH algorithm possesses an embarrassingly parallel structure and avoids repeated scans of the full dataset in iterations, and is thus feasible for big data problems. Compared to the popular divide-and-combine method, BMH can be generally more efficient as it can asymptotically integrate the whole data information into a single simulation run. The BMH algorithm is very flexible. Like the Metropolis-Hastings algorithm, it can serve as a basic building block for developing advanced MCMC algorithms that are feasible for big data problems. This is illustrated in the paper by the tempering BMH algorithm, which can be viewed as a combination of parallel tempering and the BMH algorithm. BMH can also be used for model selection and optimization by combining with reversible jump MCMC and simulated annealing, respectively. PMID:29033469

Bayesian screening for active compounds in high-dimensional chemical spaces combining property descriptors and molecular fingerprints.

PubMed

Vogt, Martin; Bajorath, Jürgen

2008-01-01

Bayesian classifiers are increasingly being used to distinguish active from inactive compounds and search large databases for novel active molecules. We introduce an approach to directly combine the contributions of property descriptors and molecular fingerprints in the search for active compounds that is based on a Bayesian framework. Conventionally, property descriptors and fingerprints are used as alternative features for virtual screening methods. Following the approach introduced here, probability distributions of descriptor values and fingerprint bit settings are calculated for active and database molecules and the divergence between the resulting combined distributions is determined as a measure of biological activity. In test calculations on a large number of compound activity classes, this methodology was found to consistently perform better than similarity searching using fingerprints and multiple reference compounds or Bayesian screening calculations using probability distributions calculated only from property descriptors. These findings demonstrate that there is considerable synergy between different types of property descriptors and fingerprints in recognizing diverse structure-activity relationships, at least in the context of Bayesian modeling.

Variable Discretisation for Anomaly Detection using Bayesian Networks

DTIC Science & Technology

2017-01-01

UNCLASSIFIED DST- Group –TR–3328 1 Introduction Bayesian network implementations usually require each variable to take on a finite number of mutually...UNCLASSIFIED Variable Discretisation for Anomaly Detection using Bayesian Networks Jonathan Legg National Security and ISR Division Defence Science...and Technology Group DST- Group –TR–3328 ABSTRACT Anomaly detection is the process by which low probability events are automatically found against a

Entanglement-enhanced Neyman-Pearson target detection using quantum illumination

NASA Astrophysics Data System (ADS)

Zhuang, Quntao; Zhang, Zheshen; Shapiro, Jeffrey H.

2017-08-01

Quantum illumination (QI) provides entanglement-based target detection---in an entanglement-breaking environment---whose performance is significantly better than that of optimum classical-illumination target detection. QI's performance advantage was established in a Bayesian setting with the target presumed equally likely to be absent or present and error probability employed as the performance metric. Radar theory, however, eschews that Bayesian approach, preferring the Neyman-Pearson performance criterion to avoid the difficulties of accurately assigning prior probabilities to target absence and presence and appropriate costs to false-alarm and miss errors. We have recently reported an architecture---based on sum-frequency generation (SFG) and feedforward (FF) processing---for minimum error-probability QI target detection with arbitrary prior probabilities for target absence and presence. In this paper, we use our results for FF-SFG reception to determine the receiver operating characteristic---detection probability versus false-alarm probability---for optimum QI target detection under the Neyman-Pearson criterion.

Bayesian randomized clinical trials: From fixed to adaptive design.

PubMed

Yin, Guosheng; Lam, Chi Kin; Shi, Haolun

2017-08-01

Randomized controlled studies are the gold standard for phase III clinical trials. Using α-spending functions to control the overall type I error rate, group sequential methods are well established and have been dominating phase III studies. Bayesian randomized design, on the other hand, can be viewed as a complement instead of competitive approach to the frequentist methods. For the fixed Bayesian design, the hypothesis testing can be cast in the posterior probability or Bayes factor framework, which has a direct link to the frequentist type I error rate. Bayesian group sequential design relies upon Bayesian decision-theoretic approaches based on backward induction, which is often computationally intensive. Compared with the frequentist approaches, Bayesian methods have several advantages. The posterior predictive probability serves as a useful and convenient tool for trial monitoring, and can be updated at any time as the data accrue during the trial. The Bayesian decision-theoretic framework possesses a direct link to the decision making in the practical setting, and can be modeled more realistically to reflect the actual cost-benefit analysis during the drug development process. Other merits include the possibility of hierarchical modeling and the use of informative priors, which would lead to a more comprehensive utilization of information from both historical and longitudinal data. From fixed to adaptive design, we focus on Bayesian randomized controlled clinical trials and make extensive comparisons with frequentist counterparts through numerical studies. Copyright © 2017 Elsevier Inc. All rights reserved.

Uncertainty Analysis and Parameter Estimation For Nearshore Hydrodynamic Models

NASA Astrophysics Data System (ADS)

Ardani, S.; Kaihatu, J. M.

2012-12-01

Numerical models represent deterministic approaches used for the relevant physical processes in the nearshore. Complexity of the physics of the model and uncertainty involved in the model inputs compel us to apply a stochastic approach to analyze the robustness of the model. The Bayesian inverse problem is one powerful way to estimate the important input model parameters (determined by apriori sensitivity analysis) and can be used for uncertainty analysis of the outputs. Bayesian techniques can be used to find the range of most probable parameters based on the probability of the observed data and the residual errors. In this study, the effect of input data involving lateral (Neumann) boundary conditions, bathymetry and off-shore wave conditions on nearshore numerical models are considered. Monte Carlo simulation is applied to a deterministic numerical model (the Delft3D modeling suite for coupled waves and flow) for the resulting uncertainty analysis of the outputs (wave height, flow velocity, mean sea level and etc.). Uncertainty analysis of outputs is performed by random sampling from the input probability distribution functions and running the model as required until convergence to the consistent results is achieved. The case study used in this analysis is the Duck94 experiment, which was conducted at the U.S. Army Field Research Facility at Duck, North Carolina, USA in the fall of 1994. The joint probability of model parameters relevant for the Duck94 experiments will be found using the Bayesian approach. We will further show that, by using Bayesian techniques to estimate the optimized model parameters as inputs and applying them for uncertainty analysis, we can obtain more consistent results than using the prior information for input data which means that the variation of the uncertain parameter will be decreased and the probability of the observed data will improve as well. Keywords: Monte Carlo Simulation, Delft3D, uncertainty analysis, Bayesian techniques, MCMC

Making Sense of a Negative Clinical Trial Result: A Bayesian Analysis of a Clinical Trial of Lorazepam and Diazepam for Pediatric Status Epilepticus.

PubMed

Chamberlain, Daniel B; Chamberlain, James M

2017-01-01

We demonstrate the application of a Bayesian approach to a recent negative clinical trial result. A Bayesian analysis of such a trial can provide a more useful interpretation of results and can incorporate previous evidence. This was a secondary analysis of the efficacy and safety results of the Pediatric Seizure Study, a randomized clinical trial of lorazepam versus diazepam for pediatric status epilepticus. We included the published results from the only prospective pediatric study of status in a Bayesian hierarchic model, and we performed sensitivity analyses on the amount of pooling between studies. We evaluated 3 summary analyses for the results: superiority, noninferiority (margin <-10%), and practical equivalence (within ±10%). Consistent with the original study's classic analysis of study results, we did not demonstrate superiority of lorazepam over diazepam. There is a 95% probability that the true efficacy of lorazepam is in the range of 66% to 80%. For both the efficacy and safety outcomes, there was greater than 95% probability that lorazepam is noninferior to diazepam, and there was greater than 90% probability that the 2 medications are practically equivalent. The results were largely driven by the current study because of the sample sizes of our study (n=273) and the previous pediatric study (n=61). Because Bayesian analysis estimates the probability of one or more hypotheses, such an approach can provide more useful information about the meaning of the results of a negative trial outcome. In the case of pediatric status epilepticus, it is highly likely that lorazepam is noninferior and practically equivalent to diazepam. Copyright © 2016 American College of Emergency Physicians. Published by Elsevier Inc. All rights reserved.

Confidence as Bayesian Probability: From Neural Origins to Behavior.

PubMed

Meyniel, Florent; Sigman, Mariano; Mainen, Zachary F

2015-10-07

Research on confidence spreads across several sub-fields of psychology and neuroscience. Here, we explore how a definition of confidence as Bayesian probability can unify these viewpoints. This computational view entails that there are distinct forms in which confidence is represented and used in the brain, including distributional confidence, pertaining to neural representations of probability distributions, and summary confidence, pertaining to scalar summaries of those distributions. Summary confidence is, normatively, derived or "read out" from distributional confidence. Neural implementations of readout will trade off optimality versus flexibility of routing across brain systems, allowing confidence to serve diverse cognitive functions. Copyright © 2015 Elsevier Inc. All rights reserved.

Bayesian paradox in homeland security and homeland defense

NASA Astrophysics Data System (ADS)

Jannson, Tomasz; Forrester, Thomas; Wang, Wenjian

2011-06-01

In this paper we discuss a rather surprising result of Bayesian inference analysis: performance of a broad variety of sensors depends not only on a sensor system itself, but also on CONOPS parameters in such a way that even an excellent sensor system can perform poorly if absolute probabilities of a threat (target) are lower than a false alarm probability. This result, which we call Bayesian paradox, holds not only for binary sensors as discussed in the lead author's previous papers, but also for a more general class of multi-target sensors, discussed also in this paper. Examples include: ATR (automatic target recognition), luggage X-ray inspection for explosives, medical diagnostics, car engine diagnostics, judicial decisions, and many other issues.

Uncertainty plus Prior Equals Rational Bias: An Intuitive Bayesian Probability Weighting Function

ERIC Educational Resources Information Center

Fennell, John; Baddeley, Roland

2012-01-01

Empirical research has shown that when making choices based on probabilistic options, people behave as if they overestimate small probabilities, underestimate large probabilities, and treat positive and negative outcomes differently. These distortions have been modeled using a nonlinear probability weighting function, which is found in several…

Feasibility of streamlining an interactive Bayesian-based diagnostic support tool designed for clinical practice

NASA Astrophysics Data System (ADS)

Chen, Po-Hao; Botzolakis, Emmanuel; Mohan, Suyash; Bryan, R. N.; Cook, Tessa

2016-03-01

In radiology, diagnostic errors occur either through the failure of detection or incorrect interpretation. Errors are estimated to occur in 30-35% of all exams and contribute to 40-54% of medical malpractice litigations. In this work, we focus on reducing incorrect interpretation of known imaging features. Existing literature categorizes cognitive bias leading a radiologist to an incorrect diagnosis despite having correctly recognized the abnormal imaging features: anchoring bias, framing effect, availability bias, and premature closure. Computational methods make a unique contribution, as they do not exhibit the same cognitive biases as a human. Bayesian networks formalize the diagnostic process. They modify pre-test diagnostic probabilities using clinical and imaging features, arriving at a post-test probability for each possible diagnosis. To translate Bayesian networks to clinical practice, we implemented an entirely web-based open-source software tool. In this tool, the radiologist first selects a network of choice (e.g. basal ganglia). Then, large, clearly labeled buttons displaying salient imaging features are displayed on the screen serving both as a checklist and for input. As the radiologist inputs the value of an extracted imaging feature, the conditional probabilities of each possible diagnosis are updated. The software presents its level of diagnostic discrimination using a Pareto distribution chart, updated with each additional imaging feature. Active collaboration with the clinical radiologist is a feasible approach to software design and leads to design decisions closely coupling the complex mathematics of conditional probability in Bayesian networks with practice.

Trending in Probability of Collision Measurements via a Bayesian Zero-Inflated Beta Mixed Model

NASA Technical Reports Server (NTRS)

Vallejo, Jonathon; Hejduk, Matt; Stamey, James

2015-01-01

We investigate the performance of a generalized linear mixed model in predicting the Probabilities of Collision (Pc) for conjunction events. Specifically, we apply this model to the log(sub 10) transformation of these probabilities and argue that this transformation yields values that can be considered bounded in practice. Additionally, this bounded random variable, after scaling, is zero-inflated. Consequently, we model these values using the zero-inflated Beta distribution, and utilize the Bayesian paradigm and the mixed model framework to borrow information from past and current events. This provides a natural way to model the data and provides a basis for answering questions of interest, such as what is the likelihood of observing a probability of collision equal to the effective value of zero on a subsequent observation.

Recent Transmission Clustering of HIV-1 C and CRF17_BF Strains Characterized by NNRTI-Related Mutations among Newly Diagnosed Men in Central Italy

PubMed Central

Orchi, Nicoletta; Gori, Caterina; Bertoli, Ada; Forbici, Federica; Montella, Francesco; Pennica, Alfredo; De Carli, Gabriella; Giuliani, Massimo; Continenza, Fabio; Pinnetti, Carmela; Nicastri, Emanuele; Ceccherini-Silberstein, Francesca; Mastroianni, Claudio Maria; Girardi, Enrico; Andreoni, Massimo; Antinori, Andrea; Santoro, Maria Mercedes; Perno, Carlo Federico

2015-01-01

Background Increased evidence of relevant HIV-1 epidemic transmission in European countries is being reported, with an increased circulation of non-B-subtypes. Here, we present two recent HIV-1 non-B transmission clusters characterized by NNRTI-related amino-acidic mutations among newly diagnosed HIV-1 infected men, living in Rome (Central-Italy). Methods Pol and V3 sequences were available at the time of diagnosis for all individuals. Maximum-Likelihood and Bayesian phylogenetic-trees with bootstrap and Bayesian-probability supports defined transmission-clusters. HIV-1 drug-resistance and V3-tropism were also evaluated. Results Among 534 new HIV-1 non-B cases, diagnosed from 2011 to 2014, in Central-Italy, 35 carried virus gathering in two distinct clusters, including 27 HIV-1 C and 8 CRF17_BF subtypes, respectively. Both clusters were centralized in Rome, and their origin was estimated to have been after 2007. All individuals within both clusters were males and 37.1% of them had been recently-infected. While C-cluster was entirely composed by Italian men-who-have-sex-with-men, with a median-age of 34 years (IQR:30–39), individuals in CRF17_BF-cluster were older, with a median-age of 51 years (IQR:48–59) and almost all reported sexual-contacts with men and women. All carried R5-tropic viruses, with evidence of atypical or resistance amino-acidic mutations related to NNRTI-drugs (K103Q in C-cluster, and K101E+E138K in CRF17_BF-cluster). Conclusions These two epidemiological clusters provided evidence of a strong and recent circulation of C and CRF17_BF strains in central Italy, characterized by NNRTI-related mutations among men engaging in high-risk behaviours. These findings underline the role of molecular epidemiology in identifying groups at increased risk of HIV-1 transmission, and in enhancing additional prevention efforts. PMID:26270824

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.

Quantum Bayesian perspective for intelligence reservoir characterization, monitoring and management

NASA Astrophysics Data System (ADS)

Lozada Aguilar, Miguel Ángel; Khrennikov, Andrei; Oleschko, Klaudia; de Jesús Correa, María

2017-10-01

The paper starts with a brief review of the literature about uncertainty in geological, geophysical and petrophysical data. In particular, we present the viewpoints of experts in geophysics on the application of Bayesian inference and subjective probability. Then we present arguments that the use of classical probability theory (CP) does not match completely the structure of geophysical data. We emphasize that such data are characterized by contextuality and non-Kolmogorovness (the impossibility to use the CP model), incompleteness as well as incompatibility of some geophysical measurements. These characteristics of geophysical data are similar to the characteristics of quantum physical data. Notwithstanding all this, contextuality can be seen as a major deviation of quantum theory from classical physics. In particular, the contextual probability viewpoint is the essence of the Växjö interpretation of quantum mechanics. We propose to use quantum probability (QP) for decision-making during the characterization, modelling, exploring and management of the intelligent hydrocarbon reservoir. Quantum Bayesianism (QBism), one of the recently developed information interpretations of quantum theory, can be used as the interpretational basis for such QP decision-making in geology, geophysics and petroleum projects design and management. This article is part of the themed issue `Second quantum revolution: foundational questions'.

Fuzzy Bayesian Network-Bow-Tie Analysis of Gas Leakage during Biomass Gasification

PubMed Central

Yan, Fang; Xu, Kaili; Yao, Xiwen; Li, Yang

2016-01-01

Biomass gasification technology has been rapidly developed recently. But fire and poisoning accidents caused by gas leakage restrict the development and promotion of biomass gasification. Therefore, probabilistic safety assessment (PSA) is necessary for biomass gasification system. Subsequently, Bayesian network-bow-tie (BN-bow-tie) analysis was proposed by mapping bow-tie analysis into Bayesian network (BN). Causes of gas leakage and the accidents triggered by gas leakage can be obtained by bow-tie analysis, and BN was used to confirm the critical nodes of accidents by introducing corresponding three importance measures. Meanwhile, certain occurrence probability of failure was needed in PSA. In view of the insufficient failure data of biomass gasification, the occurrence probability of failure which cannot be obtained from standard reliability data sources was confirmed by fuzzy methods based on expert judgment. An improved approach considered expert weighting to aggregate fuzzy numbers included triangular and trapezoidal numbers was proposed, and the occurrence probability of failure was obtained. Finally, safety measures were indicated based on the obtained critical nodes. The theoretical occurrence probabilities in one year of gas leakage and the accidents caused by it were reduced to 1/10.3 of the original values by these safety measures. PMID:27463975

Using indirect comparisons to compare interventions within a Cochrane review: a tool for comparative effectiveness research.

PubMed

Agapova, Maria; Devine, Emily B; Nguyen, Hiep; Wolf, Fredric M; Inoue, Lurdes Y T

2014-07-01

Assessing relative performance among competing interventions is an important part of comparative effectiveness research. Bayesian indirect comparisons add information to existing Cochrane reviews, such as which intervention is likely to perform best. However, heterogeneity variance priors may influence results and, potentially, clinical guidance. We highlight the features of Bayesian indirect comparisons using a case study of a Cochrane review update in asthma care. The probability that one self-management educational intervention outperforms others is estimated. Simulation studies investigate the effect of heterogeneity variance prior distributions. Results suggest a 55% probability that individual education is best, followed by combination (39%) and group (6%). The intervention with few trials was sensitive to prior distributions. Bayesian indirect comparisons updates of Cochrane reviews are valuable comparative effectiveness research tools.

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

Gagné, Jonathan; Lafrenière, David; Doyon, René

We present Bayesian Analysis for Nearby Young AssociatioNs II (BANYAN II), a modified Bayesian analysis for assessing the membership of later-than-M5 objects to any of several Nearby Young Associations (NYAs). In addition to using kinematic information (from sky position and proper motion), this analysis exploits 2MASS-WISE color-magnitude diagrams in which old and young objects follow distinct sequences. As an improvement over our earlier work, the spatial and kinematic distributions for each association are now modeled as ellipsoids whose axes need not be aligned with the Galactic coordinate axes, and we use prior probabilities matching the expected populations of the NYAsmore » considered versus field stars. We present an extensive contamination analysis to characterize the performance of our new method. We find that Bayesian probabilities are generally representative of contamination rates, except when a parallax measurement is considered. In this case contamination rates become significantly smaller and hence Bayesian probabilities for NYA memberships are pessimistic. We apply this new algorithm to a sample of 158 objects from the literature that are either known to display spectroscopic signs of youth or have unusually red near-infrared colors for their spectral type. Based on our analysis, we identify 25 objects as new highly probable candidates to NYAs, including a new M7.5 bona fide member to Tucana-Horologium, making it the latest-type member. In addition, we reveal that a known L2γ dwarf is co-moving with a bright M5 dwarf, and we show for the first time that two of the currently known ultra red L dwarfs are strong candidates to the AB Doradus moving group. Several objects identified here as highly probable members to NYAs could be free-floating planetary-mass objects if their membership is confirmed.« less

On the use of posterior predictive probabilities and prediction uncertainty to tailor informative sampling for parasitological surveillance in livestock.

PubMed

Musella, Vincenzo; Rinaldi, Laura; Lagazio, Corrado; Cringoli, Giuseppe; Biggeri, Annibale; Catelan, Dolores

2014-09-15

Model-based geostatistics and Bayesian approaches are appropriate in the context of Veterinary Epidemiology when point data have been collected by valid study designs. The aim is to predict a continuous infection risk surface. Little work has been done on the use of predictive infection probabilities at farm unit level. In this paper we show how to use predictive infection probability and related uncertainty from a Bayesian kriging model to draw a informative samples from the 8794 geo-referenced sheep farms of the Campania region (southern Italy). Parasitological data come from a first cross-sectional survey carried out to study the spatial distribution of selected helminths in sheep farms. A grid sampling was performed to select the farms for coprological examinations. Faecal samples were collected for 121 sheep farms and the presence of 21 different helminths were investigated using the FLOTAC technique. The 21 responses are very different in terms of geographical distribution and prevalence of infection. The observed prevalence range is from 0.83% to 96.69%. The distributions of the posterior predictive probabilities for all the 21 parasites are very heterogeneous. We show how the results of the Bayesian kriging model can be used to plan a second wave survey. Several alternatives can be chosen depending on the purposes of the second survey: weight by posterior predictive probabilities, their uncertainty or combining both information. The proposed Bayesian kriging model is simple, and the proposed samping strategy represents a useful tool to address targeted infection control treatments and surbveillance campaigns. It is easily extendable to other fields of research. Copyright © 2014 Elsevier B.V. All rights reserved.

Pick a Sample.

ERIC Educational Resources Information Center

Peterson, Ivars

1991-01-01

A method that enables people to obtain the benefits of statistics and probability theory without the shortcomings of conventional methods because it is free of mathematical formulas and is easy to understand and use is described. A resampling technique called the "bootstrap" is discussed in terms of application and development. (KR)

Improved Correction of Misclassification Bias With Bootstrap Imputation.

PubMed

van Walraven, Carl

2018-07-01

Diagnostic codes used in administrative database research can create bias due to misclassification. Quantitative bias analysis (QBA) can correct for this bias, requires only code sensitivity and specificity, but may return invalid results. Bootstrap imputation (BI) can also address misclassification bias but traditionally requires multivariate models to accurately estimate disease probability. This study compared misclassification bias correction using QBA and BI. Serum creatinine measures were used to determine severe renal failure status in 100,000 hospitalized patients. Prevalence of severe renal failure in 86 patient strata and its association with 43 covariates was determined and compared with results in which renal failure status was determined using diagnostic codes (sensitivity 71.3%, specificity 96.2%). Differences in results (misclassification bias) were then corrected with QBA or BI (using progressively more complex methods to estimate disease probability). In total, 7.4% of patients had severe renal failure. Imputing disease status with diagnostic codes exaggerated prevalence estimates [median relative change (range), 16.6% (0.8%-74.5%)] and its association with covariates [median (range) exponentiated absolute parameter estimate difference, 1.16 (1.01-2.04)]. QBA produced invalid results 9.3% of the time and increased bias in estimates of both disease prevalence and covariate associations. BI decreased misclassification bias with increasingly accurate disease probability estimates. QBA can produce invalid results and increase misclassification bias. BI avoids invalid results and can importantly decrease misclassification bias when accurate disease probability estimates are used.

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.

MapReduce Based Parallel Bayesian Network for Manufacturing Quality Control

NASA Astrophysics Data System (ADS)

Zheng, Mao-Kuan; Ming, Xin-Guo; Zhang, Xian-Yu; Li, Guo-Ming

2017-09-01

Increasing complexity of industrial products and manufacturing processes have challenged conventional statistics based quality management approaches in the circumstances of dynamic production. A Bayesian network and big data analytics integrated approach for manufacturing process quality analysis and control is proposed. Based on Hadoop distributed architecture and MapReduce parallel computing model, big volume and variety quality related data generated during the manufacturing process could be dealt with. Artificial intelligent algorithms, including Bayesian network learning, classification and reasoning, are embedded into the Reduce process. Relying on the ability of the Bayesian network in dealing with dynamic and uncertain problem and the parallel computing power of MapReduce, Bayesian network of impact factors on quality are built based on prior probability distribution and modified with posterior probability distribution. A case study on hull segment manufacturing precision management for ship and offshore platform building shows that computing speed accelerates almost directly proportionally to the increase of computing nodes. It is also proved that the proposed model is feasible for locating and reasoning of root causes, forecasting of manufacturing outcome, and intelligent decision for precision problem solving. The integration of bigdata analytics and BN method offers a whole new perspective in manufacturing quality control.

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.

Hyperspectral techniques in analysis of oral dosage forms.

PubMed

Hamilton, Sara J; Lowell, Amanda E; Lodder, Robert A

2002-10-01

Pharmaceutical oral dosage forms are used in this paper to test the sensitivity and spatial resolution of hyperspectral imaging instruments. The first experiment tested the hypothesis that a near-infrared (IR) tunable diode-based remote sensing system is capable of monitoring degradation of hard gelatin capsules at a relatively long distance (0.5 km). Spectra from the capsules were used to differentiate among capsules exposed to an atmosphere containing 150 ppb formaldehyde for 0, 2, 4, and 8 h. Robust median-based principal component regression with Bayesian inference was employed for outlier detection. The second experiment tested the hypothesis that near-IR imaging spectrometry of tablets permits the identification and composition of multiple individual tablets to be determined simultaneously. A near-IR camera was used to collect thousands of spectra simultaneously from a field of blister-packaged tablets. The number of tablets that a typical near-IR camera can currently analyze simultaneously was estimated to be approximately 1300. The bootstrap error-adjusted single-sample technique chemometric-imaging algorithm was used to draw probability-density contour plots that revealed tablet composition. The single-capsule analysis provides an indication of how far apart the sample and instrumentation can be and still maintain adequate signal-to-noise ratio (S/N), while the multiple-tablet imaging experiment gives an indication of how many samples can be analyzed simultaneously while maintaining an adequate S/N and pixel coverage on each sample.

Bayesian approach to inverse statistical mechanics.

PubMed

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Bayesian approach to inverse statistical mechanics

NASA Astrophysics Data System (ADS)

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

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...

The Importance of Proving the Null

ERIC Educational Resources Information Center

Gallistel, C. R.

2009-01-01

Null hypotheses are simple, precise, and theoretically important. Conventional statistical analysis cannot support them; Bayesian analysis can. The challenge in a Bayesian analysis is to formulate a suitably vague alternative, because the vaguer the alternative is (the more it spreads out the unit mass of prior probability), the more the null is…

Common quandaries and their practical solutions in Bayesian network modeling

Treesearch

Bruce G. Marcot

2017-01-01

Use and popularity of Bayesian network (BN) modeling has greatly expanded in recent years, but many common problems remain. Here, I summarize key problems in BN model construction and interpretation,along with suggested practical solutions. Problems in BN model construction include parameterizing probability values, variable definition, complex network structures,...

Spectral Bayesian Knowledge Tracing

ERIC Educational Resources Information Center

Falakmasir, Mohammad; Yudelson, Michael; Ritter, Steve; Koedinger, Ken

2015-01-01

Bayesian Knowledge Tracing (BKT) has been in wide use for modeling student skill acquisition in Intelligent Tutoring Systems (ITS). BKT tracks and updates student's latent mastery of a skill as a probability distribution of a binary variable. BKT does so by accounting for observed student successes in applying the skill correctly, where success is…

Bayesian Estimation of the DINA Model with Gibbs Sampling

ERIC Educational Resources Information Center

Culpepper, Steven Andrew

2015-01-01

A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…

On the Bayesian Nonparametric Generalization of IRT-Type Models

ERIC Educational Resources Information Center

San Martin, Ernesto; Jara, Alejandro; Rolin, Jean-Marie; Mouchart, Michel

2011-01-01

We study the identification and consistency of Bayesian semiparametric IRT-type models, where the uncertainty on the abilities' distribution is modeled using a prior distribution on the space of probability measures. We show that for the semiparametric Rasch Poisson counts model, simple restrictions ensure the identification of a general…

IMPLICATIONS OF USING ROBUST BAYESIAN ANALYSIS TO REPRESENT DIVERSE SOURCES OF UNCERTAINTY IN INTEGRATED ASSESSMENT

EPA Science Inventory

In our previous research, we showed that robust Bayesian methods can be used in environmental modeling to define a set of probability distributions for key parameters that captures the effects of expert disagreement, ambiguity, or ignorance. This entire set can then be update...

Bayesian Modeling of a Human MMORPG Player

NASA Astrophysics Data System (ADS)

Synnaeve, Gabriel; Bessière, Pierre

2011-03-01

This paper describes an application of Bayesian programming to the control of an autonomous avatar in a multiplayer role-playing game (the example is based on World of Warcraft). We model a particular task, which consists of choosing what to do and to select which target in a situation where allies and foes are present. We explain the model in Bayesian programming and show how we could learn the conditional probabilities from data gathered during human-played sessions.

Bayesian Cherry Picking Revisited

NASA Astrophysics Data System (ADS)

Garrett, Anthony J. M.; Prozesky, Victor M.; Padayachee, J.

2004-04-01

Tins are marketed as containing nine cherries. To fill the tins, cherries are fed into a drum containing twelve holes through which air is sucked; either zero, one or two cherries stick in each hole. Dielectric measurements are then made on each hole. Three outcomes are distinguished: empty hole (which is reliable); one cherry (which indicates one cherry with high probability, or two cherries with a complementary low probability known from calibration); or an uncertain number (which also indicates one cherry or two, with known probabilities that are quite similar). A choice can be made from which holes simultaneously to discharge contents into the tin. The sum and product rules of probability are applied in a Bayesian manner to find the distribution for the number of cherries in the tin. Based on this distribution, ways are discussed to optimise the number to nine cherries.

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.

Updating: Learning versus Supposing

ERIC Educational Resources Information Center

Zhao, Jiaying; Crupi, Vincenzo; Tentori, Katya; Fitelson, Branden; Osherson, Daniel

2012-01-01

Bayesian orthodoxy posits a tight relationship between conditional probability and updating. Namely, the probability of an event "A" after learning "B" should equal the conditional probability of "A" given "B" prior to learning "B". We examine whether ordinary judgment conforms to the orthodox view. In three experiments we found substantial…

Asking better questions: How presentation formats influence information search.

PubMed

Wu, Charley M; Meder, Björn; Filimon, Flavia; Nelson, Jonathan D

2017-08-01

While the influence of presentation formats have been widely studied in Bayesian reasoning tasks, we present the first systematic investigation of how presentation formats influence information search decisions. Four experiments were conducted across different probabilistic environments, where subjects (N = 2,858) chose between 2 possible search queries, each with binary probabilistic outcomes, with the goal of maximizing classification accuracy. We studied 14 different numerical and visual formats for presenting information about the search environment, constructed across 6 design features that have been prominently related to improvements in Bayesian reasoning accuracy (natural frequencies, posteriors, complement, spatial extent, countability, and part-to-whole information). The posterior variants of the icon array and bar graph formats led to the highest proportion of correct responses, and were substantially better than the standard probability format. Results suggest that presenting information in terms of posterior probabilities and visualizing natural frequencies using spatial extent (a perceptual feature) were especially helpful in guiding search decisions, although environments with a mixture of probabilistic and certain outcomes were challenging across all formats. Subjects who made more accurate probability judgments did not perform better on the search task, suggesting that simple decision heuristics may be used to make search decisions without explicitly applying Bayesian inference to compute probabilities. We propose a new take-the-difference (TTD) heuristic that identifies the accuracy-maximizing query without explicit computation of posterior probabilities. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

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.

Software Supportability Risk Assessment in OT&E (Operational Test and Evaluation): Literature Review, Current Research Review, and Data Base Assemblage.

DTIC Science & Technology

1984-09-28

variables before simula- tion of model - Search for reality checks a, - Express uncertainty as a probability density distribution. a. H2 a, H-22 TWIF... probability that the software con- tains errors. This prior is updated as test failure data are accumulated. Only a p of 1 (software known to contain...discusssed; both parametric and nonparametric versions are presented. It is shown by the author that the bootstrap underlies the jackknife method and

Robust Statistics and Regularization for Feature Extraction and UXO Discrimination

DTIC Science & Technology

2011-07-01

July 11, 2011 real data we find that this technique has an improved probability of finding all ordnance in a test data set, relative to previously...many sites. Tests on larger data sets should still be carried out. In previous work we considered a bootstrapping approach to selecting the operating...Marginalizing over x we obtain the probability that the ith order statistic in the test data belongs to the T class (55) P (T |x(i)) = ∞∫ −∞ P (T |x)p(x

Bayesian Redshift Classification of Emission-line Galaxies with Photometric Equivalent Widths

NASA Astrophysics Data System (ADS)

Leung, Andrew S.; Acquaviva, Viviana; Gawiser, Eric; Ciardullo, Robin; Komatsu, Eiichiro; Malz, A. I.; Zeimann, Gregory R.; Bridge, Joanna S.; Drory, Niv; Feldmeier, John J.; Finkelstein, Steven L.; Gebhardt, Karl; Gronwall, Caryl; Hagen, Alex; Hill, Gary J.; Schneider, Donald P.

2017-07-01

We present a Bayesian approach to the redshift classification of emission-line galaxies when only a single emission line is detected spectroscopically. We consider the case of surveys for high-redshift Lyα-emitting galaxies (LAEs), which have traditionally been classified via an inferred rest-frame equivalent width (EW {W}{Lyα }) greater than 20 Å. Our Bayesian method relies on known prior probabilities in measured emission-line luminosity functions and EW distributions for the galaxy populations, and returns the probability that an object in question is an LAE given the characteristics observed. This approach will be directly relevant for the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX), which seeks to classify ˜106 emission-line galaxies into LAEs and low-redshift [{{O}} {{II}}] emitters. For a simulated HETDEX catalog with realistic measurement noise, our Bayesian method recovers 86% of LAEs missed by the traditional {W}{Lyα } > 20 Å cutoff over 2 < z < 3, outperforming the EW cut in both contamination and incompleteness. This is due to the method’s ability to trade off between the two types of binary classification error by adjusting the stringency of the probability requirement for classifying an observed object as an LAE. In our simulations of HETDEX, this method reduces the uncertainty in cosmological distance measurements by 14% with respect to the EW cut, equivalent to recovering 29% more cosmological information. Rather than using binary object labels, this method enables the use of classification probabilities in large-scale structure analyses. It can be applied to narrowband emission-line surveys as well as upcoming large spectroscopic surveys including Euclid and WFIRST.

Statistics provide guidance for indigenous organic carbon detection on Mars missions.

PubMed

Sephton, Mark A; Carter, Jonathan N

2014-08-01

Data from the Viking and Mars Science Laboratory missions indicate the presence of organic compounds that are not definitively martian in origin. Both contamination and confounding mineralogies have been suggested as alternatives to indigenous organic carbon. Intuitive thought suggests that we are repeatedly obtaining data that confirms the same level of uncertainty. Bayesian statistics may suggest otherwise. If an organic detection method has a true positive to false positive ratio greater than one, then repeated organic matter detection progressively increases the probability of indigeneity. Bayesian statistics also reveal that methods with higher ratios of true positives to false positives give higher overall probabilities and that detection of organic matter in a sample with a higher prior probability of indigenous organic carbon produces greater confidence. Bayesian statistics, therefore, provide guidance for the planning and operation of organic carbon detection activities on Mars. Suggestions for future organic carbon detection missions and instruments are as follows: (i) On Earth, instruments should be tested with analog samples of known organic content to determine their true positive to false positive ratios. (ii) On the mission, for an instrument with a true positive to false positive ratio above one, it should be recognized that each positive detection of organic carbon will result in a progressive increase in the probability of indigenous organic carbon being present; repeated measurements, therefore, can overcome some of the deficiencies of a less-than-definitive test. (iii) For a fixed number of analyses, the highest true positive to false positive ratio method or instrument will provide the greatest probability that indigenous organic carbon is present. (iv) On Mars, analyses should concentrate on samples with highest prior probability of indigenous organic carbon; intuitive desires to contrast samples of high prior probability and low prior probability of indigenous organic carbon should be resisted.

From least squares to multilevel modeling: A graphical introduction to Bayesian inference

NASA Astrophysics Data System (ADS)

Loredo, Thomas J.

2016-01-01

This tutorial presentation will introduce some of the key ideas and techniques involved in applying Bayesian methods to problems in astrostatistics. The focus will be on the big picture: understanding the foundations (interpreting probability, Bayes's theorem, the law of total probability and marginalization), making connections to traditional methods (propagation of errors, least squares, chi-squared, maximum likelihood, Monte Carlo simulation), and highlighting problems where a Bayesian approach can be particularly powerful (Poisson processes, density estimation and curve fitting with measurement error). The "graphical" component of the title reflects an emphasis on pictorial representations of some of the math, but also on the use of graphical models (multilevel or hierarchical models) for analyzing complex data. Code for some examples from the talk will be available to participants, in Python and in the Stan probabilistic programming language.

Frequentist and Bayesian Orbital Parameter Estimaton from Radial Velocity Data Using RVLIN, BOOTTRAN, and RUN DMC

NASA Astrophysics Data System (ADS)

Nelson, Benjamin Earl; Wright, Jason Thomas; Wang, Sharon

2015-08-01

For this hack session, we will present three tools used in analyses of radial velocity exoplanet systems. RVLIN is a set of IDL routines used to quickly fit an arbitrary number of Keplerian curves to radial velocity data to find adequate parameter point estimates. BOOTTRAN is an IDL-based extension of RVLIN to provide orbital parameter uncertainties using bootstrap based on a Keplerian model. RUN DMC is a highly parallelized Markov chain Monte Carlo algorithm that employs an n-body model, primarily used for dynamically complex or poorly constrained exoplanet systems. We will compare the performance of these tools and their applications to various exoplanet systems.

The impossibility of probabilities

NASA Astrophysics Data System (ADS)

Zimmerman, Peter D.

2017-11-01

This paper discusses the problem of assigning probabilities to the likelihood of nuclear terrorism events, in particular examining the limitations of using Bayesian priors for this purpose. It suggests an alternate approach to analyzing the threat of nuclear terrorism.

A Framework for Final Drive Simultaneous Failure Diagnosis Based on Fuzzy Entropy and Sparse Bayesian Extreme Learning Machine

PubMed Central

Ye, Qing; Pan, Hao; Liu, Changhua

2015-01-01

This research proposes a novel framework of final drive simultaneous failure diagnosis containing feature extraction, training paired diagnostic models, generating decision threshold, and recognizing simultaneous failure modes. In feature extraction module, adopt wavelet package transform and fuzzy entropy to reduce noise interference and extract representative features of failure mode. Use single failure sample to construct probability classifiers based on paired sparse Bayesian extreme learning machine which is trained only by single failure modes and have high generalization and sparsity of sparse Bayesian learning approach. To generate optimal decision threshold which can convert probability output obtained from classifiers into final simultaneous failure modes, this research proposes using samples containing both single and simultaneous failure modes and Grid search method which is superior to traditional techniques in global optimization. Compared with other frequently used diagnostic approaches based on support vector machine and probability neural networks, experiment results based on F 1-measure value verify that the diagnostic accuracy and efficiency of the proposed framework which are crucial for simultaneous failure diagnosis are superior to the existing approach. PMID:25722717

Nonparametric Bayesian Modeling for Automated Database Schema Matching

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

Ferragut, Erik M; Laska, Jason A

2015-01-01

The problem of merging databases arises in many government and commercial applications. Schema matching, a common first step, identifies equivalent fields between databases. We introduce a schema matching framework that builds nonparametric Bayesian models for each field and compares them by computing the probability that a single model could have generated both fields. Our experiments show that our method is more accurate and faster than the existing instance-based matching algorithms in part because of the use of nonparametric Bayesian models.

Inverse and forward modeling under uncertainty using MRE-based Bayesian approach

NASA Astrophysics Data System (ADS)

Hou, Z.; Rubin, Y.

2004-12-01

A stochastic inverse approach for subsurface characterization is proposed and applied to shallow vadose zone at a winery field site in north California and to a gas reservoir at the Ormen Lange field site in the North Sea. The approach is formulated in a Bayesian-stochastic framework, whereby the unknown parameters are identified in terms of their statistical moments or their probabilities. Instead of the traditional single-valued estimation /prediction provided by deterministic methods, the approach gives a probability distribution for an unknown parameter. This allows calculating the mean, the mode, and the confidence interval, which is useful for a rational treatment of uncertainty and its consequences. The approach also allows incorporating data of various types and different error levels, including measurements of state variables as well as information such as bounds on or statistical moments of the unknown parameters, which may represent prior information. To obtain minimally subjective prior probabilities required for the Bayesian approach, the principle of Minimum Relative Entropy (MRE) is employed. The approach is tested in field sites for flow parameters identification and soil moisture estimation in the vadose zone and for gas saturation estimation at great depth below the ocean floor. Results indicate the potential of coupling various types of field data within a MRE-based Bayesian formalism for improving the estimation of the parameters of interest.

Bayesian Finite Mixtures for Nonlinear Modeling of Educational Data.

ERIC Educational Resources Information Center

Tirri, Henry; And Others

A Bayesian approach for finding latent classes in data is discussed. The approach uses finite mixture models to describe the underlying structure in the data and demonstrate that the possibility of using full joint probability models raises interesting new prospects for exploratory data analysis. The concepts and methods discussed are illustrated…

Predicting forest insect flight activity: A Bayesian network approach

Treesearch

Stephen M. Pawson; Bruce G. Marcot; Owen G. Woodberry

2017-01-01

Daily flight activity patterns of forest insects are influenced by temporal and meteorological conditions. Temperature and time of day are frequently cited as key drivers of activity; however, complex interactions between multiple contributing factors have also been proposed. Here, we report individual Bayesian network models to assess the probability of flight...

Single-Case Time Series with Bayesian Analysis: A Practitioner's Guide.

ERIC Educational Resources Information Center

Jones, W. Paul

2003-01-01

This article illustrates a simplified time series analysis for use by the counseling researcher practitioner in single-case baseline plus intervention studies with a Bayesian probability analysis to integrate findings from replications. The C statistic is recommended as a primary analysis tool with particular relevance in the context of actual…

Using Discrete Loss Functions and Weighted Kappa for Classification: An Illustration Based on Bayesian Network Analysis

ERIC Educational Resources Information Center

Zwick, Rebecca; Lenaburg, Lubella

2009-01-01

In certain data analyses (e.g., multiple discriminant analysis and multinomial log-linear modeling), classification decisions are made based on the estimated posterior probabilities that individuals belong to each of several distinct categories. In the Bayesian network literature, this type of classification is often accomplished by assigning…

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…

Inverse Bayesian inference as a key of consciousness featuring a macroscopic quantum logical structure.

PubMed

Gunji, Yukio-Pegio; Shinohara, Shuji; Haruna, Taichi; Basios, Vasileios

2017-02-01

To overcome the dualism between mind and matter and to implement consciousness in science, a physical entity has to be embedded with a measurement process. Although quantum mechanics have been regarded as a candidate for implementing consciousness, nature at its macroscopic level is inconsistent with quantum mechanics. We propose a measurement-oriented inference system comprising Bayesian and inverse Bayesian inferences. While Bayesian inference contracts probability space, the newly defined inverse one relaxes the space. These two inferences allow an agent to make a decision corresponding to an immediate change in their environment. They generate a particular pattern of joint probability for data and hypotheses, comprising multiple diagonal and noisy matrices. This is expressed as a nondistributive orthomodular lattice equivalent to quantum logic. We also show that an orthomodular lattice can reveal information generated by inverse syllogism as well as the solutions to the frame and symbol-grounding problems. Our model is the first to connect macroscopic cognitive processes with the mathematical structure of quantum mechanics with no additional assumptions. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Discriminative Bayesian Dictionary Learning for Classification.

PubMed

Akhtar, Naveed; Shafait, Faisal; Mian, Ajmal

2016-12-01

We propose a Bayesian approach to learn discriminative dictionaries for sparse representation of data. The proposed approach infers probability distributions over the atoms of a discriminative dictionary using a finite approximation of Beta Process. It also computes sets of Bernoulli distributions that associate class labels to the learned dictionary atoms. This association signifies the selection probabilities of the dictionary atoms in the expansion of class-specific data. Furthermore, the non-parametric character of the proposed approach allows it to infer the correct size of the dictionary. We exploit the aforementioned Bernoulli distributions in separately learning a linear classifier. The classifier uses the same hierarchical Bayesian model as the dictionary, which we present along the analytical inference solution for Gibbs sampling. For classification, a test instance is first sparsely encoded over the learned dictionary and the codes are fed to the classifier. We performed experiments for face and action recognition; and object and scene-category classification using five public datasets and compared the results with state-of-the-art discriminative sparse representation approaches. Experiments show that the proposed Bayesian approach consistently outperforms the existing approaches.

Quantum Bayesian perspective for intelligence reservoir characterization, monitoring and management.

PubMed

Lozada Aguilar, Miguel Ángel; Khrennikov, Andrei; Oleschko, Klaudia; de Jesús Correa, María

2017-11-13

The paper starts with a brief review of the literature about uncertainty in geological, geophysical and petrophysical data. In particular, we present the viewpoints of experts in geophysics on the application of Bayesian inference and subjective probability. Then we present arguments that the use of classical probability theory (CP) does not match completely the structure of geophysical data. We emphasize that such data are characterized by contextuality and non-Kolmogorovness (the impossibility to use the CP model), incompleteness as well as incompatibility of some geophysical measurements. These characteristics of geophysical data are similar to the characteristics of quantum physical data. Notwithstanding all this, contextuality can be seen as a major deviation of quantum theory from classical physics. In particular, the contextual probability viewpoint is the essence of the Växjö interpretation of quantum mechanics. We propose to use quantum probability (QP) for decision-making during the characterization, modelling, exploring and management of the intelligent hydrocarbon reservoir Quantum Bayesianism (QBism), one of the recently developed information interpretations of quantum theory, can be used as the interpretational basis for such QP decision-making in geology, geophysics and petroleum projects design and management.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).

Neural Mechanisms for Integrating Prior Knowledge and Likelihood in Value-Based Probabilistic Inference

PubMed Central

Ting, Chih-Chung; Yu, Chia-Chen; Maloney, Laurence T.

2015-01-01

In Bayesian decision theory, knowledge about the probabilities of possible outcomes is captured by a prior distribution and a likelihood function. The prior reflects past knowledge and the likelihood summarizes current sensory information. The two combined (integrated) form a posterior distribution that allows estimation of the probability of different possible outcomes. In this study, we investigated the neural mechanisms underlying Bayesian integration using a novel lottery decision task in which both prior knowledge and likelihood information about reward probability were systematically manipulated on a trial-by-trial basis. Consistent with Bayesian integration, as sample size increased, subjects tended to weigh likelihood information more compared with prior information. Using fMRI in humans, we found that the medial prefrontal cortex (mPFC) correlated with the mean of the posterior distribution, a statistic that reflects the integration of prior knowledge and likelihood of reward probability. Subsequent analysis revealed that both prior and likelihood information were represented in mPFC and that the neural representations of prior and likelihood in mPFC reflected changes in the behaviorally estimated weights assigned to these different sources of information in response to changes in the environment. Together, these results establish the role of mPFC in prior-likelihood integration and highlight its involvement in representing and integrating these distinct sources of information. PMID:25632152

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.

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.

Natural frequencies facilitate diagnostic inferences of managers

PubMed Central

Hoffrage, Ulrich; Hafenbrädl, Sebastian; Bouquet, Cyril

2015-01-01

In Bayesian inference tasks, information about base rates as well as hit rate and false-alarm rate needs to be integrated according to Bayes’ rule after the result of a diagnostic test became known. Numerous studies have found that presenting information in a Bayesian inference task in terms of natural frequencies leads to better performance compared to variants with information presented in terms of probabilities or percentages. Natural frequencies are the tallies in a natural sample in which hit rate and false-alarm rate are not normalized with respect to base rates. The present research replicates the beneficial effect of natural frequencies with four tasks from the domain of management, and with management students as well as experienced executives as participants. The percentage of Bayesian responses was almost twice as high when information was presented in natural frequencies compared to a presentation in terms of percentages. In contrast to most tasks previously studied, the majority of numerical responses were lower than the Bayesian solutions. Having heard of Bayes’ rule prior to the study did not affect Bayesian performance. An implication of our work is that textbooks explaining Bayes’ rule should teach how to represent information in terms of natural frequencies instead of how to plug probabilities or percentages into a formula. PMID:26157397

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.

Probability, statistics, and computational science.

PubMed

Beerenwinkel, Niko; Siebourg, Juliane

2012-01-01

In this chapter, we review basic concepts from probability theory and computational statistics that are fundamental to evolutionary genomics. We provide a very basic introduction to statistical modeling and discuss general principles, including maximum likelihood and Bayesian inference. Markov chains, hidden Markov models, and Bayesian network models are introduced in more detail as they occur frequently and in many variations in genomics applications. In particular, we discuss efficient inference algorithms and methods for learning these models from partially observed data. Several simple examples are given throughout the text, some of which point to models that are discussed in more detail in subsequent chapters.

Determination of the priority indexes for the oil refinery wastewater treatment process

NASA Astrophysics Data System (ADS)

Chesnokova, M. G.; Myshlyavtsev, A. V.; Kriga, A. S.; Shaporenko, A. P.; Markelov, V. V.

2017-08-01

The wastewater biological treatment intensity and effectiveness are influenced by many factors: temperature, pH, presence and concentration of toxic substances, the biomass concentration et al. Regulation of them allows controlling the biological treatment process. Using the Bayesian theorem the link between changes was determined and the wastewater indexes normative limits exceeding influence for activated sludge characteristics alteration probability was evaluated. The estimation of total, or aposterioric, priority index presence probability, which characterizes the wastewater treatment level, is an important way to use the Bayesian theorem in activated sludge swelling prediction at the oil refinery biological treatment unit.

Probabilistic safety analysis of earth retaining structures during earthquakes

NASA Astrophysics Data System (ADS)

Grivas, D. A.; Souflis, C.

1982-07-01

A procedure is presented for determining the probability of failure of Earth retaining structures under static or seismic conditions. Four possible modes of failure (overturning, base sliding, bearing capacity, and overall sliding) are examined and their combined effect is evaluated with the aid of combinatorial analysis. The probability of failure is shown to be a more adequate measure of safety than the customary factor of safety. As Earth retaining structures may fail in four distinct modes, a system analysis can provide a single estimate for the possibility of failure. A Bayesian formulation of the safety retaining walls is found to provide an improved measure for the predicted probability of failure under seismic loading. The presented Bayesian analysis can account for the damage incurred to a retaining wall during an earthquake to provide an improved estimate for its probability of failure during future seismic events.

The Role of Simulation Approaches in Statistics

ERIC Educational Resources Information Center

Wood, Michael

2005-01-01

This article explores the uses of a simulation model (the two bucket story)--implemented by a stand-alone computer program, or an Excel workbook (both on the web)--that can be used for deriving bootstrap confidence intervals, and simulating various probability distributions. The strengths of the model are its generality, the fact that it provides…

How Transitional Probabilities and the Edge Effect Contribute to Listeners' Phonological Bootstrapping Success

ERIC Educational Resources Information Center

Sohail, Juwairia; Johnson, Elizabeth K.

2016-01-01

Much of what we know about the development of listeners' word segmentation strategies originates from the artificial language-learning literature. However, many artificial speech streams designed to study word segmentation lack a salient cue found in all natural languages: utterance boundaries. In this study, participants listened to a…

Probabilistic mapping of descriptive health status responses onto health state utilities using Bayesian networks: an empirical analysis converting SF-12 into EQ-5D utility index in a national US sample.

PubMed

Le, Quang A; Doctor, Jason N

2011-05-01

As quality-adjusted life years have become the standard metric in health economic evaluations, mapping health-profile or disease-specific measures onto preference-based measures to obtain quality-adjusted life years has become a solution when health utilities are not directly available. However, current mapping methods are limited due to their predictive validity, reliability, and/or other methodological issues. We employ probability theory together with a graphical model, called a Bayesian network, to convert health-profile measures into preference-based measures and to compare the results to those estimated with current mapping methods. A sample of 19,678 adults who completed both the 12-item Short Form Health Survey (SF-12v2) and EuroQoL 5D (EQ-5D) questionnaires from the 2003 Medical Expenditure Panel Survey was split into training and validation sets. Bayesian networks were constructed to explore the probabilistic relationships between each EQ-5D domain and 12 items of the SF-12v2. The EQ-5D utility scores were estimated on the basis of the predicted probability of each response level of the 5 EQ-5D domains obtained from the Bayesian inference process using the following methods: Monte Carlo simulation, expected utility, and most-likely probability. Results were then compared with current mapping methods including multinomial logistic regression, ordinary least squares, and censored least absolute deviations. The Bayesian networks consistently outperformed other mapping models in the overall sample (mean absolute error=0.077, mean square error=0.013, and R overall=0.802), in different age groups, number of chronic conditions, and ranges of the EQ-5D index. Bayesian networks provide a new robust and natural approach to map health status responses into health utility measures for health economic evaluations.

Intervals for posttest probabilities: a comparison of 5 methods.

PubMed

Mossman, D; Berger, J O

2001-01-01

Several medical articles discuss methods of constructing confidence intervals for single proportions and the likelihood ratio, but scant attention has been given to the systematic study of intervals for the posterior odds, or the positive predictive value, of a test. The authors describe 5 methods of constructing confidence intervals for posttest probabilities when estimates of sensitivity, specificity, and the pretest probability of a disorder are derived from empirical data. They then evaluate each method to determine how well the intervals' coverage properties correspond to their nominal value. When the estimates of pretest probabilities, sensitivity, and specificity are derived from more than 80 subjects and are not close to 0 or 1, all methods generate intervals with appropriate coverage properties. When these conditions are not met, however, the best-performing method is an objective Bayesian approach implemented by a simple simulation using a spreadsheet. Physicians and investigators can generate accurate confidence intervals for posttest probabilities in small-sample situations using the objective Bayesian approach.

Prior elicitation and Bayesian analysis of the Steroids for Corneal Ulcers Trial.

PubMed

See, Craig W; Srinivasan, Muthiah; Saravanan, Somu; Oldenburg, Catherine E; Esterberg, Elizabeth J; Ray, Kathryn J; Glaser, Tanya S; Tu, Elmer Y; Zegans, Michael E; McLeod, Stephen D; Acharya, Nisha R; Lietman, Thomas M

2012-12-01

To elicit expert opinion on the use of adjunctive corticosteroid therapy in bacterial corneal ulcers. To perform a Bayesian analysis of the Steroids for Corneal Ulcers Trial (SCUT), using expert opinion as a prior probability. The SCUT was a placebo-controlled trial assessing visual outcomes in patients receiving topical corticosteroids or placebo as adjunctive therapy for bacterial keratitis. Questionnaires were conducted at scientific meetings in India and North America to gauge expert consensus on the perceived benefit of corticosteroids as adjunct treatment. Bayesian analysis, using the questionnaire data as a prior probability and the primary outcome of SCUT as a likelihood, was performed. For comparison, an additional Bayesian analysis was performed using the results of the SCUT pilot study as a prior distribution. Indian respondents believed there to be a 1.21 Snellen line improvement, and North American respondents believed there to be a 1.24 line improvement with corticosteroid therapy. The SCUT primary outcome found a non-significant 0.09 Snellen line benefit with corticosteroid treatment. The results of the Bayesian analysis estimated a slightly greater benefit than did the SCUT primary analysis (0.19 lines verses 0.09 lines). Indian and North American experts had similar expectations on the effectiveness of corticosteroids in bacterial corneal ulcers; that corticosteroids would markedly improve visual outcomes. Bayesian analysis produced results very similar to those produced by the SCUT primary analysis. The similarity in result is likely due to the large sample size of SCUT and helps validate the results of SCUT.

Detangling complex relationships in forensic data: principles and use of causal networks and their application to clinical forensic science.

PubMed

Lefèvre, Thomas; Lepresle, Aude; Chariot, Patrick

2015-09-01

The search for complex, nonlinear relationships and causality in data is hindered by the availability of techniques in many domains, including forensic science. Linear multivariable techniques are useful but present some shortcomings. In the past decade, Bayesian approaches have been introduced in forensic science. To date, authors have mainly focused on providing an alternative to classical techniques for quantifying effects and dealing with uncertainty. Causal networks, including Bayesian networks, can help detangle complex relationships in data. A Bayesian network estimates the joint probability distribution of data and graphically displays dependencies between variables and the circulation of information between these variables. In this study, we illustrate the interest in utilizing Bayesian networks for dealing with complex data through an application in clinical forensic science. Evaluating the functional impairment of assault survivors is a complex task for which few determinants are known. As routinely estimated in France, the duration of this impairment can be quantified by days of 'Total Incapacity to Work' ('Incapacité totale de travail,' ITT). In this study, we used a Bayesian network approach to identify the injury type, victim category and time to evaluation as the main determinants of the 'Total Incapacity to Work' (TIW). We computed the conditional probabilities associated with the TIW node and its parents. We compared this approach with a multivariable analysis, and the results of both techniques were converging. Thus, Bayesian networks should be considered a reliable means to detangle complex relationships in data.

A Defence of the AR4’s Bayesian Approach to Quantifying Uncertainty

NASA Astrophysics Data System (ADS)

Vezer, M. A.

2009-12-01

The field of climate change research is a kimberlite pipe filled with philosophic diamonds waiting to be mined and analyzed by philosophers. Within the scientific literature on climate change, there is much philosophical dialogue regarding the methods and implications of climate studies. To this date, however, discourse regarding the philosophy of climate science has been confined predominately to scientific - rather than philosophical - investigations. In this paper, I hope to bring one such issue to the surface for explicit philosophical analysis: The purpose of this paper is to address a philosophical debate pertaining to the expressions of uncertainty in the International Panel on Climate Change (IPCC) Fourth Assessment Report (AR4), which, as will be noted, has received significant attention in scientific journals and books, as well as sporadic glances from the popular press. My thesis is that the AR4’s Bayesian method of uncertainty analysis and uncertainty expression is justifiable on pragmatic grounds: it overcomes problems associated with vagueness, thereby facilitating communication between scientists and policy makers such that the latter can formulate decision analyses in response to the views of the former. Further, I argue that the most pronounced criticisms against the AR4’s Bayesian approach, which are outlined below, are misguided. §1 Introduction Central to AR4 is a list of terms related to uncertainty that in colloquial conversations would be considered vague. The IPCC attempts to reduce the vagueness of its expressions of uncertainty by calibrating uncertainty terms with numerical probability values derived from a subjective Bayesian methodology. This style of analysis and expression has stimulated some controversy, as critics reject as inappropriate and even misleading the association of uncertainty terms with Bayesian probabilities. [...] The format of the paper is as follows. The investigation begins (§2) with an explanation of background considerations relevant to the IPCC and its use of uncertainty expressions. It then (§3) outlines some general philosophical worries regarding vague expressions and (§4) relates those worries to the AR4 and its method of dealing with them, which is a subjective Bayesian probability analysis. The next phase of the paper (§5) examines the notions of ‘objective’ and ‘subjective’ probability interpretations and compares the IPCC’s subjective Bayesian strategy with a frequentist approach. It then (§6) addresses objections to that methodology, and concludes (§7) that those objections are wrongheaded.

Reducing the Uncertainty in Atlantic Meridional Overturning Circulation Projections Using Bayesian Model Averaging

NASA Astrophysics Data System (ADS)

Olson, R.; An, S. I.

2016-12-01

Atlantic Meridional Overturning Circulation (AMOC) in the ocean might slow down in the future, which can lead to a host of climatic effects in North Atlantic and throughout the world. Despite improvements in climate models and availability of new observations, AMOC projections remain uncertain. Here we constrain CMIP5 multi-model ensemble output with observations of a recently developed AMOC index to provide improved Bayesian predictions of future AMOC. Specifically, we first calculate yearly AMOC index loosely based on Rahmstorf et al. (2015) for years 1880—2004 for both observations, and the CMIP5 models for which relevant output is available. We then assign a weight to each model based on a Bayesian Model Averaging method that accounts for differential model skill in terms of both mean state and variability. We include the temporal autocorrelation in climate model errors, and account for the uncertainty in the parameters of our statistical model. We use the weights to provide future weighted projections of AMOC, and compare them to un-weighted ones. Our projections use bootstrapping to account for uncertainty in internal AMOC variability. We also perform spectral and other statistical analyses to show that AMOC index variability, both in models and in observations, is consistent with red noise. Our results improve on and complement previous work by using a new ensemble of climate models, a different observational metric, and an improved Bayesian weighting method that accounts for differential model skill at reproducing internal variability. Reference: Rahmstorf, S., Box, J. E., Feulner, G., Mann, M. E., Robinson, A., Rutherford, S., & Schaffernicht, E. J. (2015). Exceptional twentieth-century slowdown in atlantic ocean overturning circulation. Nature Climate Change, 5(5), 475-480. doi:10.1038/nclimate2554

Bayesian, maximum parsimony and UPGMA models for inferring the phylogenies of antelopes using mitochondrial markers.

PubMed

Khan, Haseeb A; Arif, Ibrahim A; Bahkali, Ali H; Al Farhan, Ahmad H; Al Homaidan, Ali A

2008-10-06

This investigation was aimed to compare the inference of antelope phylogenies resulting from the 16S rRNA, cytochrome-b (cyt-b) and d-loop segments of mitochondrial DNA using three different computational models including Bayesian (BA), maximum parsimony (MP) and unweighted pair group method with arithmetic mean (UPGMA). The respective nucleotide sequences of three Oryx species (Oryx leucoryx, Oryx dammah and Oryx gazella) and an out-group (Addax nasomaculatus) were aligned and subjected to BA, MP and UPGMA models for comparing the topologies of respective phylogenetic trees. The 16S rRNA region possessed the highest frequency of conserved sequences (97.65%) followed by cyt-b (94.22%) and d-loop (87.29%). There were few transitions (2.35%) and none transversions in 16S rRNA as compared to cyt-b (5.61% transitions and 0.17% transversions) and d-loop (11.57% transitions and 1.14% transversions) while comparing the four taxa. All the three mitochondrial segments clearly differentiated the genus Addax from Oryx using the BA or UPGMA models. The topologies of all the gamma-corrected Bayesian trees were identical irrespective of the marker type. The UPGMA trees resulting from 16S rRNA and d-loop sequences were also identical (Oryx dammah grouped with Oryx leucoryx) to Bayesian trees except that the UPGMA tree based on cyt-b showed a slightly different phylogeny (Oryx dammah grouped with Oryx gazella) with a low bootstrap support. However, the MP model failed to differentiate the genus Addax from Oryx. These findings demonstrate the efficiency and robustness of BA and UPGMA methods for phylogenetic analysis of antelopes using mitochondrial markers.

Bayesian, Maximum Parsimony and UPGMA Models for Inferring the Phylogenies of Antelopes Using Mitochondrial Markers

PubMed Central

Khan, Haseeb A.; Arif, Ibrahim A.; Bahkali, Ali H.; Al Farhan, Ahmad H.; Al Homaidan, Ali A.

2008-01-01

This investigation was aimed to compare the inference of antelope phylogenies resulting from the 16S rRNA, cytochrome-b (cyt-b) and d-loop segments of mitochondrial DNA using three different computational models including Bayesian (BA), maximum parsimony (MP) and unweighted pair group method with arithmetic mean (UPGMA). The respective nucleotide sequences of three Oryx species (Oryx leucoryx, Oryx dammah and Oryx gazella) and an out-group (Addax nasomaculatus) were aligned and subjected to BA, MP and UPGMA models for comparing the topologies of respective phylogenetic trees. The 16S rRNA region possessed the highest frequency of conserved sequences (97.65%) followed by cyt-b (94.22%) and d-loop (87.29%). There were few transitions (2.35%) and none transversions in 16S rRNA as compared to cyt-b (5.61% transitions and 0.17% transversions) and d-loop (11.57% transitions and 1.14% transversions) while comparing the four taxa. All the three mitochondrial segments clearly differentiated the genus Addax from Oryx using the BA or UPGMA models. The topologies of all the gamma-corrected Bayesian trees were identical irrespective of the marker type. The UPGMA trees resulting from 16S rRNA and d-loop sequences were also identical (Oryx dammah grouped with Oryx leucoryx) to Bayesian trees except that the UPGMA tree based on cyt-b showed a slightly different phylogeny (Oryx dammah grouped with Oryx gazella) with a low bootstrap support. However, the MP model failed to differentiate the genus Addax from Oryx. These findings demonstrate the efficiency and robustness of BA and UPGMA methods for phylogenetic analysis of antelopes using mitochondrial markers. PMID:19204824

Editorial: Bayesian benefits for child psychology and psychiatry researchers.

PubMed

Oldehinkel, Albertine J

2016-09-01

For many scientists, performing statistical tests has become an almost automated routine. However, p-values are frequently used and interpreted incorrectly; and even when used appropriately, p-values tend to provide answers that do not match researchers' questions and hypotheses well. Bayesian statistics present an elegant and often more suitable alternative. The Bayesian approach has rarely been applied in child psychology and psychiatry research so far, but the development of user-friendly software packages and tutorials has placed it well within reach now. Because Bayesian analyses require a more refined definition of hypothesized probabilities of possible outcomes than the classical approach, going Bayesian may offer the additional benefit of sparkling the development and refinement of theoretical models in our field. © 2016 Association for Child and Adolescent Mental Health.

Quantum-Like Representation of Non-Bayesian Inference

NASA Astrophysics Data System (ADS)

Asano, M.; Basieva, I.; Khrennikov, A.; Ohya, M.; Tanaka, Y.

2013-01-01

This research is related to the problem of "irrational decision making or inference" that have been discussed in cognitive psychology. There are some experimental studies, and these statistical data cannot be described by classical probability theory. The process of decision making generating these data cannot be reduced to the classical Bayesian inference. For this problem, a number of quantum-like coginitive models of decision making was proposed. Our previous work represented in a natural way the classical Bayesian inference in the frame work of quantum mechanics. By using this representation, in this paper, we try to discuss the non-Bayesian (irrational) inference that is biased by effects like the quantum interference. Further, we describe "psychological factor" disturbing "rationality" as an "environment" correlating with the "main system" of usual Bayesian inference.

Uncertain deduction and conditional reasoning.

PubMed

Evans, Jonathan St B T; Thompson, Valerie A; Over, David E

2015-01-01

There has been a paradigm shift in the psychology of deductive reasoning. Many researchers no longer think it is appropriate to ask people to assume premises and decide what necessarily follows, with the results evaluated by binary extensional logic. Most every day and scientific inference is made from more or less confidently held beliefs and not assumptions, and the relevant normative standard is Bayesian probability theory. We argue that the study of "uncertain deduction" should directly ask people to assign probabilities to both premises and conclusions, and report an experiment using this method. We assess this reasoning by two Bayesian metrics: probabilistic validity and coherence according to probability theory. On both measures, participants perform above chance in conditional reasoning, but they do much better when statements are grouped as inferences, rather than evaluated in separate tasks.

PyBetVH: A Python tool for probabilistic volcanic hazard assessment and for generation of Bayesian hazard curves and maps

NASA Astrophysics Data System (ADS)

Tonini, Roberto; Sandri, Laura; Anne Thompson, Mary

2015-06-01

PyBetVH is a completely new, free, open-source and cross-platform software implementation of the Bayesian Event Tree for Volcanic Hazard (BET_VH), a tool for estimating the probability of any magmatic hazardous phenomenon occurring in a selected time frame, accounting for all the uncertainties. New capabilities of this implementation include the ability to calculate hazard curves which describe the distribution of the exceedance probability as a function of intensity (e.g., tephra load) on a grid of points covering the target area. The computed hazard curves are (i) absolute (accounting for the probability of eruption in a given time frame, and for all the possible vent locations and eruptive sizes) and (ii) Bayesian (computed at different percentiles, in order to quantify the epistemic uncertainty). Such curves allow representation of the full information contained in the probabilistic volcanic hazard assessment (PVHA) and are well suited to become a main input to quantitative risk analyses. PyBetVH allows for interactive visualization of both the computed hazard curves, and the corresponding Bayesian hazard/probability maps. PyBetVH is designed to minimize the efforts of end users, making PVHA results accessible to people who may be less experienced in probabilistic methodologies, e.g. decision makers. The broad compatibility of Python language has also allowed PyBetVH to be installed on the VHub cyber-infrastructure, where it can be run online or downloaded at no cost. PyBetVH can be used to assess any type of magmatic hazard from any volcano. Here we illustrate how to perform a PVHA through PyBetVH using the example of analyzing tephra fallout from the Okataina Volcanic Centre (OVC), New Zealand, and highlight the range of outputs that the tool can generate.

Predicting Rotator Cuff Tears Using Data Mining and Bayesian Likelihood Ratios

PubMed Central

Lu, Hsueh-Yi; Huang, Chen-Yuan; Su, Chwen-Tzeng; Lin, Chen-Chiang

2014-01-01

Objectives Rotator cuff tear is a common cause of shoulder diseases. Correct diagnosis of rotator cuff tears can save patients from further invasive, costly and painful tests. This study used predictive data mining and Bayesian theory to improve the accuracy of diagnosing rotator cuff tears by clinical examination alone. Methods In this retrospective study, 169 patients who had a preliminary diagnosis of rotator cuff tear on the basis of clinical evaluation followed by confirmatory MRI between 2007 and 2011 were identified. MRI was used as a reference standard to classify rotator cuff tears. The predictor variable was the clinical assessment results, which consisted of 16 attributes. This study employed 2 data mining methods (ANN and the decision tree) and a statistical method (logistic regression) to classify the rotator cuff diagnosis into “tear” and “no tear” groups. Likelihood ratio and Bayesian theory were applied to estimate the probability of rotator cuff tears based on the results of the prediction models. Results Our proposed data mining procedures outperformed the classic statistical method. The correction rate, sensitivity, specificity and area under the ROC curve of predicting a rotator cuff tear were statistical better in the ANN and decision tree models compared to logistic regression. Based on likelihood ratios derived from our prediction models, Fagan's nomogram could be constructed to assess the probability of a patient who has a rotator cuff tear using a pretest probability and a prediction result (tear or no tear). Conclusions Our predictive data mining models, combined with likelihood ratios and Bayesian theory, appear to be good tools to classify rotator cuff tears as well as determine the probability of the presence of the disease to enhance diagnostic decision making for rotator cuff tears. PMID:24733553

QUEST - A Bayesian adaptive psychometric method

NASA Technical Reports Server (NTRS)

Watson, A. B.; Pelli, D. G.

1983-01-01

An adaptive psychometric procedure that places each trial at the current most probable Bayesian estimate of threshold is described. The procedure takes advantage of the common finding that the human psychometric function is invariant in form when expressed as a function of log intensity. The procedure is simple, fast, and efficient, and may be easily implemented on any computer.

A General Structure for Legal Arguments about Evidence Using Bayesian Networks

ERIC Educational Resources Information Center

Fenton, Norman; Neil, Martin; Lagnado, David A.

2013-01-01

A Bayesian network (BN) is a graphical model of uncertainty that is especially well suited to legal arguments. It enables us to visualize and model dependencies between different hypotheses and pieces of evidence and to calculate the revised probability beliefs about all uncertain factors when any piece of new evidence is presented. Although BNs…

XID+: Next generation XID development

NASA Astrophysics Data System (ADS)

Hurley, Peter

2017-04-01

XID+ is a prior-based source extraction tool which carries out photometry in the Herschel SPIRE (Spectral and Photometric Imaging Receiver) maps at the positions of known sources. It uses a probabilistic Bayesian framework that provides a natural framework in which to include prior information, and uses the Bayesian inference tool Stan to obtain the full posterior probability distribution on flux estimates.

Locally Bayesian Learning with Applications to Retrospective Revaluation and Highlighting

ERIC Educational Resources Information Center

Kruschke, John K.

2006-01-01

A scheme is described for locally Bayesian parameter updating in models structured as successions of component functions. The essential idea is to back-propagate the target data to interior modules, such that an interior component's target is the input to the next component that maximizes the probability of the next component's target. Each layer…

Bayesian Ideal Types: Integration of Psychometric Data for Visually Impaired Persons.

ERIC Educational Resources Information Center

Jones, W. P.

1991-01-01

A model is proposed for the clinical synthesis of data from psychological tests of persons with visual impairments. The model integrates the concepts of the ideal type and Bayesian probability and compares actual test scores with ideal scores through use of a pattern similarity coefficient. A pilot study with Business Enterprise Program operators…

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.

Bayesian soft X-ray tomography using non-stationary Gaussian Processes

NASA Astrophysics Data System (ADS)

Li, Dong; Svensson, J.; Thomsen, H.; Medina, F.; Werner, A.; Wolf, R.

2013-08-01

In this study, a Bayesian based non-stationary Gaussian Process (GP) method for the inference of soft X-ray emissivity distribution along with its associated uncertainties has been developed. For the investigation of equilibrium condition and fast magnetohydrodynamic behaviors in nuclear fusion plasmas, it is of importance to infer, especially in the plasma center, spatially resolved soft X-ray profiles from a limited number of noisy line integral measurements. For this ill-posed inversion problem, Bayesian probability theory can provide a posterior probability distribution over all possible solutions under given model assumptions. Specifically, the use of a non-stationary GP to model the emission allows the model to adapt to the varying length scales of the underlying diffusion process. In contrast to other conventional methods, the prior regularization is realized in a probability form which enhances the capability of uncertainty analysis, in consequence, scientists who concern the reliability of their results will benefit from it. Under the assumption of normally distributed noise, the posterior distribution evaluated at a discrete number of points becomes a multivariate normal distribution whose mean and covariance are analytically available, making inversions and calculation of uncertainty fast. Additionally, the hyper-parameters embedded in the model assumption can be optimized through a Bayesian Occam's Razor formalism and thereby automatically adjust the model complexity. This method is shown to produce convincing reconstructions and good agreements with independently calculated results from the Maximum Entropy and Equilibrium-Based Iterative Tomography Algorithm methods.

Bayesian soft X-ray tomography using non-stationary Gaussian Processes.

PubMed

Li, Dong; Svensson, J; Thomsen, H; Medina, F; Werner, A; Wolf, R

2013-08-01

In this study, a Bayesian based non-stationary Gaussian Process (GP) method for the inference of soft X-ray emissivity distribution along with its associated uncertainties has been developed. For the investigation of equilibrium condition and fast magnetohydrodynamic behaviors in nuclear fusion plasmas, it is of importance to infer, especially in the plasma center, spatially resolved soft X-ray profiles from a limited number of noisy line integral measurements. For this ill-posed inversion problem, Bayesian probability theory can provide a posterior probability distribution over all possible solutions under given model assumptions. Specifically, the use of a non-stationary GP to model the emission allows the model to adapt to the varying length scales of the underlying diffusion process. In contrast to other conventional methods, the prior regularization is realized in a probability form which enhances the capability of uncertainty analysis, in consequence, scientists who concern the reliability of their results will benefit from it. Under the assumption of normally distributed noise, the posterior distribution evaluated at a discrete number of points becomes a multivariate normal distribution whose mean and covariance are analytically available, making inversions and calculation of uncertainty fast. Additionally, the hyper-parameters embedded in the model assumption can be optimized through a Bayesian Occam's Razor formalism and thereby automatically adjust the model complexity. This method is shown to produce convincing reconstructions and good agreements with independently calculated results from the Maximum Entropy and Equilibrium-Based Iterative Tomography Algorithm methods.

Exoplanet Biosignatures: A Framework for Their Assessment.

PubMed

Catling, David C; Krissansen-Totton, Joshua; Kiang, Nancy Y; Crisp, David; Robinson, Tyler D; DasSarma, Shiladitya; Rushby, Andrew J; Del Genio, Anthony; Bains, William; Domagal-Goldman, Shawn

2018-04-20

Finding life on exoplanets from telescopic observations is an ultimate goal of exoplanet science. Life produces gases and other substances, such as pigments, which can have distinct spectral or photometric signatures. Whether or not life is found with future data must be expressed with probabilities, requiring a framework of biosignature assessment. We present a framework in which we advocate using biogeochemical "Exo-Earth System" models to simulate potential biosignatures in spectra or photometry. Given actual observations, simulations are used to find the Bayesian likelihoods of those data occurring for scenarios with and without life. The latter includes "false positives" wherein abiotic sources mimic biosignatures. Prior knowledge of factors influencing planetary inhabitation, including previous observations, is combined with the likelihoods to give the Bayesian posterior probability of life existing on a given exoplanet. Four components of observation and analysis are necessary. (1) Characterization of stellar (e.g., age and spectrum) and exoplanetary system properties, including "external" exoplanet parameters (e.g., mass and radius), to determine an exoplanet's suitability for life. (2) Characterization of "internal" exoplanet parameters (e.g., climate) to evaluate habitability. (3) Assessment of potential biosignatures within the environmental context (components 1-2), including corroborating evidence. (4) Exclusion of false positives. We propose that resulting posterior Bayesian probabilities of life's existence map to five confidence levels, ranging from "very likely" (90-100%) to "very unlikely" (<10%) inhabited. Key Words: Bayesian statistics-Biosignatures-Drake equation-Exoplanets-Habitability-Planetary science. Astrobiology 18, xxx-xxx.

Public opinion by a poll process: model study and Bayesian view

NASA Astrophysics Data System (ADS)

Lee, Hyun Keun; Kim, Yong Woon

2018-05-01

We study the formation of public opinion in a poll process where the current score is open to the public. The voters are assumed to vote probabilistically for or against their own preference considering the group opinion collected up to then in the score. The poll-score probability is found to follow the beta distribution in the large polls limit. We demonstrate that various poll results, even those contradictory to the population preference, are possible with non-zero probability density and that such deviations are readily triggered by initial bias. It is mentioned that our poll model can be understood in the Bayesian viewpoint.

Bayesian approach for peak detection in two-dimensional chromatography.

PubMed

Vivó-Truyols, Gabriel

2012-03-20

A new method for peak detection in two-dimensional chromatography is presented. In a first step, the method starts with a conventional one-dimensional peak detection algorithm to detect modulated peaks. In a second step, a sophisticated algorithm is constructed to decide which of the individual one-dimensional peaks have been originated from the same compound and should then be arranged in a two-dimensional peak. The merging algorithm is based on Bayesian inference. The user sets prior information about certain parameters (e.g., second-dimension retention time variability, first-dimension band broadening, chromatographic noise). On the basis of these priors, the algorithm calculates the probability of myriads of peak arrangements (i.e., ways of merging one-dimensional peaks), finding which of them holds the highest value. Uncertainty in each parameter can be accounted by adapting conveniently its probability distribution function, which in turn may change the final decision of the most probable peak arrangement. It has been demonstrated that the Bayesian approach presented in this paper follows the chromatographers' intuition. The algorithm has been applied and tested with LC × LC and GC × GC data and takes around 1 min to process chromatograms with several thousands of peaks.

Bayesian structural inference for hidden processes.

PubMed

Strelioff, Christopher C; Crutchfield, James P

2014-04-01

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ε-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be ε-machines, irrespective of estimated transition probabilities. Properties of ε-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.

Bayesian structural inference for hidden processes

NASA Astrophysics Data System (ADS)

Strelioff, Christopher C.; Crutchfield, James P.

2014-04-01

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ɛ-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be ɛ-machines, irrespective of estimated transition probabilities. Properties of ɛ-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.

Reliability modelling and analysis of a multi-state element based on a dynamic Bayesian network

NASA Astrophysics Data System (ADS)

Li, Zhiqiang; Xu, Tingxue; Gu, Junyuan; Dong, Qi; Fu, Linyu

2018-04-01

This paper presents a quantitative reliability modelling and analysis method for multi-state elements based on a combination of the Markov process and a dynamic Bayesian network (DBN), taking perfect repair, imperfect repair and condition-based maintenance (CBM) into consideration. The Markov models of elements without repair and under CBM are established, and an absorbing set is introduced to determine the reliability of the repairable element. According to the state-transition relations between the states determined by the Markov process, a DBN model is built. In addition, its parameters for series and parallel systems, namely, conditional probability tables, can be calculated by referring to the conditional degradation probabilities. Finally, the power of a control unit in a failure model is used as an example. A dynamic fault tree (DFT) is translated into a Bayesian network model, and subsequently extended to a DBN. The results show the state probabilities of an element and the system without repair, with perfect and imperfect repair, and under CBM, with an absorbing set plotted by differential equations and verified. Through referring forward, the reliability value of the control unit is determined in different kinds of modes. Finally, weak nodes are noted in the control unit.

Itô-SDE MCMC method for Bayesian characterization of errors associated with data limitations in stochastic expansion methods for uncertainty quantification

NASA Astrophysics Data System (ADS)

Arnst, M.; Abello Álvarez, B.; Ponthot, J.-P.; Boman, R.

2017-11-01

This paper is concerned with the characterization and the propagation of errors associated with data limitations in polynomial-chaos-based stochastic methods for uncertainty quantification. Such an issue can arise in uncertainty quantification when only a limited amount of data is available. When the available information does not suffice to accurately determine the probability distributions that must be assigned to the uncertain variables, the Bayesian method for assigning these probability distributions becomes attractive because it allows the stochastic model to account explicitly for insufficiency of the available information. In previous work, such applications of the Bayesian method had already been implemented by using the Metropolis-Hastings and Gibbs Markov Chain Monte Carlo (MCMC) methods. In this paper, we present an alternative implementation, which uses an alternative MCMC method built around an Itô stochastic differential equation (SDE) that is ergodic for the Bayesian posterior. We draw together from the mathematics literature a number of formal properties of this Itô SDE that lend support to its use in the implementation of the Bayesian method, and we describe its discretization, including the choice of the free parameters, by using the implicit Euler method. We demonstrate the proposed methodology on a problem of uncertainty quantification in a complex nonlinear engineering application relevant to metal forming.

Statistical inferences with jointly type-II censored samples from two Pareto distributions

NASA Astrophysics Data System (ADS)

Abu-Zinadah, Hanaa H.

2017-08-01

In the several fields of industries the product comes from more than one production line, which is required to work the comparative life tests. This problem requires sampling of the different production lines, then the joint censoring scheme is appeared. In this article we consider the life time Pareto distribution with jointly type-II censoring scheme. The maximum likelihood estimators (MLE) and the corresponding approximate confidence intervals as well as the bootstrap confidence intervals of the model parameters are obtained. Also Bayesian point and credible intervals of the model parameters are presented. The life time data set is analyzed for illustrative purposes. Monte Carlo results from simulation studies are presented to assess the performance of our proposed method.

The Inverse Bagging Algorithm: Anomaly Detection by Inverse Bootstrap Aggregating

NASA Astrophysics Data System (ADS)

Vischia, Pietro; Dorigo, Tommaso

2017-03-01

For data sets populated by a very well modeled process and by another process of unknown probability density function (PDF), a desired feature when manipulating the fraction of the unknown process (either for enhancing it or suppressing it) consists in avoiding to modify the kinematic distributions of the well modeled one. A bootstrap technique is used to identify sub-samples rich in the well modeled process, and classify each event according to the frequency of it being part of such sub-samples. Comparisons with general MVA algorithms will be shown, as well as a study of the asymptotic properties of the method, making use of a public domain data set that models a typical search for new physics as performed at hadronic colliders such as the Large Hadron Collider (LHC).

UNIFORMLY MOST POWERFUL BAYESIAN TESTS

PubMed Central

Johnson, Valen E.

2014-01-01

Uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all tests of a given size. In this article, the notion of uniformly most powerful tests is extended to the Bayesian setting by defining uniformly most powerful Bayesian tests to be tests that maximize the probability that the Bayes factor, in favor of the alternative hypothesis, exceeds a specified threshold. Like their classical counterpart, uniformly most powerful Bayesian tests are most easily defined in one-parameter exponential family models, although extensions outside of this class are possible. The connection between uniformly most powerful tests and uniformly most powerful Bayesian tests can be used to provide an approximate calibration between p-values and Bayes factors. Finally, issues regarding the strong dependence of resulting Bayes factors and p-values on sample size are discussed. PMID:24659829

Novel method to construct large-scale design space in lubrication process utilizing Bayesian estimation based on a small-scale design-of-experiment and small sets of large-scale manufacturing data.

PubMed

Maeda, Jin; Suzuki, Tatsuya; Takayama, Kozo

2012-12-01

A large-scale design space was constructed using a Bayesian estimation method with a small-scale design of experiments (DoE) and small sets of large-scale manufacturing data without enforcing a large-scale DoE. The small-scale DoE was conducted using various Froude numbers (X(1)) and blending times (X(2)) in the lubricant blending process for theophylline tablets. The response surfaces, design space, and their reliability of the compression rate of the powder mixture (Y(1)), tablet hardness (Y(2)), and dissolution rate (Y(3)) on a small scale were calculated using multivariate spline interpolation, a bootstrap resampling technique, and self-organizing map clustering. The constant Froude number was applied as a scale-up rule. Three experiments under an optimal condition and two experiments under other conditions were performed on a large scale. The response surfaces on the small scale were corrected to those on a large scale by Bayesian estimation using the large-scale results. Large-scale experiments under three additional sets of conditions showed that the corrected design space was more reliable than that on the small scale, even if there was some discrepancy in the pharmaceutical quality between the manufacturing scales. This approach is useful for setting up a design space in pharmaceutical development when a DoE cannot be performed at a commercial large manufacturing scale.

Design space construction of multiple dose-strength tablets utilizing bayesian estimation based on one set of design-of-experiments.

PubMed

Maeda, Jin; Suzuki, Tatsuya; Takayama, Kozo

2012-01-01

Design spaces for multiple dose strengths of tablets were constructed using a Bayesian estimation method with one set of design of experiments (DoE) of only the highest dose-strength tablet. The lubricant blending process for theophylline tablets with dose strengths of 100, 50, and 25 mg is used as a model manufacturing process in order to construct design spaces. The DoE was conducted using various Froude numbers (X(1)) and blending times (X(2)) for theophylline 100-mg tablet. The response surfaces, design space, and their reliability of the compression rate of the powder mixture (Y(1)), tablet hardness (Y(2)), and dissolution rate (Y(3)) of the 100-mg tablet were calculated using multivariate spline interpolation, a bootstrap resampling technique, and self-organizing map clustering. Three experiments under an optimal condition and two experiments under other conditions were performed using 50- and 25-mg tablets, respectively. The response surfaces of the highest-strength tablet were corrected to those of the lower-strength tablets by Bayesian estimation using the manufacturing data of the lower-strength tablets. Experiments under three additional sets of conditions of lower-strength tablets showed that the corrected design space made it possible to predict the quality of lower-strength tablets more precisely than the design space of the highest-strength tablet. This approach is useful for constructing design spaces of tablets with multiple strengths.

Enhancing a Short Measure of Big Five Personality Traits with Bayesian Scaling

ERIC Educational Resources Information Center

Jones, W. Paul

2014-01-01

A study in a university clinic/laboratory investigated adaptive Bayesian scaling as a supplement to interpretation of scores on the Mini-IPIP. A "probability of belonging" in categories of low, medium, or high on each of the Big Five traits was calculated after each item response and continued until all items had been used or until a…

Bayesian model checking: A comparison of tests

NASA Astrophysics Data System (ADS)

Lucy, L. B.

2018-06-01

Two procedures for checking Bayesian models are compared using a simple test problem based on the local Hubble expansion. Over four orders of magnitude, p-values derived from a global goodness-of-fit criterion for posterior probability density functions agree closely with posterior predictive p-values. The former can therefore serve as an effective proxy for the difficult-to-calculate posterior predictive p-values.

Bayesian adaptive phase II screening design for combination trials.

PubMed

Cai, Chunyan; Yuan, Ying; Johnson, Valen E

2013-01-01

Trials of combination therapies for the treatment of cancer are playing an increasingly important role in the battle against this disease. To more efficiently handle the large number of combination therapies that must be tested, we propose a novel Bayesian phase II adaptive screening design to simultaneously select among possible treatment combinations involving multiple agents. Our design is based on formulating the selection procedure as a Bayesian hypothesis testing problem in which the superiority of each treatment combination is equated to a single hypothesis. During the trial conduct, we use the current values of the posterior probabilities of all hypotheses to adaptively allocate patients to treatment combinations. Simulation studies show that the proposed design substantially outperforms the conventional multiarm balanced factorial trial design. The proposed design yields a significantly higher probability for selecting the best treatment while allocating substantially more patients to efficacious treatments. The proposed design is most appropriate for the trials combining multiple agents and screening out the efficacious combination to be further investigated. The proposed Bayesian adaptive phase II screening design substantially outperformed the conventional complete factorial design. Our design allocates more patients to better treatments while providing higher power to identify the best treatment at the end of the trial.

Bayesian methods for outliers detection in GNSS time series

NASA Astrophysics Data System (ADS)

Qianqian, Zhang; Qingming, Gui

2013-07-01

This article is concerned with the problem of detecting outliers in GNSS time series based on Bayesian statistical theory. Firstly, a new model is proposed to simultaneously detect different types of outliers based on the conception of introducing different types of classification variables corresponding to the different types of outliers; the problem of outlier detection is converted into the computation of the corresponding posterior probabilities, and the algorithm for computing the posterior probabilities based on standard Gibbs sampler is designed. Secondly, we analyze the reasons of masking and swamping about detecting patches of additive outliers intensively; an unmasking Bayesian method for detecting additive outlier patches is proposed based on an adaptive Gibbs sampler. Thirdly, the correctness of the theories and methods proposed above is illustrated by simulated data and then by analyzing real GNSS observations, such as cycle slips detection in carrier phase data. Examples illustrate that the Bayesian methods for outliers detection in GNSS time series proposed by this paper are not only capable of detecting isolated outliers but also capable of detecting additive outlier patches. Furthermore, it can be successfully used to process cycle slips in phase data, which solves the problem of small cycle slips.

The Approximate Bayesian Computation methods in the localization of the atmospheric contamination source

NASA Astrophysics Data System (ADS)

Kopka, P.; Wawrzynczak, A.; Borysiewicz, M.

2015-09-01

In many areas of application, a central problem is a solution to the inverse problem, especially estimation of the unknown model parameters to model the underlying dynamics of a physical system precisely. In this situation, the Bayesian inference is a powerful tool to combine observed data with prior knowledge to gain the probability distribution of searched parameters. We have applied the modern methodology named Sequential Approximate Bayesian Computation (S-ABC) to the problem of tracing the atmospheric contaminant source. The ABC is technique commonly used in the Bayesian analysis of complex models and dynamic system. Sequential methods can significantly increase the efficiency of the ABC. In the presented algorithm, the input data are the on-line arriving concentrations of released substance registered by distributed sensor network from OVER-LAND ATMOSPHERIC DISPERSION (OLAD) experiment. The algorithm output are the probability distributions of a contamination source parameters i.e. its particular location, release rate, speed and direction of the movement, start time and duration. The stochastic approach presented in this paper is completely general and can be used in other fields where the parameters of the model bet fitted to the observable data should be found.

Reclassification of the butternut canker fungus, Sirococcus clavigignenti-juglandacearum, into the genus Ophiognomonia.

PubMed

Broders, K D; Boland, G J

2011-01-01

Sirococcus clavigignenti-juglandacearum (Sc-j), which causes a canker disease on butternut, is largely responsible for the decline of this tree in the United States and Canada. The original description of the species was based on anamorphic characters because the teleomorph is unknown. Recent phylogenetic investigations have found that Sc-j is not a member of the genus Sirococcus, and accurate taxonomic classification is required. The objective of this study is to use sequence data to determine the phylogenetic placement of Sc-j within the Gnomoniaceae, Diaporthales. Isolates were recovered from infected Juglans ailantifolia var. cordiformis (heartnut), Juglans cinerea (butternut), and Juglans nigra (black walnut) in Ontario and the eastern United States. The genes coding for β-tubulin, actin, calmodulin, internal transcribed spacers 1 and 2, and the translation elongation factor 1-alpha from 28 isolates of Sc-j and representatives of the major lineages within the Gnomoniaceae were evaluated. There was no difference in the sequences of the five genes among the isolates of Sc-j studied, indicating a recent introduction followed by asexual reproduction and spread via conidia. The phylogenetic analyses demonstrate this fungus does not belong to the genus Sirococcus, and provides strong support (99% MP and 100% NJ bootstrap values, and 100% Bayesian posterior probabilities) for its inclusion in the genus Ophiognomonia, thereby supporting a reclassification of the butternut canker fungus to Ophiognomonia clavigignenti-juglandacearum. Copyright © 2010 The British Mycological Society. Published by Elsevier Ltd. All rights reserved.

The evolutionary history of seahorses (Syngnathidae: Hippocampus): molecular data suggest a West Pacific origin and two invasions of the Atlantic Ocean.

PubMed

Teske, Peter R; Cherry, Michael I; Matthee, Conrad A

2004-02-01

Sequence data derived from four markers (the nuclear RP1 and Aldolase and the mitochondrial 16S rRNA and cytochrome b genes) were used to determine the phylogenetic relationships among 32 species belonging to the genus Hippocampus. There were marked differences in the rate of evolution among these gene fragments, with Aldolase evolving the slowest and the mtDNA cytochrome b gene the fastest. The RP1 gene recovered the highest number of nodes supported by >70% bootstrap values from parsimony analysis and >95% posterior probabilities from Bayesian inference. The combined analysis based on 2317 nucleotides resulted in the most robust phylogeny. A distinct phylogenetic split was identified between the pygmy seahorse, Hippocampus bargibanti, and a clade including all other species. Three species from the western Pacific Ocean included in our study, namely H. bargibanti, H. breviceps, and H. abdominalis occupy basal positions in the phylogeny. This and the high species richness in the region suggests that the genus evolved somewhere in the West Pacific. There is also fairly strong molecular support for the remaining species being subdivided into three main evolutionary lineages: two West Pacific clades and a clade of species present in both the Indo-Pacific and the Atlantic Ocean. The phylogeny obtained herein suggests at least two independent colonization events of the Atlantic Ocean, once before the closure of the Tethyan seaway, and once afterwards.

Uncertain deduction and conditional reasoning

PubMed Central

Evans, Jonathan St. B. T.; Thompson, Valerie A.; Over, David E.

2015-01-01

There has been a paradigm shift in the psychology of deductive reasoning. Many researchers no longer think it is appropriate to ask people to assume premises and decide what necessarily follows, with the results evaluated by binary extensional logic. Most every day and scientific inference is made from more or less confidently held beliefs and not assumptions, and the relevant normative standard is Bayesian probability theory. We argue that the study of “uncertain deduction” should directly ask people to assign probabilities to both premises and conclusions, and report an experiment using this method. We assess this reasoning by two Bayesian metrics: probabilistic validity and coherence according to probability theory. On both measures, participants perform above chance in conditional reasoning, but they do much better when statements are grouped as inferences, rather than evaluated in separate tasks. PMID:25904888

The double slit experiment and the time reversed fire alarm

NASA Astrophysics Data System (ADS)

Halabi, Tarek

2011-03-01

When both slits of the double slit experiment are open, closing one paradoxically increases the detection rate at some points on the detection screen. Feynman famously warned that temptation to "understand" such a puzzling feature only draws us into blind alleys. Nevertheless, we gain insight into this feature by drawing an analogy between the double slit experiment and a time reversed fire alarm. Much as closing the slit increases probability of a future detection, ruling out fire drill scenarios, having heard the fire alarm, increases probability of a past fire (using Bayesian inference). Classically, Bayesian inference is associated with computing probabilities of past events. We therefore identify this feature of the double slit experiment with a time reversed thermodynamic arrow. We believe that much of the enigma of quantum mechanics is simply due to some variation of time's arrow.

A New Bayesian Approach for Estimating the Presence of a Suspected Compound in Routine Screening Analysis.

PubMed

Woldegebriel, Michael; Vivó-Truyols, Gabriel

2016-10-04

A novel method for compound identification in liquid chromatography-high resolution mass spectrometry (LC-HRMS) is proposed. The method, based on Bayesian statistics, accommodates all possible uncertainties involved, from instrumentation up to data analysis into a single model yielding the probability of the compound of interest being present/absent in the sample. This approach differs from the classical methods in two ways. First, it is probabilistic (instead of deterministic); hence, it computes the probability that the compound is (or is not) present in a sample. Second, it answers the hypothesis "the compound is present", opposed to answering the question "the compound feature is present". This second difference implies a shift in the way data analysis is tackled, since the probability of interfering compounds (i.e., isomers and isobaric compounds) is also taken into account.

Prior Elicitation and Bayesian Analysis of the Steroids for Corneal Ulcers Trial

PubMed Central

See, Craig W.; Srinivasan, Muthiah; Saravanan, Somu; Oldenburg, Catherine E.; Esterberg, Elizabeth J.; Ray, Kathryn J.; Glaser, Tanya S.; Tu, Elmer Y.; Zegans, Michael E.; McLeod, Stephen D.; Acharya, Nisha R.; Lietman, Thomas M.

2013-01-01

Purpose To elicit expert opinion on the use of adjunctive corticosteroid therapy in bacterial corneal ulcers. To perform a Bayesian analysis of the Steroids for Corneal Ulcers Trial (SCUT), using expert opinion as a prior probability. Methods The SCUT was a placebo-controlled trial assessing visual outcomes in patients receiving topical corticosteroids or placebo as adjunctive therapy for bacterial keratitis. Questionnaires were conducted at scientific meetings in India and North America to gauge expert consensus on the perceived benefit of corticosteroids as adjunct treatment. Bayesian analysis, using the questionnaire data as a prior probability and the primary outcome of SCUT as a likelihood, was performed. For comparison, an additional Bayesian analysis was performed using the results of the SCUT pilot study as a prior distribution. Results Indian respondents believed there to be a 1.21 Snellen line improvement, and North American respondents believed there to be a 1.24 line improvement with corticosteroid therapy. The SCUT primary outcome found a non-significant 0.09 Snellen line benefit with corticosteroid treatment. The results of the Bayesian analysis estimated a slightly greater benefit than did the SCUT primary analysis (0.19 lines verses 0.09 lines). Conclusion Indian and North American experts had similar expectations on the effectiveness of corticosteroids in bacterial corneal ulcers; that corticosteroids would markedly improve visual outcomes. Bayesian analysis produced results very similar to those produced by the SCUT primary analysis. The similarity in result is likely due to the large sample size of SCUT and helps validate the results of SCUT. PMID:23171211

Application of bayesian networks to real-time flood risk estimation

NASA Astrophysics Data System (ADS)

Garrote, L.; Molina, M.; Blasco, G.

2003-04-01

This paper presents the application of a computational paradigm taken from the field of artificial intelligence - the bayesian network - to model the behaviour of hydrologic basins during floods. The final goal of this research is to develop representation techniques for hydrologic simulation models in order to define, develop and validate a mechanism, supported by a software environment, oriented to build decision models for the prediction and management of river floods in real time. The emphasis is placed on providing decision makers with tools to incorporate their knowledge of basin behaviour, usually formulated in terms of rainfall-runoff models, in the process of real-time decision making during floods. A rainfall-runoff model is only a step in the process of decision making. If a reliable rainfall forecast is available and the rainfall-runoff model is well calibrated, decisions can be based mainly on model results. However, in most practical situations, uncertainties in rainfall forecasts or model performance have to be incorporated in the decision process. The computation paradigm adopted for the simulation of hydrologic processes is the bayesian network. A bayesian network is a directed acyclic graph that represents causal influences between linked variables. Under this representation, uncertain qualitative variables are related through causal relations quantified with conditional probabilities. The solution algorithm allows the computation of the expected probability distribution of unknown variables conditioned to the observations. An approach to represent hydrologic processes by bayesian networks with temporal and spatial extensions is presented in this paper, together with a methodology for the development of bayesian models using results produced by deterministic hydrologic simulation models

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.

Probabilistic sensitivity analysis for decision trees with multiple branches: use of the Dirichlet distribution in a Bayesian framework.

PubMed

Briggs, Andrew H; Ades, A E; Price, Martin J

2003-01-01

In structuring decision models of medical interventions, it is commonly recommended that only 2 branches be used for each chance node to avoid logical inconsistencies that can arise during sensitivity analyses if the branching probabilities do not sum to 1. However, information may be naturally available in an unconditional form, and structuring a tree in conditional form may complicate rather than simplify the sensitivity analysis of the unconditional probabilities. Current guidance emphasizes using probabilistic sensitivity analysis, and a method is required to provide probabilistic probabilities over multiple branches that appropriately represents uncertainty while satisfying the requirement that mutually exclusive event probabilities should sum to 1. The authors argue that the Dirichlet distribution, the multivariate equivalent of the beta distribution, is appropriate for this purpose and illustrate its use for generating a fully probabilistic transition matrix for a Markov model. Furthermore, they demonstrate that by adopting a Bayesian approach, the problem of observing zero counts for transitions of interest can be overcome.

The maximum entropy method of moments and Bayesian probability theory

NASA Astrophysics Data System (ADS)

Bretthorst, G. Larry

2013-08-01

The problem of density estimation occurs in many disciplines. For example, in MRI it is often necessary to classify the types of tissues in an image. To perform this classification one must first identify the characteristics of the tissues to be classified. These characteristics might be the intensity of a T1 weighted image and in MRI many other types of characteristic weightings (classifiers) may be generated. In a given tissue type there is no single intensity that characterizes the tissue, rather there is a distribution of intensities. Often this distributions can be characterized by a Gaussian, but just as often it is much more complicated. Either way, estimating the distribution of intensities is an inference problem. In the case of a Gaussian distribution, one must estimate the mean and standard deviation. However, in the Non-Gaussian case the shape of the density function itself must be inferred. Three common techniques for estimating density functions are binned histograms [1, 2], kernel density estimation [3, 4], and the maximum entropy method of moments [5, 6]. In the introduction, the maximum entropy method of moments will be reviewed. Some of its problems and conditions under which it fails will be discussed. Then in later sections, the functional form of the maximum entropy method of moments probability distribution will be incorporated into Bayesian probability theory. It will be shown that Bayesian probability theory solves all of the problems with the maximum entropy method of moments. One gets posterior probabilities for the Lagrange multipliers, and, finally, one can put error bars on the resulting estimated density function.

When Mommy Comes to the Rescue of Statistics: Infants Combine Top-Down and Bottom-Up Cues to Segment Speech

ERIC Educational Resources Information Center

Mersad, Karima; Nazzi, Thierry

2012-01-01

Transitional Probability (TP) computations are regarded as a powerful learning mechanism that is functional early in development and has been proposed as an initial bootstrapping device for speech segmentation. However, a recent study casts doubt on the robustness of early statistical word-learning. Johnson and Tyler (2010) showed that when…

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

Efficient Effects-Based Military Planning Final Report

DTIC Science & Technology

2010-11-13

using probabilistic infer- ence methods,” in Proc. 8th Annu. Conf. Uncertainty Artificial Intelli - gence (UAI), Stanford, CA. San Mateo, CA: Morgan...Imprecise Probabilities, the 24th Conference on Uncertainty in Artificial Intelligence (UAI), 2008. 7. Yan Tong and Qiang Ji, Learning Bayesian Networks...Bayesian Networks using Constraints Cassio P. de Campos cassiopc@acm.org Dalle Molle Institute for Artificial Intelligence Galleria 2, Manno 6928

A Bayesian account of quantum histories

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

Marlow, Thomas

2006-05-15

We investigate whether quantum history theories can be consistent with Bayesian reasoning and whether such an analysis helps clarify the interpretation of such theories. First, we summarise and extend recent work categorising two different approaches to formalising multi-time measurements in quantum theory. The standard approach consists of describing an ordered series of measurements in terms of history propositions with non-additive 'probabilities.' The non-standard approach consists of defining multi-time measurements to consist of sets of exclusive and exhaustive history propositions and recovering the single-time exclusivity of results when discussing single-time history propositions. We analyse whether such history propositions can be consistentmore » with Bayes' rule. We show that certain class of histories are given a natural Bayesian interpretation, namely, the linearly positive histories originally introduced by Goldstein and Page. Thus, we argue that this gives a certain amount of interpretational clarity to the non-standard approach. We also attempt a justification of our analysis using Cox's axioms of probability theory.« less

A Bayesian Approach for Sensor Optimisation in Impact Identification

PubMed Central

Mallardo, Vincenzo; Sharif Khodaei, Zahra; Aliabadi, Ferri M. H.

2016-01-01

This paper presents a Bayesian approach for optimizing the position of sensors aimed at impact identification in composite structures under operational conditions. The uncertainty in the sensor data has been represented by statistical distributions of the recorded signals. An optimisation strategy based on the genetic algorithm is proposed to find the best sensor combination aimed at locating impacts on composite structures. A Bayesian-based objective function is adopted in the optimisation procedure as an indicator of the performance of meta-models developed for different sensor combinations to locate various impact events. To represent a real structure under operational load and to increase the reliability of the Structural Health Monitoring (SHM) system, the probability of malfunctioning sensors is included in the optimisation. The reliability and the robustness of the procedure is tested with experimental and numerical examples. Finally, the proposed optimisation algorithm is applied to a composite stiffened panel for both the uniform and non-uniform probability of impact occurrence. PMID:28774064

Bayesian time series analysis of segments of the Rocky Mountain trumpeter swan population

USGS Publications Warehouse

Wright, Christopher K.; Sojda, Richard S.; Goodman, Daniel

2002-01-01

A Bayesian time series analysis technique, the dynamic linear model, was used to analyze counts of Trumpeter Swans (Cygnus buccinator) summering in Idaho, Montana, and Wyoming from 1931 to 2000. For the Yellowstone National Park segment of white birds (sub-adults and adults combined) the estimated probability of a positive growth rate is 0.01. The estimated probability of achieving the Subcommittee on Rocky Mountain Trumpeter Swans 2002 population goal of 40 white birds for the Yellowstone segment is less than 0.01. Outside of Yellowstone National Park, Wyoming white birds are estimated to have a 0.79 probability of a positive growth rate with a 0.05 probability of achieving the 2002 objective of 120 white birds. In the Centennial Valley in southwest Montana, results indicate a probability of 0.87 that the white bird population is growing at a positive rate with considerable uncertainty. The estimated probability of achieving the 2002 Centennial Valley objective of 160 white birds is 0.14 but under an alternative model falls to 0.04. The estimated probability that the Targhee National Forest segment of white birds has a positive growth rate is 0.03. In Idaho outside of the Targhee National Forest, white birds are estimated to have a 0.97 probability of a positive growth rate with a 0.18 probability of attaining the 2002 goal of 150 white birds.

Bootstrap percolation on spatial networks

NASA Astrophysics Data System (ADS)

Gao, Jian; Zhou, Tao; Hu, Yanqing

2015-10-01

Bootstrap percolation is a general representation of some networked activation process, which has found applications in explaining many important social phenomena, such as the propagation of information. Inspired by some recent findings on spatial structure of online social networks, here we study bootstrap percolation on undirected spatial networks, with the probability density function of long-range links’ lengths being a power law with tunable exponent. Setting the size of the giant active component as the order parameter, we find a parameter-dependent critical value for the power-law exponent, above which there is a double phase transition, mixed of a second-order phase transition and a hybrid phase transition with two varying critical points, otherwise there is only a second-order phase transition. We further find a parameter-independent critical value around -1, about which the two critical points for the double phase transition are almost constant. To our surprise, this critical value -1 is just equal or very close to the values of many real online social networks, including LiveJournal, HP Labs email network, Belgian mobile phone network, etc. This work helps us in better understanding the self-organization of spatial structure of online social networks, in terms of the effective function for information spreading.

A resampling strategy based on bootstrap to reduce the effect of large blunders in GPS absolute positioning

NASA Astrophysics Data System (ADS)

Angrisano, Antonio; Maratea, Antonio; Gaglione, Salvatore

2018-01-01

In the absence of obstacles, a GPS device is generally able to provide continuous and accurate estimates of position, while in urban scenarios buildings can generate multipath and echo-only phenomena that severely affect the continuity and the accuracy of the provided estimates. Receiver autonomous integrity monitoring (RAIM) techniques are able to reduce the negative consequences of large blunders in urban scenarios, but require both a good redundancy and a low contamination to be effective. In this paper a resampling strategy based on bootstrap is proposed as an alternative to RAIM, in order to estimate accurately position in case of low redundancy and multiple blunders: starting with the pseudorange measurement model, at each epoch the available measurements are bootstrapped—that is random sampled with replacement—and the generated a posteriori empirical distribution is exploited to derive the final position. Compared to standard bootstrap, in this paper the sampling probabilities are not uniform, but vary according to an indicator of the measurement quality. The proposed method has been compared with two different RAIM techniques on a data set collected in critical conditions, resulting in a clear improvement on all considered figures of merit.

The influence of baseline marijuana use on treatment of cocaine dependence: application of an informative-priors bayesian approach.

PubMed

Green, Charles; Schmitz, Joy; Lindsay, Jan; Pedroza, Claudia; Lane, Scott; Agnelli, Rob; Kjome, Kimberley; Moeller, F Gerard

2012-01-01

Marijuana use is prevalent among patients with cocaine dependence and often non-exclusionary in clinical trials of potential cocaine medications. The dual-focus of this study was to (1) examine the moderating effect of baseline marijuana use on response to treatment with levodopa/carbidopa for cocaine dependence; and (2) apply an informative-priors, Bayesian approach for estimating the probability of a subgroup-by-treatment interaction effect. A secondary data analysis of two previously published, double-blind, randomized controlled trials provided complete data for the historical (Study 1: N = 64 placebo), and current (Study 2: N = 113) data sets. Negative binomial regression evaluated Treatment Effectiveness Scores (TES) as a function of medication condition (levodopa/carbidopa, placebo), baseline marijuana use (days in past 30), and their interaction. Bayesian analysis indicated that there was a 96% chance that baseline marijuana use predicts differential response to treatment with levodopa/carbidopa. Simple effects indicated that among participants receiving levodopa/carbidopa the probability that baseline marijuana confers harm in terms of reducing TES was 0.981; whereas the probability that marijuana confers harm within the placebo condition was 0.163. For every additional day of marijuana use reported at baseline, participants in the levodopa/carbidopa condition demonstrated a 5.4% decrease in TES; while participants in the placebo condition demonstrated a 4.9% increase in TES. The potential moderating effect of marijuana on cocaine treatment response should be considered in future trial designs. Applying Bayesian subgroup analysis proved informative in characterizing this patient-treatment interaction effect.

The Influence of Baseline Marijuana Use on Treatment of Cocaine Dependence: Application of an Informative-Priors Bayesian Approach

PubMed Central

Green, Charles; Schmitz, Joy; Lindsay, Jan; Pedroza, Claudia; Lane, Scott; Agnelli, Rob; Kjome, Kimberley; Moeller, F. Gerard

2012-01-01

Background: Marijuana use is prevalent among patients with cocaine dependence and often non-exclusionary in clinical trials of potential cocaine medications. The dual-focus of this study was to (1) examine the moderating effect of baseline marijuana use on response to treatment with levodopa/carbidopa for cocaine dependence; and (2) apply an informative-priors, Bayesian approach for estimating the probability of a subgroup-by-treatment interaction effect. Method: A secondary data analysis of two previously published, double-blind, randomized controlled trials provided complete data for the historical (Study 1: N = 64 placebo), and current (Study 2: N = 113) data sets. Negative binomial regression evaluated Treatment Effectiveness Scores (TES) as a function of medication condition (levodopa/carbidopa, placebo), baseline marijuana use (days in past 30), and their interaction. Results: Bayesian analysis indicated that there was a 96% chance that baseline marijuana use predicts differential response to treatment with levodopa/carbidopa. Simple effects indicated that among participants receiving levodopa/carbidopa the probability that baseline marijuana confers harm in terms of reducing TES was 0.981; whereas the probability that marijuana confers harm within the placebo condition was 0.163. For every additional day of marijuana use reported at baseline, participants in the levodopa/carbidopa condition demonstrated a 5.4% decrease in TES; while participants in the placebo condition demonstrated a 4.9% increase in TES. Conclusion: The potential moderating effect of marijuana on cocaine treatment response should be considered in future trial designs. Applying Bayesian subgroup analysis proved informative in characterizing this patient-treatment interaction effect. PMID:23115553

A Bayesian taxonomic classification method for 16S rRNA gene sequences with improved species-level accuracy.

PubMed

Gao, Xiang; Lin, Huaiying; Revanna, Kashi; Dong, Qunfeng

2017-05-10

Species-level classification for 16S rRNA gene sequences remains a serious challenge for microbiome researchers, because existing taxonomic classification tools for 16S rRNA gene sequences either do not provide species-level classification, or their classification results are unreliable. The unreliable results are due to the limitations in the existing methods which either lack solid probabilistic-based criteria to evaluate the confidence of their taxonomic assignments, or use nucleotide k-mer frequency as the proxy for sequence similarity measurement. We have developed a method that shows significantly improved species-level classification results over existing methods. Our method calculates true sequence similarity between query sequences and database hits using pairwise sequence alignment. Taxonomic classifications are assigned from the species to the phylum levels based on the lowest common ancestors of multiple database hits for each query sequence, and further classification reliabilities are evaluated by bootstrap confidence scores. The novelty of our method is that the contribution of each database hit to the taxonomic assignment of the query sequence is weighted by a Bayesian posterior probability based upon the degree of sequence similarity of the database hit to the query sequence. Our method does not need any training datasets specific for different taxonomic groups. Instead only a reference database is required for aligning to the query sequences, making our method easily applicable for different regions of the 16S rRNA gene or other phylogenetic marker genes. Reliable species-level classification for 16S rRNA or other phylogenetic marker genes is critical for microbiome research. Our software shows significantly higher classification accuracy than the existing tools and we provide probabilistic-based confidence scores to evaluate the reliability of our taxonomic classification assignments based on multiple database matches to query sequences. Despite its higher computational costs, our method is still suitable for analyzing large-scale microbiome datasets for practical purposes. Furthermore, our method can be applied for taxonomic classification of any phylogenetic marker gene sequences. Our software, called BLCA, is freely available at https://github.com/qunfengdong/BLCA .

Instruction in information structuring improves Bayesian judgment in intelligence analysts.

PubMed

Mandel, David R

2015-01-01

An experiment was conducted to test the effectiveness of brief instruction in information structuring (i.e., representing and integrating information) for improving the coherence of probability judgments and binary choices among intelligence analysts. Forty-three analysts were presented with comparable sets of Bayesian judgment problems before and immediately after instruction. After instruction, analysts' probability judgments were more coherent (i.e., more additive and compliant with Bayes theorem). Instruction also improved the coherence of binary choices regarding category membership: after instruction, subjects were more likely to invariably choose the category to which they assigned the higher probability of a target's membership. The research provides a rare example of evidence-based validation of effectiveness in instruction to improve the statistical assessment skills of intelligence analysts. Such instruction could also be used to improve the assessment quality of other types of experts who are required to integrate statistical information or make probabilistic assessments.

Determining open cluster membership. A Bayesian framework for quantitative member classification

NASA Astrophysics Data System (ADS)

Stott, Jonathan J.

2018-01-01

Aims: My goal is to develop a quantitative algorithm for assessing open cluster membership probabilities. The algorithm is designed to work with single-epoch observations. In its simplest form, only one set of program images and one set of reference images are required. Methods: The algorithm is based on a two-stage joint astrometric and photometric assessment of cluster membership probabilities. The probabilities were computed within a Bayesian framework using any available prior information. Where possible, the algorithm emphasizes simplicity over mathematical sophistication. Results: The algorithm was implemented and tested against three observational fields using published survey data. M 67 and NGC 654 were selected as cluster examples while a third, cluster-free, field was used for the final test data set. The algorithm shows good quantitative agreement with the existing surveys and has a false-positive rate significantly lower than the astrometric or photometric methods used individually.

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.

Geostatistics and Bayesian updating for transmissivity estimation in a multiaquifer system in Manitoba, Canada.

PubMed

Kennedy, Paula L; Woodbury, Allan D

2002-01-01

In ground water flow and transport modeling, the heterogeneous nature of porous media has a considerable effect on the resulting flow and solute transport. Some method of generating the heterogeneous field from a limited dataset of uncertain measurements is required. Bayesian updating is one method that interpolates from an uncertain dataset using the statistics of the underlying probability distribution function. In this paper, Bayesian updating was used to determine the heterogeneous natural log transmissivity field for a carbonate and a sandstone aquifer in southern Manitoba. It was determined that the transmissivity in m2/sec followed a natural log normal distribution for both aquifers with a mean of -7.2 and - 8.0 for the carbonate and sandstone aquifers, respectively. The variograms were calculated using an estimator developed by Li and Lake (1994). Fractal nature was not evident in the variogram from either aquifer. The Bayesian updating heterogeneous field provided good results even in cases where little data was available. A large transmissivity zone in the sandstone aquifer was created by the Bayesian procedure, which is not a reflection of any deterministic consideration, but is a natural outcome of updating a prior probability distribution function with observations. The statistical model returns a result that is very reasonable; that is homogeneous in regions where little or no information is available to alter an initial state. No long range correlation trends or fractal behavior of the log-transmissivity field was observed in either aquifer over a distance of about 300 km.

A Bayesian approach to reliability and confidence

NASA Technical Reports Server (NTRS)

Barnes, Ron

1989-01-01

The historical evolution of NASA's interest in quantitative measures of reliability assessment is outlined. The introduction of some quantitative methodologies into the Vehicle Reliability Branch of the Safety, Reliability and Quality Assurance (SR and QA) Division at Johnson Space Center (JSC) was noted along with the development of the Extended Orbiter Duration--Weakest Link study which will utilize quantitative tools for a Bayesian statistical analysis. Extending the earlier work of NASA sponsor, Richard Heydorn, researchers were able to produce a consistent Bayesian estimate for the reliability of a component and hence by a simple extension for a system of components in some cases where the rate of failure is not constant but varies over time. Mechanical systems in general have this property since the reliability usually decreases markedly as the parts degrade over time. While they have been able to reduce the Bayesian estimator to a simple closed form for a large class of such systems, the form for the most general case needs to be attacked by the computer. Once a table is generated for this form, researchers will have a numerical form for the general solution. With this, the corresponding probability statements about the reliability of a system can be made in the most general setting. Note that the utilization of uniform Bayesian priors represents a worst case scenario in the sense that as researchers incorporate more expert opinion into the model, they will be able to improve the strength of the probability calculations.

Bayesian ionospheric multi-instrument 3D tomography

NASA Astrophysics Data System (ADS)

Norberg, Johannes; Vierinen, Juha; Roininen, Lassi

2017-04-01

The tomographic reconstruction of ionospheric electron densities is an inverse problem that cannot be solved without relatively strong regularising additional information. % Especially the vertical electron density profile is determined predominantly by the regularisation. % %Often utilised regularisations in ionospheric tomography include smoothness constraints and iterative methods with initial ionospheric models. % Despite its crucial role, the regularisation is often hidden in the algorithm as a numerical procedure without physical understanding. % % The Bayesian methodology provides an interpretative approach for the problem, as the regularisation can be given in a physically meaningful and quantifiable prior probability distribution. % The prior distribution can be based on ionospheric physics, other available ionospheric measurements and their statistics. % Updating the prior with measurements results as the posterior distribution that carries all the available information combined. % From the posterior distribution, the most probable state of the ionosphere can then be solved with the corresponding probability intervals. % Altogether, the Bayesian methodology provides understanding on how strong the given regularisation is, what is the information gained with the measurements and how reliable the final result is. % In addition, the combination of different measurements and temporal development can be taken into account in a very intuitive way. However, a direct implementation of the Bayesian approach requires inversion of large covariance matrices resulting in computational infeasibility. % In the presented method, Gaussian Markov random fields are used to form a sparse matrix approximations for the covariances. % The approach makes the problem computationally feasible while retaining the probabilistic and physical interpretation. Here, the Bayesian method with Gaussian Markov random fields is applied for ionospheric 3D tomography over Northern Europe. % Multi-instrument measurements are utilised from TomoScand receiver network for Low Earth orbit beacon satellite signals, GNSS receiver networks, as well as from EISCAT ionosondes and incoherent scatter radars. % %The performance is demonstrated in three-dimensional spatial domain with temporal development also taken into account.

Phylogenetic reconstruction using four low-copy nuclear loci strongly supports a polyphyletic origin of the genus Sorghum

PubMed Central

Hawkins, Jennifer S.; Ramachandran, Dhanushya; Henderson, Ashley; Freeman, Jasmine; Carlise, Michael; Harris, Alex; Willison-Headley, Zachary

2015-01-01

Background and Aims Sorghum is an essential grain crop whose evolutionary placement within the Andropogoneae has been the subject of scrutiny for decades. Early studies using cytogenetic and morphological data point to a poly- or paraphyletic origin of the genus; however, acceptance of poly- or paraphyly has been met with resistance. This study aimed to address the species relationships within Sorghum, in addition to the placement of Sorghum within the tribe, using a phylogenetic approach and employing broad taxon sampling. Methods From 16 diverse Sorghum species, eight low-copy nuclear loci were sequenced that are known to play a role in morphological diversity and have been previously used to study evolutionary relationships in grasses. Further, the data for four of these loci were combined with those from 57 members of the Andropogoneae in order to determine the placement of Sorghum within the tribe. Both maximum likelihood and Bayesian analyses were performed on multilocus concatenated data matrices. Key Results The Sorghum-specific topology provides strong support for two major lineages, in alignment with earlier studies employing chloroplast and internal transcribed spacer (ITS) markers. Clade I is composed of the Eu-, Chaeto- and Heterosorghum, while clade II contains the Stipo- and Parasorghum. When combined with data from the Andropogoneae, Clade II resolves as sister to a clade containing Miscanthus and Saccharum with high posterior probability and bootstrap support, and to the exclusion of Clade I. Conclusions The results provide compelling evidence for a two-lineage polyphyletic ancestry of Sorghum within the larger Andropogoneae, i.e. the derivation of the two major Sorghum clades from a unique common ancestor. Rejection of monophyly in previous molecular studies is probably due to limited taxon sampling outside of the genus. The clade consisting of Para- and Stiposorghum resolves as sister to Miscanthus and Saccharum with strong node support. PMID:26141132

Generic phylogeny, historical biogeography and character evolution of the cosmopolitan aquatic plant family Hydrocharitaceae.

PubMed

Chen, Ling-Yun; Chen, Jin-Ming; Gituru, Robert Wahiti; Wang, Qing-Feng

2012-03-10

Hydrocharitaceae is a fully aquatic monocot family, consists of 18 genera with approximately 120 species. The family includes both fresh and marine aquatics and exhibits great diversity in form and habit including annual and perennial life histories; submersed, partially submersed and floating leaf habits and linear to orbicular leaf shapes. The family has a cosmopolitan distribution and is well represented in the Tertiary fossil record in Europe. At present, the historical biogeography of the family is not well understood and the generic relationships remain controversial. In this study we investigated the phylogeny and biogeography of Hydrocharitaceae by integrating fossils and DNA sequences from eight genes. We also conducted ancestral state reconstruction for three morphological characters. Phylogenetic analyses produced a phylogeny with most branches strongly supported by bootstrap values greater than 95 and Bayesian posterior probability values of 1.0. Stratiotes is the first diverging lineage with the remaining genera in two clades, one clade consists of Lagarosiphon, Ottelia, Blyxa, Apalanthe, Elodea and Egeria; and the other consists of Hydrocharis-Limnobium, Thalassia, Enhalus, Halophila, Najas, Hydrilla, Vallisneria, Nechamandra and Maidenia. Biogeographic analyses (DIVA, Mesquite) and divergence time estimates (BEAST) resolved the most recent common ancestor of Hydrocharitaceae as being in Asia during the Late Cretaceous and Palaeocene (54.7-72.6 Ma). Dispersals (including long-distance dispersal and migrations through Tethys seaway and land bridges) probably played major roles in the intercontinental distribution of this family. Ancestral state reconstruction suggested that in Hydrocharitaceae evolution of dioecy is bidirectional, viz., from dioecy to hermaphroditism, and from hermaphroditism to dioecy, and that the aerial-submerged leaf habit and short-linear leaf shape are the ancestral states. Our study has shed light on the previously controversial generic phylogeny of Hydrocharitaceae. The study has resolved the historical biogeography of this family and supported dispersal as the most likely explanation for the intercontinental distribution. We have also provided valuable information for understanding the evolution of breeding system and leaf phenotype in aquatic monocots.

Reliability modelling and analysis of a multi-state element based on a dynamic Bayesian network

PubMed Central

Xu, Tingxue; Gu, Junyuan; Dong, Qi; Fu, Linyu

2018-01-01

This paper presents a quantitative reliability modelling and analysis method for multi-state elements based on a combination of the Markov process and a dynamic Bayesian network (DBN), taking perfect repair, imperfect repair and condition-based maintenance (CBM) into consideration. The Markov models of elements without repair and under CBM are established, and an absorbing set is introduced to determine the reliability of the repairable element. According to the state-transition relations between the states determined by the Markov process, a DBN model is built. In addition, its parameters for series and parallel systems, namely, conditional probability tables, can be calculated by referring to the conditional degradation probabilities. Finally, the power of a control unit in a failure model is used as an example. A dynamic fault tree (DFT) is translated into a Bayesian network model, and subsequently extended to a DBN. The results show the state probabilities of an element and the system without repair, with perfect and imperfect repair, and under CBM, with an absorbing set plotted by differential equations and verified. Through referring forward, the reliability value of the control unit is determined in different kinds of modes. Finally, weak nodes are noted in the control unit. PMID:29765629

Robust Bayesian Experimental Design for Conceptual Model Discrimination

NASA Astrophysics Data System (ADS)

Pham, H. V.; Tsai, F. T. C.

2015-12-01

A robust Bayesian optimal experimental design under uncertainty is presented to provide firm information for model discrimination, given the least number of pumping wells and observation wells. Firm information is the maximum information of a system can be guaranteed from an experimental design. The design is based on the Box-Hill expected entropy decrease (EED) before and after the experiment design and the Bayesian model averaging (BMA) framework. A max-min programming is introduced to choose the robust design that maximizes the minimal Box-Hill EED subject to that the highest expected posterior model probability satisfies a desired probability threshold. The EED is calculated by the Gauss-Hermite quadrature. The BMA method is used to predict future observations and to quantify future observation uncertainty arising from conceptual and parametric uncertainties in calculating EED. Monte Carlo approach is adopted to quantify the uncertainty in the posterior model probabilities. The optimal experimental design is tested by a synthetic 5-layer anisotropic confined aquifer. Nine conceptual groundwater models are constructed due to uncertain geological architecture and boundary condition. High-performance computing is used to enumerate all possible design solutions in order to identify the most plausible groundwater model. Results highlight the impacts of scedasticity in future observation data as well as uncertainty sources on potential pumping and observation locations.

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

The Role of Probability-Based Inference in an Intelligent Tutoring System.

ERIC Educational Resources Information Center

Mislevy, Robert J.; Gitomer, Drew H.

Probability-based inference in complex networks of interdependent variables is an active topic in statistical research, spurred by such diverse applications as forecasting, pedigree analysis, troubleshooting, and medical diagnosis. This paper concerns the role of Bayesian inference networks for updating student models in intelligent tutoring…

ChemStable: a web server for rule-embedded naïve Bayesian learning approach to predict compound stability.

PubMed

Liu, Zhihong; Zheng, Minghao; Yan, Xin; Gu, Qiong; Gasteiger, Johann; Tijhuis, Johan; Maas, Peter; Li, Jiabo; Xu, Jun

2014-09-01

Predicting compound chemical stability is important because unstable compounds can lead to either false positive or to false negative conclusions in bioassays. Experimental data (COMDECOM) measured from DMSO/H2O solutions stored at 50 °C for 105 days were used to predicted stability by applying rule-embedded naïve Bayesian learning, based upon atom center fragment (ACF) features. To build the naïve Bayesian classifier, we derived ACF features from 9,746 compounds in the COMDECOM dataset. By recursively applying naïve Bayesian learning from the data set, each ACF is assigned with an expected stable probability (p(s)) and an unstable probability (p(uns)). 13,340 ACFs, together with their p(s) and p(uns) data, were stored in a knowledge base for use by the Bayesian classifier. For a given compound, its ACFs were derived from its structure connection table with the same protocol used to drive ACFs from the training data. Then, the Bayesian classifier assigned p(s) and p(uns) values to the compound ACFs by a structural pattern recognition algorithm, which was implemented in-house. Compound instability is calculated, with Bayes' theorem, based upon the p(s) and p(uns) values of the compound ACFs. We were able to achieve performance with an AUC value of 84% and a tenfold cross validation accuracy of 76.5%. To reduce false negatives, a rule-based approach has been embedded in the classifier. The rule-based module allows the program to improve its predictivity by expanding its compound instability knowledge base, thus further reducing the possibility of false negatives. To our knowledge, this is the first in silico prediction service for the prediction of the stabilities of organic compounds.

On the uncertainty in single molecule fluorescent lifetime and energy emission measurements

NASA Technical Reports Server (NTRS)

Brown, Emery N.; Zhang, Zhenhua; Mccollom, Alex D.

1995-01-01

Time-correlated single photon counting has recently been combined with mode-locked picosecond pulsed excitation to measure the fluorescent lifetimes and energy emissions of single molecules in a flow stream. Maximum likelihood (ML) and least square methods agree and are optimal when the number of detected photons is large however, in single molecule fluorescence experiments the number of detected photons can be less than 20, 67% of those can be noise and the detection time is restricted to 10 nanoseconds. Under the assumption that the photon signal and background noise are two independent inhomogeneous poisson processes, we derive the exact joint arrival time probably density of the photons collected in a single counting experiment performed in the presence of background noise. The model obviates the need to bin experimental data for analysis, and makes it possible to analyze formally the effect of background noise on the photon detection experiment using both ML or Bayesian methods. For both methods we derive the joint and marginal probability densities of the fluorescent lifetime and fluorescent emission. the ML and Bayesian methods are compared in an analysis of simulated single molecule fluorescence experiments of Rhodamine 110 using different combinations of expected background nose and expected fluorescence emission. While both the ML or Bayesian procedures perform well for analyzing fluorescence emissions, the Bayesian methods provide more realistic measures of uncertainty in the fluorescent lifetimes. The Bayesian methods would be especially useful for measuring uncertainty in fluorescent lifetime estimates in current single molecule flow stream experiments where the expected fluorescence emission is low. Both the ML and Bayesian algorithms can be automated for applications in molecular biology.

On the Uncertainty in Single Molecule Fluorescent Lifetime and Energy Emission Measurements

NASA Technical Reports Server (NTRS)

Brown, Emery N.; Zhang, Zhenhua; McCollom, Alex D.

1996-01-01

Time-correlated single photon counting has recently been combined with mode-locked picosecond pulsed excitation to measure the fluorescent lifetimes and energy emissions of single molecules in a flow stream. Maximum likelihood (ML) and least squares methods agree and are optimal when the number of detected photons is large, however, in single molecule fluorescence experiments the number of detected photons can be less than 20, 67 percent of those can be noise, and the detection time is restricted to 10 nanoseconds. Under the assumption that the photon signal and background noise are two independent inhomogeneous Poisson processes, we derive the exact joint arrival time probability density of the photons collected in a single counting experiment performed in the presence of background noise. The model obviates the need to bin experimental data for analysis, and makes it possible to analyze formally the effect of background noise on the photon detection experiment using both ML or Bayesian methods. For both methods we derive the joint and marginal probability densities of the fluorescent lifetime and fluorescent emission. The ML and Bayesian methods are compared in an analysis of simulated single molecule fluorescence experiments of Rhodamine 110 using different combinations of expected background noise and expected fluorescence emission. While both the ML or Bayesian procedures perform well for analyzing fluorescence emissions, the Bayesian methods provide more realistic measures of uncertainty in the fluorescent lifetimes. The Bayesian methods would be especially useful for measuring uncertainty in fluorescent lifetime estimates in current single molecule flow stream experiments where the expected fluorescence emission is low. Both the ML and Bayesian algorithms can be automated for applications in molecular biology.

Potential Use of a Bayesian Network for Discriminating Flash Type from Future GOES-R Geostationary Lightning Mapper (GLM) data

NASA Technical Reports Server (NTRS)

Solakiewiz, Richard; Koshak, William

2008-01-01

Continuous monitoring of the ratio of cloud flashes to ground flashes may provide a better understanding of thunderstorm dynamics, intensification, and evolution, and it may be useful in severe weather warning. The National Lighting Detection Network TM (NLDN) senses ground flashes with exceptional detection efficiency and accuracy over most of the continental United States. A proposed Geostationary Lightning Mapper (GLM) aboard the Geostationary Operational Environmental Satellite (GOES-R) will look at the western hemisphere, and among the lightning data products to be made available will be the fundamental optical flash parameters for both cloud and ground flashes: radiance, area, duration, number of optical groups, and number of optical events. Previous studies have demonstrated that the optical flash parameter statistics of ground and cloud lightning, which are observable from space, are significantly different. This study investigates a Bayesian network methodology for discriminating lightning flash type (ground or cloud) using the lightning optical data and ancillary GOES-R data. A Directed Acyclic Graph (DAG) is set up with lightning as a "root" and data observed by GLM as the "leaves." This allows for a direct calculation of the joint probability distribution function for the lighting type and radiance, area, etc. Initially, the conditional probabilities that will be required can be estimated from the Lightning Imaging Sensor (LIS) and the Optical Transient Detector (OTD) together with NLDN data. Directly manipulating the joint distribution will yield the conditional probability that a lightning flash is a ground flash given the evidence, which consists of the observed lightning optical data [and possibly cloud data retrieved from the GOES-R Advanced Baseline Imager (ABI) in a more mature Bayesian network configuration]. Later, actual GLM and NLDN data can be used to refine the estimates of the conditional probabilities used in the model; i.e., the Bayesian network is a learning network. Methods for efficient calculation of the conditional probabilities (e.g., an algorithm using junction trees), finding data conflicts, goodness of fit, and dealing with missing data will also be addressed.

On the use of Bayesian Monte-Carlo in evaluation of nuclear data

NASA Astrophysics Data System (ADS)

De Saint Jean, Cyrille; Archier, Pascal; Privas, Edwin; Noguere, Gilles

2017-09-01

As model parameters, necessary ingredients of theoretical models, are not always predicted by theory, a formal mathematical framework associated to the evaluation work is needed to obtain the best set of parameters (resonance parameters, optical models, fission barrier, average width, multigroup cross sections) with Bayesian statistical inference by comparing theory to experiment. The formal rule related to this methodology is to estimate the posterior density probability function of a set of parameters by solving an equation of the following type: pdf(posterior) ˜ pdf(prior) × a likelihood function. A fitting procedure can be seen as an estimation of the posterior density probability of a set of parameters (referred as x→?) knowing a prior information on these parameters and a likelihood which gives the probability density function of observing a data set knowing x→?. To solve this problem, two major paths could be taken: add approximations and hypothesis and obtain an equation to be solved numerically (minimum of a cost function or Generalized least Square method, referred as GLS) or use Monte-Carlo sampling of all prior distributions and estimate the final posterior distribution. Monte Carlo methods are natural solution for Bayesian inference problems. They avoid approximations (existing in traditional adjustment procedure based on chi-square minimization) and propose alternative in the choice of probability density distribution for priors and likelihoods. This paper will propose the use of what we are calling Bayesian Monte Carlo (referred as BMC in the rest of the manuscript) in the whole energy range from thermal, resonance and continuum range for all nuclear reaction models at these energies. Algorithms will be presented based on Monte-Carlo sampling and Markov chain. The objectives of BMC are to propose a reference calculation for validating the GLS calculations and approximations, to test probability density distributions effects and to provide the framework of finding global minimum if several local minimums exist. Application to resolved resonance, unresolved resonance and continuum evaluation as well as multigroup cross section data assimilation will be presented.

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.

A Bayesian Method for Evaluating and Discovering Disease Loci Associations

PubMed Central

Jiang, Xia; Barmada, M. Michael; Cooper, Gregory F.; Becich, Michael J.

2011-01-01

Background A genome-wide association study (GWAS) typically involves examining representative SNPs in individuals from some population. A GWAS data set can concern a million SNPs and may soon concern billions. Researchers investigate the association of each SNP individually with a disease, and it is becoming increasingly commonplace to also analyze multi-SNP associations. Techniques for handling so many hypotheses include the Bonferroni correction and recently developed Bayesian methods. These methods can encounter problems. Most importantly, they are not applicable to a complex multi-locus hypothesis which has several competing hypotheses rather than only a null hypothesis. A method that computes the posterior probability of complex hypotheses is a pressing need. Methodology/Findings We introduce the Bayesian network posterior probability (BNPP) method which addresses the difficulties. The method represents the relationship between a disease and SNPs using a directed acyclic graph (DAG) model, and computes the likelihood of such models using a Bayesian network scoring criterion. The posterior probability of a hypothesis is computed based on the likelihoods of all competing hypotheses. The BNPP can not only be used to evaluate a hypothesis that has previously been discovered or suspected, but also to discover new disease loci associations. The results of experiments using simulated and real data sets are presented. Our results concerning simulated data sets indicate that the BNPP exhibits both better evaluation and discovery performance than does a p-value based method. For the real data sets, previous findings in the literature are confirmed and additional findings are found. Conclusions/Significance We conclude that the BNPP resolves a pressing problem by providing a way to compute the posterior probability of complex multi-locus hypotheses. A researcher can use the BNPP to determine the expected utility of investigating a hypothesis further. Furthermore, we conclude that the BNPP is a promising method for discovering disease loci associations. PMID:21853025

Exoplanet Biosignatures: Future Directions

PubMed Central

Bains, William; Cronin, Leroy; DasSarma, Shiladitya; Danielache, Sebastian; Domagal-Goldman, Shawn; Kacar, Betul; Kiang, Nancy Y.; Lenardic, Adrian; Reinhard, Christopher T.; Moore, William; Schwieterman, Edward W.; Shkolnik, Evgenya L.; Smith, Harrison B.

2018-01-01

Abstract We introduce a Bayesian method for guiding future directions for detection of life on exoplanets. We describe empirical and theoretical work necessary to place constraints on the relevant likelihoods, including those emerging from better understanding stellar environment, planetary climate and geophysics, geochemical cycling, the universalities of physics and chemistry, the contingencies of evolutionary history, the properties of life as an emergent complex system, and the mechanisms driving the emergence of life. We provide examples for how the Bayesian formalism could guide future search strategies, including determining observations to prioritize or deciding between targeted searches or larger lower resolution surveys to generate ensemble statistics and address how a Bayesian methodology could constrain the prior probability of life with or without a positive detection. Key Words: Exoplanets—Biosignatures—Life detection—Bayesian analysis. Astrobiology 18, 779–824. PMID:29938538

Exoplanet Biosignatures: Future Directions.

PubMed

Walker, Sara I; Bains, William; Cronin, Leroy; DasSarma, Shiladitya; Danielache, Sebastian; Domagal-Goldman, Shawn; Kacar, Betul; Kiang, Nancy Y; Lenardic, Adrian; Reinhard, Christopher T; Moore, William; Schwieterman, Edward W; Shkolnik, Evgenya L; Smith, Harrison B

2018-06-01

We introduce a Bayesian method for guiding future directions for detection of life on exoplanets. We describe empirical and theoretical work necessary to place constraints on the relevant likelihoods, including those emerging from better understanding stellar environment, planetary climate and geophysics, geochemical cycling, the universalities of physics and chemistry, the contingencies of evolutionary history, the properties of life as an emergent complex system, and the mechanisms driving the emergence of life. We provide examples for how the Bayesian formalism could guide future search strategies, including determining observations to prioritize or deciding between targeted searches or larger lower resolution surveys to generate ensemble statistics and address how a Bayesian methodology could constrain the prior probability of life with or without a positive detection. Key Words: Exoplanets-Biosignatures-Life detection-Bayesian analysis. Astrobiology 18, 779-824.

A fast combination method in DSmT and its application to recommender system

PubMed Central

Liu, Yihai

2018-01-01

In many applications involving epistemic uncertainties usually modeled by belief functions, it is often necessary to approximate general (non-Bayesian) basic belief assignments (BBAs) to subjective probabilities (called Bayesian BBAs). This necessity occurs if one needs to embed the fusion result in a system based on the probabilistic framework and Bayesian inference (e.g. tracking systems), or if one needs to make a decision in the decision making problems. In this paper, we present a new fast combination method, called modified rigid coarsening (MRC), to obtain the final Bayesian BBAs based on hierarchical decomposition (coarsening) of the frame of discernment. Regarding this method, focal elements with probabilities are coarsened efficiently to reduce computational complexity in the process of combination by using disagreement vector and a simple dichotomous approach. In order to prove the practicality of our approach, this new approach is applied to combine users’ soft preferences in recommender systems (RSs). Additionally, in order to make a comprehensive performance comparison, the proportional conflict redistribution rule #6 (PCR6) is regarded as a baseline in a range of experiments. According to the results of experiments, MRC is more effective in accuracy of recommendations compared to original Rigid Coarsening (RC) method and comparable in computational time. PMID:29351297

Natural frequencies improve Bayesian reasoning in simple and complex inference tasks

PubMed Central

Hoffrage, Ulrich; Krauss, Stefan; Martignon, Laura; Gigerenzer, Gerd

2015-01-01

Representing statistical information in terms of natural frequencies rather than probabilities improves performance in Bayesian inference tasks. This beneficial effect of natural frequencies has been demonstrated in a variety of applied domains such as medicine, law, and education. Yet all the research and applications so far have been limited to situations where one dichotomous cue is used to infer which of two hypotheses is true. Real-life applications, however, often involve situations where cues (e.g., medical tests) have more than one value, where more than two hypotheses (e.g., diseases) are considered, or where more than one cue is available. In Study 1, we show that natural frequencies, compared to information stated in terms of probabilities, consistently increase the proportion of Bayesian inferences made by medical students in four conditions—three cue values, three hypotheses, two cues, or three cues—by an average of 37 percentage points. In Study 2, we show that teaching natural frequencies for simple tasks with one dichotomous cue and two hypotheses leads to a transfer of learning to complex tasks with three cue values and two cues, with a proportion of 40 and 81% correct inferences, respectively. Thus, natural frequencies facilitate Bayesian reasoning in a much broader class of situations than previously thought. PMID:26528197

A Bayesian joint probability modeling approach for seasonal forecasting of streamflows at multiple sites

NASA Astrophysics Data System (ADS)

Wang, Q. J.; Robertson, D. E.; Chiew, F. H. S.

2009-05-01

Seasonal forecasting of streamflows can be highly valuable for water resources management. In this paper, a Bayesian joint probability (BJP) modeling approach for seasonal forecasting of streamflows at multiple sites is presented. A Box-Cox transformed multivariate normal distribution is proposed to model the joint distribution of future streamflows and their predictors such as antecedent streamflows and El Niño-Southern Oscillation indices and other climate indicators. Bayesian inference of model parameters and uncertainties is implemented using Markov chain Monte Carlo sampling, leading to joint probabilistic forecasts of streamflows at multiple sites. The model provides a parametric structure for quantifying relationships between variables, including intersite correlations. The Box-Cox transformed multivariate normal distribution has considerable flexibility for modeling a wide range of predictors and predictands. The Bayesian inference formulated allows the use of data that contain nonconcurrent and missing records. The model flexibility and data-handling ability means that the BJP modeling approach is potentially of wide practical application. The paper also presents a number of statistical measures and graphical methods for verification of probabilistic forecasts of continuous variables. Results for streamflows at three river gauges in the Murrumbidgee River catchment in southeast Australia show that the BJP modeling approach has good forecast quality and that the fitted model is consistent with observed data.

Bayesian adaptive phase II screening design for combination trials

PubMed Central

Cai, Chunyan; Yuan, Ying; Johnson, Valen E

2013-01-01

Background Trials of combination therapies for the treatment of cancer are playing an increasingly important role in the battle against this disease. To more efficiently handle the large number of combination therapies that must be tested, we propose a novel Bayesian phase II adaptive screening design to simultaneously select among possible treatment combinations involving multiple agents. Methods Our design is based on formulating the selection procedure as a Bayesian hypothesis testing problem in which the superiority of each treatment combination is equated to a single hypothesis. During the trial conduct, we use the current values of the posterior probabilities of all hypotheses to adaptively allocate patients to treatment combinations. Results Simulation studies show that the proposed design substantially outperforms the conventional multiarm balanced factorial trial design. The proposed design yields a significantly higher probability for selecting the best treatment while allocating substantially more patients to efficacious treatments. Limitations The proposed design is most appropriate for the trials combining multiple agents and screening out the efficacious combination to be further investigated. Conclusions The proposed Bayesian adaptive phase II screening design substantially outperformed the conventional complete factorial design. Our design allocates more patients to better treatments while providing higher power to identify the best treatment at the end of the trial. PMID:23359875

Copula-based assessment of the relationship between food peaks and flood volumes using information on historical floods by Bayesian Monte Carlo Markov Chain simulations

NASA Astrophysics Data System (ADS)

Gaál, Ladislav; Szolgay, Ján.; Bacigál, Tomáå.¡; Kohnová, Silvia

2010-05-01

Copula-based estimation methods of hydro-climatological extremes have increasingly been gaining attention of researchers and practitioners in the last couple of years. Unlike the traditional estimation methods which are based on bivariate cumulative distribution functions (CDFs), copulas are a relatively flexible tool of statistics that allow for modelling dependencies between two or more variables such as flood peaks and flood volumes without making strict assumptions on the marginal distributions. The dependence structure and the reliability of the joint estimates of hydro-climatological extremes, mainly in the right tail of the joint CDF not only depends on the particular copula adopted but also on the data available for the estimation of the marginal distributions of the individual variables. Generally, data samples for frequency modelling have limited temporal extent, which is a considerable drawback of frequency analyses in practice. Therefore, it is advised to deal with statistical methods that improve any part of the process of copula construction and result in more reliable design values of hydrological variables. The scarcity of the data sample mostly in the extreme tail of the joint CDF can be bypassed, e.g., by using a considerably larger amount of simulated data by rainfall-runoff analysis or by including historical information on the variables under study. The latter approach of data extension is used here to make the quantile estimates of the individual marginals of the copula more reliable. In the presented paper it is proposed to use historical information in the frequency analysis of the marginal distributions in the framework of Bayesian Monte Carlo Markov Chain (MCMC) simulations. Generally, a Bayesian approach allows for a straightforward combination of different sources of information on floods (e.g. flood data from systematic measurements and historical flood records, respectively) in terms of a product of the corresponding likelihood functions. On the other hand, the MCMC algorithm is a numerical approach for sampling from the likelihood distributions. The Bayesian MCMC methods therefore provide an attractive way to estimate the uncertainty in parameters and quantile metrics of frequency distributions. The applicability of the method is demonstrated in a case study of the hydroelectric power station Orlík on the Vltava River. This site has a key role in the flood prevention of Prague, the capital city of the Czech Republic. The record length of the available flood data is 126 years from the period 1877-2002, while the flood event observed in 2002 that caused extensive damages and numerous casualties is treated as a historic one. To estimate the joint probabilities of flood peaks and volumes, different copulas are fitted and their goodness-of-fit are evaluated by bootstrap simulations. Finally, selected quantiles of flood volumes conditioned on given flood peaks are derived and compared with those obtained by the traditional method used in the practice of water management specialists of the Vltava River.

Bayesics

NASA Astrophysics Data System (ADS)

Skilling, John

2005-11-01

This tutorial gives a basic overview of Bayesian methodology, from its axiomatic foundation through the conventional development of data analysis and model selection to its rôle in quantum mechanics, and ending with some comments on inference in general human affairs. The central theme is that probability calculus is the unique language within which we can develop models of our surroundings that have predictive capability. These models are patterns of belief; there is no need to claim external reality. 1. Logic and probability 2. Probability and inference 3. Probability and model selection 4. Prior probabilities 5. Probability and frequency 6. Probability and quantum mechanics 7. Probability and fundamentalism 8. Probability and deception 9. Prediction and truth

Geotechnical parameter spatial distribution stochastic analysis based on multi-precision information assimilation

NASA Astrophysics Data System (ADS)

Wang, C.; Rubin, Y.

2014-12-01

Spatial distribution of important geotechnical parameter named compression modulus Es contributes considerably to the understanding of the underlying geological processes and the adequate assessment of the Es mechanics effects for differential settlement of large continuous structure foundation. These analyses should be derived using an assimilating approach that combines in-situ static cone penetration test (CPT) with borehole experiments. To achieve such a task, the Es distribution of stratum of silty clay in region A of China Expo Center (Shanghai) is studied using the Bayesian-maximum entropy method. This method integrates rigorously and efficiently multi-precision of different geotechnical investigations and sources of uncertainty. Single CPT samplings were modeled as a rational probability density curve by maximum entropy theory. Spatial prior multivariate probability density function (PDF) and likelihood PDF of the CPT positions were built by borehole experiments and the potential value of the prediction point, then, preceding numerical integration on the CPT probability density curves, the posterior probability density curve of the prediction point would be calculated by the Bayesian reverse interpolation framework. The results were compared between Gaussian Sequential Stochastic Simulation and Bayesian methods. The differences were also discussed between single CPT samplings of normal distribution and simulated probability density curve based on maximum entropy theory. It is shown that the study of Es spatial distributions can be improved by properly incorporating CPT sampling variation into interpolation process, whereas more informative estimations are generated by considering CPT Uncertainty for the estimation points. Calculation illustrates the significance of stochastic Es characterization in a stratum, and identifies limitations associated with inadequate geostatistical interpolation techniques. This characterization results will provide a multi-precision information assimilation method of other geotechnical parameters.

Bayesian network models for error detection in radiotherapy plans

NASA Astrophysics Data System (ADS)

Kalet, Alan M.; Gennari, John H.; Ford, Eric C.; Phillips, Mark H.

2015-04-01

The purpose of this study is to design and develop a probabilistic network for detecting errors in radiotherapy plans for use at the time of initial plan verification. Our group has initiated a multi-pronged approach to reduce these errors. We report on our development of Bayesian models of radiotherapy plans. Bayesian networks consist of joint probability distributions that define the probability of one event, given some set of other known information. Using the networks, we find the probability of obtaining certain radiotherapy parameters, given a set of initial clinical information. A low probability in a propagated network then corresponds to potential errors to be flagged for investigation. To build our networks we first interviewed medical physicists and other domain experts to identify the relevant radiotherapy concepts and their associated interdependencies and to construct a network topology. Next, to populate the network’s conditional probability tables, we used the Hugin Expert software to learn parameter distributions from a subset of de-identified data derived from a radiation oncology based clinical information database system. These data represent 4990 unique prescription cases over a 5 year period. Under test case scenarios with approximately 1.5% introduced error rates, network performance produced areas under the ROC curve of 0.88, 0.98, and 0.89 for the lung, brain and female breast cancer error detection networks, respectively. Comparison of the brain network to human experts performance (AUC of 0.90 ± 0.01) shows the Bayes network model performs better than domain experts under the same test conditions. Our results demonstrate the feasibility and effectiveness of comprehensive probabilistic models as part of decision support systems for improved detection of errors in initial radiotherapy plan verification procedures.

Bayesian networks for maritime traffic accident prevention: benefits and challenges.

PubMed

Hänninen, Maria

2014-12-01

Bayesian networks are quantitative modeling tools whose applications to the maritime traffic safety context are becoming more popular. This paper discusses the utilization of Bayesian networks in maritime safety modeling. Based on literature and the author's own experiences, the paper studies what Bayesian networks can offer to maritime accident prevention and safety modeling and discusses a few challenges in their application to this context. It is argued that the capability of representing rather complex, not necessarily causal but uncertain relationships makes Bayesian networks an attractive modeling tool for the maritime safety and accidents. Furthermore, as the maritime accident and safety data is still rather scarce and has some quality problems, the possibility to combine data with expert knowledge and the easy way of updating the model after acquiring more evidence further enhance their feasibility. However, eliciting the probabilities from the maritime experts might be challenging and the model validation can be tricky. It is concluded that with the utilization of several data sources, Bayesian updating, dynamic modeling, and hidden nodes for latent variables, Bayesian networks are rather well-suited tools for the maritime safety management and decision-making. Copyright © 2014 Elsevier Ltd. All rights reserved.

Assessment of accident severity in the construction industry using the Bayesian theorem.

PubMed

Alizadeh, Seyed Shamseddin; Mortazavi, Seyed Bagher; Mehdi Sepehri, Mohammad

2015-01-01

Construction is a major source of employment in many countries. In construction, workers perform a great diversity of activities, each one with a specific associated risk. The aim of this paper is to identify workers who are at risk of accidents with severe consequences and classify these workers to determine appropriate control measures. We defined 48 groups of workers and used the Bayesian theorem to estimate posterior probabilities about the severity of accidents at the level of individuals in construction sector. First, the posterior probabilities of injuries based on four variables were provided. Then the probabilities of injury for 48 groups of workers were determined. With regard to marginal frequency of injury, slight injury (0.856), fatal injury (0.086) and severe injury (0.058) had the highest probability of occurrence. It was observed that workers with <1 year's work experience (0.168) had the highest probability of injury occurrence. The first group of workers, who were extensively exposed to risk of severe and fatal accidents, involved workers ≥ 50 years old, married, with 1-5 years' work experience, who had no past accident experience. The findings provide a direction for more effective safety strategies and occupational accident prevention and emergency programmes.

Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method.

PubMed

Nangia, Shikha; Jasper, Ahren W; Miller, Thomas F; Truhlar, Donald G

2004-02-22

The most widely used algorithm for Monte Carlo sampling of electronic transitions in trajectory surface hopping (TSH) calculations is the so-called anteater algorithm, which is inefficient for sampling low-probability nonadiabatic events. We present a new sampling scheme (called the army ants algorithm) for carrying out TSH calculations that is applicable to systems with any strength of coupling. The army ants algorithm is a form of rare event sampling whose efficiency is controlled by an input parameter. By choosing a suitable value of the input parameter the army ants algorithm can be reduced to the anteater algorithm (which is efficient for strongly coupled cases), and by optimizing the parameter the army ants algorithm may be efficiently applied to systems with low-probability events. To demonstrate the efficiency of the army ants algorithm, we performed atom-diatom scattering calculations on a model system involving weakly coupled electronic states. Fully converged quantum mechanical calculations were performed, and the probabilities for nonadiabatic reaction and nonreactive deexcitation (quenching) were found to be on the order of 10(-8). For such low-probability events the anteater sampling scheme requires a large number of trajectories ( approximately 10(10)) to obtain good statistics and converged semiclassical results. In contrast by using the new army ants algorithm converged results were obtained by running 10(5) trajectories. Furthermore, the results were found to be in excellent agreement with the quantum mechanical results. Sampling errors were estimated using the bootstrap method, which is validated for use with the army ants algorithm. (c) 2004 American Institute of Physics.

Bayesian models: A statistical primer for ecologists

USGS Publications Warehouse

Hobbs, N. Thompson; Hooten, Mevin B.

2015-01-01

Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods—in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach.Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals.This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management.Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticiansCovers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and moreDeemphasizes computer coding in favor of basic principlesExplains how to write out properly factored statistical expressions representing Bayesian models

An at-site flood estimation method in the context of nonstationarity II. Statistical analysis of floods in Quebec

NASA Astrophysics Data System (ADS)

Gado, Tamer A.; Nguyen, Van-Thanh-Van

2016-04-01

This paper, the second of a two-part paper, investigates the nonstationary behaviour of flood peaks in Quebec (Canada) by analyzing the annual maximum flow series (AMS) available for the common 1966-2001 period from a network of 32 watersheds. Temporal trends in the mean of flood peaks were examined by the nonparametric Mann-Kendall test. The significance of the detected trends over the whole province is also assessed by a bootstrap test that preserves the cross-correlation structure of the network. Furthermore, The LM-NS method (introduced in the first part) is used to parametrically model the AMS, investigating its applicability to real data, to account for temporal trends in the moments of the time series. In this study two probability distributions (GEV & Gumbel) were selected to model four different types of time-varying moments of the historical time series considered, comprising eight competing models. The selected models are: two stationary models (GEV0 & Gumbel0), two nonstationary models in the mean as a linear function of time (GEV1 & Gumbel1), two nonstationary models in the mean as a parabolic function of time (GEV2 & Gumbel2), and two nonstationary models in the mean and the log standard deviation as linear functions of time (GEV11 & Gumbel11). The eight models were applied to flood data available for each watershed and their performance was compared to identify the best model for each location. The comparative methodology involves two phases: (1) a descriptive ability based on likelihood-based optimality criteria such as the Bayesian Information Criterion (BIC) and the deviance statistic; and (2) a predictive ability based on the residual bootstrap. According to the Mann-Kendall test and the LM-NS method, a quarter of the analyzed stations show significant trends in the AMS. All of the significant trends are negative, indicating decreasing flood magnitudes in Quebec. It was found that the LM-NS method could provide accurate flood estimates in the context of nonstationarity. The results have indicated the importance of taking into consideration the nonstationary behaviour of the flood series in order to improve the quality of flood estimation. The results also provided a general impression on the possible impacts of climate change on flood estimation in the Quebec province.

Association of earthquakes and faults in the San Francisco Bay area using Bayesian inference

USGS Publications Warehouse

Wesson, R.L.; Bakun, W.H.; Perkins, D.M.

2003-01-01

Bayesian inference provides a method to use seismic intensity data or instrumental locations, together with geologic and seismologic data, to make quantitative estimates of the probabilities that specific past earthquakes are associated with specific faults. Probability density functions are constructed for the location of each earthquake, and these are combined with prior probabilities through Bayes' theorem to estimate the probability that an earthquake is associated with a specific fault. Results using this method are presented here for large, preinstrumental, historical earthquakes and for recent earthquakes with instrumental locations in the San Francisco Bay region. The probabilities for individual earthquakes can be summed to construct a probabilistic frequency-magnitude relationship for a fault segment. Other applications of the technique include the estimation of the probability of background earthquakes, that is, earthquakes not associated with known or considered faults, and the estimation of the fraction of the total seismic moment associated with earthquakes less than the characteristic magnitude. Results for the San Francisco Bay region suggest that potentially damaging earthquakes with magnitudes less than the characteristic magnitudes should be expected. Comparisons of earthquake locations and the surface traces of active faults as determined from geologic data show significant disparities, indicating that a complete understanding of the relationship between earthquakes and faults remains elusive.

Sharing the Diagnostic Process in the Clinical Teaching Environment: A Case Study

ERIC Educational Resources Information Center

Cuello-Garcia; Carlos

2005-01-01

Revealing or visualizing the thinking involved in making clinical decisions is a challenge. A case study is presented with a visual implement for sharing the diagnostic process. This technique adapts the Bayesian approach to the case presentation. Pretest probabilities and likelihood ratios are gathered to obtain post-test probabilities of every…

Experimental and statistical study on fracture boundary of non-irradiated Zircaloy-4 cladding tube under LOCA conditions

NASA Astrophysics Data System (ADS)

Narukawa, Takafumi; Yamaguchi, Akira; Jang, Sunghyon; Amaya, Masaki

2018-02-01

For estimating fracture probability of fuel cladding tube under loss-of-coolant accident conditions of light-water-reactors, laboratory-scale integral thermal shock tests were conducted on non-irradiated Zircaloy-4 cladding tube specimens. Then, the obtained binary data with respect to fracture or non-fracture of the cladding tube specimen were analyzed statistically. A method to obtain the fracture probability curve as a function of equivalent cladding reacted (ECR) was proposed using Bayesian inference for generalized linear models: probit, logit, and log-probit models. Then, model selection was performed in terms of physical characteristics and information criteria, a widely applicable information criterion and a widely applicable Bayesian information criterion. As a result, it was clarified that the log-probit model was the best among the three models to estimate the fracture probability in terms of the degree of prediction accuracy for both next data to be obtained and the true model. Using the log-probit model, it was shown that 20% ECR corresponded to a 5% probability level with a 95% confidence of fracture of the cladding tube specimens.

A fuzzy Bayesian network approach to quantify the human behaviour during an evacuation

NASA Astrophysics Data System (ADS)

Ramli, Nurulhuda; Ghani, Noraida Abdul; Ahmad, Nazihah

2016-06-01

Bayesian Network (BN) has been regarded as a successful representation of inter-relationship of factors affecting human behavior during an emergency. This paper is an extension of earlier work of quantifying the variables involved in the BN model of human behavior during an evacuation using a well-known direct probability elicitation technique. To overcome judgment bias and reduce the expert's burden in providing precise probability values, a new approach for the elicitation technique is required. This study proposes a new fuzzy BN approach for quantifying human behavior during an evacuation. Three major phases of methodology are involved, namely 1) development of qualitative model representing human factors during an evacuation, 2) quantification of BN model using fuzzy probability and 3) inferencing and interpreting the BN result. A case study of three inter-dependencies of human evacuation factors such as danger assessment ability, information about the threat and stressful conditions are used to illustrate the application of the proposed method. This approach will serve as an alternative to the conventional probability elicitation technique in understanding the human behavior during an evacuation.

Supernova Cosmology Inference with Probabilistic Photometric Redshifts (SCIPPR)

NASA Astrophysics Data System (ADS)

Peters, Christina; Malz, Alex; Hlozek, Renée

2018-01-01

The Bayesian Estimation Applied to Multiple Species (BEAMS) framework employs probabilistic supernova type classifications to do photometric SN cosmology. This work extends BEAMS to replace high-confidence spectroscopic redshifts with photometric redshift probability density functions, a capability that will be essential in the era the Large Synoptic Survey Telescope and other next-generation photometric surveys where it will not be possible to perform spectroscopic follow up on every SN. We present the Supernova Cosmology Inference with Probabilistic Photometric Redshifts (SCIPPR) Bayesian hierarchical model for constraining the cosmological parameters from photometric lightcurves and host galaxy photometry, which includes selection effects and is extensible to uncertainty in the redshift-dependent supernova type proportions. We create a pair of realistic mock catalogs of joint posteriors over supernova type, redshift, and distance modulus informed by photometric supernova lightcurves and over redshift from simulated host galaxy photometry. We perform inference under our model to obtain a joint posterior probability distribution over the cosmological parameters and compare our results with other methods, namely: a spectroscopic subset, a subset of high probability photometrically classified supernovae, and reducing the photometric redshift probability to a single measurement and error bar.

Comparison of three Bayesian methods to estimate posttest probability in patients undergoing exercise stress testing

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

Morise, A.P.; Duval, R.D.

To determine whether recent refinements in Bayesian methods have led to improved diagnostic ability, 3 methods using Bayes' theorem and the independence assumption for estimating posttest probability after exercise stress testing were compared. Each method differed in the number of variables considered in the posttest probability estimate (method A = 5, method B = 6 and method C = 15). Method C is better known as CADENZA. There were 436 patients (250 men and 186 women) who underwent stress testing (135 had concurrent thallium scintigraphy) followed within 2 months by coronary arteriography. Coronary artery disease ((CAD), at least 1 vesselmore » with greater than or equal to 50% diameter narrowing) was seen in 169 (38%). Mean pretest probabilities using each method were not different. However, the mean posttest probabilities for CADENZA were significantly greater than those for method A or B (p less than 0.0001). Each decile of posttest probability was compared to the actual prevalence of CAD in that decile. At posttest probabilities less than or equal to 20%, there was underestimation of CAD. However, at posttest probabilities greater than or equal to 60%, there was overestimation of CAD by all methods, especially CADENZA. Comparison of sensitivity and specificity at every fifth percentile of posttest probability revealed that CADENZA was significantly more sensitive and less specific than methods A and B. Therefore, at lower probability thresholds, CADENZA was a better screening method. However, methods A or B still had merit as a means to confirm higher probabilities generated by CADENZA (especially greater than or equal to 60%).« less

Bayesian probability analysis: a prospective demonstration of its clinical utility in diagnosing coronary disease

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

Detrano, R.; Yiannikas, J.; Salcedo, E.E.

One hundred fifty-four patients referred for coronary arteriography were prospectively studied with stress electrocardiography, stress thallium scintigraphy, cine fluoroscopy (for coronary calcifications), and coronary angiography. Pretest probabilities of coronary disease were determined based on age, sex, and type of chest pain. These and pooled literature values for the conditional probabilities of test results based on disease state were used in Bayes theorem to calculate posttest probabilities of disease. The results of the three noninvasive tests were compared for statistical independence, a necessary condition for their simultaneous use in Bayes theorem. The test results were found to demonstrate pairwise independence inmore » patients with and those without disease. Some dependencies that were observed between the test results and the clinical variables of age and sex were not sufficient to invalidate application of the theorem. Sixty-eight of the study patients had at least one major coronary artery obstruction of greater than 50%. When these patients were divided into low-, intermediate-, and high-probability subgroups according to their pretest probabilities, noninvasive test results analyzed by Bayesian probability analysis appropriately advanced 17 of them by at least one probability subgroup while only seven were moved backward. Of the 76 patients without disease, 34 were appropriately moved into a lower probability subgroup while 10 were incorrectly moved up. We conclude that posttest probabilities calculated from Bayes theorem more accurately classified patients with and without disease than did pretest probabilities, thus demonstrating the utility of the theorem in this application.« less

Comparing energy sources for surgical ablation of atrial fibrillation: a Bayesian network meta-analysis of randomized, controlled trials.

PubMed

Phan, Kevin; Xie, Ashleigh; Kumar, Narendra; Wong, Sophia; Medi, Caroline; La Meir, Mark; Yan, Tristan D

2015-08-01

Simplified maze procedures involving radiofrequency, cryoenergy and microwave energy sources have been increasingly utilized for surgical treatment of atrial fibrillation as an alternative to the traditional cut-and-sew approach. In the absence of direct comparisons, a Bayesian network meta-analysis is another alternative to assess the relative effect of different treatments, using indirect evidence. A Bayesian meta-analysis of indirect evidence was performed using 16 published randomized trials identified from 6 databases. Rank probability analysis was used to rank each intervention in terms of their probability of having the best outcome. Sinus rhythm prevalence beyond the 12-month follow-up was similar between the cut-and-sew, microwave and radiofrequency approaches, which were all ranked better than cryoablation (respectively, 39, 36, and 25 vs 1%). The cut-and-sew maze was ranked worst in terms of mortality outcomes compared with microwave, radiofrequency and cryoenergy (2 vs 19, 34, and 24%, respectively). The cut-and-sew maze procedure was associated with significantly lower stroke rates compared with microwave ablation [odds ratio <0.01; 95% confidence interval 0.00, 0.82], and ranked the best in terms of pacemaker requirements compared with microwave, radiofrequency and cryoenergy (81 vs 14, and 1, <0.01% respectively). Bayesian rank probability analysis shows that the cut-and-sew approach is associated with the best outcomes in terms of sinus rhythm prevalence and stroke outcomes, and remains the gold standard approach for AF treatment. Given the limitations of indirect comparison analysis, these results should be viewed with caution and not over-interpreted. © The Author 2014. Published by Oxford University Press on behalf of the European Association for Cardio-Thoracic Surgery. All rights reserved.

A critique of statistical hypothesis testing in clinical research

PubMed Central

Raha, Somik

2011-01-01

Many have documented the difficulty of using the current paradigm of Randomized Controlled Trials (RCTs) to test and validate the effectiveness of alternative medical systems such as Ayurveda. This paper critiques the applicability of RCTs for all clinical knowledge-seeking endeavors, of which Ayurveda research is a part. This is done by examining statistical hypothesis testing, the underlying foundation of RCTs, from a practical and philosophical perspective. In the philosophical critique, the two main worldviews of probability are that of the Bayesian and the frequentist. The frequentist worldview is a special case of the Bayesian worldview requiring the unrealistic assumptions of knowing nothing about the universe and believing that all observations are unrelated to each other. Many have claimed that the first belief is necessary for science, and this claim is debunked by comparing variations in learning with different prior beliefs. Moving beyond the Bayesian and frequentist worldviews, the notion of hypothesis testing itself is challenged on the grounds that a hypothesis is an unclear distinction, and assigning a probability on an unclear distinction is an exercise that does not lead to clarity of action. This critique is of the theory itself and not any particular application of statistical hypothesis testing. A decision-making frame is proposed as a way of both addressing this critique and transcending ideological debates on probability. An example of a Bayesian decision-making approach is shown as an alternative to statistical hypothesis testing, utilizing data from a past clinical trial that studied the effect of Aspirin on heart attacks in a sample population of doctors. As a big reason for the prevalence of RCTs in academia is legislation requiring it, the ethics of legislating the use of statistical methods for clinical research is also examined. PMID:22022152

A bootstrap method for estimating uncertainty of water quality trends

USGS Publications Warehouse

Hirsch, Robert M.; Archfield, Stacey A.; DeCicco, Laura

2015-01-01

Estimation of the direction and magnitude of trends in surface water quality remains a problem of great scientific and practical interest. The Weighted Regressions on Time, Discharge, and Season (WRTDS) method was recently introduced as an exploratory data analysis tool to provide flexible and robust estimates of water quality trends. This paper enhances the WRTDS method through the introduction of the WRTDS Bootstrap Test (WBT), an extension of WRTDS that quantifies the uncertainty in WRTDS-estimates of water quality trends and offers various ways to visualize and communicate these uncertainties. Monte Carlo experiments are applied to estimate the Type I error probabilities for this method. WBT is compared to other water-quality trend-testing methods appropriate for data sets of one to three decades in length with sampling frequencies of 6–24 observations per year. The software to conduct the test is in the EGRETci R-package.

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.

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.

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.

Path integration mediated systematic search: a Bayesian model.

PubMed

Vickerstaff, Robert J; Merkle, Tobias

2012-08-21

The systematic search behaviour is a backup system that increases the chances of desert ants finding their nest entrance after foraging when the path integrator has failed to guide them home accurately enough. Here we present a mathematical model of the systematic search that is based on extensive behavioural studies in North African desert ants Cataglyphis fortis. First, a simple search heuristic utilising Bayesian inference and a probability density function is developed. This model, which optimises the short-term nest detection probability, is then compared to three simpler search heuristics and to recorded search patterns of Cataglyphis ants. To compare the different searches a method to quantify search efficiency is established as well as an estimate of the error rate in the ants' path integrator. We demonstrate that the Bayesian search heuristic is able to automatically adapt to increasing levels of positional uncertainty to produce broader search patterns, just as desert ants do, and that it outperforms the three other search heuristics tested. The searches produced by it are also arguably the most similar in appearance to the ant's searches. Copyright © 2012 Elsevier Ltd. All rights reserved.

Credible occurrence probabilities for extreme geophysical events: earthquakes, volcanic eruptions, magnetic storms

USGS Publications Warehouse

Love, Jeffrey J.

2012-01-01

Statistical analysis is made of rare, extreme geophysical events recorded in historical data -- counting the number of events $k$ with sizes that exceed chosen thresholds during specific durations of time $\\tau$. Under transformations that stabilize data and model-parameter variances, the most likely Poisson-event occurrence rate, $k/\\tau$, applies for frequentist inference and, also, for Bayesian inference with a Jeffreys prior that ensures posterior invariance under changes of variables. Frequentist confidence intervals and Bayesian (Jeffreys) credibility intervals are approximately the same and easy to calculate: $(1/\\tau)[(\\sqrt{k} - z/2)^{2},(\\sqrt{k} + z/2)^{2}]$, where $z$ is a parameter that specifies the width, $z=1$ ($z=2$) corresponding to $1\\sigma$, $68.3\\%$ ($2\\sigma$, $95.4\\%$). If only a few events have been observed, as is usually the case for extreme events, then these "error-bar" intervals might be considered to be relatively wide. From historical records, we estimate most likely long-term occurrence rates, 10-yr occurrence probabilities, and intervals of frequentist confidence and Bayesian credibility for large earthquakes, explosive volcanic eruptions, and magnetic storms.

Efficient Posterior Probability Mapping Using Savage-Dickey Ratios

PubMed Central

Penny, William D.; Ridgway, Gerard R.

2013-01-01

Statistical Parametric Mapping (SPM) is the dominant paradigm for mass-univariate analysis of neuroimaging data. More recently, a Bayesian approach termed Posterior Probability Mapping (PPM) has been proposed as an alternative. PPM offers two advantages: (i) inferences can be made about effect size thus lending a precise physiological meaning to activated regions, (ii) regions can be declared inactive. This latter facility is most parsimoniously provided by PPMs based on Bayesian model comparisons. To date these comparisons have been implemented by an Independent Model Optimization (IMO) procedure which separately fits null and alternative models. This paper proposes a more computationally efficient procedure based on Savage-Dickey approximations to the Bayes factor, and Taylor-series approximations to the voxel-wise posterior covariance matrices. Simulations show the accuracy of this Savage-Dickey-Taylor (SDT) method to be comparable to that of IMO. Results on fMRI data show excellent agreement between SDT and IMO for second-level models, and reasonable agreement for first-level models. This Savage-Dickey test is a Bayesian analogue of the classical SPM-F and allows users to implement model comparison in a truly interactive manner. PMID:23533640

Should Perioperative Supplemental Oxygen Be Routinely Recommended for Surgical Patients? A Bayesian Meta-analysis

PubMed Central

Kao, Lillian S.; Millas, Stefanos G.; Pedroza, Claudia; Tyson, Jon E.; Lally, Kevin P.

2012-01-01

Objective The purpose of this study is to use updated data and Bayesian methods to evaluate the effectiveness of hyperoxia to reduce surgical site infections (SSIs) and/or mortality in both colorectal and all surgical patients. Because few trials assessed potential harms of hyperoxia, hazards were not included. Background Use of hyperoxia to reduce SSIs is controversial. Three recent meta-analyses have had conflicting conclusions. Methods A systematic literature search and review were performed. Traditional fixed-effect and random-effects meta-analyses and Bayesian meta-analysis were performed to evaluate SSIs and mortality. Results Traditional meta-analysis yielded a relative risk of an SSI with hyperoxia among all surgery patients of 0.84 (95% confidence interval, CI, 0.73–0.97) and 0.84 (95% CI 0.61–1.16) for the fixed-effect and random effects models respectively. The probabilities of any risk reduction in SSIs among all surgery patients were 77%, 81%, and 83% for skeptical, neutral, and enthusiastic priors. Subset analysis of colorectal surgery patients increased the probabilities to 86%, 89%, and 92%. The probabilities of at least a 10% reduction were 57%, 62%, and 68% for all surgical patients and 71%, 75%, and 80% among the colorectal surgery subset. Conclusions There is a moderately high probability of a benefit to hyperoxia in reducing SSIs in colorectal surgery patients; however, the magnitude of benefit is relatively small and might not exceed treatment hazards. Further studies should focus on generalizability to other patient populations or on treatment hazards and other outcomes. PMID:23160100

The critically endangered forest owlet Heteroglaux blewitti is nested within the currently recognized Athene clade: A century-old debate addressed.

PubMed

Koparde, Pankaj; Mehta, Prachi; Reddy, Sushma; Ramakrishnan, Uma; Mukherjee, Shomita; Robin, V V

2018-01-01

Range-restricted species generally have specific niche requirements and may often have unique evolutionary histories. Unfortunately, many of these species severely lack basic research, resulting in poor conservation strategies. The phylogenetic relationship of the Critically Endangered Forest Owlet Heteroglaux blewitti has been the subject of a century-old debate. The current classifications based on non-phylogenetic comparisons of morphology place the small owls of Asia into three genera, namely, Athene, Glaucidium, and Heteroglaux. Based on morphological and anatomical data, H. blewitti has been alternatively hypothesized to belong within Athene, Glaucidium, or its own monotypic genus Heteroglaux. To test these competing hypotheses, we sequenced six loci (~4300 bp data) and performed phylogenetic analyses of owlets. Mitochondrial and nuclear trees were not congruent in their placement of H. blewitti. However, both mitochondrial and nuclear combined datasets showed strong statistical support with high maximum likelihood bootstrap (>/ = 90) and Bayesian posterior probability values (>/ = 0.98) for H. blewitti being nested in the currently recognized Athene group, but not sister to Indian A. brama. The divergence of H. blewitti from its sister taxa was between 4.3 and 5.7 Ma coinciding with a period of drastic climatic changes in the Indian subcontinent. This study presented the first genetic analysis of H. blewitti, a Critically Endangered species, and addressed the long debate on the relationships of the Athene-Heteroglaux-Glaucidium complex. We recommend further studies with more data and complete taxon sampling to understand the biogeography of Indian Athene species.

The critically endangered forest owlet Heteroglaux blewitti is nested within the currently recognized Athene clade: A century-old debate addressed

PubMed Central

Mehta, Prachi; Reddy, Sushma; Ramakrishnan, Uma

2018-01-01

Range-restricted species generally have specific niche requirements and may often have unique evolutionary histories. Unfortunately, many of these species severely lack basic research, resulting in poor conservation strategies. The phylogenetic relationship of the Critically Endangered Forest Owlet Heteroglaux blewitti has been the subject of a century-old debate. The current classifications based on non-phylogenetic comparisons of morphology place the small owls of Asia into three genera, namely, Athene, Glaucidium, and Heteroglaux. Based on morphological and anatomical data, H. blewitti has been alternatively hypothesized to belong within Athene, Glaucidium, or its own monotypic genus Heteroglaux. To test these competing hypotheses, we sequenced six loci (~4300 bp data) and performed phylogenetic analyses of owlets. Mitochondrial and nuclear trees were not congruent in their placement of H. blewitti. However, both mitochondrial and nuclear combined datasets showed strong statistical support with high maximum likelihood bootstrap (>/ = 90) and Bayesian posterior probability values (>/ = 0.98) for H. blewitti being nested in the currently recognized Athene group, but not sister to Indian A. brama. The divergence of H. blewitti from its sister taxa was between 4.3 and 5.7 Ma coinciding with a period of drastic climatic changes in the Indian subcontinent. This study presented the first genetic analysis of H. blewitti, a Critically Endangered species, and addressed the long debate on the relationships of the Athene-Heteroglaux-Glaucidium complex. We recommend further studies with more data and complete taxon sampling to understand the biogeography of Indian Athene species. PMID:29401484

Morphological and molecular data reveal a new species of Neoechinorhynchus (Acanthocephala: Neoechinorhynchidae) from Dormitator maculatus in the Gulf of Mexico.

PubMed

Pinacho-Pinacho, Carlos Daniel; Sereno-Uribe, Ana L; García-Varela, Martín

2014-12-01

Neoechinorhynchus (Neoechinorhynchus) mexicoensis sp. n. is described from the intestine of Dormitator maculatus (Bloch 1792) collected in 5 coastal localities from the Gulf of Mexico. The new species is mainly distinguished from the other 33 described species of Neoechinorhynchus from the Americas associated with freshwater, marine and brackish fishes by having smaller middle and posterior hooks and possessing a small proboscis with three rows of six hooks each, apical hooks longer than other hooks and extending to the same level as the posterior hooks, 1 giant nucleus in the ventral body wall and females with eggs longer than other congeneric species. Sequences of the internal transcribed spacer (ITS) and the large subunit (LSU) of ribosomal DNA including the domain D2+D3 were used independently to corroborate the morphological distinction among the new species and other congeneric species associated with freshwater and brackish water fish from Mexico. The genetic divergence estimated among congeneric species ranged from 7.34 to 44% for ITS and from 1.65 to 32.9% for LSU. Maximum likelihood and Bayesian inference analyses with each dataset showed that the 25 specimens analyzed from 5 localities of the coast of the Gulf of Mexico parasitizing D. maculatus represent an independent clade with strong bootstrap support and posterior probabilities. The morphological evidence, plus the monophyly in the phylogenetic analyses, indicates that the acanthocephalans collected from intestine of D. maculatus from the Gulf of Mexico represent a new species, herein named N. (N.) mexicoensis sp. n. Copyright © 2014. Published by Elsevier Ireland Ltd.

Phylogeny of Neoparamoeba strains isolated from marine fish and invertebrates as inferred from SSU rDNA sequences.

PubMed

Dyková, Iva; Nowak, Barbara; Pecková, Hana; Fiala, Ivan; Crosbie, Philip; Dvoráková, Helena

2007-02-08

We characterised 9 strains selected from primary isolates referable to Paramoeba/Neoparamoeba spp. Based on ultrastructural study, 5 strains isolated from fish (amoebic gill disease [AGD]-affected Atlantic salmon and dead southern bluefin tuna), 1 strain from netting of a floating sea cage and 3 strains isolated from invertebrates (sea urchins and crab) were assigned to the genus Neoparamoeba Page, 1987. Phylogenetic analyses based on SSU rDNA sequences revealed affiliations of newly introduced and previously analysed Neoparamoeba strains. Three strains from the invertebrates and 2 out of 3 strains from gills of southern bluefin tunas were members of the N. branchiphila clade, while the remaining, fish-isolated strains, as well as the fish cage strain, clustered within the clade of N. pemaquidensis. These findings and previous reports point to the possibility that N. pemaquidensis and N. branchiphila can affect both fish and invertebrates. A new potential fish host, southern bluefin tuna, was included in the list of farmed fish endangered by N. branchiphila. The sequence of P. eilhardi (Culture Collection of Algae and Protozoa [CCAP] strain 1560/2) appeared in all analyses among sequences of strain representatives of Neoparamoeba species, in a position well supported by bootstrap value, Bremer index and Bayesian posterior probability. Our research shows that isolation of additional strains from invertebrates and further analyses of relations between molecular data and morphological characters of the genera Paramoeba and Neoparamoeba are required. This complexity needs to be considered when attempting to define molecular markers for identification of Paramoeba/Neoparamoeba species in tissues of fish and invertebrates.

A search for evidence of solar rotation in Super-Kamiokande solar neutrino dataset

NASA Astrophysics Data System (ADS)

Desai, Shantanu; Liu, Dawei W.

2016-09-01

We apply the generalized Lomb-Scargle (LS) periodogram, proposed by Zechmeister and Kurster, to the solar neutrino data from Super-Kamiokande (Super-K) using data from its first five years. For each peak in the LS periodogram, we evaluate the statistical significance in two different ways. The first method involves calculating the False Alarm Probability (FAP) using non-parametric bootstrap resampling, and the second method is by calculating the difference in Bayesian Information Criterion (BIC) between the null hypothesis, viz. the data contains only noise, compared to the hypothesis that the data contains a peak at a given frequency. Using these methods, we scan the frequency range between 7-14 cycles per year to look for any peaks caused by solar rotation, since this is the proposed explanation for the statistically significant peaks found by Sturrock and collaborators in the Super-K dataset. From our analysis, we do confirm that similar to Sturrock et al, the maximum peak occurs at a frequency of 9.42/year, corresponding to a period of 38.75 days. The FAP for this peak is about 1.5% and the difference in BIC (between pure white noise and this peak) is about 4.8. We note that the significance depends on the frequency band used to search for peaks and hence it is important to use a search band appropriate for solar rotation. However, The significance of this peak based on the value of BIC is marginal and more data is needed to confirm if the peak persists and is real.

Nomogram Prediction of Overall Survival After Curative Irradiation for Uterine Cervical Cancer

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

Seo, YoungSeok; Yoo, Seong Yul; Kim, Mi-Sook

Purpose: The purpose of this study was to develop a nomogram capable of predicting the probability of 5-year survival after radical radiotherapy (RT) without chemotherapy for uterine cervical cancer. Methods and Materials: We retrospectively analyzed 549 patients that underwent radical RT for uterine cervical cancer between March 1994 and April 2002 at our institution. Multivariate analysis using Cox proportional hazards regression was performed and this Cox model was used as the basis for the devised nomogram. The model was internally validated for discrimination and calibration by bootstrap resampling. Results: By multivariate regression analysis, the model showed that age, hemoglobin levelmore » before RT, Federation Internationale de Gynecologie Obstetrique (FIGO) stage, maximal tumor diameter, lymph node status, and RT dose at Point A significantly predicted overall survival. The survival prediction model demonstrated good calibration and discrimination. The bootstrap-corrected concordance index was 0.67. The predictive ability of the nomogram proved to be superior to FIGO stage (p = 0.01). Conclusions: The devised nomogram offers a significantly better level of discrimination than the FIGO staging system. In particular, it improves predictions of survival probability and could be useful for counseling patients, choosing treatment modalities and schedules, and designing clinical trials. However, before this nomogram is used clinically, it should be externally validated.« less

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

Information Theoretic Studies and Assessment of Space Object Identification

DTIC Science & Technology

2014-03-24

localization are contained in Ref. [5]. 1.7.1 A Bayesian MPE Based Analysis of 2D Point-Source-Pair Superresolution In a second recently submitted paper [6], a...related problem of the optical superresolution (OSR) of a pair of equal-brightness point sources separated spatially by a distance (or angle) smaller...1403.4897 [physics.optics] (19 March 2014). 6. S. Prasad, “Asymptotics of Bayesian error probability and 2D pair superresolution ,” submitted to Opt. Express

Prediction of community prevalence of human onchocerciasis in the Amazonian onchocerciasis focus: Bayesian approach.

PubMed Central

Carabin, Hélène; Escalona, Marisela; Marshall, Clare; Vivas-Martínez, Sarai; Botto, Carlos; Joseph, Lawrence; Basáñez, María-Gloria

2003-01-01

OBJECTIVE: To develop a Bayesian hierarchical model for human onchocerciasis with which to explore the factors that influence prevalence of microfilariae in the Amazonian focus of onchocerciasis and predict the probability of any community being at least mesoendemic (>20% prevalence of microfilariae), and thus in need of priority ivermectin treatment. METHODS: Models were developed with data from 732 individuals aged > or =15 years who lived in 29 Yanomami communities along four rivers of the south Venezuelan Orinoco basin. The models' abilities to predict prevalences of microfilariae in communities were compared. The deviance information criterion, Bayesian P-values, and residual values were used to select the best model with an approximate cross-validation procedure. FINDINGS: A three-level model that acknowledged clustering of infection within communities performed best, with host age and sex included at the individual level, a river-dependent altitude effect at the community level, and additional clustering of communities along rivers. This model correctly classified 25/29 (86%) villages with respect to their need for priority ivermectin treatment. CONCLUSION: Bayesian methods are a flexible and useful approach for public health research and control planning. Our model acknowledges the clustering of infection within communities, allows investigation of links between individual- or community-specific characteristics and infection, incorporates additional uncertainty due to missing covariate data, and informs policy decisions by predicting the probability that a new community is at least mesoendemic. PMID:12973640

Prediction of community prevalence of human onchocerciasis in the Amazonian onchocerciasis focus: Bayesian approach.

PubMed

Carabin, Hélène; Escalona, Marisela; Marshall, Clare; Vivas-Martínez, Sarai; Botto, Carlos; Joseph, Lawrence; Basáñez, María-Gloria

2003-01-01

To develop a Bayesian hierarchical model for human onchocerciasis with which to explore the factors that influence prevalence of microfilariae in the Amazonian focus of onchocerciasis and predict the probability of any community being at least mesoendemic (>20% prevalence of microfilariae), and thus in need of priority ivermectin treatment. Models were developed with data from 732 individuals aged > or =15 years who lived in 29 Yanomami communities along four rivers of the south Venezuelan Orinoco basin. The models' abilities to predict prevalences of microfilariae in communities were compared. The deviance information criterion, Bayesian P-values, and residual values were used to select the best model with an approximate cross-validation procedure. A three-level model that acknowledged clustering of infection within communities performed best, with host age and sex included at the individual level, a river-dependent altitude effect at the community level, and additional clustering of communities along rivers. This model correctly classified 25/29 (86%) villages with respect to their need for priority ivermectin treatment. Bayesian methods are a flexible and useful approach for public health research and control planning. Our model acknowledges the clustering of infection within communities, allows investigation of links between individual- or community-specific characteristics and infection, incorporates additional uncertainty due to missing covariate data, and informs policy decisions by predicting the probability that a new community is at least mesoendemic.

Family History as an Indicator of Risk for Reading Disability.

ERIC Educational Resources Information Center

Volger, George P.; And Others

1984-01-01

Self-reported reading ability of parents of 174 reading-disabled children and of 182 controls was used to estimate the probability that a child will become reading disabled. Using Bayesian inverse probability analysis, it was found that the risk for reading disability is increased substantially if either parent has had difficulty in learning to…

Comparison of three-parameter probability distributions for representing annual extreme and partial duration precipitation series

NASA Astrophysics Data System (ADS)

Wilks, Daniel S.

1993-10-01

Performance of 8 three-parameter probability distributions for representing annual extreme and partial duration precipitation data at stations in the northeastern and southeastern United States is investigated. Particular attention is paid to fidelity on the right tail, through use of a bootstrap procedure simulating extrapolation on the right tail beyond the data. It is found that the beta-κ distribution best describes the extreme right tail of annual extreme series, and the beta-P distribution is best for the partial duration data. The conventionally employed two-parameter Gumbel distribution is found to substantially underestimate probabilities associated with the larger precipitation amounts for both annual extreme and partial duration data. Fitting the distributions using left-censored data did not result in improved fits to the right tail.

Bayesian probability of success for clinical trials using historical data

PubMed Central

Ibrahim, Joseph G.; Chen, Ming-Hui; Lakshminarayanan, Mani; Liu, Guanghan F.; Heyse, Joseph F.

2015-01-01

Developing sophisticated statistical methods for go/no-go decisions is crucial for clinical trials, as planning phase III or phase IV trials is costly and time consuming. In this paper, we develop a novel Bayesian methodology for determining the probability of success of a treatment regimen on the basis of the current data of a given trial. We introduce a new criterion for calculating the probability of success that allows for inclusion of covariates as well as allowing for historical data based on the treatment regimen, and patient characteristics. A new class of prior distributions and covariate distributions is developed to achieve this goal. The methodology is quite general and can be used with univariate or multivariate continuous or discrete data, and it generalizes Chuang-Stein’s work. This methodology will be invaluable for informing the scientist on the likelihood of success of the compound, while including the information of covariates for patient characteristics in the trial population for planning future pre-market or post-market trials. PMID:25339499

Competing risk models in reliability systems, an exponential distribution model with Bayesian analysis approach

NASA Astrophysics Data System (ADS)

Iskandar, I.

2018-03-01

The exponential distribution is the most widely used reliability analysis. This distribution is very suitable for representing the lengths of life of many cases and is available in a simple statistical form. The characteristic of this distribution is a constant hazard rate. The exponential distribution is the lower rank of the Weibull distributions. In this paper our effort is to introduce the basic notions that constitute an exponential competing risks model in reliability analysis using Bayesian analysis approach and presenting their analytic methods. The cases are limited to the models with independent causes of failure. A non-informative prior distribution is used in our analysis. This model describes the likelihood function and follows with the description of the posterior function and the estimations of the point, interval, hazard function, and reliability. The net probability of failure if only one specific risk is present, crude probability of failure due to a specific risk in the presence of other causes, and partial crude probabilities are also included.

Modeling Women's Menstrual Cycles using PICI Gates in Bayesian Network.

PubMed

Zagorecki, Adam; Łupińska-Dubicka, Anna; Voortman, Mark; Druzdzel, Marek J

2016-03-01

A major difficulty in building Bayesian network (BN) models is the size of conditional probability tables, which grow exponentially in the number of parents. One way of dealing with this problem is through parametric conditional probability distributions that usually require only a number of parameters that is linear in the number of parents. In this paper, we introduce a new class of parametric models, the Probabilistic Independence of Causal Influences (PICI) models, that aim at lowering the number of parameters required to specify local probability distributions, but are still capable of efficiently modeling a variety of interactions. A subset of PICI models is decomposable and this leads to significantly faster inference as compared to models that cannot be decomposed. We present an application of the proposed method to learning dynamic BNs for modeling a woman's menstrual cycle. We show that PICI models are especially useful for parameter learning from small data sets and lead to higher parameter accuracy than when learning CPTs.

Bayesian probability of success for clinical trials using historical data.

PubMed

Ibrahim, Joseph G; Chen, Ming-Hui; Lakshminarayanan, Mani; Liu, Guanghan F; Heyse, Joseph F

2015-01-30

Developing sophisticated statistical methods for go/no-go decisions is crucial for clinical trials, as planning phase III or phase IV trials is costly and time consuming. In this paper, we develop a novel Bayesian methodology for determining the probability of success of a treatment regimen on the basis of the current data of a given trial. We introduce a new criterion for calculating the probability of success that allows for inclusion of covariates as well as allowing for historical data based on the treatment regimen, and patient characteristics. A new class of prior distributions and covariate distributions is developed to achieve this goal. The methodology is quite general and can be used with univariate or multivariate continuous or discrete data, and it generalizes Chuang-Stein's work. This methodology will be invaluable for informing the scientist on the likelihood of success of the compound, while including the information of covariates for patient characteristics in the trial population for planning future pre-market or post-market trials. Copyright © 2014 John Wiley & Sons, Ltd.

Gravity dual for a model of perception

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

Nakayama, Yu, E-mail: nakayama@berkeley.edu

2011-01-15

One of the salient features of human perception is its invariance under dilatation in addition to the Euclidean group, but its non-invariance under special conformal transformation. We investigate a holographic approach to the information processing in image discrimination with this feature. We claim that a strongly coupled analogue of the statistical model proposed by Bialek and Zee can be holographically realized in scale invariant but non-conformal Euclidean geometries. We identify the Bayesian probability distribution of our generalized Bialek-Zee model with the GKPW partition function of the dual gravitational system. We provide a concrete example of the geometric configuration based onmore » a vector condensation model coupled with the Euclidean Einstein-Hilbert action. From the proposed geometry, we study sample correlation functions to compute the Bayesian probability distribution.« less

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.

Using Bayesian Adaptive Trial Designs for Comparative Effectiveness Research: A Virtual Trial Execution.

PubMed

Luce, Bryan R; Connor, Jason T; Broglio, Kristine R; Mullins, C Daniel; Ishak, K Jack; Saunders, Elijah; Davis, Barry R

2016-09-20

Bayesian and adaptive clinical trial designs offer the potential for more efficient processes that result in lower sample sizes and shorter trial durations than traditional designs. To explore the use and potential benefits of Bayesian adaptive clinical trial designs in comparative effectiveness research. Virtual execution of ALLHAT (Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial) as if it had been done according to a Bayesian adaptive trial design. Comparative effectiveness trial of antihypertensive medications. Patient data sampled from the more than 42 000 patients enrolled in ALLHAT with publicly available data. Number of patients randomly assigned between groups, trial duration, observed numbers of events, and overall trial results and conclusions. The Bayesian adaptive approach and original design yielded similar overall trial conclusions. The Bayesian adaptive trial randomly assigned more patients to the better-performing group and would probably have ended slightly earlier. This virtual trial execution required limited resampling of ALLHAT patients for inclusion in RE-ADAPT (REsearch in ADAptive methods for Pragmatic Trials). Involvement of a data monitoring committee and other trial logistics were not considered. In a comparative effectiveness research trial, Bayesian adaptive trial designs are a feasible approach and potentially generate earlier results and allocate more patients to better-performing groups. National Heart, Lung, and Blood Institute.

Latent class profile of psychiatric symptoms and treatment utilization in a sample of patients with co-occurring disorders.

PubMed

Villalobos-Gallegos, Luis; Marín-Navarrete, Rodrigo; Roncero, Calos; González-Cantú, Hugo

2017-01-01

To identify symptom-based subgroups within a sample of patients with co-occurring disorders (CODs) and to analyze intersubgroup differences in mental health services utilization. Two hundred and fifteen patients with COD from an addiction clinic completed the Symptom Checklist 90-Revised. Subgroups were determined using latent class profile analysis. Services utilization data were collected from electronic records during a 3-year span. The five-class model obtained the best fit (Bayesian information criteria [BIC] = 3,546.95; adjusted BIC = 3,363.14; bootstrapped likelihood ratio test p < 0.0001). Differences between classes were quantitative, and groups were labeled according to severity: mild (26%), mild-moderate (28.8%), moderate (18.6%), moderate-severe (17.2%), and severe (9.3%). A significant time by class interaction was obtained (chi-square [χ2[15

Confidence Intervals for Laboratory Sonic Boom Annoyance Tests

NASA Technical Reports Server (NTRS)

Rathsam, Jonathan; Christian, Andrew

2016-01-01

Commercial supersonic flight is currently forbidden over land because sonic booms have historically caused unacceptable annoyance levels in overflown communities. NASA is providing data and expertise to noise regulators as they consider relaxing the ban for future quiet supersonic aircraft. One deliverable NASA will provide is a predictive model for indoor annoyance to aid in setting an acceptable quiet sonic boom threshold. A laboratory study was conducted to determine how indoor vibrations caused by sonic booms affect annoyance judgments. The test method required finding the point of subjective equality (PSE) between sonic boom signals that cause vibrations and signals not causing vibrations played at various amplitudes. This presentation focuses on a few statistical techniques for estimating the interval around the PSE. The techniques examined are the Delta Method, Parametric and Nonparametric Bootstrapping, and Bayesian Posterior Estimation.

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.

Using Bayesian Networks for Candidate Generation in Consistency-based Diagnosis

NASA Technical Reports Server (NTRS)

Narasimhan, Sriram; Mengshoel, Ole

2008-01-01

Consistency-based diagnosis relies heavily on the assumption that discrepancies between model predictions and sensor observations can be detected accurately. When sources of uncertainty like sensor noise and model abstraction exist robust schemes have to be designed to make a binary decision on whether predictions are consistent with observations. This risks the occurrence of false alarms and missed alarms when an erroneous decision is made. Moreover when multiple sensors (with differing sensing properties) are available the degree of match between predictions and observations can be used to guide the search for fault candidates. In this paper we propose a novel approach to handle this problem using Bayesian networks. In the consistency- based diagnosis formulation, automatically generated Bayesian networks are used to encode a probabilistic measure of fit between predictions and observations. A Bayesian network inference algorithm is used to compute most probable fault candidates.

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.

Bayesian truncation errors in chiral effective field theory: model checking and accounting for correlations

NASA Astrophysics Data System (ADS)

Melendez, Jordan; Wesolowski, Sarah; Furnstahl, Dick

2017-09-01

Chiral effective field theory (EFT) predictions are necessarily truncated at some order in the EFT expansion, which induces an error that must be quantified for robust statistical comparisons to experiment. A Bayesian model yields posterior probability distribution functions for these errors based on expectations of naturalness encoded in Bayesian priors and the observed order-by-order convergence pattern of the EFT. As a general example of a statistical approach to truncation errors, the model was applied to chiral EFT for neutron-proton scattering using various semi-local potentials of Epelbaum, Krebs, and Meißner (EKM). Here we discuss how our model can learn correlation information from the data and how to perform Bayesian model checking to validate that the EFT is working as advertised. Supported in part by NSF PHY-1614460 and DOE NUCLEI SciDAC DE-SC0008533.

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.

Improving default risk prediction using Bayesian model uncertainty techniques.

PubMed

Kazemi, Reza; Mosleh, Ali

2012-11-01

Credit risk is the potential exposure of a creditor to an obligor's failure or refusal to repay the debt in principal or interest. The potential of exposure is measured in terms of probability of default. Many models have been developed to estimate credit risk, with rating agencies dating back to the 19th century. They provide their assessment of probability of default and transition probabilities of various firms in their annual reports. Regulatory capital requirements for credit risk outlined by the Basel Committee on Banking Supervision have made it essential for banks and financial institutions to develop sophisticated models in an attempt to measure credit risk with higher accuracy. The Bayesian framework proposed in this article uses the techniques developed in physical sciences and engineering for dealing with model uncertainty and expert accuracy to obtain improved estimates of credit risk and associated uncertainties. The approach uses estimates from one or more rating agencies and incorporates their historical accuracy (past performance data) in estimating future default risk and transition probabilities. Several examples demonstrate that the proposed methodology can assess default probability with accuracy exceeding the estimations of all the individual models. Moreover, the methodology accounts for potentially significant departures from "nominal predictions" due to "upsetting events" such as the 2008 global banking crisis. © 2012 Society for Risk Analysis.

Imprecise Probability Methods for Weapons UQ

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

Picard, Richard Roy; Vander Wiel, Scott Alan

Building on recent work in uncertainty quanti cation, we examine the use of imprecise probability methods to better characterize expert knowledge and to improve on misleading aspects of Bayesian analysis with informative prior distributions. Quantitative approaches to incorporate uncertainties in weapons certi cation are subject to rigorous external peer review, and in this regard, certain imprecise probability methods are well established in the literature and attractive. These methods are illustrated using experimental data from LANL detonator impact testing.

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.

A bayesian approach to classification criteria for spectacled eiders

USGS Publications Warehouse

Taylor, B.L.; Wade, P.R.; Stehn, R.A.; Cochrane, J.F.

1996-01-01

To facilitate decisions to classify species according to risk of extinction, we used Bayesian methods to analyze trend data for the Spectacled Eider, an arctic sea duck. Trend data from three independent surveys of the Yukon-Kuskokwim Delta were analyzed individually and in combination to yield posterior distributions for population growth rates. We used classification criteria developed by the recovery team for Spectacled Eiders that seek to equalize errors of under- or overprotecting the species. We conducted both a Bayesian decision analysis and a frequentist (classical statistical inference) decision analysis. Bayesian decision analyses are computationally easier, yield basically the same results, and yield results that are easier to explain to nonscientists. With the exception of the aerial survey analysis of the 10 most recent years, both Bayesian and frequentist methods indicated that an endangered classification is warranted. The discrepancy between surveys warrants further research. Although the trend data are abundance indices, we used a preliminary estimate of absolute abundance to demonstrate how to calculate extinction distributions using the joint probability distributions for population growth rate and variance in growth rate generated by the Bayesian analysis. Recent apparent increases in abundance highlight the need for models that apply to declining and then recovering species.

Bayesian Latent Class Analysis Tutorial.

PubMed

Li, Yuelin; Lord-Bessen, Jennifer; Shiyko, Mariya; Loeb, Rebecca

2018-01-01

This article is a how-to guide on Bayesian computation using Gibbs sampling, demonstrated in the context of Latent Class Analysis (LCA). It is written for students in quantitative psychology or related fields who have a working knowledge of Bayes Theorem and conditional probability and have experience in writing computer programs in the statistical language R . The overall goals are to provide an accessible and self-contained tutorial, along with a practical computation tool. We begin with how Bayesian computation is typically described in academic articles. Technical difficulties are addressed by a hypothetical, worked-out example. We show how Bayesian computation can be broken down into a series of simpler calculations, which can then be assembled together to complete a computationally more complex model. The details are described much more explicitly than what is typically available in elementary introductions to Bayesian modeling so that readers are not overwhelmed by the mathematics. Moreover, the provided computer program shows how Bayesian LCA can be implemented with relative ease. The computer program is then applied in a large, real-world data set and explained line-by-line. We outline the general steps in how to extend these considerations to other methodological applications. We conclude with suggestions for further readings.

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.

A Bayesian network approach to the database search problem in criminal proceedings

PubMed Central

2012-01-01

Background The ‘database search problem’, that is, the strengthening of a case - in terms of probative value - against an individual who is found as a result of a database search, has been approached during the last two decades with substantial mathematical analyses, accompanied by lively debate and centrally opposing conclusions. This represents a challenging obstacle in teaching but also hinders a balanced and coherent discussion of the topic within the wider scientific and legal community. This paper revisits and tracks the associated mathematical analyses in terms of Bayesian networks. Their derivation and discussion for capturing probabilistic arguments that explain the database search problem are outlined in detail. The resulting Bayesian networks offer a distinct view on the main debated issues, along with further clarity. Methods As a general framework for representing and analyzing formal arguments in probabilistic reasoning about uncertain target propositions (that is, whether or not a given individual is the source of a crime stain), this paper relies on graphical probability models, in particular, Bayesian networks. This graphical probability modeling approach is used to capture, within a single model, a series of key variables, such as the number of individuals in a database, the size of the population of potential crime stain sources, and the rarity of the corresponding analytical characteristics in a relevant population. Results This paper demonstrates the feasibility of deriving Bayesian network structures for analyzing, representing, and tracking the database search problem. The output of the proposed models can be shown to agree with existing but exclusively formulaic approaches. Conclusions The proposed Bayesian networks allow one to capture and analyze the currently most well-supported but reputedly counter-intuitive and difficult solution to the database search problem in a way that goes beyond the traditional, purely formulaic expressions. The method’s graphical environment, along with its computational and probabilistic architectures, represents a rich package that offers analysts and discussants with additional modes of interaction, concise representation, and coherent communication. PMID:22849390

Artificial and Bayesian Neural Networks

PubMed

Korhani Kangi, Azam; Bahrampour, Abbas

2018-02-26

Introduction and purpose: In recent years the use of neural networks without any premises for investigation of prognosis in analyzing survival data has increased. Artificial neural networks (ANN) use small processors with a continuous network to solve problems inspired by the human brain. Bayesian neural networks (BNN) constitute a neural-based approach to modeling and non-linearization of complex issues using special algorithms and statistical methods. Gastric cancer incidence is the first and third ranking for men and women in Iran, respectively. The aim of the present study was to assess the value of an artificial neural network and a Bayesian neural network for modeling and predicting of probability of gastric cancer patient death. Materials and Methods: In this study, we used information on 339 patients aged from 20 to 90 years old with positive gastric cancer, referred to Afzalipoor and Shahid Bahonar Hospitals in Kerman City from 2001 to 2015. The three layers perceptron neural network (ANN) and the Bayesian neural network (BNN) were used for predicting the probability of mortality using the available data. To investigate differences between the models, sensitivity, specificity, accuracy and the area under receiver operating characteristic curves (AUROCs) were generated. Results: In this study, the sensitivity and specificity of the artificial neural network and Bayesian neural network models were 0.882, 0.903 and 0.954, 0.909, respectively. Prediction accuracy and the area under curve ROC for the two models were 0.891, 0.944 and 0.935, 0.961. The age at diagnosis of gastric cancer was most important for predicting survival, followed by tumor grade, morphology, gender, smoking history, opium consumption, receiving chemotherapy, presence of metastasis, tumor stage, receiving radiotherapy, and being resident in a village. Conclusion: The findings of the present study indicated that the Bayesian neural network is preferable to an artificial neural network for predicting survival of gastric cancer patients in Iran. Creative Commons Attribution License

Impact of censoring on learning Bayesian networks in survival modelling.

PubMed

Stajduhar, Ivan; Dalbelo-Basić, Bojana; Bogunović, Nikola

2009-11-01

Bayesian networks are commonly used for presenting uncertainty and covariate interactions in an easily interpretable way. Because of their efficient inference and ability to represent causal relationships, they are an excellent choice for medical decision support systems in diagnosis, treatment, and prognosis. Although good procedures for learning Bayesian networks from data have been defined, their performance in learning from censored survival data has not been widely studied. In this paper, we explore how to use these procedures to learn about possible interactions between prognostic factors and their influence on the variate of interest. We study how censoring affects the probability of learning correct Bayesian network structures. Additionally, we analyse the potential usefulness of the learnt models for predicting the time-independent probability of an event of interest. We analysed the influence of censoring with a simulation on synthetic data sampled from randomly generated Bayesian networks. We used two well-known methods for learning Bayesian networks from data: a constraint-based method and a score-based method. We compared the performance of each method under different levels of censoring to those of the naive Bayes classifier and the proportional hazards model. We did additional experiments on several datasets from real-world medical domains. The machine-learning methods treated censored cases in the data as event-free. We report and compare results for several commonly used model evaluation metrics. On average, the proportional hazards method outperformed other methods in most censoring setups. As part of the simulation study, we also analysed structural similarities of the learnt networks. Heavy censoring, as opposed to no censoring, produces up to a 5% surplus and up to 10% missing total arcs. It also produces up to 50% missing arcs that should originally be connected to the variate of interest. Presented methods for learning Bayesian networks from data can be used to learn from censored survival data in the presence of light censoring (up to 20%) by treating censored cases as event-free. Given intermediate or heavy censoring, the learnt models become tuned to the majority class and would thus require a different approach.

Bayesian approach to non-Gaussian field statistics for diffusive broadband terahertz pulses.

PubMed

Pearce, Jeremy; Jian, Zhongping; Mittleman, Daniel M

2005-11-01

We develop a closed-form expression for the probability distribution function for the field components of a diffusive broadband wave propagating through a random medium. We consider each spectral component to provide an individual observation of a random variable, the configurationally averaged spectral intensity. Since the intensity determines the variance of the field distribution at each frequency, this random variable serves as the Bayesian prior that determines the form of the non-Gaussian field statistics. This model agrees well with experimental results.

Bayesian Inference in Satellite Gravity Inversion

NASA Technical Reports Server (NTRS)

Kis, K. I.; Taylor, Patrick T.; Wittmann, G.; Kim, Hyung Rae; Torony, B.; Mayer-Guerr, T.

2005-01-01

To solve a geophysical inverse problem means applying measurements to determine the parameters of the selected model. The inverse problem is formulated as the Bayesian inference. The Gaussian probability density functions are applied in the Bayes's equation. The CHAMP satellite gravity data are determined at the altitude of 400 kilometer altitude over the South part of the Pannonian basin. The model of interpretation is the right vertical cylinder. The parameters of the model are obtained from the minimum problem solved by the Simplex method.

Proceedings of the Conference on the Design of Experiments in Army Research, Development and Testing (29th)

DTIC Science & Technology

1984-06-01

SEQUENTIAL TESTING (Bldg. A, Room C) 1300-1330 ’ 1330-1415 1415-1445 1445-1515 BREAK 1515-1545 A TRUNCATED SEQUENTIAL PROBABILITY RATIO TEST J...suicide optical data operational testing reliability random numbers bootstrap methods missing data sequential testing fire support complex computer model carcinogenesis studies EUITION Of 1 NOV 68 I% OBSOLETE a ...contributed papers can be ascertained from the titles of the

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

A Bayesian framework for extracting human gait using strong prior knowledge.

PubMed

Zhou, Ziheng; Prügel-Bennett, Adam; Damper, Robert I

2006-11-01

Extracting full-body motion of walking people from monocular video sequences in complex, real-world environments is an important and difficult problem, going beyond simple tracking, whose satisfactory solution demands an appropriate balance between use of prior knowledge and learning from data. We propose a consistent Bayesian framework for introducing strong prior knowledge into a system for extracting human gait. In this work, the strong prior is built from a simple articulated model having both time-invariant (static) and time-variant (dynamic) parameters. The model is easily modified to cater to situations such as walkers wearing clothing that obscures the limbs. The statistics of the parameters are learned from high-quality (indoor laboratory) data and the Bayesian framework then allows us to "bootstrap" to accurate gait extraction on the noisy images typical of cluttered, outdoor scenes. To achieve automatic fitting, we use a hidden Markov model to detect the phases of images in a walking cycle. We demonstrate our approach on silhouettes extracted from fronto-parallel ("sideways on") sequences of walkers under both high-quality indoor and noisy outdoor conditions. As well as high-quality data with synthetic noise and occlusions added, we also test walkers with rucksacks, skirts, and trench coats. Results are quantified in terms of chamfer distance and average pixel error between automatically extracted body points and corresponding hand-labeled points. No one part of the system is novel in itself, but the overall framework makes it feasible to extract gait from very much poorer quality image sequences than hitherto. This is confirmed by comparing person identification by gait using our method and a well-established baseline recognition algorithm.

Dynamic Bayesian Network Modeling of the Interplay between EGFR and Hedgehog Signaling.

PubMed

Fröhlich, Holger; Bahamondez, Gloria; Götschel, Frank; Korf, Ulrike

2015-01-01

Aberrant activation of sonic Hegdehog (SHH) signaling has been found to disrupt cellular differentiation in many human cancers and to increase proliferation. The SHH pathway is known to cross-talk with EGFR dependent signaling. Recent studies experimentally addressed this interplay in Daoy cells, which are presumable a model system for medulloblastoma, a highly malignant brain tumor that predominately occurs in children. Currently ongoing are several clinical trials for different solid cancers, which are designed to validate the clinical benefits of targeting the SHH in combination with other pathways. This has motivated us to investigate interactions between EGFR and SHH dependent signaling in greater depth. To our knowledge, there is no mathematical model describing the interplay between EGFR and SHH dependent signaling in medulloblastoma so far. Here we come up with a fully probabilistic approach using Dynamic Bayesian Networks (DBNs). To build our model, we made use of literature based knowledge describing SHH and EGFR signaling and integrated gene expression (Illumina) and cellular location dependent time series protein expression data (Reverse Phase Protein Arrays). We validated our model by sub-sampling training data and making Bayesian predictions on the left out test data. Our predictions focusing on key transcription factors and p70S6K, showed a high level of concordance with experimental data. Furthermore, the stability of our model was tested by a parametric bootstrap approach. Stable network features were in agreement with published data. Altogether we believe that our model improved our understanding of the interplay between two highly oncogenic signaling pathways in Daoy cells. This may open new perspectives for the future therapy of Hedghog/EGF-dependent solid tumors.

Identifying causal networks linking cancer processes and anti-tumor immunity using Bayesian network inference and metagene constructs.

PubMed

Kaiser, Jacob L; Bland, Cassidy L; Klinke, David J

2016-03-01

Cancer arises from a deregulation of both intracellular and intercellular networks that maintain system homeostasis. Identifying the architecture of these networks and how they are changed in cancer is a pre-requisite for designing drugs to restore homeostasis. Since intercellular networks only appear in intact systems, it is difficult to identify how these networks become altered in human cancer using many of the common experimental models. To overcome this, we used the diversity in normal and malignant human tissue samples from the Cancer Genome Atlas (TCGA) database of human breast cancer to identify the topology associated with intercellular networks in vivo. To improve the underlying biological signals, we constructed Bayesian networks using metagene constructs, which represented groups of genes that are concomitantly associated with different immune and cancer states. We also used bootstrap resampling to establish the significance associated with the inferred networks. In short, we found opposing relationships between cell proliferation and epithelial-to-mesenchymal transformation (EMT) with regards to macrophage polarization. These results were consistent across multiple carcinomas in that proliferation was associated with a type 1 cell-mediated anti-tumor immune response and EMT was associated with a pro-tumor anti-inflammatory response. To address the identifiability of these networks from other datasets, we could identify the relationship between EMT and macrophage polarization with fewer samples when the Bayesian network was generated from malignant samples alone. However, the relationship between proliferation and macrophage polarization was identified with fewer samples when the samples were taken from a combination of the normal and malignant samples. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:470-479, 2016. © 2016 American Institute of Chemical Engineers.

A Bayesian Meta-Analysis of the Effect of Alcohol Use on HCV-Treatment Outcomes with a Comparison of Resampling Methods to Assess Uncertainty in Parameter Estimates.

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

Cauthen, Katherine Regina; Lambert, Gregory Joseph; Finley, Patrick D.

There is mounting evidence that alcohol use is significantly linked to lower HCV treatment response rates in interferon-based therapies, though some of the evidence is conflicting. Furthermore, although health care providers recommend reducing or abstaining from alcohol use prior to treatment, many patients do not succeed in doing so. The goal of this meta-analysis was to systematically review and summarize the Englishlanguage literature up through January 30, 2015 regarding the relationship between alcohol use and HCV treatment outcomes, among patients who were not required to abstain from alcohol use in order to receive treatment. Seven pertinent articles studying 1,751 HCV-infectedmore » patients were identified. Log-ORs of HCV treatment response for heavy alcohol use and light alcohol use were calculated and compared. We employed a hierarchical Bayesian meta-analytic model to accommodate the small sample size. The summary estimate for the log-OR of HCV treatment response was -0.775 with a 95% credible interval of (-1.397, -0.236). The results of the Bayesian meta-analysis are slightly more conservative compared to those obtained from a boot-strapped, random effects model. We found evidence of heterogeneity (Q = 14.489, p = 0.025), accounting for 60.28% of the variation among log-ORs. Meta-regression to capture the sources of this heterogeneity did not identify any of the covariates investigated as significant. This meta-analysis confirms that heavy alcohol use is associated with decreased HCV treatment response compared to lighter levels of alcohol use. Further research is required to characterize the mechanism by which alcohol use affects HCV treatment response.« less

Analysis of trend changes in Northern African palaeo-climate by using Bayesian inference

NASA Astrophysics Data System (ADS)

Schütz, Nadine; Trauth, Martin H.; Holschneider, Matthias

2010-05-01

Climate variability of Northern Africa is of high interest due to climate-evolutionary linkages under study. The reconstruction of the palaeo-climate over long time scales, including the expected linkages (> 3 Ma), is mainly accessible by proxy data from deep sea drilling cores. By concentrating on published data sets, we try to decipher rhythms and trends to detect correlations between different proxy time series by advanced mathematical methods. Our preliminary data is dust concentration, as an indicator for climatic changes such as humidity, from the ODP sites 659, 721 and 967 situated around Northern Africa. Our interest is in challenging the available time series with advanced statistical methods to detect significant trend changes and to compare different model assumptions. For that purpose, we want to avoid the rescaling of the time axis to obtain equidistant time steps for filtering methods. Additionally we demand an plausible description of the errors for the estimated parameters, in terms of confidence intervals. Finally, depending on what model we restrict on, we also want an insight in the parameter structure of the assumed models. To gain this information, we focus on Bayesian inference by formulating the problem as a linear mixed model, so that the expectation and deviation are of linear structure. By using the Bayesian method we can formulate the posteriori density as a function of the model parameters and calculate this probability density in the parameter space. Depending which parameters are of interest, we analytically and numerically marginalize the posteriori with respect to the remaining parameters of less interest. We apply a simple linear mixed model to calculate the posteriori densities of the ODP sites 659 and 721 concerning the last 5 Ma at maximum. From preliminary calculations on these data sets, we can confirm results gained by the method of breakfit regression combined with block bootstrapping ([1]). We obtain a significant change point around (1.63 - 1.82) Ma, which correlates with a global climate transition due to the establishment of the Walker circulation ([2]). Furthermore we detect another significant change point around (2.7 - 3.2) Ma, which correlates with the end of the Pliocene warm period (permanent El Niño-like conditions) and the onset of a colder global climate ([3], [4]). The discussion on the algorithm, the results of calculated confidence intervals, the available information about the applied model in the parameter space and the comparison of multiple change point models will be presented. [1] Trauth, M.H., et al., Quaternary Science Reviews, 28, 2009 [2] Wara, M.W., et al., Science, Vol. 309, 2005 [3] Chiang, J.C.H., Annual Review of Earth and Planetary Sciences, Vol. 37, 2009 [4] deMenocal, P., Earth and Planetary Science Letters, 220, 2004

Suspected pulmonary embolism and lung scan interpretation: Trial of a Bayesian reporting method

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

Becker, D.M.; Philbrick, J.T.; Schoonover, F.W.

The objective of this research is to determine whether a Bayesian method of lung scan (LS) reporting could influence the management of patients with suspected pulmonary embolism (PE). The study is performed by the following: (1) A descriptive study of the diagnostic process for suspected PE using the new reporting method; (2) a non-experimental evaluation of the reporting method comparing prospective patients and historical controls; and (3) a survey of physicians' reactions to the reporting innovation. Of 148 consecutive patients enrolled at the time of LS, 129 were completely evaluated; 75 patients scanned the previous year served as controls. Themore » LS results of patients with suspected PE were reported as posttest probabilities of PE calculated from physician-provided pretest probabilities and the likelihood ratios for PE of LS interpretations. Despite the Bayesian intervention, the confirmation or exclusion of PE was often based on inconclusive evidence. PE was considered by the clinician to be ruled out in 98% of patients with posttest probabilities less than 25% and ruled in for 95% of patients with posttest probabilities greater than 75%. Prospective patients and historical controls were similar in terms of tests ordered after the LS (e.g., pulmonary angiography). Patients with intermediate or indeterminate lung scan results had the highest proportion of subsequent testing. Most physicians (80%) found the reporting innovation to be helpful, either because it confirmed clinical judgement (94 cases) or because it led to additional testing (7 cases). Despite the probabilistic guidance provided by the study, the diagnosis of PE was often neither clearly established nor excluded. While physicians appreciated the innovation and were not confused by the terminology, their clinical decision making was not clearly enhanced.« less

BCM: toolkit for Bayesian analysis of Computational Models using samplers.

PubMed

Thijssen, Bram; Dijkstra, Tjeerd M H; Heskes, Tom; Wessels, Lodewyk F A

2016-10-21

Computational models in biology are characterized by a large degree of uncertainty. This uncertainty can be analyzed with Bayesian statistics, however, the sampling algorithms that are frequently used for calculating Bayesian statistical estimates are computationally demanding, and each algorithm has unique advantages and disadvantages. It is typically unclear, before starting an analysis, which algorithm will perform well on a given computational model. We present BCM, a toolkit for the Bayesian analysis of Computational Models using samplers. It provides efficient, multithreaded implementations of eleven algorithms for sampling from posterior probability distributions and for calculating marginal likelihoods. BCM includes tools to simplify the process of model specification and scripts for visualizing the results. The flexible architecture allows it to be used on diverse types of biological computational models. In an example inference task using a model of the cell cycle based on ordinary differential equations, BCM is significantly more efficient than existing software packages, allowing more challenging inference problems to be solved. BCM represents an efficient one-stop-shop for computational modelers wishing to use sampler-based Bayesian statistics.

The researcher and the consultant: from testing to probability statements.

PubMed

Hamra, Ghassan B; Stang, Andreas; Poole, Charles

2015-09-01

In the first instalment of this series, Stang and Poole provided an overview of Fisher significance testing (ST), Neyman-Pearson null hypothesis testing (NHT), and their unfortunate and unintended offspring, null hypothesis significance testing. In addition to elucidating the distinction between the first two and the evolution of the third, the authors alluded to alternative models of statistical inference; namely, Bayesian statistics. Bayesian inference has experienced a revival in recent decades, with many researchers advocating for its use as both a complement and an alternative to NHT and ST. This article will continue in the direction of the first instalment, providing practicing researchers with an introduction to Bayesian inference. Our work will draw on the examples and discussion of the previous dialogue.

Spectral likelihood expansions for Bayesian inference

NASA Astrophysics Data System (ADS)

Nagel, Joseph B.; Sudret, Bruno

2016-03-01

A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this spectral likelihood expansion all statistical quantities of interest can be calculated semi-analytically. The posterior is formally represented as the product of a reference density and a linear combination of polynomial basis functions. Both the model evidence and the posterior moments are related to the expansion coefficients. This formulation avoids Markov chain Monte Carlo simulation and allows one to make use of linear least squares instead. The pros and cons of spectral Bayesian inference are discussed and demonstrated on the basis of simple applications from classical statistics and inverse modeling.

Incremental diagnostic quality gain of CTA over V/Q scan in the assessment of pulmonary embolism by means of a Wells score Bayesian model: results from the ACDC collaboration.

PubMed

Cochon, Laila; McIntyre, Kaitlin; Nicolás, José M; Baez, Amado Alejandro

2017-08-01

Our objective was to evaluate the diagnostic value of computed tomography angiography (CTA) and ventilation perfusion (V/Q) scan in the assessment of pulmonary embolism (PE) by means of a Bayesian statistical model. Wells criteria defined pretest probability. Sensitivity and specificity of CTA and V/Q scan for PE were derived from pooled meta-analysis data. Likelihood ratios calculated for CTA and V/Q were inserted in the nomogram. Absolute (ADG) and relative diagnostic gains (RDG) were analyzed comparing post- and pretest probability. Comparative gain difference was calculated for CTA ADG over V/Q scan integrating ANOVA p value set at 0.05. The sensitivity for CT was 86.0% (95% CI: 80.2%, 92.1%) and specificity of 93.7% (95% CI: 91.1%, 96.3%). The V/Q scan yielded a sensitivity of 96% (95% CI: 95%, 97%) and a specificity of 97% (95% CI: 96%, 98%). Bayes nomogram results for CTA were low risk and yielded a posttest probability of 71.1%, an ADG of 56.1%, and an RDG of 374%, moderate-risk posttest probability was 85.1%, an ADG of 56.1%, and an RDG of 193.4%, and high-risk posttest probability was 95.2%, an ADG of 36.2%, and an RDG of 61.35%. The comparative gain difference for low-risk population was 46.1%; in moderate-risk 41.6%; and in high-risk a 22.1% superiority. ANOVA analysis for LR+ and LR- showed no significant difference (p = 0.8745, p = 0.9841 respectively). This Bayesian model demonstrated a superiority of CTA when compared to V/Q scan for the diagnosis of pulmonary embolism. Low-risk patients are recognized to have a superior overall comparative gain favoring CTA.

Data Analysis Techniques for Physical Scientists

NASA Astrophysics Data System (ADS)

Pruneau, Claude A.

2017-10-01

Preface; How to read this book; 1. The scientific method; Part I. Foundation in Probability and Statistics: 2. Probability; 3. Probability models; 4. Classical inference I: estimators; 5. Classical inference II: optimization; 6. Classical inference III: confidence intervals and statistical tests; 7. Bayesian inference; Part II. Measurement Techniques: 8. Basic measurements; 9. Event reconstruction; 10. Correlation functions; 11. The multiple facets of correlation functions; 12. Data correction methods; Part III. Simulation Techniques: 13. Monte Carlo methods; 14. Collision and detector modeling; List of references; Index.

BM-Map: Bayesian Mapping of Multireads for Next-Generation Sequencing Data

PubMed Central

Ji, Yuan; Xu, Yanxun; Zhang, Qiong; Tsui, Kam-Wah; Yuan, Yuan; Norris, Clift; Liang, Shoudan; Liang, Han

2011-01-01

Summary Next-generation sequencing (NGS) technology generates millions of short reads, which provide valuable information for various aspects of cellular activities and biological functions. A key step in NGS applications (e.g., RNA-Seq) is to map short reads to correct genomic locations within the source genome. While most reads are mapped to a unique location, a significant proportion of reads align to multiple genomic locations with equal or similar numbers of mismatches; these are called multireads. The ambiguity in mapping the multireads may lead to bias in downstream analyses. Currently, most practitioners discard the multireads in their analysis, resulting in a loss of valuable information, especially for the genes with similar sequences. To refine the read mapping, we develop a Bayesian model that computes the posterior probability of mapping a multiread to each competing location. The probabilities are used for downstream analyses, such as the quantification of gene expression. We show through simulation studies and RNA-Seq analysis of real life data that the Bayesian method yields better mapping than the current leading methods. We provide a C++ program for downloading that is being packaged into a user-friendly software. PMID:21517792

A bayesian analysis for identifying DNA copy number variations using a compound poisson process.

PubMed

Chen, Jie; Yiğiter, Ayten; Wang, Yu-Ping; Deng, Hong-Wen

2010-01-01

To study chromosomal aberrations that may lead to cancer formation or genetic diseases, the array-based Comparative Genomic Hybridization (aCGH) technique is often used for detecting DNA copy number variants (CNVs). Various methods have been developed for gaining CNVs information based on aCGH data. However, most of these methods make use of the log-intensity ratios in aCGH data without taking advantage of other information such as the DNA probe (e.g., biomarker) positions/distances contained in the data. Motivated by the specific features of aCGH data, we developed a novel method that takes into account the estimation of a change point or locus of the CNV in aCGH data with its associated biomarker position on the chromosome using a compound Poisson process. We used a Bayesian approach to derive the posterior probability for the estimation of the CNV locus. To detect loci of multiple CNVs in the data, a sliding window process combined with our derived Bayesian posterior probability was proposed. To evaluate the performance of the method in the estimation of the CNV locus, we first performed simulation studies. Finally, we applied our approach to real data from aCGH experiments, demonstrating its applicability.

A Method of Face Detection with Bayesian Probability

NASA Astrophysics Data System (ADS)

Sarker, Goutam

2010-10-01

The objective of face detection is to identify all images which contain a face, irrespective of its orientation, illumination conditions etc. This is a hard problem, because the faces are highly variable in size, shape lighting conditions etc. Many methods have been designed and developed to detect faces in a single image. The present paper is based on one `Appearance Based Method' which relies on learning the facial and non facial features from image examples. This in its turn is based on statistical analysis of examples and counter examples of facial images and employs Bayesian Conditional Classification Rule to detect the probability of belongingness of a face (or non-face) within an image frame. The detection rate of the present system is very high and thereby the number of false positive and false negative detection is substantially low.

Bayesian operational modal analysis with asynchronous data, part I: Most probable value

NASA Astrophysics Data System (ADS)

Zhu, Yi-Chen; Au, Siu-Kui

2018-01-01

In vibration tests, multiple sensors are used to obtain detailed mode shape information about the tested structure. Time synchronisation among data channels is required in conventional modal identification approaches. Modal identification can be more flexibly conducted if this is not required. Motivated by the potential gain in feasibility and economy, this work proposes a Bayesian frequency domain method for modal identification using asynchronous 'output-only' ambient data, i.e. 'operational modal analysis'. It provides a rigorous means for identifying the global mode shape taking into account the quality of the measured data and their asynchronous nature. This paper (Part I) proposes an efficient algorithm for determining the most probable values of modal properties. The method is validated using synthetic and laboratory data. The companion paper (Part II) investigates identification uncertainty and challenges in applications to field vibration data.

Screening for SNPs with Allele-Specific Methylation based on Next-Generation Sequencing Data.

PubMed

Hu, Bo; Ji, Yuan; Xu, Yaomin; Ting, Angela H

2013-05-01

Allele-specific methylation (ASM) has long been studied but mainly documented in the context of genomic imprinting and X chromosome inactivation. Taking advantage of the next-generation sequencing technology, we conduct a high-throughput sequencing experiment with four prostate cell lines to survey the whole genome and identify single nucleotide polymorphisms (SNPs) with ASM. A Bayesian approach is proposed to model the counts of short reads for each SNP conditional on its genotypes of multiple subjects, leading to a posterior probability of ASM. We flag SNPs with high posterior probabilities of ASM by accounting for multiple comparisons based on posterior false discovery rates. Applying the Bayesian approach to the in-house prostate cell line data, we identify 269 SNPs as candidates of ASM. A simulation study is carried out to demonstrate the quantitative performance of the proposed approach.

Physician Bayesian updating from personal beliefs about the base rate and likelihood ratio.

PubMed

Rottman, Benjamin Margolin

2017-02-01

Whether humans can accurately make decisions in line with Bayes' rule has been one of the most important yet contentious topics in cognitive psychology. Though a number of paradigms have been used for studying Bayesian updating, rarely have subjects been allowed to use their own preexisting beliefs about the prior and the likelihood. A study is reported in which physicians judged the posttest probability of a diagnosis for a patient vignette after receiving a test result, and the physicians' posttest judgments were compared to the normative posttest calculated from their own beliefs in the sensitivity and false positive rate of the test (likelihood ratio) and prior probability of the diagnosis. On the one hand, the posttest judgments were strongly related to the physicians' beliefs about both the prior probability as well as the likelihood ratio, and the priors were used considerably more strongly than in previous research. On the other hand, both the prior and the likelihoods were still not used quite as much as they should have been, and there was evidence of other nonnormative aspects to the updating, such as updating independent of the likelihood beliefs. By focusing on how physicians use their own prior beliefs for Bayesian updating, this study provides insight into how well experts perform probabilistic inference in settings in which they rely upon their own prior beliefs rather than experimenter-provided cues. It suggests that there is reason to be optimistic about experts' abilities, but that there is still considerable need for improvement.

A general Bayesian framework for calibrating and evaluating stochastic models of annual multi-site hydrological data

NASA Astrophysics Data System (ADS)

Frost, Andrew J.; Thyer, Mark A.; Srikanthan, R.; Kuczera, George

2007-07-01

SummaryMulti-site simulation of hydrological data are required for drought risk assessment of large multi-reservoir water supply systems. In this paper, a general Bayesian framework is presented for the calibration and evaluation of multi-site hydrological data at annual timescales. Models included within this framework are the hidden Markov model (HMM) and the widely used lag-1 autoregressive (AR(1)) model. These models are extended by the inclusion of a Box-Cox transformation and a spatial correlation function in a multi-site setting. Parameter uncertainty is evaluated using Markov chain Monte Carlo techniques. Models are evaluated by their ability to reproduce a range of important extreme statistics and compared using Bayesian model selection techniques which evaluate model probabilities. The case study, using multi-site annual rainfall data situated within catchments which contribute to Sydney's main water supply, provided the following results: Firstly, in terms of model probabilities and diagnostics, the inclusion of the Box-Cox transformation was preferred. Secondly the AR(1) and HMM performed similarly, while some other proposed AR(1)/HMM models with regionally pooled parameters had greater posterior probability than these two models. The practical significance of parameter and model uncertainty was illustrated using a case study involving drought security analysis for urban water supply. It was shown that ignoring parameter uncertainty resulted in a significant overestimate of reservoir yield and an underestimation of system vulnerability to severe drought.

Machine health prognostics using the Bayesian-inference-based probabilistic indication and high-order particle filtering framework

NASA Astrophysics Data System (ADS)

Yu, Jianbo

2015-12-01

Prognostics is much efficient to achieve zero-downtime performance, maximum productivity and proactive maintenance of machines. Prognostics intends to assess and predict the time evolution of machine health degradation so that machine failures can be predicted and prevented. A novel prognostics system is developed based on the data-model-fusion scheme using the Bayesian inference-based self-organizing map (SOM) and an integration of logistic regression (LR) and high-order particle filtering (HOPF). In this prognostics system, a baseline SOM is constructed to model the data distribution space of healthy machine under an assumption that predictable fault patterns are not available. Bayesian inference-based probability (BIP) derived from the baseline SOM is developed as a quantification indication of machine health degradation. BIP is capable of offering failure probability for the monitored machine, which has intuitionist explanation related to health degradation state. Based on those historic BIPs, the constructed LR and its modeling noise constitute a high-order Markov process (HOMP) to describe machine health propagation. HOPF is used to solve the HOMP estimation to predict the evolution of the machine health in the form of a probability density function (PDF). An on-line model update scheme is developed to adapt the Markov process changes to machine health dynamics quickly. The experimental results on a bearing test-bed illustrate the potential applications of the proposed system as an effective and simple tool for machine health prognostics.

A Bayesian Framework of Uncertainties Integration in 3D Geological Model

NASA Astrophysics Data System (ADS)

Liang, D.; Liu, X.

2017-12-01

3D geological model can describe complicated geological phenomena in an intuitive way while its application may be limited by uncertain factors. Great progress has been made over the years, lots of studies decompose the uncertainties of geological model to analyze separately, while ignored the comprehensive impacts of multi-source uncertainties. Great progress has been made over the years, while lots of studies ignored the comprehensive impacts of multi-source uncertainties when analyzed them item by item from each source. To evaluate the synthetical uncertainty, we choose probability distribution to quantify uncertainty, and propose a bayesian framework of uncertainties integration. With this framework, we integrated data errors, spatial randomness, and cognitive information into posterior distribution to evaluate synthetical uncertainty of geological model. Uncertainties propagate and cumulate in modeling process, the gradual integration of multi-source uncertainty is a kind of simulation of the uncertainty propagation. Bayesian inference accomplishes uncertainty updating in modeling process. Maximum entropy principle makes a good effect on estimating prior probability distribution, which ensures the prior probability distribution subjecting to constraints supplied by the given information with minimum prejudice. In the end, we obtained a posterior distribution to evaluate synthetical uncertainty of geological model. This posterior distribution represents the synthetical impact of all the uncertain factors on the spatial structure of geological model. The framework provides a solution to evaluate synthetical impact on geological model of multi-source uncertainties and a thought to study uncertainty propagation mechanism in geological modeling.

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.

Estimating reach-specific fish movement probabilities in rivers with a Bayesian state-space model: application to sea lamprey passage and capture at dams

USGS Publications Warehouse

Holbrook, Christopher M.; Johnson, Nicholas S.; Steibel, Juan P.; Twohey, Michael B.; Binder, Thomas R.; Krueger, Charles C.; Jones, Michael L.

2014-01-01

Improved methods are needed to evaluate barriers and traps for control and assessment of invasive sea lamprey (Petromyzon marinus) in the Great Lakes. A Bayesian state-space model provided reach-specific probabilities of movement, including trap capture and dam passage, for 148 acoustic tagged invasive sea lamprey in the lower Cheboygan River, Michigan, a tributary to Lake Huron. Reach-specific movement probabilities were combined to obtain estimates of spatial distribution and abundance needed to evaluate a barrier and trap complex for sea lamprey control and assessment. Of an estimated 21 828 – 29 300 adult sea lampreys in the river, 0%–2%, or 0–514 untagged lampreys, could have passed upstream of the dam, and 46%–61% were caught in the trap. Although no tagged lampreys passed above the dam (0/148), our sample size was not sufficient to consider the lock and dam a complete barrier to sea lamprey. Results also showed that existing traps are in good locations because 83%–96% of the population was vulnerable to existing traps. However, only 52%–69% of lampreys vulnerable to traps were caught, suggesting that traps can be improved. The approach used in this study was a novel use of Bayesian state-space models that may have broader applications, including evaluation of barriers for other invasive species (e.g., Asian carp (Hypophthalmichthys spp.)) and fish passage structures for other diadromous fishes.

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.

A fast Monte Carlo EM algorithm for estimation in latent class model analysis with an application to assess diagnostic accuracy for cervical neoplasia in women with AGC

PubMed Central

Kang, Le; Carter, Randy; Darcy, Kathleen; Kauderer, James; Liao, Shu-Yuan

2013-01-01

In this article we use a latent class model (LCM) with prevalence modeled as a function of covariates to assess diagnostic test accuracy in situations where the true disease status is not observed, but observations on three or more conditionally independent diagnostic tests are available. A fast Monte Carlo EM (MCEM) algorithm with binary (disease) diagnostic data is implemented to estimate parameters of interest; namely, sensitivity, specificity, and prevalence of the disease as a function of covariates. To obtain standard errors for confidence interval construction of estimated parameters, the missing information principle is applied to adjust information matrix estimates. We compare the adjusted information matrix based standard error estimates with the bootstrap standard error estimates both obtained using the fast MCEM algorithm through an extensive Monte Carlo study. Simulation demonstrates that the adjusted information matrix approach estimates the standard error similarly with the bootstrap methods under certain scenarios. The bootstrap percentile intervals have satisfactory coverage probabilities. We then apply the LCM analysis to a real data set of 122 subjects from a Gynecologic Oncology Group (GOG) study of significant cervical lesion (S-CL) diagnosis in women with atypical glandular cells of undetermined significance (AGC) to compare the diagnostic accuracy of a histology-based evaluation, a CA-IX biomarker-based test and a human papillomavirus (HPV) DNA test. PMID:24163493

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

Bayesian network representing system dynamics in risk analysis of nuclear systems

NASA Astrophysics Data System (ADS)

Varuttamaseni, Athi

2011-12-01

A dynamic Bayesian network (DBN) model is used in conjunction with the alternating conditional expectation (ACE) regression method to analyze the risk associated with the loss of feedwater accident coupled with a subsequent initiation of the feed and bleed operation in the Zion-1 nuclear power plant. The use of the DBN allows the joint probability distribution to be factorized, enabling the analysis to be done on many simpler network structures rather than on one complicated structure. The construction of the DBN model assumes conditional independence relations among certain key reactor parameters. The choice of parameter to model is based on considerations of the macroscopic balance statements governing the behavior of the reactor under a quasi-static assumption. The DBN is used to relate the peak clad temperature to a set of independent variables that are known to be important in determining the success of the feed and bleed operation. A simple linear relationship is then used to relate the clad temperature to the core damage probability. To obtain a quantitative relationship among different nodes in the DBN, surrogates of the RELAP5 reactor transient analysis code are used. These surrogates are generated by applying the ACE algorithm to output data obtained from about 50 RELAP5 cases covering a wide range of the selected independent variables. These surrogates allow important safety parameters such as the fuel clad temperature to be expressed as a function of key reactor parameters such as the coolant temperature and pressure together with important independent variables such as the scram delay time. The time-dependent core damage probability is calculated by sampling the independent variables from their probability distributions and propagate the information up through the Bayesian network to give the clad temperature. With the knowledge of the clad temperature and the assumption that the core damage probability has a one-to-one relationship to it, we have calculated the core damage probably as a function of transient time. The use of the DBN model in combination with ACE allows risk analysis to be performed with much less effort than if the analysis were done using the standard techniques.

OGLE-2008-BLG-355Lb: A massive planet around a late-type star

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

Koshimoto, N.; Sumi, T.; Fukagawa, M.

2014-06-20

We report the discovery of a massive planet, OGLE-2008-BLG-355Lb. The light curve analysis indicates a planet:host mass ratio of q = 0.0118 ± 0.0006 at a separation of 0.877 ± 0.010 Einstein radii. We do not measure a significant microlensing parallax signal and do not have high angular resolution images that could detect the planetary host star. Therefore, we do not have a direct measurement of the host star mass. A Bayesian analysis, assuming that all host stars have equal probability to host a planet with the measured mass ratio, implies a host star mass of M{sub h}=0.37{sub −0.17}{sup +0.30}more » M{sub ⊙} and a companion of mass M{sub P}=4.6{sub −2.2}{sup +3.7}M{sub J}, at a projected separation of r{sub ⊥}=1.70{sub −0.30}{sup +0.29} AU. The implied distance to the planetary system is D {sub L} = 6.8 ± 1.1 kpc. A planetary system with the properties preferred by the Bayesian analysis may be a challenge to the core accretion model of planet formation, as the core accretion model predicts that massive planets are far more likely to form around more massive host stars. This core accretion model prediction is not consistent with our Bayesian prior of an equal probability of host stars of all masses to host a planet with the measured mass ratio. Thus, if the core accretion model prediction is right, we should expect that follow-up high angular resolution observations will detect a host star with a mass in the upper part of the range allowed by the Bayesian analysis. That is, the host would probably be a K or G dwarf.« less

Comparison of bootstrap approaches for estimation of uncertainties of DTI parameters.

PubMed

Chung, SungWon; Lu, Ying; Henry, Roland G

2006-11-01

Bootstrap is an empirical non-parametric statistical technique based on data resampling that has been used to quantify uncertainties of diffusion tensor MRI (DTI) parameters, useful in tractography and in assessing DTI methods. The current bootstrap method (repetition bootstrap) used for DTI analysis performs resampling within the data sharing common diffusion gradients, requiring multiple acquisitions for each diffusion gradient. Recently, wild bootstrap was proposed that can be applied without multiple acquisitions. In this paper, two new approaches are introduced called residual bootstrap and repetition bootknife. We show that repetition bootknife corrects for the large bias present in the repetition bootstrap method and, therefore, better estimates the standard errors. Like wild bootstrap, residual bootstrap is applicable to single acquisition scheme, and both are based on regression residuals (called model-based resampling). Residual bootstrap is based on the assumption that non-constant variance of measured diffusion-attenuated signals can be modeled, which is actually the assumption behind the widely used weighted least squares solution of diffusion tensor. The performances of these bootstrap approaches were compared in terms of bias, variance, and overall error of bootstrap-estimated standard error by Monte Carlo simulation. We demonstrate that residual bootstrap has smaller biases and overall errors, which enables estimation of uncertainties with higher accuracy. Understanding the properties of these bootstrap procedures will help us to choose the optimal approach for estimating uncertainties that can benefit hypothesis testing based on DTI parameters, probabilistic fiber tracking, and optimizing DTI methods.

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.

Incorporating uncertainty into medical decision making: an approach to unexpected test results.

PubMed

Bianchi, Matt T; Alexander, Brian M; Cash, Sydney S

2009-01-01

The utility of diagnostic tests derives from the ability to translate the population concepts of sensitivity and specificity into information that will be useful for the individual patient: the predictive value of the result. As the array of available diagnostic testing broadens, there is a temptation to de-emphasize history and physical findings and defer to the objective rigor of technology. However, diagnostic test interpretation is not always straightforward. One significant barrier to routine use of probability-based test interpretation is the uncertainty inherent in pretest probability estimation, the critical first step of Bayesian reasoning. The context in which this uncertainty presents the greatest challenge is when test results oppose clinical judgment. It is this situation when decision support would be most helpful. The authors propose a simple graphical approach that incorporates uncertainty in pretest probability and has specific application to the interpretation of unexpected results. This method quantitatively demonstrates how uncertainty in disease probability may be amplified when test results are unexpected (opposing clinical judgment), even for tests with high sensitivity and specificity. The authors provide a simple nomogram for determining whether an unexpected test result suggests that one should "switch diagnostic sides.'' This graphical framework overcomes the limitation of pretest probability uncertainty in Bayesian analysis and guides decision making when it is most challenging: interpretation of unexpected test results.

A Bayesian Developmental Approach to Robotic Goal-Based Imitation Learning.

PubMed

Chung, Michael Jae-Yoon; Friesen, Abram L; Fox, Dieter; Meltzoff, Andrew N; Rao, Rajesh P N

2015-01-01

A fundamental challenge in robotics today is building robots that can learn new skills by observing humans and imitating human actions. We propose a new Bayesian approach to robotic learning by imitation inspired by the developmental hypothesis that children use self-experience to bootstrap the process of intention recognition and goal-based imitation. Our approach allows an autonomous agent to: (i) learn probabilistic models of actions through self-discovery and experience, (ii) utilize these learned models for inferring the goals of human actions, and (iii) perform goal-based imitation for robotic learning and human-robot collaboration. Such an approach allows a robot to leverage its increasing repertoire of learned behaviors to interpret increasingly complex human actions and use the inferred goals for imitation, even when the robot has very different actuators from humans. We demonstrate our approach using two different scenarios: (i) a simulated robot that learns human-like gaze following behavior, and (ii) a robot that learns to imitate human actions in a tabletop organization task. In both cases, the agent learns a probabilistic model of its own actions, and uses this model for goal inference and goal-based imitation. We also show that the robotic agent can use its probabilistic model to seek human assistance when it recognizes that its inferred actions are too uncertain, risky, or impossible to perform, thereby opening the door to human-robot collaboration.

A Bayesian Developmental Approach to Robotic Goal-Based Imitation Learning

PubMed Central

Chung, Michael Jae-Yoon; Friesen, Abram L.; Fox, Dieter; Meltzoff, Andrew N.; Rao, Rajesh P. N.

2015-01-01

A fundamental challenge in robotics today is building robots that can learn new skills by observing humans and imitating human actions. We propose a new Bayesian approach to robotic learning by imitation inspired by the developmental hypothesis that children use self-experience to bootstrap the process of intention recognition and goal-based imitation. Our approach allows an autonomous agent to: (i) learn probabilistic models of actions through self-discovery and experience, (ii) utilize these learned models for inferring the goals of human actions, and (iii) perform goal-based imitation for robotic learning and human-robot collaboration. Such an approach allows a robot to leverage its increasing repertoire of learned behaviors to interpret increasingly complex human actions and use the inferred goals for imitation, even when the robot has very different actuators from humans. We demonstrate our approach using two different scenarios: (i) a simulated robot that learns human-like gaze following behavior, and (ii) a robot that learns to imitate human actions in a tabletop organization task. In both cases, the agent learns a probabilistic model of its own actions, and uses this model for goal inference and goal-based imitation. We also show that the robotic agent can use its probabilistic model to seek human assistance when it recognizes that its inferred actions are too uncertain, risky, or impossible to perform, thereby opening the door to human-robot collaboration. PMID:26536366

THREAT ANTICIPATION AND DECEPTIVE REASONING USING BAYESIAN BELIEF NETWORKS

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

Allgood, Glenn O; Olama, Mohammed M; Lake, Joe E

Recent events highlight the need for tools to anticipate threats posed by terrorists. Assessing these threats requires combining information from disparate data sources such as analytic models, simulations, historical data, sensor networks, and user judgments. These disparate data can be combined in a coherent, analytically defensible, and understandable manner using a Bayesian belief network (BBN). In this paper, we develop a BBN threat anticipatory model based on a deceptive reasoning algorithm using a network engineering process that treats the probability distributions of the BBN nodes within the broader context of the system development process.

Entropic Inference

NASA Astrophysics Data System (ADS)

Caticha, Ariel

2011-03-01

In this tutorial we review the essential arguments behing entropic inference. We focus on the epistemological notion of information and its relation to the Bayesian beliefs of rational agents. The problem of updating from a prior to a posterior probability distribution is tackled through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting method of Maximum relative Entropy (ME), includes as special cases both MaxEnt and Bayes' rule, and therefore unifies the two themes of these workshops—the Maximum Entropy and the Bayesian methods—into a single general inference scheme.

An inquiry into computer understanding

NASA Technical Reports Server (NTRS)

Cheeseman, Peter

1988-01-01

The paper examines issues connected with the choice of the best method for representing and reasoning about common sense. McDermott (1978) has shown that a direct translation of common sense reasoning into logical form leads to insurmountable difficulties. It is shown, in the present work, that if Bayesian probability is used instead of logic as the language of such reasoning, none of the technical difficulties found in using logic arise. Bayesian inference is applied to a simple example of linguistic information to illustrate the potential of this type of inference for artificial intelligence.

Source Detection with Bayesian Inference on ROSAT All-Sky Survey Data Sample

NASA Astrophysics Data System (ADS)

Guglielmetti, F.; Voges, W.; Fischer, R.; Boese, G.; Dose, V.

2004-07-01

We employ Bayesian inference for the joint estimation of sources and background on ROSAT All-Sky Survey (RASS) data. The probabilistic method allows for detection improvement of faint extended celestial sources compared to the Standard Analysis Software System (SASS). Background maps were estimated in a single step together with the detection of sources without pixel censoring. Consistent uncertainties of background and sources are provided. The source probability is evaluated for single pixels as well as for pixel domains to enhance source detection of weak and extended sources.

Multiple utility constrained multi-objective programs using Bayesian theory

NASA Astrophysics Data System (ADS)

Abbasian, Pooneh; Mahdavi-Amiri, Nezam; Fazlollahtabar, Hamed

2018-03-01

A utility function is an important tool for representing a DM's preference. We adjoin utility functions to multi-objective optimization problems. In current studies, usually one utility function is used for each objective function. Situations may arise for a goal to have multiple utility functions. Here, we consider a constrained multi-objective problem with each objective having multiple utility functions. We induce the probability of the utilities for each objective function using Bayesian theory. Illustrative examples considering dependence and independence of variables are worked through to demonstrate the usefulness of the proposed model.

Bayesian operational modal analysis with asynchronous data, Part II: Posterior uncertainty

NASA Astrophysics Data System (ADS)

Zhu, Yi-Chen; Au, Siu-Kui

2018-01-01

A Bayesian modal identification method has been proposed in the companion paper that allows the most probable values of modal parameters to be determined using asynchronous ambient vibration data. This paper investigates the identification uncertainty of modal parameters in terms of their posterior covariance matrix. Computational issues are addressed. Analytical expressions are derived to allow the posterior covariance matrix to be evaluated accurately and efficiently. Synthetic, laboratory and field data examples are presented to verify the consistency, investigate potential modelling error and demonstrate practical applications.

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

Tucker, Susan L.; Liu, H. Helen; Wang, Shulian

Purpose: The aim of this study was to investigate the effect of radiation dose distribution in the lung on the risk of postoperative pulmonary complications among esophageal cancer patients. Methods and Materials: We analyzed data from 110 patients with esophageal cancer treated with concurrent chemoradiotherapy followed by surgery at our institution from 1998 to 2003. The endpoint for analysis was postsurgical pneumonia or acute respiratory distress syndrome. Dose-volume histograms (DVHs) and dose-mass histograms (DMHs) for the whole lung were used to fit normal-tissue complication probability (NTCP) models, and the quality of fits were compared using bootstrap analysis. Results: Normal-tissue complicationmore » probability modeling identified that the risk of postoperative pulmonary complications was most significantly associated with small absolute volumes of lung spared from doses {>=}5 Gy (VS5), that is, exposed to doses <5 Gy. However, bootstrap analysis found no significant difference between the quality of this model and fits based on other dosimetric parameters, including mean lung dose, effective dose, and relative volume of lung receiving {>=}5 Gy, probably because of correlations among these factors. The choice of DVH vs. DMH or the use of fractionation correction did not significantly affect the results of the NTCP modeling. The parameter values estimated for the Lyman NTCP model were as follows (with 95% confidence intervals in parentheses): n = 1.85 (0.04, {infinity}), m = 0.55 (0.22, 1.02), and D {sub 5} = 17.5 Gy (9.4 Gy, 102 Gy). Conclusions: In this cohort of esophageal cancer patients, several dosimetric parameters including mean lung dose, effective dose, and absolute volume of lung receiving <5 Gy provided similar descriptions of the risk of postoperative pulmonary complications as a function of Radiation dose distribution in the lung.« less

Variance estimation when using inverse probability of treatment weighting (IPTW) with survival analysis.

PubMed

Austin, Peter C

2016-12-30

Propensity score methods are used to reduce the effects of observed confounding when using observational data to estimate the effects of treatments or exposures. A popular method of using the propensity score is inverse probability of treatment weighting (IPTW). When using this method, a weight is calculated for each subject that is equal to the inverse of the probability of receiving the treatment that was actually received. These weights are then incorporated into the analyses to minimize the effects of observed confounding. Previous research has found that these methods result in unbiased estimation when estimating the effect of treatment on survival outcomes. However, conventional methods of variance estimation were shown to result in biased estimates of standard error. In this study, we conducted an extensive set of Monte Carlo simulations to examine different methods of variance estimation when using a weighted Cox proportional hazards model to estimate the effect of treatment. We considered three variance estimation methods: (i) a naïve model-based variance estimator; (ii) a robust sandwich-type variance estimator; and (iii) a bootstrap variance estimator. We considered estimation of both the average treatment effect and the average treatment effect in the treated. We found that the use of a bootstrap estimator resulted in approximately correct estimates of standard errors and confidence intervals with the correct coverage rates. The other estimators resulted in biased estimates of standard errors and confidence intervals with incorrect coverage rates. Our simulations were informed by a case study examining the effect of statin prescribing on mortality. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Phylogenetic evidence for the ancient Himalayan wolf: towards a clarification of its taxonomic status based on genetic sampling from western Nepal

PubMed Central

Kaden, Jennifer; Joshi, Jyoti; Bhattarai, Susmita; Kusi, Naresh; Sillero-Zubiri, Claudio; Macdonald, David W.

2017-01-01

Wolves in the Himalayan region form a monophyletic lineage distinct from the present-day Holarctic grey wolf Canis lupus spp. (Linnaeus 1758) found across Eurasia and North America. Here, we analyse phylogenetic relationships and the geographic distribution of mitochondrial DNA haplotypes of the contemporary Himalayan wolf (proposed in previous studies as Canis himalayensis) found in Central Asia. We combine genetic data from a living Himalayan wolf population collected in northwestern Nepal in this study with already published genetic data, and confirm the Himalayan wolf lineage based on mitochondrial genomic data (508 bp cytochrome b and 242 bp D-loop), and X- and Y-linked zinc-finger protein gene (ZFX and ZFY) sequences. We then compare the genetic profile of the Himalayan wolf lineage found in northwestern Nepal with canid reference sequences from around the globe with maximum likelihood and Bayesian phylogeny building methods to demonstrate that the Himalayan wolf forms a distinct monophyletic clade supported by posterior probabilities/bootstrap for D-loop of greater than 0.92/85 and cytochrome b greater than 0.99/93. The Himalayan wolf shows a unique Y-chromosome (ZFY) haplotype, and shares an X-chromosome haplotype (ZFX) with the newly postulated African wolf. Our results imply that the Himalayan wolf distribution range extends from the Himalayan range north across the Tibetan Plateau up to the Qinghai Lakes region in Qinghai Province in the People's Republic of China. Based on its phylogenetic distinction and its older age of divergence relative to the Holarctic grey wolf, the Himalayan wolf merits formal classification as a distinct taxon of special conservation concern. PMID:28680672

Whose statistical reasoning is facilitated by a causal structure intervention?

PubMed

McNair, Simon; Feeney, Aidan

2015-02-01

People often struggle when making Bayesian probabilistic estimates on the basis of competing sources of statistical evidence. Recently, Krynski and Tenenbaum (Journal of Experimental Psychology: General, 136, 430-450, 2007) proposed that a causal Bayesian framework accounts for peoples' errors in Bayesian reasoning and showed that, by clarifying the causal relations among the pieces of evidence, judgments on a classic statistical reasoning problem could be significantly improved. We aimed to understand whose statistical reasoning is facilitated by the causal structure intervention. In Experiment 1, although we observed causal facilitation effects overall, the effect was confined to participants high in numeracy. We did not find an overall facilitation effect in Experiment 2 but did replicate the earlier interaction between numerical ability and the presence or absence of causal content. This effect held when we controlled for general cognitive ability and thinking disposition. Our results suggest that clarifying causal structure facilitates Bayesian judgments, but only for participants with sufficient understanding of basic concepts in probability and statistics.

Bayesian sample size calculations in phase II clinical trials using a mixture of informative priors.

PubMed

Gajewski, Byron J; Mayo, Matthew S

2006-08-15

A number of researchers have discussed phase II clinical trials from a Bayesian perspective. A recent article by Mayo and Gajewski focuses on sample size calculations, which they determine by specifying an informative prior distribution and then calculating a posterior probability that the true response will exceed a prespecified target. In this article, we extend these sample size calculations to include a mixture of informative prior distributions. The mixture comes from several sources of information. For example consider information from two (or more) clinicians. The first clinician is pessimistic about the drug and the second clinician is optimistic. We tabulate the results for sample size design using the fact that the simple mixture of Betas is a conjugate family for the Beta- Binomial model. We discuss the theoretical framework for these types of Bayesian designs and show that the Bayesian designs in this paper approximate this theoretical framework. Copyright 2006 John Wiley & Sons, Ltd.

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.

Assessment of Manual Operation Time for the Manufacturing of Thin Film Transistor Liquid Crystal Display: A Bayesian Approach

NASA Astrophysics Data System (ADS)

Shen, Chien-wen

2009-01-01

During the processes of TFT-LCD manufacturing, steps like visual inspection of panel surface defects still heavily rely on manual operations. As the manual inspection time of TFT-LCD manufacturing could range from 4 hours to 1 day, the reliability of time forecasting is thus important for production planning, scheduling and customer response. This study would like to propose a practical and easy-to-implement prediction model through the approach of Bayesian networks for time estimation of manual operated procedures in TFT-LCD manufacturing. Given the lack of prior knowledge about manual operation time, algorithms of necessary path condition and expectation-maximization are used for structural learning and estimation of conditional probability distributions respectively. This study also applied Bayesian inference to evaluate the relationships between explanatory variables and manual operation time. With the empirical applications of this proposed forecasting model, approach of Bayesian networks demonstrates its practicability and prediction accountability.

Bayesian analyses of seasonal runoff forecasts

NASA Astrophysics Data System (ADS)

Krzysztofowicz, R.; Reese, S.

1991-12-01

Forecasts of seasonal snowmelt runoff volume provide indispensable information for rational decision making by water project operators, irrigation district managers, and farmers in the western United States. Bayesian statistical models and communication frames have been researched in order to enhance the forecast information disseminated to the users, and to characterize forecast skill from the decision maker's point of view. Four products are presented: (i) a Bayesian Processor of Forecasts, which provides a statistical filter for calibrating the forecasts, and a procedure for estimating the posterior probability distribution of the seasonal runoff; (ii) the Bayesian Correlation Score, a new measure of forecast skill, which is related monotonically to the ex ante economic value of forecasts for decision making; (iii) a statistical predictor of monthly cumulative runoffs within the snowmelt season, conditional on the total seasonal runoff forecast; and (iv) a framing of the forecast message that conveys the uncertainty associated with the forecast estimates to the users. All analyses are illustrated with numerical examples of forecasts for six gauging stations from the period 1971 1988.

Application of a predictive Bayesian model to environmental accounting.

PubMed

Anex, R P; Englehardt, J D

2001-03-30

Environmental accounting techniques are intended to capture important environmental costs and benefits that are often overlooked in standard accounting practices. Environmental accounting methods themselves often ignore or inadequately represent large but highly uncertain environmental costs and costs conditioned by specific prior events. Use of a predictive Bayesian model is demonstrated for the assessment of such highly uncertain environmental and contingent costs. The predictive Bayesian approach presented generates probability distributions for the quantity of interest (rather than parameters thereof). A spreadsheet implementation of a previously proposed predictive Bayesian model, extended to represent contingent costs, is described and used to evaluate whether a firm should undertake an accelerated phase-out of its PCB containing transformers. Variability and uncertainty (due to lack of information) in transformer accident frequency and severity are assessed simultaneously using a combination of historical accident data, engineering model-based cost estimates, and subjective judgement. Model results are compared using several different risk measures. Use of the model for incorporation of environmental risk management into a company's overall risk management strategy is discussed.

Bayesian evidence computation for model selection in non-linear geoacoustic inference problems.

PubMed

Dettmer, Jan; Dosso, Stan E; Osler, John C

2010-12-01

This paper applies a general Bayesian inference approach, based on Bayesian evidence computation, to geoacoustic inversion of interface-wave dispersion data. Quantitative model selection is carried out by computing the evidence (normalizing constants) for several model parameterizations using annealed importance sampling. The resulting posterior probability density estimate is compared to estimates obtained from Metropolis-Hastings sampling to ensure consistent results. The approach is applied to invert interface-wave dispersion data collected on the Scotian Shelf, off the east coast of Canada for the sediment shear-wave velocity profile. Results are consistent with previous work on these data but extend the analysis to a rigorous approach including model selection and uncertainty analysis. The results are also consistent with core samples and seismic reflection measurements carried out in the area.

Fast model updating coupling Bayesian inference and PGD model reduction

NASA Astrophysics Data System (ADS)

Rubio, Paul-Baptiste; Louf, François; Chamoin, Ludovic

2018-04-01

The paper focuses on a coupled Bayesian-Proper Generalized Decomposition (PGD) approach for the real-time identification and updating of numerical models. The purpose is to use the most general case of Bayesian inference theory in order to address inverse problems and to deal with different sources of uncertainties (measurement and model errors, stochastic parameters). In order to do so with a reasonable CPU cost, the idea is to replace the direct model called for Monte-Carlo sampling by a PGD reduced model, and in some cases directly compute the probability density functions from the obtained analytical formulation. This procedure is first applied to a welding control example with the updating of a deterministic parameter. In the second application, the identification of a stochastic parameter is studied through a glued assembly example.

Gaussian process surrogates for failure detection: A Bayesian experimental design approach

NASA Astrophysics Data System (ADS)

Wang, Hongqiao; Lin, Guang; Li, Jinglai

2016-05-01

An important task of uncertainty quantification is to identify the probability of undesired events, in particular, system failures, caused by various sources of uncertainties. In this work we consider the construction of Gaussian process surrogates for failure detection and failure probability estimation. In particular, we consider the situation that the underlying computer models are extremely expensive, and in this setting, determining the sampling points in the state space is of essential importance. We formulate the problem as an optimal experimental design for Bayesian inferences of the limit state (i.e., the failure boundary) and propose an efficient numerical scheme to solve the resulting optimization problem. In particular, the proposed limit-state inference method is capable of determining multiple sampling points at a time, and thus it is well suited for problems where multiple computer simulations can be performed in parallel. The accuracy and performance of the proposed method is demonstrated by both academic and practical examples.

Screening for SNPs with Allele-Specific Methylation based on Next-Generation Sequencing Data

PubMed Central

Hu, Bo; Xu, Yaomin

2013-01-01

Allele-specific methylation (ASM) has long been studied but mainly documented in the context of genomic imprinting and X chromosome inactivation. Taking advantage of the next-generation sequencing technology, we conduct a high-throughput sequencing experiment with four prostate cell lines to survey the whole genome and identify single nucleotide polymorphisms (SNPs) with ASM. A Bayesian approach is proposed to model the counts of short reads for each SNP conditional on its genotypes of multiple subjects, leading to a posterior probability of ASM. We flag SNPs with high posterior probabilities of ASM by accounting for multiple comparisons based on posterior false discovery rates. Applying the Bayesian approach to the in-house prostate cell line data, we identify 269 SNPs as candidates of ASM. A simulation study is carried out to demonstrate the quantitative performance of the proposed approach. PMID:23710259

Integrated Data Analysis for Fusion: A Bayesian Tutorial for Fusion Diagnosticians

NASA Astrophysics Data System (ADS)

Dinklage, Andreas; Dreier, Heiko; Fischer, Rainer; Gori, Silvio; Preuss, Roland; Toussaint, Udo von

2008-03-01

Integrated Data Analysis (IDA) offers a unified way of combining information relevant to fusion experiments. Thereby, IDA meets with typical issues arising in fusion data analysis. In IDA, all information is consistently formulated as probability density functions quantifying uncertainties in the analysis within the Bayesian probability theory. For a single diagnostic, IDA allows the identification of faulty measurements and improvements in the setup. For a set of diagnostics, IDA gives joint error distributions allowing the comparison and integration of different diagnostics results. Validation of physics models can be performed by model comparison techniques. Typical data analysis applications benefit from IDA capabilities of nonlinear error propagation, the inclusion of systematic effects and the comparison of different physics models. Applications range from outlier detection, background discrimination, model assessment and design of diagnostics. In order to cope with next step fusion device requirements, appropriate techniques are explored for fast analysis applications.

Fermi's paradox, extraterrestrial life and the future of humanity: a Bayesian analysis

NASA Astrophysics Data System (ADS)

Verendel, Vilhelm; Häggström, Olle

2017-01-01

The Great Filter interpretation of Fermi's great silence asserts that Npq is not a very large number, where N is the number of potentially life-supporting planets in the observable universe, p is the probability that a randomly chosen such planet develops intelligent life to the level of present-day human civilization, and q is the conditional probability that it then goes on to develop a technological supercivilization visible all over the observable universe. Evidence suggests that N is huge, which implies that pq is very small. Hanson (1998) and Bostrom (2008) have argued that the discovery of extraterrestrial life would point towards p not being small and therefore a very small q, which can be seen as bad news for humanity's prospects of colonizing the universe. Here we investigate whether a Bayesian analysis supports their argument, and the answer turns out to depend critically on the choice of prior distribution.

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

A Variational Bayes Genomic-Enabled Prediction Model with Genotype × Environment Interaction

PubMed Central

Montesinos-López, Osval A.; Montesinos-López, Abelardo; Crossa, José; Montesinos-López, José Cricelio; Luna-Vázquez, Francisco Javier; Salinas-Ruiz, Josafhat; Herrera-Morales, José R.; Buenrostro-Mariscal, Raymundo

2017-01-01

There are Bayesian and non-Bayesian genomic models that take into account G×E interactions. However, the computational cost of implementing Bayesian models is high, and becomes almost impossible when the number of genotypes, environments, and traits is very large, while, in non-Bayesian models, there are often important and unsolved convergence problems. The variational Bayes method is popular in machine learning, and, by approximating the probability distributions through optimization, it tends to be faster than Markov Chain Monte Carlo methods. For this reason, in this paper, we propose a new genomic variational Bayes version of the Bayesian genomic model with G×E using half-t priors on each standard deviation (SD) term to guarantee highly noninformative and posterior inferences that are not sensitive to the choice of hyper-parameters. We show the complete theoretical derivation of the full conditional and the variational posterior distributions, and their implementations. We used eight experimental genomic maize and wheat data sets to illustrate the new proposed variational Bayes approximation, and compared its predictions and implementation time with a standard Bayesian genomic model with G×E. Results indicated that prediction accuracies are slightly higher in the standard Bayesian model with G×E than in its variational counterpart, but, in terms of computation time, the variational Bayes genomic model with G×E is, in general, 10 times faster than the conventional Bayesian genomic model with G×E. For this reason, the proposed model may be a useful tool for researchers who need to predict and select genotypes in several environments. PMID:28391241

A Variational Bayes Genomic-Enabled Prediction Model with Genotype × Environment Interaction.

PubMed

Montesinos-López, Osval A; Montesinos-López, Abelardo; Crossa, José; Montesinos-López, José Cricelio; Luna-Vázquez, Francisco Javier; Salinas-Ruiz, Josafhat; Herrera-Morales, José R; Buenrostro-Mariscal, Raymundo

2017-06-07

There are Bayesian and non-Bayesian genomic models that take into account G×E interactions. However, the computational cost of implementing Bayesian models is high, and becomes almost impossible when the number of genotypes, environments, and traits is very large, while, in non-Bayesian models, there are often important and unsolved convergence problems. The variational Bayes method is popular in machine learning, and, by approximating the probability distributions through optimization, it tends to be faster than Markov Chain Monte Carlo methods. For this reason, in this paper, we propose a new genomic variational Bayes version of the Bayesian genomic model with G×E using half-t priors on each standard deviation (SD) term to guarantee highly noninformative and posterior inferences that are not sensitive to the choice of hyper-parameters. We show the complete theoretical derivation of the full conditional and the variational posterior distributions, and their implementations. We used eight experimental genomic maize and wheat data sets to illustrate the new proposed variational Bayes approximation, and compared its predictions and implementation time with a standard Bayesian genomic model with G×E. Results indicated that prediction accuracies are slightly higher in the standard Bayesian model with G×E than in its variational counterpart, but, in terms of computation time, the variational Bayes genomic model with G×E is, in general, 10 times faster than the conventional Bayesian genomic model with G×E. For this reason, the proposed model may be a useful tool for researchers who need to predict and select genotypes in several environments. Copyright © 2017 Montesinos-López et al.

Generic phylogeny, historical biogeography and character evolution of the cosmopolitan aquatic plant family Hydrocharitaceae

PubMed Central

2012-01-01

Background Hydrocharitaceae is a fully aquatic monocot family, consists of 18 genera with approximately 120 species. The family includes both fresh and marine aquatics and exhibits great diversity in form and habit including annual and perennial life histories; submersed, partially submersed and floating leaf habits and linear to orbicular leaf shapes. The family has a cosmopolitan distribution and is well represented in the Tertiary fossil record in Europe. At present, the historical biogeography of the family is not well understood and the generic relationships remain controversial. In this study we investigated the phylogeny and biogeography of Hydrocharitaceae by integrating fossils and DNA sequences from eight genes. We also conducted ancestral state reconstruction for three morphological characters. Results Phylogenetic analyses produced a phylogeny with most branches strongly supported by bootstrap values greater than 95 and Bayesian posterior probability values of 1.0. Stratiotes is the first diverging lineage with the remaining genera in two clades, one clade consists of Lagarosiphon, Ottelia, Blyxa, Apalanthe, Elodea and Egeria; and the other consists of Hydrocharis-Limnobium, Thalassia, Enhalus, Halophila, Najas, Hydrilla, Vallisneria, Nechamandra and Maidenia. Biogeographic analyses (DIVA, Mesquite) and divergence time estimates (BEAST) resolved the most recent common ancestor of Hydrocharitaceae as being in Asia during the Late Cretaceous and Palaeocene (54.7-72.6 Ma). Dispersals (including long-distance dispersal and migrations through Tethys seaway and land bridges) probably played major roles in the intercontinental distribution of this family. Ancestral state reconstruction suggested that in Hydrocharitaceae evolution of dioecy is bidirectional, viz., from dioecy to hermaphroditism, and from hermaphroditism to dioecy, and that the aerial-submerged leaf habit and short-linear leaf shape are the ancestral states. Conclusions Our study has shed light on the previously controversial generic phylogeny of Hydrocharitaceae. The study has resolved the historical biogeography of this family and supported dispersal as the most likely explanation for the intercontinental distribution. We have also provided valuable information for understanding the evolution of breeding system and leaf phenotype in aquatic monocots. PMID:22404786

Entropy-Bayesian Inversion of Time-Lapse Tomographic GPR data for Monitoring Dielectric Permittivity and Soil Moisture Variations

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

Hou, Z; Terry, N; Hubbard, S S

2013-02-12

In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniquenessmore » and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability distribution functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSim) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes advantage of the spatial-temporal correlation of the state variables. We first apply the inversion framework to a static synthetic example and then to a time-lapse GPR tomographic dataset collected during a dynamic experiment conducted at the Hanford Site in Richland, WA. We demonstrate that the MRE-Bayesian inversion enables us to merge various data types, quantify uncertainty, evaluate nonlinear models, and produce more detailed and better resolved estimates than straight-ray based inversion; therefore, it has the potential to improve estimates of inter-wellbore dielectric permittivity and soil moisture content and to monitor their temporal dynamics more accurately.« less

Entropy-Bayesian Inversion of Time-Lapse Tomographic GPR data for Monitoring Dielectric Permittivity and Soil Moisture Variations

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

Hou, Zhangshuan; Terry, Neil C.; Hubbard, Susan S.

2013-02-22

In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniquenessmore » and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability density functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSIM) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes advantage of the spatial-temporal correlation of the state variables. We first apply the inversion framework to a static synthetic example and then to a time-lapse GPR tomographic dataset collected during a dynamic experiment conducted at the Hanford Site in Richland, WA. We demonstrate that the MRE-Bayesian inversion enables us to merge various data types, quantify uncertainty, evaluate nonlinear models, and produce more detailed and better resolved estimates than straight-ray based inversion; therefore, it has the potential to improve estimates of inter-wellbore dielectric permittivity and soil moisture content and to monitor their temporal dynamics more accurately.« less

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 Inference and Online Learning in Poisson Neuronal Networks.

PubMed

Huang, Yanping; Rao, Rajesh P N

2016-08-01

Motivated by the growing evidence for Bayesian computation in the brain, we show how a two-layer recurrent network of Poisson neurons can perform both approximate Bayesian inference and learning for any hidden Markov model. The lower-layer sensory neurons receive noisy measurements of hidden world states. The higher-layer neurons infer a posterior distribution over world states via Bayesian inference from inputs generated by sensory neurons. We demonstrate how such a neuronal network with synaptic plasticity can implement a form of Bayesian inference similar to Monte Carlo methods such as particle filtering. Each spike in a higher-layer neuron represents a sample of a particular hidden world state. The spiking activity across the neural population approximates the posterior distribution over hidden states. In this model, variability in spiking is regarded not as a nuisance but as an integral feature that provides the variability necessary for sampling during inference. We demonstrate how the network can learn the likelihood model, as well as the transition probabilities underlying the dynamics, using a Hebbian learning rule. We present results illustrating the ability of the network to perform inference and learning for arbitrary hidden Markov models.

Bayesian feature selection for high-dimensional linear regression via the Ising approximation with applications to genomics.

PubMed

Fisher, Charles K; Mehta, Pankaj

2015-06-01

Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and computationally intensive when the number of variables approaches or exceeds the number of samples, as is often the case for many genomic datasets. Here, we introduce a new approach--the Bayesian Ising Approximation (BIA)-to rapidly calculate posterior probabilities for feature relevance in L2 penalized linear regression. In the regime where the regression problem is strongly regularized by the prior, we show that computing the marginal posterior probabilities for features is equivalent to computing the magnetizations of an Ising model with weak couplings. Using a mean field approximation, we show it is possible to rapidly compute the feature selection path described by the posterior probabilities as a function of the L2 penalty. We present simulations and analytical results illustrating the accuracy of the BIA on some simple regression problems. Finally, we demonstrate the applicability of the BIA to high-dimensional regression by analyzing a gene expression dataset with nearly 30 000 features. These results also highlight the impact of correlations between features on Bayesian feature selection. An implementation of the BIA in C++, along with data for reproducing our gene expression analyses, are freely available at http://physics.bu.edu/∼pankajm/BIACode. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

A quantum probability framework for human probabilistic inference.

PubMed

Trueblood, Jennifer S; Yearsley, James M; Pothos, Emmanuel M

2017-09-01

There is considerable variety in human inference (e.g., a doctor inferring the presence of a disease, a juror inferring the guilt of a defendant, or someone inferring future weight loss based on diet and exercise). As such, people display a wide range of behaviors when making inference judgments. Sometimes, people's judgments appear Bayesian (i.e., normative), but in other cases, judgments deviate from the normative prescription of classical probability theory. How can we combine both Bayesian and non-Bayesian influences in a principled way? We propose a unified explanation of human inference using quantum probability theory. In our approach, we postulate a hierarchy of mental representations, from 'fully' quantum to 'fully' classical, which could be adopted in different situations. In our hierarchy of models, moving from the lowest level to the highest involves changing assumptions about compatibility (i.e., how joint events are represented). Using results from 3 experiments, we show that our modeling approach explains 5 key phenomena in human inference including order effects, reciprocity (i.e., the inverse fallacy), memorylessness, violations of the Markov condition, and antidiscounting. As far as we are aware, no existing theory or model can explain all 5 phenomena. We also explore transitions in our hierarchy, examining how representations change from more quantum to more classical. We show that classical representations provide a better account of data as individuals gain familiarity with a task. We also show that representations vary between individuals, in a way that relates to a simple measure of cognitive style, the Cognitive Reflection Test. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Bayesian regression analyses of radiation modality effects on pericardial and pleural effusion and survival in esophageal cancer.

PubMed

He, Liru; Chapple, Andrew; Liao, Zhongxing; Komaki, Ritsuko; Thall, Peter F; Lin, Steven H

2016-10-01

To evaluate radiation modality effects on pericardial effusion (PCE), pleural effusion (PE) and survival in esophageal cancer (EC) patients. We analyzed data from 470 EC patients treated with definitive concurrent chemoradiotherapy (CRT). Bayesian semi-competing risks (SCR) regression models were fit to assess effects of radiation modality and prognostic covariates on the risks of PCE and PE, and death either with or without these preceding events. Bayesian piecewise exponential regression models were fit for overall survival, the time to PCE or death, and the time to PE or death. All models included propensity score as a covariate to correct for potential selection bias. Median times to onset of PCE and PE after RT were 7.1 and 6.1months for IMRT, and 6.5 and 5.4months for 3DCRT, respectively. Compared to 3DCRT, the IMRT group had significantly lower risks of PE, PCE, and death. The respective probabilities of a patient being alive without either PCE or PE at 3-years and 5-years were 0.29 and 0.21 for IMRT compared to 0.13 and 0.08 for 3DCRT. In the SCR regression analyses, IMRT was associated with significantly lower risks of PCE (HR=0.26) and PE (HR=0.49), and greater overall survival (probability of beneficial effect (pbe)>0.99), after controlling for known clinical prognostic factors. IMRT reduces the incidence and postpones the onset of PCE and PE, and increases survival probability, compared to 3DCRT. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

A Risk Assessment of Antibiotic Pan-Drug-Resistance in the UK: Bayesian Analysis of an Expert Elicitation Study

PubMed Central

Carter, Daniel; Charlett, André; Conti, Stefano; Robotham, Julie V.; Johnson, Alan P.; Livermore, David M.; Fowler, Tom; Sharland, Mike; Hopkins, Susan; Woodford, Neil; Burgess, Philip; Dobra, Stephen

2017-01-01

To inform the UK antimicrobial resistance strategy, a risk assessment was undertaken of the likelihood, over a five-year time-frame, of the emergence and widespread dissemination of pan-drug-resistant (PDR) Gram-negative bacteria that would pose a major public health threat by compromising effective healthcare delivery. Subsequent impact over five- and 20-year time-frames was assessed in terms of morbidity and mortality attributable to PDR Gram-negative bacteraemia. A Bayesian approach, combining available data with expert prior opinion, was used to determine the probability of the emergence, persistence and spread of PDR bacteria. Overall probability was modelled using Monte Carlo simulation. Estimates of impact were also obtained using Bayesian methods. The estimated probability of widespread occurrence of PDR pathogens within five years was 0.2 (95% credibility interval (CrI): 0.07–0.37). Estimated annual numbers of PDR Gram-negative bacteraemias at five and 20 years were 6800 (95% CrI: 400–58,600) and 22,800 (95% CrI: 1500–160,000), respectively; corresponding estimates of excess deaths were 1900 (95% CrI: 0–23,000) and 6400 (95% CrI: 0–64,000). Over 20 years, cumulative estimates indicate 284,000 (95% CrI: 17,000–1,990,000) cases of PDR Gram-negative bacteraemia, leading to an estimated 79,000 (95% CrI: 0–821,000) deaths. This risk assessment reinforces the need for urgent national and international action to tackle antibiotic resistance. PMID:28272350

Robust Bayesian Algorithm for Targeted Compound Screening in Forensic Toxicology.

PubMed

Woldegebriel, Michael; Gonsalves, John; van Asten, Arian; Vivó-Truyols, Gabriel

2016-02-16

As part of forensic toxicological investigation of cases involving unexpected death of an individual, targeted or untargeted xenobiotic screening of post-mortem samples is normally conducted. To this end, liquid chromatography (LC) coupled to high-resolution mass spectrometry (MS) is typically employed. For data analysis, almost all commonly applied algorithms are threshold-based (frequentist). These algorithms examine the value of a certain measurement (e.g., peak height) to decide whether a certain xenobiotic of interest (XOI) is present/absent, yielding a binary output. Frequentist methods pose a problem when several sources of information [e.g., shape of the chromatographic peak, isotopic distribution, estimated mass-to-charge ratio (m/z), adduct, etc.] need to be combined, requiring the approach to make arbitrary decisions at substep levels of data analysis. We hereby introduce a novel Bayesian probabilistic algorithm for toxicological screening. The method tackles the problem with a different strategy. It is not aimed at reaching a final conclusion regarding the presence of the XOI, but it estimates its probability. The algorithm effectively and efficiently combines all possible pieces of evidence from the chromatogram and calculates the posterior probability of the presence/absence of XOI features. This way, the model can accommodate more information by updating the probability if extra evidence is acquired. The final probabilistic result assists the end user to make a final decision with respect to the presence/absence of the xenobiotic. The Bayesian method was validated and found to perform better (in terms of false positives and false negatives) than the vendor-supplied software package.

Non-monophyly and intricate morphological evolution within the avian family Cettiidae revealed by multilocus analysis of a taxonomically densely sampled dataset

PubMed Central

2011-01-01

Background The avian family Cettiidae, including the genera Cettia, Urosphena, Tesia, Abroscopus and Tickellia and Orthotomus cucullatus, has recently been proposed based on analysis of a small number of loci and species. The close relationship of most of these taxa was unexpected, and called for a comprehensive study based on multiple loci and dense taxon sampling. In the present study, we infer the relationships of all except one of the species in this family using one mitochondrial and three nuclear loci. We use traditional gene tree methods (Bayesian inference, maximum likelihood bootstrapping, parsimony bootstrapping), as well as a recently developed Bayesian species tree approach (*BEAST) that accounts for lineage sorting processes that might produce discordance between gene trees. We also analyse mitochondrial DNA for a larger sample, comprising multiple individuals and a large number of subspecies of polytypic species. Results There are many topological incongruences among the single-locus trees, although none of these is strongly supported. The multi-locus tree inferred using concatenated sequences and the species tree agree well with each other, and are overall well resolved and well supported by the data. The main discrepancy between these trees concerns the most basal split. Both methods infer the genus Cettia to be highly non-monophyletic, as it is scattered across the entire family tree. Deep intraspecific divergences are revealed, and one or two species and one subspecies are inferred to be non-monophyletic (differences between methods). Conclusions The molecular phylogeny presented here is strongly inconsistent with the traditional, morphology-based classification. The remarkably high degree of non-monophyly in the genus Cettia is likely to be one of the most extraordinary examples of misconceived relationships in an avian genus. The phylogeny suggests instances of parallel evolution, as well as highly unequal rates of morphological divergence in different lineages. This complex morphological evolution apparently misled earlier taxonomists. These results underscore the well-known but still often neglected problem of basing classifications on overall morphological similarity. Based on the molecular data, a revised taxonomy is proposed. Although the traditional and species tree methods inferred much the same tree in the present study, the assumption by species tree methods that all species are monophyletic is a limitation in these methods, as some currently recognized species might have more complex histories. PMID:22142197

Assessment of groundwater level estimation uncertainty using sequential Gaussian simulation and Bayesian bootstrapping

NASA Astrophysics Data System (ADS)

Varouchakis, Emmanouil; Hristopulos, Dionissios

2015-04-01

Space-time geostatistical approaches can improve the reliability of dynamic groundwater level models in areas with limited spatial and temporal data. Space-time residual Kriging (STRK) is a reliable method for spatiotemporal interpolation that can incorporate auxiliary information. The method usually leads to an underestimation of the prediction uncertainty. The uncertainty of spatiotemporal models is usually estimated by determining the space-time Kriging variance or by means of cross validation analysis. For de-trended data the former is not usually applied when complex spatiotemporal trend functions are assigned. A Bayesian approach based on the bootstrap idea and sequential Gaussian simulation are employed to determine the uncertainty of the spatiotemporal model (trend and covariance) parameters. These stochastic modelling approaches produce multiple realizations, rank the prediction results on the basis of specified criteria and capture the range of the uncertainty. The correlation of the spatiotemporal residuals is modeled using a non-separable space-time variogram based on the Spartan covariance family (Hristopulos and Elogne 2007, Varouchakis and Hristopulos 2013). We apply these simulation methods to investigate the uncertainty of groundwater level variations. The available dataset consists of bi-annual (dry and wet hydrological period) groundwater level measurements in 15 monitoring locations for the time period 1981 to 2010. The space-time trend function is approximated using a physical law that governs the groundwater flow in the aquifer in the presence of pumping. The main objective of this research is to compare the performance of two simulation methods for prediction uncertainty estimation. In addition, we investigate the performance of the Spartan spatiotemporal covariance function for spatiotemporal geostatistical analysis. Hristopulos, D.T. and Elogne, S.N. 2007. Analytic properties and covariance functions for a new class of generalized Gibbs random fields. IΕΕΕ Transactions on Information Theory, 53:4667-4467. Varouchakis, E.A. and Hristopulos, D.T. 2013. Improvement of groundwater level prediction in sparsely gauged basins using physical laws and local geographic features as auxiliary variables. Advances in Water Resources, 52:34-49. Research supported by the project SPARTA 1591: "Development of Space-Time Random Fields based on Local Interaction Models and Applications in the Processing of Spatiotemporal Datasets". "SPARTA" is implemented under the "ARISTEIA" Action of the operational programme Education and Lifelong Learning and is co-funded by the European Social Fund (ESF) and National Resources.

Developing a spatial-statistical model and map of historical malaria prevalence in Botswana using a staged variable selection procedure

PubMed Central

Craig, Marlies H; Sharp, Brian L; Mabaso, Musawenkosi LH; Kleinschmidt, Immo

2007-01-01

Background Several malaria risk maps have been developed in recent years, many from the prevalence of infection data collated by the MARA (Mapping Malaria Risk in Africa) project, and using various environmental data sets as predictors. Variable selection is a major obstacle due to analytical problems caused by over-fitting, confounding and non-independence in the data. Testing and comparing every combination of explanatory variables in a Bayesian spatial framework remains unfeasible for most researchers. The aim of this study was to develop a malaria risk map using a systematic and practicable variable selection process for spatial analysis and mapping of historical malaria risk in Botswana. Results Of 50 potential explanatory variables from eight environmental data themes, 42 were significantly associated with malaria prevalence in univariate logistic regression and were ranked by the Akaike Information Criterion. Those correlated with higher-ranking relatives of the same environmental theme, were temporarily excluded. The remaining 14 candidates were ranked by selection frequency after running automated step-wise selection procedures on 1000 bootstrap samples drawn from the data. A non-spatial multiple-variable model was developed through step-wise inclusion in order of selection frequency. Previously excluded variables were then re-evaluated for inclusion, using further step-wise bootstrap procedures, resulting in the exclusion of another variable. Finally a Bayesian geo-statistical model using Markov Chain Monte Carlo simulation was fitted to the data, resulting in a final model of three predictor variables, namely summer rainfall, mean annual temperature and altitude. Each was independently and significantly associated with malaria prevalence after allowing for spatial correlation. This model was used to predict malaria prevalence at unobserved locations, producing a smooth risk map for the whole country. Conclusion We have produced a highly plausible and parsimonious model of historical malaria risk for Botswana from point-referenced data from a 1961/2 prevalence survey of malaria infection in 1–14 year old children. After starting with a list of 50 potential variables we ended with three highly plausible predictors, by applying a systematic and repeatable staged variable selection procedure that included a spatial analysis, which has application for other environmentally determined infectious diseases. All this was accomplished using general-purpose statistical software. PMID:17892584

Evaluating experimental design for soil-plant model selection using a Bootstrap Filter and Bayesian model averaging

NASA Astrophysics Data System (ADS)

Wöhling, T.; Schöniger, A.; Geiges, A.; Nowak, W.; Gayler, S.

2013-12-01

The objective selection of appropriate models for realistic simulations of coupled soil-plant processes is a challenging task since the processes are complex, not fully understood at larger scales, and highly non-linear. Also, comprehensive data sets are scarce, and measurements are uncertain. In the past decades, a variety of different models have been developed that exhibit a wide range of complexity regarding their approximation of processes in the coupled model compartments. We present a method for evaluating experimental design for maximum confidence in the model selection task. The method considers uncertainty in parameters, measurements and model structures. Advancing the ideas behind Bayesian Model Averaging (BMA), we analyze the changes in posterior model weights and posterior model choice uncertainty when more data are made available. This allows assessing the power of different data types, data densities and data locations in identifying the best model structure from among a suite of plausible models. The models considered in this study are the crop models CERES, SUCROS, GECROS and SPASS, which are coupled to identical routines for simulating soil processes within the modelling framework Expert-N. The four models considerably differ in the degree of detail at which crop growth and root water uptake are represented. Monte-Carlo simulations were conducted for each of these models considering their uncertainty in soil hydraulic properties and selected crop model parameters. Using a Bootstrap Filter (BF), the models were then conditioned on field measurements of soil moisture, matric potential, leaf-area index, and evapotranspiration rates (from eddy-covariance measurements) during a vegetation period of winter wheat at a field site at the Swabian Alb in Southwestern Germany. Following our new method, we derived model weights when using all data or different subsets thereof. We discuss to which degree the posterior mean outperforms the prior mean and all individual posterior models, how informative the data types were for reducing prediction uncertainty of evapotranspiration and deep drainage, and how well the model structure can be identified based on the different data types and subsets. We further analyze the impact of measurement uncertainty und systematic model errors on the effective sample size of the BF and the resulting model weights.

Bayes in biological anthropology.

PubMed

Konigsberg, Lyle W; Frankenberg, Susan R

2013-12-01

In this article, we both contend and illustrate that biological anthropologists, particularly in the Americas, often think like Bayesians but act like frequentists when it comes to analyzing a wide variety of data. In other words, while our research goals and perspectives are rooted in probabilistic thinking and rest on prior knowledge, we often proceed to use statistical hypothesis tests and confidence interval methods unrelated (or tenuously related) to the research questions of interest. We advocate for applying Bayesian analyses to a number of different bioanthropological questions, especially since many of the programming and computational challenges to doing so have been overcome in the past two decades. To facilitate such applications, this article explains Bayesian principles and concepts, and provides concrete examples of Bayesian computer simulations and statistics that address questions relevant to biological anthropology, focusing particularly on bioarchaeology and forensic anthropology. It also simultaneously reviews the use of Bayesian methods and inference within the discipline to date. This article is intended to act as primer to Bayesian methods and inference in biological anthropology, explaining the relationships of various methods to likelihoods or probabilities and to classical statistical models. Our contention is not that traditional frequentist statistics should be rejected outright, but that there are many situations where biological anthropology is better served by taking a Bayesian approach. To this end it is hoped that the examples provided in this article will assist researchers in choosing from among the broad array of statistical methods currently available. Copyright © 2013 Wiley Periodicals, Inc.

Bayesian probabilistic approach for inverse source determination from limited and noisy chemical or biological sensor concentration measurements

NASA Astrophysics Data System (ADS)

Yee, Eugene

2007-04-01

Although a great deal of research effort has been focused on the forward prediction of the dispersion of contaminants (e.g., chemical and biological warfare agents) released into the turbulent atmosphere, much less work has been directed toward the inverse prediction of agent source location and strength from the measured concentration, even though the importance of this problem for a number of practical applications is obvious. In general, the inverse problem of source reconstruction is ill-posed and unsolvable without additional information. It is demonstrated that a Bayesian probabilistic inferential framework provides a natural and logically consistent method for source reconstruction from a limited number of noisy concentration data. In particular, the Bayesian approach permits one to incorporate prior knowledge about the source as well as additional information regarding both model and data errors. The latter enables a rigorous determination of the uncertainty in the inference of the source parameters (e.g., spatial location, emission rate, release time, etc.), hence extending the potential of the methodology as a tool for quantitative source reconstruction. A model (or, source-receptor relationship) that relates the source distribution to the concentration data measured by a number of sensors is formulated, and Bayesian probability theory is used to derive the posterior probability density function of the source parameters. A computationally efficient methodology for determination of the likelihood function for the problem, based on an adjoint representation of the source-receptor relationship, is described. Furthermore, we describe the application of efficient stochastic algorithms based on Markov chain Monte Carlo (MCMC) for sampling from the posterior distribution of the source parameters, the latter of which is required to undertake the Bayesian computation. The Bayesian inferential methodology for source reconstruction is validated against real dispersion data for two cases involving contaminant dispersion in highly disturbed flows over urban and complex environments where the idealizations of horizontal homogeneity and/or temporal stationarity in the flow cannot be applied to simplify the problem. Furthermore, the methodology is applied to the case of reconstruction of multiple sources.

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

Uncertainty in action-value estimation affects both action choice and learning rate of the choice behaviors of rats

PubMed Central

Funamizu, Akihiro; Ito, Makoto; Doya, Kenji; Kanzaki, Ryohei; Takahashi, Hirokazu

2012-01-01

The estimation of reward outcomes for action candidates is essential for decision making. In this study, we examined whether and how the uncertainty in reward outcome estimation affects the action choice and learning rate. We designed a choice task in which rats selected either the left-poking or right-poking hole and received a reward of a food pellet stochastically. The reward probabilities of the left and right holes were chosen from six settings (high, 100% vs. 66%; mid, 66% vs. 33%; low, 33% vs. 0% for the left vs. right holes, and the opposites) in every 20–549 trials. We used Bayesian Q-learning models to estimate the time course of the probability distribution of action values and tested if they better explain the behaviors of rats than standard Q-learning models that estimate only the mean of action values. Model comparison by cross-validation revealed that a Bayesian Q-learning model with an asymmetric update for reward and non-reward outcomes fit the choice time course of the rats best. In the action-choice equation of the Bayesian Q-learning model, the estimated coefficient for the variance of action value was positive, meaning that rats were uncertainty seeking. Further analysis of the Bayesian Q-learning model suggested that the uncertainty facilitated the effective learning rate. These results suggest that the rats consider uncertainty in action-value estimation and that they have an uncertainty-seeking action policy and uncertainty-dependent modulation of the effective learning rate. PMID:22487046

Meta-analysis of the effect of natural frequencies on Bayesian reasoning.

PubMed

McDowell, Michelle; Jacobs, Perke

2017-12-01

The natural frequency facilitation effect describes the finding that people are better able to solve descriptive Bayesian inference tasks when represented as joint frequencies obtained through natural sampling, known as natural frequencies, than as conditional probabilities. The present meta-analysis reviews 20 years of research seeking to address when, why, and for whom natural frequency formats are most effective. We review contributions from research associated with the 2 dominant theoretical perspectives, the ecological rationality framework and nested-sets theory, and test potential moderators of the effect. A systematic review of relevant literature yielded 35 articles representing 226 performance estimates. These estimates were statistically integrated using a bivariate mixed-effects model that yields summary estimates of average performances across the 2 formats and estimates of the effects of different study characteristics on performance. These study characteristics range from moderators representing individual characteristics (e.g., numeracy, expertise), to methodological differences (e.g., use of incentives, scoring criteria) and features of problem representation (e.g., short menu format, visual aid). Short menu formats (less computationally complex representations showing joint-events) and visual aids demonstrated some of the strongest moderation effects, improving performance for both conditional probability and natural frequency formats. A number of methodological factors (e.g., exposure to both problem formats) were also found to affect performance rates, emphasizing the importance of a systematic approach. We suggest how research on Bayesian reasoning can be strengthened by broadening the definition of successful Bayesian reasoning to incorporate choice and process and by applying different research methodologies. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Predicting coastal cliff erosion using a Bayesian probabilistic model

USGS Publications Warehouse

Hapke, Cheryl J.; Plant, Nathaniel G.

2010-01-01

Regional coastal cliff retreat is difficult to model due to the episodic nature of failures and the along-shore variability of retreat events. There is a growing demand, however, for predictive models that can be used to forecast areas vulnerable to coastal erosion hazards. Increasingly, probabilistic models are being employed that require data sets of high temporal density to define the joint probability density function that relates forcing variables (e.g. wave conditions) and initial conditions (e.g. cliff geometry) to erosion events. In this study we use a multi-parameter Bayesian network to investigate correlations between key variables that control and influence variations in cliff retreat processes. The network uses Bayesian statistical methods to estimate event probabilities using existing observations. Within this framework, we forecast the spatial distribution of cliff retreat along two stretches of cliffed coast in Southern California. The input parameters are the height and slope of the cliff, a descriptor of material strength based on the dominant cliff-forming lithology, and the long-term cliff erosion rate that represents prior behavior. The model is forced using predicted wave impact hours. Results demonstrate that the Bayesian approach is well-suited to the forward modeling of coastal cliff retreat, with the correct outcomes forecast in 70–90% of the modeled transects. The model also performs well in identifying specific locations of high cliff erosion, thus providing a foundation for hazard mapping. This approach can be employed to predict cliff erosion at time-scales ranging from storm events to the impacts of sea-level rise at the century-scale.

[Determination of wine original regions using information fusion of NIR and MIR spectroscopy].

PubMed

Xiang, Ling-Li; Li, Meng-Hua; Li, Jing-Mingz; Li, Jun-Hui; Zhang, Lu-Da; Zhao, Long-Lian

2014-10-01

Geographical origins of wine grapes are significant factors affecting wine quality and wine prices. Tasters' evaluation is a good method but has some limitations. It is important to discriminate different wine original regions quickly and accurately. The present paper proposed a method to determine wine original regions based on Bayesian information fusion that fused near-infrared (NIR) transmission spectra information and mid-infrared (MIR) ATR spectra information of wines. This method improved the determination results by expanding the sources of analysis information. NIR spectra and MIR spectra of 153 wine samples from four different regions of grape growing were collected by near-infrared and mid-infrared Fourier transform spe trometer separately. These four different regions are Huailai, Yantai, Gansu and Changli, which areall typical geographical originals for Chinese wines. NIR and MIR discriminant models for wine regions were established using partial least squares discriminant analysis (PLS-DA) based on NIR spectra and MIR spectra separately. In PLS-DA, the regions of wine samples are presented in group of binary code. There are four wine regions in this paper, thereby using four nodes standing for categorical variables. The output nodes values for each sample in NIR and MIR models were normalized first. These values stand for the probabilities of each sample belonging to each category. They seemed as the input to the Bayesian discriminant formula as a priori probability value. The probabilities were substituteed into the Bayesian formula to get posterior probabilities, by which we can judge the new class characteristics of these samples. Considering the stability of PLS-DA models, all the wine samples were divided into calibration sets and validation sets randomly for ten times. The results of NIR and MIR discriminant models of four wine regions were as follows: the average accuracy rates of calibration sets were 78.21% (NIR) and 82.57% (MIR), and the average accuracy rates of validation sets were 82.50% (NIR) and 81.98% (MIR). After using the method proposed in this paper, the accuracy rates of calibration and validation changed to 87.11% and 90.87% separately, which all achieved better results of determination than individual spectroscopy. These results suggest that Bayesian information fusion of NIR and MIR spectra is feasible for fast identification of wine original regions.

Nested Sampling for Bayesian Model Comparison in the Context of Salmonella Disease Dynamics

PubMed Central

Dybowski, Richard; McKinley, Trevelyan J.; Mastroeni, Pietro; Restif, Olivier

2013-01-01

Understanding the mechanisms underlying the observed dynamics of complex biological systems requires the statistical assessment and comparison of multiple alternative models. Although this has traditionally been done using maximum likelihood-based methods such as Akaike's Information Criterion (AIC), Bayesian methods have gained in popularity because they provide more informative output in the form of posterior probability distributions. However, comparison between multiple models in a Bayesian framework is made difficult by the computational cost of numerical integration over large parameter spaces. A new, efficient method for the computation of posterior probabilities has recently been proposed and applied to complex problems from the physical sciences. Here we demonstrate how nested sampling can be used for inference and model comparison in biological sciences. We present a reanalysis of data from experimental infection of mice with Salmonella enterica showing the distribution of bacteria in liver cells. In addition to confirming the main finding of the original analysis, which relied on AIC, our approach provides: (a) integration across the parameter space, (b) estimation of the posterior parameter distributions (with visualisations of parameter correlations), and (c) estimation of the posterior predictive distributions for goodness-of-fit assessments of the models. The goodness-of-fit results suggest that alternative mechanistic models and a relaxation of the quasi-stationary assumption should be considered. PMID:24376528

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

A Bayesian blind survey for cold molecular gas in the Universe

NASA Astrophysics Data System (ADS)

Lentati, L.; Carilli, C.; Alexander, P.; Walter, F.; Decarli, R.

2014-10-01

A new Bayesian method for performing an image domain search for line-emitting galaxies is presented. The method uses both spatial and spectral information to robustly determine the source properties, employing either simple Gaussian, or other physically motivated models whilst using the evidence to determine the probability that the source is real. In this paper, we describe the method, and its application to both a simulated data set, and a blind survey for cold molecular gas using observations of the Hubble Deep Field-North taken with the Plateau de Bure Interferometer. We make a total of six robust detections in the survey, five of which have counterparts in other observing bands. We identify the most secure detections found in a previous investigation, while finding one new probable line source with an optical ID not seen in the previous analysis. This study acts as a pilot application of Bayesian statistics to future searches to be carried out both for low-J CO transitions of high-redshift galaxies using the Jansky Very Large Array (JVLA), and at millimetre wavelengths with Atacama Large Millimeter/submillimeter Array (ALMA), enabling the inference of robust scientific conclusions about the history of the molecular gas properties of star-forming galaxies in the Universe through cosmic time.

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

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 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.

[Bayesian approach for the cost-effectiveness evaluation of healthcare technologies].

PubMed

Berchialla, Paola; Gregori, Dario; Brunello, Franco; Veltri, Andrea; Petrinco, Michele; Pagano, Eva

2009-01-01

The development of Bayesian statistical methods for the assessment of the cost-effectiveness of health care technologies is reviewed. Although many studies adopt a frequentist approach, several authors have advocated the use of Bayesian methods in health economics. Emphasis has been placed on the advantages of the Bayesian approach, which include: (i) the ability to make more intuitive and meaningful inferences; (ii) the ability to tackle complex problems, such as allowing for the inclusion of patients who generate no cost, thanks to the availability of powerful computational algorithms; (iii) the importance of a full use of quantitative and structural prior information to produce realistic inferences. Much literature comparing the cost-effectiveness of two treatments is based on the incremental cost-effectiveness ratio. However, new methods are arising with the purpose of decision making. These methods are based on a net benefits approach. In the present context, the cost-effectiveness acceptability curves have been pointed out to be intrinsically Bayesian in their formulation. They plot the probability of a positive net benefit against the threshold cost of a unit increase in efficacy.A case study is presented in order to illustrate the Bayesian statistics in the cost-effectiveness analysis. Emphasis is placed on the cost-effectiveness acceptability curves. Advantages and disadvantages of the method described in this paper have been compared to frequentist methods and discussed.

A note on the kappa statistic for clustered dichotomous data.

PubMed

Zhou, Ming; Yang, Zhao

2014-06-30

The kappa statistic is widely used to assess the agreement between two raters. Motivated by a simulation-based cluster bootstrap method to calculate the variance of the kappa statistic for clustered physician-patients dichotomous data, we investigate its special correlation structure and develop a new simple and efficient data generation algorithm. For the clustered physician-patients dichotomous data, based on the delta method and its special covariance structure, we propose a semi-parametric variance estimator for the kappa statistic. An extensive Monte Carlo simulation study is performed to evaluate the performance of the new proposal and five existing methods with respect to the empirical coverage probability, root-mean-square error, and average width of the 95% confidence interval for the kappa statistic. The variance estimator ignoring the dependence within a cluster is generally inappropriate, and the variance estimators from the new proposal, bootstrap-based methods, and the sampling-based delta method perform reasonably well for at least a moderately large number of clusters (e.g., the number of clusters K ⩾50). The new proposal and sampling-based delta method provide convenient tools for efficient computations and non-simulation-based alternatives to the existing bootstrap-based methods. Moreover, the new proposal has acceptable performance even when the number of clusters is as small as K = 25. To illustrate the practical application of all the methods, one psychiatric research data and two simulated clustered physician-patients dichotomous data are analyzed. Copyright © 2014 John Wiley & Sons, Ltd.

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.

Protein construct storage: Bayesian variable selection and prediction with mixtures.

PubMed

Clyde, M A; Parmigiani, G

1998-07-01

Determining optimal conditions for protein storage while maintaining a high level of protein activity is an important question in pharmaceutical research. A designed experiment based on a space-filling design was conducted to understand the effects of factors affecting protein storage and to establish optimal storage conditions. Different model-selection strategies to identify important factors may lead to very different answers about optimal conditions. Uncertainty about which factors are important, or model uncertainty, can be a critical issue in decision-making. We use Bayesian variable selection methods for linear models to identify important variables in the protein storage data, while accounting for model uncertainty. We also use the Bayesian framework to build predictions based on a large family of models, rather than an individual model, and to evaluate the probability that certain candidate storage conditions are optimal.

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.

The Estimation of Tree Posterior Probabilities Using Conditional Clade Probability Distributions

PubMed Central

Larget, Bret

2013-01-01

In this article I introduce the idea of conditional independence of separated subtrees as a principle by which to estimate the posterior probability of trees using conditional clade probability distributions rather than simple sample relative frequencies. I describe an algorithm for these calculations and software which implements these ideas. I show that these alternative calculations are very similar to simple sample relative frequencies for high probability trees but are substantially more accurate for relatively low probability trees. The method allows the posterior probability of unsampled trees to be calculated when these trees contain only clades that are in other sampled trees. Furthermore, the method can be used to estimate the total probability of the set of sampled trees which provides a measure of the thoroughness of a posterior sample. [Bayesian phylogenetics; conditional clade distributions; improved accuracy; posterior probabilities of trees.] PMID:23479066

mBEEF-vdW: Robust fitting of error estimation density functionals

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

Lundgaard, Keld T.; Wellendorff, Jess; Voss, Johannes

Here, we propose a general-purpose semilocal/nonlocal exchange-correlation functional approximation, named mBEEF-vdW. The exchange is a meta generalized gradient approximation, and the correlation is a semilocal and nonlocal mixture, with the Rutgers-Chalmers approximation for van der Waals (vdW) forces. The functional is fitted within the Bayesian error estimation functional (BEEF) framework. We improve the previously used fitting procedures by introducing a robust MM-estimator based loss function, reducing the sensitivity to outliers in the datasets. To more reliably determine the optimal model complexity, we furthermore introduce a generalization of the bootstrap 0.632 estimator with hierarchical bootstrap sampling and geometric mean estimator overmore » the training datasets. Using this estimator, we show that the robust loss function leads to a 10% improvement in the estimated prediction error over the previously used least-squares loss function. The mBEEF-vdW functional is benchmarked against popular density functional approximations over a wide range of datasets relevant for heterogeneous catalysis, including datasets that were not used for its training. Overall, we find that mBEEF-vdW has a higher general accuracy than competing popular functionals, and it is one of the best performing functionals on chemisorption systems, surface energies, lattice constants, and dispersion. We also show the potential-energy curve of graphene on the nickel(111) surface, where mBEEF-vdW matches the experimental binding length. mBEEF-vdW is currently available in gpaw and other density functional theory codes through Libxc, version 3.0.0.« less

mBEEF-vdW: Robust fitting of error estimation density functionals

DOE PAGES

Lundgaard, Keld T.; Wellendorff, Jess; Voss, Johannes; ...

2016-06-15

Here, we propose a general-purpose semilocal/nonlocal exchange-correlation functional approximation, named mBEEF-vdW. The exchange is a meta generalized gradient approximation, and the correlation is a semilocal and nonlocal mixture, with the Rutgers-Chalmers approximation for van der Waals (vdW) forces. The functional is fitted within the Bayesian error estimation functional (BEEF) framework. We improve the previously used fitting procedures by introducing a robust MM-estimator based loss function, reducing the sensitivity to outliers in the datasets. To more reliably determine the optimal model complexity, we furthermore introduce a generalization of the bootstrap 0.632 estimator with hierarchical bootstrap sampling and geometric mean estimator overmore » the training datasets. Using this estimator, we show that the robust loss function leads to a 10% improvement in the estimated prediction error over the previously used least-squares loss function. The mBEEF-vdW functional is benchmarked against popular density functional approximations over a wide range of datasets relevant for heterogeneous catalysis, including datasets that were not used for its training. Overall, we find that mBEEF-vdW has a higher general accuracy than competing popular functionals, and it is one of the best performing functionals on chemisorption systems, surface energies, lattice constants, and dispersion. We also show the potential-energy curve of graphene on the nickel(111) surface, where mBEEF-vdW matches the experimental binding length. mBEEF-vdW is currently available in gpaw and other density functional theory codes through Libxc, version 3.0.0.« less

Inference of reaction rate parameters based on summary statistics from experiments

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

Khalil, Mohammad; Chowdhary, Kamaljit Singh; Safta, Cosmin

Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H 2/O 2-mechanism chain branching reaction H + O 2 → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the givenmore » summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize Gauss-Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity in the model, the consistent data sets all res ult in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogen-air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.« less

Inference of reaction rate parameters based on summary statistics from experiments

DOE PAGES

Khalil, Mohammad; Chowdhary, Kamaljit Singh; Safta, Cosmin; ...

2016-10-15

Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H 2/O 2-mechanism chain branching reaction H + O 2 → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the givenmore » summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize Gauss-Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity in the model, the consistent data sets all res ult in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogen-air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.« less

Probabilistic risk assessment for a loss of coolant accident in McMaster Nuclear Reactor and application of reliability physics model for modeling human reliability

NASA Astrophysics Data System (ADS)

Ha, Taesung

A probabilistic risk assessment (PRA) was conducted for a loss of coolant accident, (LOCA) in the McMaster Nuclear Reactor (MNR). A level 1 PRA was completed including event sequence modeling, system modeling, and quantification. To support the quantification of the accident sequence identified, data analysis using the Bayesian method and human reliability analysis (HRA) using the accident sequence evaluation procedure (ASEP) approach were performed. Since human performance in research reactors is significantly different from that in power reactors, a time-oriented HRA model (reliability physics model) was applied for the human error probability (HEP) estimation of the core relocation. This model is based on two competing random variables: phenomenological time and performance time. The response surface and direct Monte Carlo simulation with Latin Hypercube sampling were applied for estimating the phenomenological time, whereas the performance time was obtained from interviews with operators. An appropriate probability distribution for the phenomenological time was assigned by statistical goodness-of-fit tests. The human error probability (HEP) for the core relocation was estimated from these two competing quantities: phenomenological time and operators' performance time. The sensitivity of each probability distribution in human reliability estimation was investigated. In order to quantify the uncertainty in the predicted HEPs, a Bayesian approach was selected due to its capability of incorporating uncertainties in model itself and the parameters in that model. The HEP from the current time-oriented model was compared with that from the ASEP approach. Both results were used to evaluate the sensitivity of alternative huinan reliability modeling for the manual core relocation in the LOCA risk model. This exercise demonstrated the applicability of a reliability physics model supplemented with a. Bayesian approach for modeling human reliability and its potential usefulness of quantifying model uncertainty as sensitivity analysis in the PRA model.

Adaptive Randomization of Neratinib in Early Breast Cancer.

PubMed

Park, John W; Liu, Minetta C; Yee, Douglas; Yau, Christina; van 't Veer, Laura J; Symmans, W Fraser; Paoloni, Melissa; Perlmutter, Jane; Hylton, Nola M; Hogarth, Michael; DeMichele, Angela; Buxton, Meredith B; Chien, A Jo; Wallace, Anne M; Boughey, Judy C; Haddad, Tufia C; Chui, Stephen Y; Kemmer, Kathleen A; Kaplan, Henry G; Isaacs, Claudine; Nanda, Rita; Tripathy, Debasish; Albain, Kathy S; Edmiston, Kirsten K; Elias, Anthony D; Northfelt, Donald W; Pusztai, Lajos; Moulder, Stacy L; Lang, Julie E; Viscusi, Rebecca K; Euhus, David M; Haley, Barbara B; Khan, Qamar J; Wood, William C; Melisko, Michelle; Schwab, Richard; Helsten, Teresa; Lyandres, Julia; Davis, Sarah E; Hirst, Gillian L; Sanil, Ashish; Esserman, Laura J; Berry, Donald A

2016-07-07

The heterogeneity of breast cancer makes identifying effective therapies challenging. The I-SPY 2 trial, a multicenter, adaptive phase 2 trial of neoadjuvant therapy for high-risk clinical stage II or III breast cancer, evaluated multiple new agents added to standard chemotherapy to assess the effects on rates of pathological complete response (i.e., absence of residual cancer in the breast or lymph nodes at the time of surgery). We used adaptive randomization to compare standard neoadjuvant chemotherapy plus the tyrosine kinase inhibitor neratinib with control. Eligible women were categorized according to eight biomarker subtypes on the basis of human epidermal growth factor receptor 2 (HER2) status, hormone-receptor status, and risk according to a 70-gene profile. Neratinib was evaluated against control with regard to 10 biomarker signatures (prospectively defined combinations of subtypes). The primary end point was pathological complete response. Volume changes on serial magnetic resonance imaging were used to assess the likelihood of such a response in each patient. Adaptive assignment to experimental groups within each disease subtype was based on Bayesian probabilities of the superiority of the treatment over control. Enrollment in the experimental group was stopped when the 85% Bayesian predictive probability of success in a confirmatory phase 3 trial of neoadjuvant therapy reached a prespecified threshold for any biomarker signature ("graduation"). Enrollment was stopped for futility if the probability fell to below 10% for every biomarker signature. Neratinib reached the prespecified efficacy threshold with regard to the HER2-positive, hormone-receptor-negative signature. Among patients with HER2-positive, hormone-receptor-negative cancer, the mean estimated rate of pathological complete response was 56% (95% Bayesian probability interval [PI], 37 to 73%) among 115 patients in the neratinib group, as compared with 33% among 78 controls (95% PI, 11 to 54%). The final predictive probability of success in phase 3 testing was 79%. Neratinib added to standard therapy was highly likely to result in higher rates of pathological complete response than standard chemotherapy with trastuzumab among patients with HER2-positive, hormone-receptor-negative breast cancer. (Funded by QuantumLeap Healthcare Collaborative and others; I-SPY 2 TRIAL ClinicalTrials.gov number, NCT01042379.).

An agglomerative hierarchical clustering approach to visualisation in Bayesian clustering problems

PubMed Central

Dawson, Kevin J.; Belkhir, Khalid

2009-01-01

Clustering problems (including the clustering of individuals into outcrossing populations, hybrid generations, full-sib families and selfing lines) have recently received much attention in population genetics. In these clustering problems, the parameter of interest is a partition of the set of sampled individuals, - the sample partition. In a fully Bayesian approach to clustering problems of this type, our knowledge about the sample partition is represented by a probability distribution on the space of possible sample partitions. Since the number of possible partitions grows very rapidly with the sample size, we can not visualise this probability distribution in its entirety, unless the sample is very small. As a solution to this visualisation problem, we recommend using an agglomerative hierarchical clustering algorithm, which we call the exact linkage algorithm. This algorithm is a special case of the maximin clustering algorithm that we introduced previously. The exact linkage algorithm is now implemented in our software package Partition View. The exact linkage algorithm takes the posterior co-assignment probabilities as input, and yields as output a rooted binary tree, - or more generally, a forest of such trees. Each node of this forest defines a set of individuals, and the node height is the posterior co-assignment probability of this set. This provides a useful visual representation of the uncertainty associated with the assignment of individuals to categories. It is also a useful starting point for a more detailed exploration of the posterior distribution in terms of the co-assignment probabilities. PMID:19337306

Reliable evaluation of the quantal determinants of synaptic efficacy using Bayesian analysis

PubMed Central

Beato, M.

2013-01-01

Communication between neurones in the central nervous system depends on synaptic transmission. The efficacy of synapses is determined by pre- and postsynaptic factors that can be characterized using quantal parameters such as the probability of neurotransmitter release, number of release sites, and quantal size. Existing methods of estimating the quantal parameters based on multiple probability fluctuation analysis (MPFA) are limited by their requirement for long recordings to acquire substantial data sets. We therefore devised an algorithm, termed Bayesian Quantal Analysis (BQA), that can yield accurate estimates of the quantal parameters from data sets of as small a size as 60 observations for each of only 2 conditions of release probability. Computer simulations are used to compare its performance in accuracy with that of MPFA, while varying the number of observations and the simulated range in release probability. We challenge BQA with realistic complexities characteristic of complex synapses, such as increases in the intra- or intersite variances, and heterogeneity in release probabilities. Finally, we validate the method using experimental data obtained from electrophysiological recordings to show that the effect of an antagonist on postsynaptic receptors is correctly characterized by BQA by a specific reduction in the estimates of quantal size. Since BQA routinely yields reliable estimates of the quantal parameters from small data sets, it is ideally suited to identify the locus of synaptic plasticity for experiments in which repeated manipulations of the recording environment are unfeasible. PMID:23076101

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.

A Prior for Neural Networks utilizing Enclosing Spheres for Normalization

NASA Astrophysics Data System (ADS)

v. Toussaint, U.; Gori, S.; Dose, V.

2004-11-01

Neural Networks are famous for their advantageous flexibility for problems when there is insufficient knowledge to set up a proper model. On the other hand this flexibility can cause over-fitting and can hamper the generalization properties of neural networks. Many approaches to regularize NN have been suggested but most of them based on ad-hoc arguments. Employing the principle of transformation invariance we derive a general prior in accordance with the Bayesian probability theory for a class of feedforward networks. Optimal networks are determined by Bayesian model comparison verifying the applicability of this approach.

Dealing with uncertainty in landscape genetic resistance models: a case of three co-occurring marsupials.

PubMed

Dudaniec, Rachael Y; Worthington Wilmer, Jessica; Hanson, Jeffrey O; Warren, Matthew; Bell, Sarah; Rhodes, Jonathan R

2016-01-01

Landscape genetics lacks explicit methods for dealing with the uncertainty in landscape resistance estimation, which is particularly problematic when sample sizes of individuals are small. Unless uncertainty can be quantified, valuable but small data sets may be rendered unusable for conservation purposes. We offer a method to quantify uncertainty in landscape resistance estimates using multimodel inference as an improvement over single model-based inference. We illustrate the approach empirically using co-occurring, woodland-preferring Australian marsupials within a common study area: two arboreal gliders (Petaurus breviceps, and Petaurus norfolcensis) and one ground-dwelling antechinus (Antechinus flavipes). First, we use maximum-likelihood and a bootstrap procedure to identify the best-supported isolation-by-resistance model out of 56 models defined by linear and non-linear resistance functions. We then quantify uncertainty in resistance estimates by examining parameter selection probabilities from the bootstrapped data. The selection probabilities provide estimates of uncertainty in the parameters that drive the relationships between landscape features and resistance. We then validate our method for quantifying uncertainty using simulated genetic and landscape data showing that for most parameter combinations it provides sensible estimates of uncertainty. We conclude that small data sets can be informative in landscape genetic analyses provided uncertainty can be explicitly quantified. Being explicit about uncertainty in landscape genetic models will make results more interpretable and useful for conservation decision-making, where dealing with uncertainty is critical. © 2015 John Wiley & Sons Ltd.

Kolmogorov-Smirnov test for spatially correlated data

USGS Publications Warehouse

Olea, R.A.; Pawlowsky-Glahn, V.

2009-01-01

The Kolmogorov-Smirnov test is a convenient method for investigating whether two underlying univariate probability distributions can be regarded as undistinguishable from each other or whether an underlying probability distribution differs from a hypothesized distribution. Application of the test requires that the sample be unbiased and the outcomes be independent and identically distributed, conditions that are violated in several degrees by spatially continuous attributes, such as topographical elevation. A generalized form of the bootstrap method is used here for the purpose of modeling the distribution of the statistic D of the Kolmogorov-Smirnov test. The innovation is in the resampling, which in the traditional formulation of bootstrap is done by drawing from the empirical sample with replacement presuming independence. The generalization consists of preparing resamplings with the same spatial correlation as the empirical sample. This is accomplished by reading the value of unconditional stochastic realizations at the sampling locations, realizations that are generated by simulated annealing. The new approach was tested by two empirical samples taken from an exhaustive sample closely following a lognormal distribution. One sample was a regular, unbiased sample while the other one was a clustered, preferential sample that had to be preprocessed. Our results show that the p-value for the spatially correlated case is always larger that the p-value of the statistic in the absence of spatial correlation, which is in agreement with the fact that the information content of an uncorrelated sample is larger than the one for a spatially correlated sample of the same size. ?? Springer-Verlag 2008.

A comparison of bootstrap methods and an adjusted bootstrap approach for estimating the prediction error in microarray classification.

PubMed

Jiang, Wenyu; Simon, Richard

2007-12-20

This paper first provides a critical review on some existing methods for estimating the prediction error in classifying microarray data where the number of genes greatly exceeds the number of specimens. Special attention is given to the bootstrap-related methods. When the sample size n is small, we find that all the reviewed methods suffer from either substantial bias or variability. We introduce a repeated leave-one-out bootstrap (RLOOB) method that predicts for each specimen in the sample using bootstrap learning sets of size ln. We then propose an adjusted bootstrap (ABS) method that fits a learning curve to the RLOOB estimates calculated with different bootstrap learning set sizes. The ABS method is robust across the situations we investigate and provides a slightly conservative estimate for the prediction error. Even with small samples, it does not suffer from large upward bias as the leave-one-out bootstrap and the 0.632+ bootstrap, and it does not suffer from large variability as the leave-one-out cross-validation in microarray applications. Copyright (c) 2007 John Wiley & Sons, Ltd.

Probability-Based Recognition Framework for Underwater Landmarks Using Sonar Images †.

PubMed

Lee, Yeongjun; Choi, Jinwoo; Ko, Nak Yong; Choi, Hyun-Taek

2017-08-24

This paper proposes a probability-based framework for recognizing underwater landmarks using sonar images. Current recognition methods use a single image, which does not provide reliable results because of weaknesses of the sonar image such as unstable acoustic source, many speckle noises, low resolution images, single channel image, and so on. However, using consecutive sonar images, if the status-i.e., the existence and identity (or name)-of an object is continuously evaluated by a stochastic method, the result of the recognition method is available for calculating the uncertainty, and it is more suitable for various applications. Our proposed framework consists of three steps: (1) candidate selection, (2) continuity evaluation, and (3) Bayesian feature estimation. Two probability methods-particle filtering and Bayesian feature estimation-are used to repeatedly estimate the continuity and feature of objects in consecutive images. Thus, the status of the object is repeatedly predicted and updated by a stochastic method. Furthermore, we develop an artificial landmark to increase detectability by an imaging sonar, which we apply to the characteristics of acoustic waves, such as instability and reflection depending on the roughness of the reflector surface. The proposed method is verified by conducting basin experiments, and the results are presented.

Bayesian source tracking via focalization and marginalization in an uncertain Mediterranean Sea environment.

PubMed

Dosso, Stan E; Wilmut, Michael J; Nielsen, Peter L

2010-07-01

This paper applies Bayesian source tracking in an uncertain environment to Mediterranean Sea data, and investigates the resulting tracks and track uncertainties as a function of data information content (number of data time-segments, number of frequencies, and signal-to-noise ratio) and of prior information (environmental uncertainties and source-velocity constraints). To track low-level sources, acoustic data recorded for multiple time segments (corresponding to multiple source positions along the track) are inverted simultaneously. Environmental uncertainty is addressed by including unknown water-column and seabed properties as nuisance parameters in an augmented inversion. Two approaches are considered: Focalization-tracking maximizes the posterior probability density (PPD) over the unknown source and environmental parameters. Marginalization-tracking integrates the PPD over environmental parameters to obtain a sequence of joint marginal probability distributions over source coordinates, from which the most-probable track and track uncertainties can be extracted. Both approaches apply track constraints on the maximum allowable vertical and radial source velocity. The two approaches are applied for towed-source acoustic data recorded at a vertical line array at a shallow-water test site in the Mediterranean Sea where previous geoacoustic studies have been carried out.

A Bayesian Approach to Evaluating Consistency between Climate Model Output and Observations

NASA Astrophysics Data System (ADS)

Braverman, A. J.; Cressie, N.; Teixeira, J.

2010-12-01

Like other scientific and engineering problems that involve physical modeling of complex systems, climate models can be evaluated and diagnosed by comparing their output to observations of similar quantities. Though the global remote sensing data record is relatively short by climate research standards, these data offer opportunities to evaluate model predictions in new ways. For example, remote sensing data are spatially and temporally dense enough to provide distributional information that goes beyond simple moments to allow quantification of temporal and spatial dependence structures. In this talk, we propose a new method for exploiting these rich data sets using a Bayesian paradigm. For a collection of climate models, we calculate posterior probabilities its members best represent the physical system each seeks to reproduce. The posterior probability is based on the likelihood that a chosen summary statistic, computed from observations, would be obtained when the model's output is considered as a realization from a stochastic process. By exploring how posterior probabilities change with different statistics, we may paint a more quantitative and complete picture of the strengths and weaknesses of the models relative to the observations. We demonstrate our method using model output from the CMIP archive, and observations from NASA's Atmospheric Infrared Sounder.

Fast, Exact Bootstrap Principal Component Analysis for p > 1 million

PubMed Central

Fisher, Aaron; Caffo, Brian; Schwartz, Brian; Zipunnikov, Vadim

2015-01-01

Many have suggested a bootstrap procedure for estimating the sampling variability of principal component analysis (PCA) results. However, when the number of measurements per subject (p) is much larger than the number of subjects (n), calculating and storing the leading principal components from each bootstrap sample can be computationally infeasible. To address this, we outline methods for fast, exact calculation of bootstrap principal components, eigenvalues, and scores. Our methods leverage the fact that all bootstrap samples occupy the same n-dimensional subspace as the original sample. As a result, all bootstrap principal components are limited to the same n-dimensional subspace and can be efficiently represented by their low dimensional coordinates in that subspace. Several uncertainty metrics can be computed solely based on the bootstrap distribution of these low dimensional coordinates, without calculating or storing the p-dimensional bootstrap components. Fast bootstrap PCA is applied to a dataset of sleep electroencephalogram recordings (p = 900, n = 392), and to a dataset of brain magnetic resonance images (MRIs) (p ≈ 3 million, n = 352). For the MRI dataset, our method allows for standard errors for the first 3 principal components based on 1000 bootstrap samples to be calculated on a standard laptop in 47 minutes, as opposed to approximately 4 days with standard methods. PMID:27616801

Speeding Up Non-Parametric Bootstrap Computations for Statistics Based on Sample Moments in Small/Moderate Sample Size Applications

PubMed Central

Chaibub Neto, Elias

2015-01-01

In this paper we propose a vectorized implementation of the non-parametric bootstrap for statistics based on sample moments. Basically, we adopt the multinomial sampling formulation of the non-parametric bootstrap, and compute bootstrap replications of sample moment statistics by simply weighting the observed data according to multinomial counts instead of evaluating the statistic on a resampled version of the observed data. Using this formulation we can generate a matrix of bootstrap weights and compute the entire vector of bootstrap replications with a few matrix multiplications. Vectorization is particularly important for matrix-oriented programming languages such as R, where matrix/vector calculations tend to be faster than scalar operations implemented in a loop. We illustrate the application of the vectorized implementation in real and simulated data sets, when bootstrapping Pearson’s sample correlation coefficient, and compared its performance against two state-of-the-art R implementations of the non-parametric bootstrap, as well as a straightforward one based on a for loop. Our investigations spanned varying sample sizes and number of bootstrap replications. The vectorized bootstrap compared favorably against the state-of-the-art implementations in all cases tested, and was remarkably/considerably faster for small/moderate sample sizes. The same results were observed in the comparison with the straightforward implementation, except for large sample sizes, where the vectorized bootstrap was slightly slower than the straightforward implementation due to increased time expenditures in the generation of weight matrices via multinomial sampling. PMID:26125965

Particle identification in ALICE: a Bayesian approach

NASA Astrophysics Data System (ADS)

Adam, J.; Adamová, D.; Aggarwal, M. M.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, S.; Ahn, S. U.; Aiola, S.; Akindinov, A.; Alam, S. N.; Albuquerque, D. S. D.; Aleksandrov, D.; Alessandro, B.; Alexandre, D.; Alfaro Molina, R.; Alici, A.; Alkin, A.; Almaraz, J. R. M.; Alme, J.; Alt, T.; Altinpinar, S.; Altsybeev, I.; Alves Garcia Prado, C.; Andrei, C.; Andronic, A.; Anguelov, V.; Antičić, T.; Antinori, F.; Antonioli, P.; Aphecetche, L.; Appelshäuser, H.; Arcelli, S.; Arnaldi, R.; Arnold, O. W.; Arsene, I. C.; Arslandok, M.; Audurier, B.; Augustinus, A.; Averbeck, R.; Azmi, M. D.; Badalà, A.; Baek, Y. W.; Bagnasco, S.; Bailhache, R.; Bala, R.; Balasubramanian, S.; Baldisseri, A.; Baral, R. C.; Barbano, A. M.; Barbera, R.; Barile, F.; Barnaföldi, G. G.; Barnby, L. S.; Barret, V.; Bartalini, P.; Barth, K.; Bartke, J.; Bartsch, E.; Basile, M.; Bastid, N.; Basu, S.; Bathen, B.; Batigne, G.; Batista Camejo, A.; Batyunya, B.; Batzing, P. C.; Bearden, I. G.; Beck, H.; Bedda, C.; Behera, N. K.; Belikov, I.; Bellini, F.; Bello Martinez, H.; Bellwied, R.; Belmont, R.; Belmont-Moreno, E.; Belyaev, V.; Benacek, P.; Bencedi, G.; Beole, S.; Berceanu, I.; Bercuci, A.; Berdnikov, Y.; Berenyi, D.; Bertens, R. A.; Berzano, D.; Betev, L.; Bhasin, A.; Bhat, I. R.; Bhati, A. K.; Bhattacharjee, B.; Bhom, J.; Bianchi, L.; Bianchi, N.; Bianchin, C.; Bielčík, J.; Bielčíková, J.; Bilandzic, A.; Biro, G.; Biswas, R.; Biswas, S.; Bjelogrlic, S.; Blair, J. T.; Blau, D.; Blume, C.; Bock, F.; Bogdanov, A.; Bøggild, H.; Boldizsár, L.; Bombara, M.; Book, J.; Borel, H.; Borissov, A.; Borri, M.; Bossú, F.; Botta, E.; Bourjau, C.; Braun-Munzinger, P.; Bregant, M.; Breitner, T.; Broker, T. A.; Browning, T. A.; Broz, M.; Brucken, E. J.; Bruna, E.; Bruno, G. E.; Budnikov, D.; Buesching, H.; Bufalino, S.; Buncic, P.; Busch, O.; Buthelezi, Z.; Butt, J. B.; Buxton, J. T.; Cabala, J.; Caffarri, D.; Cai, X.; Caines, H.; Calero Diaz, L.; Caliva, A.; Calvo Villar, E.; Camerini, P.; Carena, F.; Carena, W.; Carnesecchi, F.; Castillo Castellanos, J.; Castro, A. J.; Casula, E. A. R.; Ceballos Sanchez, C.; Cepila, J.; Cerello, P.; Cerkala, J.; Chang, B.; Chapeland, S.; Chartier, M.; Charvet, J. L.; Chattopadhyay, S.; Chattopadhyay, S.; Chauvin, A.; Chelnokov, V.; Cherney, M.; Cheshkov, C.; Cheynis, B.; Chibante Barroso, V.; Chinellato, D. D.; Cho, S.; Chochula, P.; Choi, K.; Chojnacki, M.; Choudhury, S.; Christakoglou, P.; Christensen, C. H.; Christiansen, P.; Chujo, T.; Chung, S. U.; Cicalo, C.; Cifarelli, L.; Cindolo, F.; Cleymans, J.; Colamaria, F.; Colella, D.; Collu, A.; Colocci, M.; Conesa Balbastre, G.; Conesa del Valle, Z.; Connors, M. E.; Contreras, J. G.; Cormier, T. M.; Corrales Morales, Y.; Cortés Maldonado, I.; Cortese, P.; Cosentino, M. R.; Costa, F.; Crochet, P.; Cruz Albino, R.; Cuautle, E.; Cunqueiro, L.; Dahms, T.; Dainese, A.; Danisch, M. C.; Danu, A.; Das, D.; Das, I.; Das, S.; Dash, A.; Dash, S.; De, S.; De Caro, A.; de Cataldo, G.; de Conti, C.; de Cuveland, J.; De Falco, A.; De Gruttola, D.; De Marco, N.; De Pasquale, S.; Deisting, A.; Deloff, A.; Dénes, E.; Deplano, C.; Dhankher, P.; Di Bari, D.; Di Mauro, A.; Di Nezza, P.; Diaz Corchero, M. A.; Dietel, T.; Dillenseger, P.; Divià, R.; Djuvsland, Ø.; Dobrin, A.; Domenicis Gimenez, D.; Dönigus, B.; Dordic, O.; Drozhzhova, T.; Dubey, A. K.; Dubla, A.; Ducroux, L.; Dupieux, P.; Ehlers, R. J.; Elia, D.; Endress, E.; Engel, H.; Epple, E.; Erazmus, B.; Erdemir, I.; Erhardt, F.; Espagnon, B.; Estienne, M.; Esumi, S.; Eum, J.; Evans, D.; Evdokimov, S.; Eyyubova, G.; Fabbietti, L.; Fabris, D.; Faivre, J.; Fantoni, A.; Fasel, M.; Feldkamp, L.; Feliciello, A.; Feofilov, G.; Ferencei, J.; Fernández Téllez, A.; Ferreiro, E. G.; Ferretti, A.; Festanti, A.; Feuillard, V. J. G.; Figiel, J.; Figueredo, M. A. S.; Filchagin, S.; Finogeev, D.; Fionda, F. M.; Fiore, E. M.; Fleck, M. G.; Floris, M.; Foertsch, S.; Foka, P.; Fokin, S.; Fragiacomo, E.; Francescon, A.; Frankenfeld, U.; Fronze, G. G.; Fuchs, U.; Furget, C.; Furs, A.; Fusco Girard, M.; Gaardhøje, J. J.; Gagliardi, M.; Gago, A. M.; Gallio, M.; Gangadharan, D. R.; Ganoti, P.; Gao, C.; Garabatos, C.; Garcia-Solis, E.; Gargiulo, C.; Gasik, P.; Gauger, E. F.; Germain, M.; Gheata, A.; Gheata, M.; Ghosh, P.; Ghosh, S. K.; Gianotti, P.; Giubellino, P.; Giubilato, P.; Gladysz-Dziadus, E.; Glässel, P.; Goméz Coral, D. M.; Gomez Ramirez, A.; Gonzalez, A. S.; Gonzalez, V.; González-Zamora, P.; Gorbunov, S.; Görlich, L.; Gotovac, S.; Grabski, V.; Grachov, O. A.; Graczykowski, L. K.; Graham, K. L.; Grelli, A.; Grigoras, A.; Grigoras, C.; Grigoriev, V.; Grigoryan, A.; Grigoryan, S.; Grinyov, B.; Grion, N.; Gronefeld, J. M.; Grosse-Oetringhaus, J. F.; Grosso, R.; Guber, F.; Guernane, R.; Guerzoni, B.; Gulbrandsen, K.; Gunji, T.; Gupta, A.; Gupta, R.; Haake, R.; Haaland, Ø.; Hadjidakis, C.; Haiduc, M.; Hamagaki, H.; Hamar, G.; Hamon, J. C.; Harris, J. W.; Harton, A.; Hatzifotiadou, D.; Hayashi, S.; Heckel, S. T.; Hellbär, E.; Helstrup, H.; Herghelegiu, A.; Herrera Corral, G.; Hess, B. A.; Hetland, K. F.; Hillemanns, H.; Hippolyte, B.; Horak, D.; Hosokawa, R.; Hristov, P.; Humanic, T. J.; Hussain, N.; Hussain, T.; Hutter, D.; Hwang, D. S.; Ilkaev, R.; Inaba, M.; Incani, E.; Ippolitov, M.; Irfan, M.; Ivanov, M.; Ivanov, V.; Izucheev, V.; Jacazio, N.; Jacobs, P. M.; Jadhav, M. B.; Jadlovska, S.; Jadlovsky, J.; Jahnke, C.; Jakubowska, M. J.; Jang, H. J.; Janik, M. A.; Jayarathna, P. H. S. Y.; Jena, C.; Jena, S.; Jimenez Bustamante, R. T.; Jones, P. G.; Jusko, A.; Kalinak, P.; Kalweit, A.; Kamin, J.; Kang, J. H.; Kaplin, V.; Kar, S.; Karasu Uysal, A.; Karavichev, O.; Karavicheva, T.; Karayan, L.; Karpechev, E.; Kebschull, U.; Keidel, R.; Keijdener, D. L. D.; Keil, M.; Mohisin Khan, M.; Khan, P.; Khan, S. A.; Khanzadeev, A.; Kharlov, Y.; Kileng, B.; Kim, D. W.; Kim, D. J.; Kim, D.; Kim, H.; Kim, J. S.; Kim, M.; Kim, S.; Kim, T.; Kirsch, S.; Kisel, I.; Kiselev, S.; Kisiel, A.; Kiss, G.; Klay, J. L.; Klein, C.; Klein, J.; Klein-Bösing, C.; Klewin, S.; Kluge, A.; Knichel, M. L.; Knospe, A. G.; Kobdaj, C.; Kofarago, M.; Kollegger, T.; Kolojvari, A.; Kondratiev, V.; Kondratyeva, N.; Kondratyuk, E.; Konevskikh, A.; Kopcik, M.; Kostarakis, P.; Kour, M.; Kouzinopoulos, C.; Kovalenko, O.; Kovalenko, V.; Kowalski, M.; Koyithatta Meethaleveedu, G.; Králik, I.; Kravčáková, A.; Krivda, M.; Krizek, F.; Kryshen, E.; Krzewicki, M.; Kubera, A. M.; Kučera, V.; Kuhn, C.; Kuijer, P. G.; Kumar, A.; Kumar, J.; Kumar, L.; Kumar, S.; Kurashvili, P.; Kurepin, A.; Kurepin, A. B.; Kuryakin, A.; Kweon, M. J.; Kwon, Y.; La Pointe, S. L.; La Rocca, P.; Ladron de Guevara, P.; Lagana Fernandes, C.; Lakomov, I.; Langoy, R.; Lara, C.; Lardeux, A.; Lattuca, A.; Laudi, E.; Lea, R.; Leardini, L.; Lee, G. R.; Lee, S.; Lehas, F.; Lemmon, R. C.; Lenti, V.; Leogrande, E.; León Monzón, I.; León Vargas, H.; Leoncino, M.; Lévai, P.; Li, S.; Li, X.; Lien, J.; Lietava, R.; Lindal, S.; Lindenstruth, V.; Lippmann, C.; Lisa, M. A.; Ljunggren, H. M.; Lodato, D. F.; Loenne, P. I.; Loginov, V.; Loizides, C.; Lopez, X.; López Torres, E.; Lowe, A.; Luettig, P.; Lunardon, M.; Luparello, G.; Lutz, T. H.; Maevskaya, A.; Mager, M.; Mahajan, S.; Mahmood, S. M.; Maire, A.; Majka, R. D.; Malaev, M.; Maldonado Cervantes, I.; Malinina, L.; Mal'Kevich, D.; Malzacher, P.; Mamonov, A.; Manko, V.; Manso, F.; Manzari, V.; Marchisone, M.; Mareš, J.; Margagliotti, G. V.; Margotti, A.; Margutti, J.; Marín, A.; Markert, C.; Marquard, M.; Martin, N. A.; Martin Blanco, J.; Martinengo, P.; Martínez, M. I.; Martínez García, G.; Martinez Pedreira, M.; Mas, A.; Masciocchi, S.; Masera, M.; Masoni, A.; Mastroserio, A.; Matyja, A.; Mayer, C.; Mazer, J.; Mazzoni, M. A.; Mcdonald, D.; Meddi, F.; Melikyan, Y.; Menchaca-Rocha, A.; Meninno, E.; Mercado Pérez, J.; Meres, M.; Miake, Y.; Mieskolainen, M. M.; Mikhaylov, K.; Milano, L.; Milosevic, J.; Mischke, A.; Mishra, A. N.; Miśkowiec, D.; Mitra, J.; Mitu, C. M.; Mohammadi, N.; Mohanty, B.; Molnar, L.; Montaño Zetina, L.; Montes, E.; Moreira De Godoy, D. A.; Moreno, L. A. P.; Moretto, S.; Morreale, A.; Morsch, A.; Muccifora, V.; Mudnic, E.; Mühlheim, D.; Muhuri, S.; Mukherjee, M.; Mulligan, J. D.; Munhoz, M. G.; Munzer, R. H.; Murakami, H.; Murray, S.; Musa, L.; Musinsky, J.; Naik, B.; Nair, R.; Nandi, B. K.; Nania, R.; Nappi, E.; Naru, M. U.; Natal da Luz, H.; Nattrass, C.; Navarro, S. R.; Nayak, K.; Nayak, R.; Nayak, T. K.; Nazarenko, S.; Nedosekin, A.; Nellen, L.; Ng, F.; Nicassio, M.; Niculescu, M.; Niedziela, J.; Nielsen, B. S.; Nikolaev, S.; Nikulin, S.; Nikulin, V.; Noferini, F.; Nomokonov, P.; Nooren, G.; Noris, J. C. C.; Norman, J.; Nyanin, A.; Nystrand, J.; Oeschler, H.; Oh, S.; Oh, S. K.; Ohlson, A.; Okatan, A.; Okubo, T.; Olah, L.; Oleniacz, J.; Oliveira Da Silva, A. C.; Oliver, M. H.; Onderwaater, J.; Oppedisano, C.; Orava, R.; Oravec, M.; Ortiz Velasquez, A.; Oskarsson, A.; Otwinowski, J.; Oyama, K.; Ozdemir, M.; Pachmayer, Y.; Pagano, D.; Pagano, P.; Paić, G.; Pal, S. K.; Pan, J.; Pandey, A. K.; Papikyan, V.; Pappalardo, G. S.; Pareek, P.; Park, W. J.; Parmar, S.; Passfeld, A.; Paticchio, V.; Patra, R. N.; Paul, B.; Pei, H.; Peitzmann, T.; Pereira Da Costa, H.; Peresunko, D.; Pérez Lara, C. E.; Perez Lezama, E.; Peskov, V.; Pestov, Y.; Petráček, V.; Petrov, V.; Petrovici, M.; Petta, C.; Piano, S.; Pikna, M.; Pillot, P.; Pimentel, L. O. D. L.; Pinazza, O.; Pinsky, L.; Piyarathna, D. B.; Płoskoń, M.; Planinic, M.; Pluta, J.; Pochybova, S.; Podesta-Lerma, P. L. M.; Poghosyan, M. G.; Polichtchouk, B.; Poljak, N.; Poonsawat, W.; Pop, A.; Porteboeuf-Houssais, S.; Porter, J.; Pospisil, J.; Prasad, S. K.; Preghenella, R.; Prino, F.; Pruneau, C. A.; Pshenichnov, I.; Puccio, M.; Puddu, G.; Pujahari, P.; Punin, V.; Putschke, J.; Qvigstad, H.; Rachevski, A.; Raha, S.; Rajput, S.; Rak, J.; Rakotozafindrabe, A.; Ramello, L.; Rami, F.; Raniwala, R.; Raniwala, S.; Räsänen, S. S.; Rascanu, B. T.; Rathee, D.; Read, K. F.; Redlich, K.; Reed, R. J.; Rehman, A.; Reichelt, P.; Reidt, F.; Ren, X.; Renfordt, R.; Reolon, A. R.; Reshetin, A.; Reygers, K.; Riabov, V.; Ricci, R. A.; Richert, T.; Richter, M.; Riedler, P.; Riegler, W.; Riggi, F.; Ristea, C.; Rocco, E.; Rodríguez Cahuantzi, M.; Rodriguez Manso, A.; Røed, K.; Rogochaya, E.; Rohr, D.; Röhrich, D.; Ronchetti, F.; Ronflette, L.; Rosnet, P.; Rossi, A.; Roukoutakis, F.; Roy, A.; Roy, C.; Roy, P.; Rubio Montero, A. J.; Rui, R.; Russo, R.; Ryabinkin, E.; Ryabov, Y.; Rybicki, A.; Saarinen, S.; Sadhu, S.; Sadovsky, S.; Šafařík, K.; Sahlmuller, B.; Sahoo, P.; Sahoo, R.; Sahoo, S.; Sahu, P. K.; Saini, J.; Sakai, S.; Saleh, M. A.; Salzwedel, J.; Sambyal, S.; Samsonov, V.; Šándor, L.; Sandoval, A.; Sano, M.; Sarkar, D.; Sarkar, N.; Sarma, P.; Scapparone, E.; Scarlassara, F.; Schiaua, C.; Schicker, R.; Schmidt, C.; Schmidt, H. R.; Schuchmann, S.; Schukraft, J.; Schulc, M.; Schutz, Y.; Schwarz, K.; Schweda, K.; Scioli, G.; Scomparin, E.; Scott, R.; Šefčík, M.; Seger, J. E.; Sekiguchi, Y.; Sekihata, D.; Selyuzhenkov, I.; Senosi, K.; Senyukov, S.; Serradilla, E.; Sevcenco, A.; Shabanov, A.; Shabetai, A.; Shadura, O.; Shahoyan, R.; Shahzad, M. I.; Shangaraev, A.; Sharma, A.; Sharma, M.; Sharma, M.; Sharma, N.; Sheikh, A. I.; Shigaki, K.; Shou, Q.; Shtejer, K.; Sibiriak, Y.; Siddhanta, S.; Sielewicz, K. M.; Siemiarczuk, T.; Silvermyr, D.; Silvestre, C.; Simatovic, G.; Simonetti, G.; Singaraju, R.; Singh, R.; Singha, S.; Singhal, V.; Sinha, B. C.; Sinha, T.; Sitar, B.; Sitta, M.; Skaali, T. B.; Slupecki, M.; Smirnov, N.; Snellings, R. J. M.; Snellman, T. W.; Song, J.; Song, M.; Song, Z.; Soramel, F.; Sorensen, S.; Souza, R. D. de; Sozzi, F.; Spacek, M.; Spiriti, E.; Sputowska, I.; Spyropoulou-Stassinaki, M.; Stachel, J.; Stan, I.; Stankus, P.; Stenlund, E.; Steyn, G.; Stiller, J. H.; Stocco, D.; Strmen, P.; Suaide, A. A. P.; Sugitate, T.; Suire, C.; Suleymanov, M.; Suljic, M.; Sultanov, R.; Šumbera, M.; Sumowidagdo, S.; Szabo, A.; Szanto de Toledo, A.; Szarka, I.; Szczepankiewicz, A.; Szymanski, M.; Tabassam, U.; Takahashi, J.; Tambave, G. J.; Tanaka, N.; Tarhini, M.; Tariq, M.; Tarzila, M. G.; Tauro, A.; Tejeda Muñoz, G.; Telesca, A.; Terasaki, K.; Terrevoli, C.; Teyssier, B.; Thäder, J.; Thakur, D.; Thomas, D.; Tieulent, R.; Timmins, A. R.; Toia, A.; Trogolo, S.; Trombetta, G.; Trubnikov, V.; Trzaska, W. H.; Tsuji, T.; Tumkin, A.; Turrisi, R.; Tveter, T. S.; Ullaland, K.; Uras, A.; Usai, G. L.; Utrobicic, A.; Vala, M.; Valencia Palomo, L.; Vallero, S.; Van Der Maarel, J.; Van Hoorne, J. W.; van Leeuwen, M.; Vanat, T.; Vande Vyvre, P.; Varga, D.; Vargas, A.; Vargyas, M.; Varma, R.; Vasileiou, M.; Vasiliev, A.; Vauthier, A.; Vechernin, V.; Veen, A. M.; Veldhoen, M.; Velure, A.; Vercellin, E.; Vergara Limón, S.; Vernet, R.; Verweij, M.; Vickovic, L.; Viesti, G.; Viinikainen, J.; Vilakazi, Z.; Villalobos Baillie, O.; Villatoro Tello, A.; Vinogradov, A.; Vinogradov, L.; Vinogradov, Y.; Virgili, T.; Vislavicius, V.; Viyogi, Y. P.; Vodopyanov, A.; Völkl, M. A.; Voloshin, K.; Voloshin, S. A.; Volpe, G.; von Haller, B.; Vorobyev, I.; Vranic, D.; Vrláková, J.; Vulpescu, B.; Wagner, B.; Wagner, J.; Wang, H.; Wang, M.; Watanabe, D.; Watanabe, Y.; Weber, M.; Weber, S. G.; Weiser, D. F.; Wessels, J. P.; Westerhoff, U.; Whitehead, A. M.; Wiechula, J.; Wikne, J.; Wilk, G.; Wilkinson, J.; Williams, M. C. S.; Windelband, B.; Winn, M.; Yang, H.; Yang, P.; Yano, S.; Yasin, Z.; Yin, Z.; Yokoyama, H.; Yoo, I.-K.; Yoon, J. H.; Yurchenko, V.; Yushmanov, I.; Zaborowska, A.; Zaccolo, V.; Zaman, A.; Zampolli, C.; Zanoli, H. J. C.; Zaporozhets, S.; Zardoshti, N.; Zarochentsev, A.; Závada, P.; Zaviyalov, N.; Zbroszczyk, H.; Zgura, I. S.; Zhalov, M.; Zhang, H.; Zhang, X.; Zhang, Y.; Zhang, C.; Zhang, Z.; Zhao, C.; Zhigareva, N.; Zhou, D.; Zhou, Y.; Zhou, Z.; Zhu, H.; Zhu, J.; Zichichi, A.; Zimmermann, A.; Zimmermann, M. B.; Zinovjev, G.; Zyzak, M.

2016-05-01

We present a Bayesian approach to particle identification (PID) within the ALICE experiment. The aim is to more effectively combine the particle identification capabilities of its various detectors. After a brief explanation of the adopted methodology and formalism, the performance of the Bayesian PID approach for charged pions, kaons and protons in the central barrel of ALICE is studied. PID is performed via measurements of specific energy loss ( d E/d x) and time of flight. PID efficiencies and misidentification probabilities are extracted and compared with Monte Carlo simulations using high-purity samples of identified particles in the decay channels K0S → π-π+, φ→ K-K+, and Λ→ p π- in p-Pb collisions at √{s_{NN}}=5.02 TeV. In order to thoroughly assess the validity of the Bayesian approach, this methodology was used to obtain corrected pT spectra of pions, kaons, protons, and D0 mesons in pp collisions at √{s}=7 TeV. In all cases, the results using Bayesian PID were found to be consistent with previous measurements performed by ALICE using a standard PID approach. For the measurement of D0 → K-π+, it was found that a Bayesian PID approach gave a higher signal-to-background ratio and a similar or larger statistical significance when compared with standard PID selections, despite a reduced identification efficiency. Finally, we present an exploratory study of the measurement of Λc+ → p K-π+ in pp collisions at √{s}=7 TeV, using the Bayesian approach for the identification of its decay products.

Reply to Budowle, Ge, Chakraborty and Gill-King: use of prior odds for missing persons identifications.

PubMed

Biedermann, Alex; Taroni, Franco; Margot, Pierre

2012-01-31

Prior probabilities represent a core element of the Bayesian probabilistic approach to relatedness testing. This letter opinions on the commentary Use of prior odds for missing persons identifications by Budowle et al., published recently in this journal. Contrary to Budowle et al., we argue that the concept of prior probabilities (i) is not endowed with the notion of objectivity, (ii) is not a case for computation, and (iii) does not require new guidelines edited by the forensic DNA community--as long as probability is properly considered as an expression of personal belief.

Maritime Transportation Risk Assessment of Tianjin Port with Bayesian Belief Networks.

PubMed

Zhang, Jinfen; Teixeira, Ângelo P; Guedes Soares, C; Yan, Xinping; Liu, Kezhong

2016-06-01

This article develops a Bayesian belief network model for the prediction of accident consequences in the Tianjin port. The study starts with a statistical analysis of historical accident data of six years from 2008 to 2013. Then a Bayesian belief network is constructed to express the dependencies between the indicator variables and accident consequences. The statistics and expert knowledge are synthesized in the Bayesian belief network model to obtain the probability distribution of the consequences. By a sensitivity analysis, several indicator variables that have influence on the consequences are identified, including navigational area, ship type and time of the day. The results indicate that the consequences are most sensitive to the position where the accidents occurred, followed by time of day and ship length. The results also reflect that the navigational risk of the Tianjin port is at the acceptable level, despite that there is more room of improvement. These results can be used by the Maritime Safety Administration to take effective measures to enhance maritime safety in the Tianjin port. © 2016 Society for Risk Analysis.

Exact Bayesian p-values for a test of independence in a 2 × 2 contingency table with missing data.

PubMed

Lin, Yan; Lipsitz, Stuart R; Sinha, Debajyoti; Fitzmaurice, Garrett; Lipshultz, Steven

2017-01-01

Altham (Altham PME. Exact Bayesian analysis of a 2 × 2 contingency table, and Fisher's "exact" significance test. J R Stat Soc B 1969; 31: 261-269) showed that a one-sided p-value from Fisher's exact test of independence in a 2 × 2 contingency table is equal to the posterior probability of negative association in the 2 × 2 contingency table under a Bayesian analysis using an improper prior. We derive an extension of Fisher's exact test p-value in the presence of missing data, assuming the missing data mechanism is ignorable (i.e., missing at random or completely at random). Further, we propose Bayesian p-values for a test of independence in a 2 × 2 contingency table with missing data using alternative priors; we also present results from a simulation study exploring the Type I error rate and power of the proposed exact test p-values. An example, using data on the association between blood pressure and a cardiac enzyme, is presented to illustrate the methods.

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

Bayesian stock assessment of Pacific herring in Prince William Sound, Alaska.

PubMed

Muradian, Melissa L; Branch, Trevor A; Moffitt, Steven D; Hulson, Peter-John F

2017-01-01

The Pacific herring (Clupea pallasii) population in Prince William Sound, Alaska crashed in 1993 and has yet to recover, affecting food web dynamics in the Sound and impacting Alaskan communities. To help researchers design and implement the most effective monitoring, management, and recovery programs, a Bayesian assessment of Prince William Sound herring was developed by reformulating the current model used by the Alaska Department of Fish and Game. The Bayesian model estimated pre-fishery spawning biomass of herring age-3 and older in 2013 to be a median of 19,410 mt (95% credibility interval 12,150-31,740 mt), with a 54% probability that biomass in 2013 was below the management limit used to regulate fisheries in Prince William Sound. The main advantages of the Bayesian model are that it can more objectively weight different datasets and provide estimates of uncertainty for model parameters and outputs, unlike the weighted sum-of-squares used in the original model. In addition, the revised model could be used to manage herring stocks with a decision rule that considers both stock status and the uncertainty in stock status.

Adaptability and phenotypic stability of common bean genotypes through Bayesian inference.

PubMed

Corrêa, A M; Teodoro, P E; Gonçalves, M C; Barroso, L M A; Nascimento, M; Santos, A; Torres, F E

2016-04-27

This study used Bayesian inference to investigate the genotype x environment interaction in common bean grown in Mato Grosso do Sul State, and it also evaluated the efficiency of using informative and minimally informative a priori distributions. Six trials were conducted in randomized blocks, and the grain yield of 13 common bean genotypes was assessed. To represent the minimally informative a priori distributions, a probability distribution with high variance was used, and a meta-analysis concept was adopted to represent the informative a priori distributions. Bayes factors were used to conduct comparisons between the a priori distributions. The Bayesian inference was effective for the selection of upright common bean genotypes with high adaptability and phenotypic stability using the Eberhart and Russell method. Bayes factors indicated that the use of informative a priori distributions provided more accurate results than minimally informative a priori distributions. According to Bayesian inference, the EMGOPA-201, BAMBUÍ, CNF 4999, CNF 4129 A 54, and CNFv 8025 genotypes had specific adaptability to favorable environments, while the IAPAR 14 and IAC CARIOCA ETE genotypes had specific adaptability to unfavorable environments.

Enhanced optical alignment of a digital micro mirror device through Bayesian adaptive exploration

NASA Astrophysics Data System (ADS)

Wynne, Kevin B.; Knuth, Kevin H.; Petruccelli, Jonathan

2017-12-01

As the use of Digital Micro Mirror Devices (DMDs) becomes more prevalent in optics research, the ability to precisely locate the Fourier "footprint" of an image beam at the Fourier plane becomes a pressing need. In this approach, Bayesian adaptive exploration techniques were employed to characterize the size and position of the beam on a DMD located at the Fourier plane. It couples a Bayesian inference engine with an inquiry engine to implement the search. The inquiry engine explores the DMD by engaging mirrors and recording light intensity values based on the maximization of the expected information gain. Using the data collected from this exploration, the Bayesian inference engine updates the posterior probability describing the beam's characteristics. The process is iterated until the beam is located to within the desired precision. This methodology not only locates the center and radius of the beam with remarkable precision but accomplishes the task in far less time than a brute force search. The employed approach has applications to system alignment for both Fourier processing and coded aperture design.

Bayesian modelling of the emission spectrum of the Joint European Torus Lithium Beam Emission Spectroscopy system.

PubMed

Kwak, Sehyun; Svensson, J; Brix, M; Ghim, Y-C

2016-02-01

A Bayesian model of the emission spectrum of the JET lithium beam has been developed to infer the intensity of the Li I (2p-2s) line radiation and associated uncertainties. The detected spectrum for each channel of the lithium beam emission spectroscopy system is here modelled by a single Li line modified by an instrumental function, Bremsstrahlung background, instrumental offset, and interference filter curve. Both the instrumental function and the interference filter curve are modelled with non-parametric Gaussian processes. All free parameters of the model, the intensities of the Li line, Bremsstrahlung background, and instrumental offset, are inferred using Bayesian probability theory with a Gaussian likelihood for photon statistics and electronic background noise. The prior distributions of the free parameters are chosen as Gaussians. Given these assumptions, the intensity of the Li line and corresponding uncertainties are analytically available using a Bayesian linear inversion technique. The proposed approach makes it possible to extract the intensity of Li line without doing a separate background subtraction through modulation of the Li beam.

Bayesian stock assessment of Pacific herring in Prince William Sound, Alaska

PubMed Central

Moffitt, Steven D.; Hulson, Peter-John F.

2017-01-01

The Pacific herring (Clupea pallasii) population in Prince William Sound, Alaska crashed in 1993 and has yet to recover, affecting food web dynamics in the Sound and impacting Alaskan communities. To help researchers design and implement the most effective monitoring, management, and recovery programs, a Bayesian assessment of Prince William Sound herring was developed by reformulating the current model used by the Alaska Department of Fish and Game. The Bayesian model estimated pre-fishery spawning biomass of herring age-3 and older in 2013 to be a median of 19,410 mt (95% credibility interval 12,150–31,740 mt), with a 54% probability that biomass in 2013 was below the management limit used to regulate fisheries in Prince William Sound. The main advantages of the Bayesian model are that it can more objectively weight different datasets and provide estimates of uncertainty for model parameters and outputs, unlike the weighted sum-of-squares used in the original model. In addition, the revised model could be used to manage herring stocks with a decision rule that considers both stock status and the uncertainty in stock status. PMID:28222151

Probabilistic hindcasts and projections of the coupled climate, carbon cycle and Atlantic meridional overturning circulation system: a Bayesian fusion of century-scale observations with a simple model

NASA Astrophysics Data System (ADS)

Urban, Nathan M.; Keller, Klaus

2010-10-01

How has the Atlantic Meridional Overturning Circulation (AMOC) varied over the past centuries and what is the risk of an anthropogenic AMOC collapse? We report probabilistic projections of the future climate which improve on previous AMOC projection studies by (i) greatly expanding the considered observational constraints and (ii) carefully sampling the tail areas of the parameter probability distribution function (pdf). We use a Bayesian inversion to constrain a simple model of the coupled climate, carbon cycle and AMOC systems using observations to derive multicentury hindcasts and projections. Our hindcasts show considerable skill in representing the observational constraints. We show that robust AMOC risk estimates can require carefully sampling the parameter pdfs. We find a low probability of experiencing an AMOC collapse within the 21st century for a business-as-usual emissions scenario. The probability of experiencing an AMOC collapse within two centuries is 1/10. The probability of crossing a forcing threshold and triggering a future AMOC collapse (by 2300) is approximately 1/30 in the 21st century and over 1/3 in the 22nd. Given the simplicity of the model structure and uncertainty in the forcing assumptions, our analysis should be considered a proof of concept and the quantitative conclusions subject to severe caveats.

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

Bayesian statistics and Monte Carlo methods

NASA Astrophysics Data System (ADS)

Koch, K. R.

2018-03-01

The Bayesian approach allows an intuitive way to derive the methods of statistics. Probability is defined as a measure of the plausibility of statements or propositions. Three rules are sufficient to obtain the laws of probability. If the statements refer to the numerical values of variables, the so-called random variables, univariate and multivariate distributions follow. They lead to the point estimation by which unknown quantities, i.e. unknown parameters, are computed from measurements. The unknown parameters are random variables, they are fixed quantities in traditional statistics which is not founded on Bayes' theorem. Bayesian statistics therefore recommends itself for Monte Carlo methods, which generate random variates from given distributions. Monte Carlo methods, of course, can also be applied in traditional statistics. The unknown parameters, are introduced as functions of the measurements, and the Monte Carlo methods give the covariance matrix and the expectation of these functions. A confidence region is derived where the unknown parameters are situated with a given probability. Following a method of traditional statistics, hypotheses are tested by determining whether a value for an unknown parameter lies inside or outside the confidence region. The error propagation of a random vector by the Monte Carlo methods is presented as an application. If the random vector results from a nonlinearly transformed vector, its covariance matrix and its expectation follow from the Monte Carlo estimate. This saves a considerable amount of derivatives to be computed, and errors of the linearization are avoided. The Monte Carlo method is therefore efficient. If the functions of the measurements are given by a sum of two or more random vectors with different multivariate distributions, the resulting distribution is generally not known. TheMonte Carlo methods are then needed to obtain the covariance matrix and the expectation of the sum.

qPR: An adaptive partial-report procedure based on Bayesian inference.

PubMed

Baek, Jongsoo; Lesmes, Luis Andres; Lu, Zhong-Lin

2016-08-01

Iconic memory is best assessed with the partial report procedure in which an array of letters appears briefly on the screen and a poststimulus cue directs the observer to report the identity of the cued letter(s). Typically, 6-8 cue delays or 600-800 trials are tested to measure the iconic memory decay function. Here we develop a quick partial report, or qPR, procedure based on a Bayesian adaptive framework to estimate the iconic memory decay function with much reduced testing time. The iconic memory decay function is characterized by an exponential function and a joint probability distribution of its three parameters. Starting with a prior of the parameters, the method selects the stimulus to maximize the expected information gain in the next test trial. It then updates the posterior probability distribution of the parameters based on the observer's response using Bayesian inference. The procedure is reiterated until either the total number of trials or the precision of the parameter estimates reaches a certain criterion. Simulation studies showed that only 100 trials were necessary to reach an average absolute bias of 0.026 and a precision of 0.070 (both in terms of probability correct). A psychophysical validation experiment showed that estimates of the iconic memory decay function obtained with 100 qPR trials exhibited good precision (the half width of the 68.2% credible interval = 0.055) and excellent agreement with those obtained with 1,600 trials of the conventional method of constant stimuli procedure (RMSE = 0.063). Quick partial-report relieves the data collection burden in characterizing iconic memory and makes it possible to assess iconic memory in clinical populations.

Isotopic reconstruction of the weaning process in the archaeological population of Canímar Abajo, Cuba: A Bayesian probability mixing model approach

PubMed Central

Roksandic, Mirjana; Nikitović, Dejana; Rodríguez Suárez, Roberto; Smith, David; Kanik, Nadine; García Jordá, Dailys; Buhay, William M.

2017-01-01

The general lack of well-preserved juvenile skeletal remains from Caribbean archaeological sites has, in the past, prevented evaluations of juvenile dietary changes. Canímar Abajo (Cuba), with a large number of well-preserved juvenile and adult skeletal remains, provided a unique opportunity to fully assess juvenile paleodiets from an ancient Caribbean population. Ages for the start and the end of weaning and possible food sources used for weaning were inferred by combining the results of two Bayesian probability models that help to reduce some of the uncertainties inherent to bone collagen isotope based paleodiet reconstructions. Bone collagen (31 juveniles, 18 adult females) was used for carbon and nitrogen isotope analyses. The isotope results were assessed using two Bayesian probability models: Weaning Ages Reconstruction with Nitrogen isotopes and Stable Isotope Analyses in R. Breast milk seems to have been the most important protein source until two years of age with some supplementary food such as tropical fruits and root cultigens likely introduced earlier. After two, juvenile diets were likely continuously supplemented by starch rich foods such as root cultigens and legumes. By the age of three, the model results suggest that the weaning process was completed. Additional indications suggest that animal marine/riverine protein and maize, while part of the Canímar Abajo female diets, were likely not used to supplement juvenile diets. The combined use of both models here provided a more complete assessment of the weaning process for an ancient Caribbean population, indicating not only the start and end ages of weaning but also the relative importance of different food sources for different age juveniles. PMID:28459816

Modeling Dynamic Contrast-Enhanced MRI Data with a Constrained Local AIF.

PubMed

Duan, Chong; Kallehauge, Jesper F; Pérez-Torres, Carlos J; Bretthorst, G Larry; Beeman, Scott C; Tanderup, Kari; Ackerman, Joseph J H; Garbow, Joel R

2018-02-01

This study aims to develop a constrained local arterial input function (cL-AIF) to improve quantitative analysis of dynamic contrast-enhanced (DCE)-magnetic resonance imaging (MRI) data by accounting for the contrast-agent bolus amplitude error in the voxel-specific AIF. Bayesian probability theory-based parameter estimation and model selection were used to compare tracer kinetic modeling employing either the measured remote-AIF (R-AIF, i.e., the traditional approach) or an inferred cL-AIF against both in silico DCE-MRI data and clinical, cervical cancer DCE-MRI data. When the data model included the cL-AIF, tracer kinetic parameters were correctly estimated from in silico data under contrast-to-noise conditions typical of clinical DCE-MRI experiments. Considering the clinical cervical cancer data, Bayesian model selection was performed for all tumor voxels of the 16 patients (35,602 voxels in total). Among those voxels, a tracer kinetic model that employed the voxel-specific cL-AIF was preferred (i.e., had a higher posterior probability) in 80 % of the voxels compared to the direct use of a single R-AIF. Maps of spatial variation in voxel-specific AIF bolus amplitude and arrival time for heterogeneous tissues, such as cervical cancer, are accessible with the cL-AIF approach. The cL-AIF method, which estimates unique local-AIF amplitude and arrival time for each voxel within the tissue of interest, provides better modeling of DCE-MRI data than the use of a single, measured R-AIF. The Bayesian-based data analysis described herein affords estimates of uncertainties for each model parameter, via posterior probability density functions, and voxel-wise comparison across methods/models, via model selection in data modeling.

Isotopic reconstruction of the weaning process in the archaeological population of Canímar Abajo, Cuba: A Bayesian probability mixing model approach.

PubMed

Chinique de Armas, Yadira; Roksandic, Mirjana; Nikitović, Dejana; Rodríguez Suárez, Roberto; Smith, David; Kanik, Nadine; García Jordá, Dailys; Buhay, William M

2017-01-01

The general lack of well-preserved juvenile skeletal remains from Caribbean archaeological sites has, in the past, prevented evaluations of juvenile dietary changes. Canímar Abajo (Cuba), with a large number of well-preserved juvenile and adult skeletal remains, provided a unique opportunity to fully assess juvenile paleodiets from an ancient Caribbean population. Ages for the start and the end of weaning and possible food sources used for weaning were inferred by combining the results of two Bayesian probability models that help to reduce some of the uncertainties inherent to bone collagen isotope based paleodiet reconstructions. Bone collagen (31 juveniles, 18 adult females) was used for carbon and nitrogen isotope analyses. The isotope results were assessed using two Bayesian probability models: Weaning Ages Reconstruction with Nitrogen isotopes and Stable Isotope Analyses in R. Breast milk seems to have been the most important protein source until two years of age with some supplementary food such as tropical fruits and root cultigens likely introduced earlier. After two, juvenile diets were likely continuously supplemented by starch rich foods such as root cultigens and legumes. By the age of three, the model results suggest that the weaning process was completed. Additional indications suggest that animal marine/riverine protein and maize, while part of the Canímar Abajo female diets, were likely not used to supplement juvenile diets. The combined use of both models here provided a more complete assessment of the weaning process for an ancient Caribbean population, indicating not only the start and end ages of weaning but also the relative importance of different food sources for different age juveniles.

Bayesian seismic inversion based on rock-physics prior modeling for the joint estimation of acoustic impedance, porosity and lithofacies

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

Passos de Figueiredo, Leandro, E-mail: leandrop.fgr@gmail.com; Grana, Dario; Santos, Marcio

We propose a Bayesian approach for seismic inversion to estimate acoustic impedance, porosity and lithofacies within the reservoir conditioned to post-stack seismic and well data. The link between elastic and petrophysical properties is given by a joint prior distribution for the logarithm of impedance and porosity, based on a rock-physics model. The well conditioning is performed through a background model obtained by well log interpolation. Two different approaches are presented: in the first approach, the prior is defined by a single Gaussian distribution, whereas in the second approach it is defined by a Gaussian mixture to represent the well datamore » multimodal distribution and link the Gaussian components to different geological lithofacies. The forward model is based on a linearized convolutional model. For the single Gaussian case, we obtain an analytical expression for the posterior distribution, resulting in a fast algorithm to compute the solution of the inverse problem, i.e. the posterior distribution of acoustic impedance and porosity as well as the facies probability given the observed data. For the Gaussian mixture prior, it is not possible to obtain the distributions analytically, hence we propose a Gibbs algorithm to perform the posterior sampling and obtain several reservoir model realizations, allowing an uncertainty analysis of the estimated properties and lithofacies. Both methodologies are applied to a real seismic dataset with three wells to obtain 3D models of acoustic impedance, porosity and lithofacies. The methodologies are validated through a blind well test and compared to a standard Bayesian inversion approach. Using the probability of the reservoir lithofacies, we also compute a 3D isosurface probability model of the main oil reservoir in the studied field.« less

qPR: An adaptive partial-report procedure based on Bayesian inference

PubMed Central

Baek, Jongsoo; Lesmes, Luis Andres; Lu, Zhong-Lin

2016-01-01

Iconic memory is best assessed with the partial report procedure in which an array of letters appears briefly on the screen and a poststimulus cue directs the observer to report the identity of the cued letter(s). Typically, 6–8 cue delays or 600–800 trials are tested to measure the iconic memory decay function. Here we develop a quick partial report, or qPR, procedure based on a Bayesian adaptive framework to estimate the iconic memory decay function with much reduced testing time. The iconic memory decay function is characterized by an exponential function and a joint probability distribution of its three parameters. Starting with a prior of the parameters, the method selects the stimulus to maximize the expected information gain in the next test trial. It then updates the posterior probability distribution of the parameters based on the observer's response using Bayesian inference. The procedure is reiterated until either the total number of trials or the precision of the parameter estimates reaches a certain criterion. Simulation studies showed that only 100 trials were necessary to reach an average absolute bias of 0.026 and a precision of 0.070 (both in terms of probability correct). A psychophysical validation experiment showed that estimates of the iconic memory decay function obtained with 100 qPR trials exhibited good precision (the half width of the 68.2% credible interval = 0.055) and excellent agreement with those obtained with 1,600 trials of the conventional method of constant stimuli procedure (RMSE = 0.063). Quick partial-report relieves the data collection burden in characterizing iconic memory and makes it possible to assess iconic memory in clinical populations. PMID:27580045

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.

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.

Comprehension and computation in Bayesian problem solving

PubMed Central

Johnson, Eric D.; Tubau, Elisabet

2015-01-01

Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian inferences relative to normalized formats (e.g., probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on “transparent” Bayesian problems varies widely, and generally remains rather unimpressive. We suggest there has been an over-focus on this representational facilitator (i.e., transparent problem structures) at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct vs. incorrect reasoners depart, and how individual differences might influence this time point. PMID:26283976

Bayesian approach for counting experiment statistics applied to a neutrino point source analysis

NASA Astrophysics Data System (ADS)

Bose, D.; Brayeur, L.; Casier, M.; de Vries, K. D.; Golup, G.; van Eijndhoven, N.

2013-12-01

In this paper we present a model independent analysis method following Bayesian statistics to analyse data from a generic counting experiment and apply it to the search for neutrinos from point sources. We discuss a test statistic defined following a Bayesian framework that will be used in the search for a signal. In case no signal is found, we derive an upper limit without the introduction of approximations. The Bayesian approach allows us to obtain the full probability density function for both the background and the signal rate. As such, we have direct access to any signal upper limit. The upper limit derivation directly compares with a frequentist approach and is robust in the case of low-counting observations. Furthermore, it allows also to account for previous upper limits obtained by other analyses via the concept of prior information without the need of the ad hoc application of trial factors. To investigate the validity of the presented Bayesian approach, we have applied this method to the public IceCube 40-string configuration data for 10 nearby blazars and we have obtained a flux upper limit, which is in agreement with the upper limits determined via a frequentist approach. Furthermore, the upper limit obtained compares well with the previously published result of IceCube, using the same data set.

BOP2: Bayesian optimal design for phase II clinical trials with simple and complex endpoints.

PubMed

Zhou, Heng; Lee, J Jack; Yuan, Ying

2017-09-20

We propose a flexible Bayesian optimal phase II (BOP2) design that is capable of handling simple (e.g., binary) and complicated (e.g., ordinal, nested, and co-primary) endpoints under a unified framework. We use a Dirichlet-multinomial model to accommodate different types of endpoints. At each interim, the go/no-go decision is made by evaluating a set of posterior probabilities of the events of interest, which is optimized to maximize power or minimize the number of patients under the null hypothesis. Unlike other existing Bayesian designs, the BOP2 design explicitly controls the type I error rate, thereby bridging the gap between Bayesian designs and frequentist designs. In addition, the stopping boundary of the BOP2 design can be enumerated prior to the onset of the trial. These features make the BOP2 design accessible to a wide range of users and regulatory agencies and particularly easy to implement in practice. Simulation studies show that the BOP2 design has favorable operating characteristics with higher power and lower risk of incorrectly terminating the trial than some existing Bayesian phase II designs. The software to implement the BOP2 design is freely available at www.trialdesign.org. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Integrating probabilistic models of perception and interactive neural networks: a historical and tutorial review

PubMed Central

McClelland, James L.

2013-01-01

This article seeks to establish a rapprochement between explicitly Bayesian models of contextual effects in perception and neural network models of such effects, particularly the connectionist interactive activation (IA) model of perception. The article is in part an historical review and in part a tutorial, reviewing the probabilistic Bayesian approach to understanding perception and how it may be shaped by context, and also reviewing ideas about how such probabilistic computations may be carried out in neural networks, focusing on the role of context in interactive neural networks, in which both bottom-up and top-down signals affect the interpretation of sensory inputs. It is pointed out that connectionist units that use the logistic or softmax activation functions can exactly compute Bayesian posterior probabilities when the bias terms and connection weights affecting such units are set to the logarithms of appropriate probabilistic quantities. Bayesian concepts such the prior, likelihood, (joint and marginal) posterior, probability matching and maximizing, and calculating vs. sampling from the posterior are all reviewed and linked to neural network computations. Probabilistic and neural network models are explicitly linked to the concept of a probabilistic generative model that describes the relationship between the underlying target of perception (e.g., the word intended by a speaker or other source of sensory stimuli) and the sensory input that reaches the perceiver for use in inferring the underlying target. It is shown how a new version of the IA model called the multinomial interactive activation (MIA) model can sample correctly from the joint posterior of a proposed generative model for perception of letters in words, indicating that interactive processing is fully consistent with principled probabilistic computation. Ways in which these computations might be realized in real neural systems are also considered. PMID:23970868

Unraveling multiple changes in complex climate time series using Bayesian inference

NASA Astrophysics Data System (ADS)

Berner, Nadine; Trauth, Martin H.; Holschneider, Matthias

2016-04-01

Change points in time series are perceived as heterogeneities in the statistical or dynamical characteristics of observations. Unraveling such transitions yields essential information for the understanding of the observed system. The precise detection and basic characterization of underlying changes is therefore of particular importance in environmental sciences. We present a kernel-based Bayesian inference approach to investigate direct as well as indirect climate observations for multiple generic transition events. In order to develop a diagnostic approach designed to capture a variety of natural processes, the basic statistical features of central tendency and dispersion are used to locally approximate a complex time series by a generic transition model. A Bayesian inversion approach is developed to robustly infer on the location and the generic patterns of such a transition. To systematically investigate time series for multiple changes occurring at different temporal scales, the Bayesian inversion is extended to a kernel-based inference approach. By introducing basic kernel measures, the kernel inference results are composed into a proxy probability to a posterior distribution of multiple transitions. Thus, based on a generic transition model a probability expression is derived that is capable to indicate multiple changes within a complex time series. We discuss the method's performance by investigating direct and indirect climate observations. The approach is applied to environmental time series (about 100 a), from the weather station in Tuscaloosa, Alabama, and confirms documented instrumentation changes. Moreover, the approach is used to investigate a set of complex terrigenous dust records from the ODP sites 659, 721/722 and 967 interpreted as climate indicators of the African region of the Plio-Pleistocene period (about 5 Ma). The detailed inference unravels multiple transitions underlying the indirect climate observations coinciding with established global climate events.

Constructive Epistemic Modeling: A Hierarchical Bayesian Model Averaging Method

NASA Astrophysics Data System (ADS)

Tsai, F. T. C.; Elshall, A. S.

2014-12-01

Constructive epistemic modeling is the idea that our understanding of a natural system through a scientific model is a mental construct that continually develops through learning about and from the model. Using the hierarchical Bayesian model averaging (HBMA) method [1], this study shows that segregating different uncertain model components through a BMA tree of posterior model probabilities, model prediction, within-model variance, between-model variance and total model variance serves as a learning tool [2]. First, the BMA tree of posterior model probabilities permits the comparative evaluation of the candidate propositions of each uncertain model component. Second, systemic model dissection is imperative for understanding the individual contribution of each uncertain model component to the model prediction and variance. Third, the hierarchical representation of the between-model variance facilitates the prioritization of the contribution of each uncertain model component to the overall model uncertainty. We illustrate these concepts using the groundwater modeling of a siliciclastic aquifer-fault system. The sources of uncertainty considered are from geological architecture, formation dip, boundary conditions and model parameters. The study shows that the HBMA analysis helps in advancing knowledge about the model rather than forcing the model to fit a particularly understanding or merely averaging several candidate models. [1] Tsai, F. T.-C., and A. S. Elshall (2013), Hierarchical Bayesian model averaging for hydrostratigraphic modeling: Uncertainty segregation and comparative evaluation. Water Resources Research, 49, 5520-5536, doi:10.1002/wrcr.20428. [2] Elshall, A.S., and F. T.-C. Tsai (2014). Constructive epistemic modeling of groundwater flow with geological architecture and boundary condition uncertainty under Bayesian paradigm, Journal of Hydrology, 517, 105-119, doi: 10.1016/j.jhydrol.2014.05.027.

Uncertainty in action-value estimation affects both action choice and learning rate of the choice behaviors of rats.

PubMed

Funamizu, Akihiro; Ito, Makoto; Doya, Kenji; Kanzaki, Ryohei; Takahashi, Hirokazu

2012-04-01

The estimation of reward outcomes for action candidates is essential for decision making. In this study, we examined whether and how the uncertainty in reward outcome estimation affects the action choice and learning rate. We designed a choice task in which rats selected either the left-poking or right-poking hole and received a reward of a food pellet stochastically. The reward probabilities of the left and right holes were chosen from six settings (high, 100% vs. 66%; mid, 66% vs. 33%; low, 33% vs. 0% for the left vs. right holes, and the opposites) in every 20-549 trials. We used Bayesian Q-learning models to estimate the time course of the probability distribution of action values and tested if they better explain the behaviors of rats than standard Q-learning models that estimate only the mean of action values. Model comparison by cross-validation revealed that a Bayesian Q-learning model with an asymmetric update for reward and non-reward outcomes fit the choice time course of the rats best. In the action-choice equation of the Bayesian Q-learning model, the estimated coefficient for the variance of action value was positive, meaning that rats were uncertainty seeking. Further analysis of the Bayesian Q-learning model suggested that the uncertainty facilitated the effective learning rate. These results suggest that the rats consider uncertainty in action-value estimation and that they have an uncertainty-seeking action policy and uncertainty-dependent modulation of the effective learning rate. © 2012 The Authors. European Journal of Neuroscience © 2012 Federation of European Neuroscience Societies and Blackwell Publishing Ltd.

Integrating probabilistic models of perception and interactive neural networks: a historical and tutorial review.

PubMed

McClelland, James L

2013-01-01

This article seeks to establish a rapprochement between explicitly Bayesian models of contextual effects in perception and neural network models of such effects, particularly the connectionist interactive activation (IA) model of perception. The article is in part an historical review and in part a tutorial, reviewing the probabilistic Bayesian approach to understanding perception and how it may be shaped by context, and also reviewing ideas about how such probabilistic computations may be carried out in neural networks, focusing on the role of context in interactive neural networks, in which both bottom-up and top-down signals affect the interpretation of sensory inputs. It is pointed out that connectionist units that use the logistic or softmax activation functions can exactly compute Bayesian posterior probabilities when the bias terms and connection weights affecting such units are set to the logarithms of appropriate probabilistic quantities. Bayesian concepts such the prior, likelihood, (joint and marginal) posterior, probability matching and maximizing, and calculating vs. sampling from the posterior are all reviewed and linked to neural network computations. Probabilistic and neural network models are explicitly linked to the concept of a probabilistic generative model that describes the relationship between the underlying target of perception (e.g., the word intended by a speaker or other source of sensory stimuli) and the sensory input that reaches the perceiver for use in inferring the underlying target. It is shown how a new version of the IA model called the multinomial interactive activation (MIA) model can sample correctly from the joint posterior of a proposed generative model for perception of letters in words, indicating that interactive processing is fully consistent with principled probabilistic computation. Ways in which these computations might be realized in real neural systems are also considered.

Bayesian uncertainty quantification in linear models for diffusion MRI.

PubMed

Sjölund, Jens; Eklund, Anders; Özarslan, Evren; Herberthson, Magnus; Bånkestad, Maria; Knutsson, Hans

2018-03-29

Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification. Copyright © 2018 Elsevier Inc. All rights reserved.

Bayesian network modeling applied to coastal geomorphology: lessons learned from a decade of experimentation and application

NASA Astrophysics Data System (ADS)

Plant, N. G.; Thieler, E. R.; Gutierrez, B.; Lentz, E. E.; Zeigler, S. L.; Van Dongeren, A.; Fienen, M. N.

2016-12-01

We evaluate the strengths and weaknesses of Bayesian networks that have been used to address scientific and decision-support questions related to coastal geomorphology. We will provide an overview of coastal geomorphology research that has used Bayesian networks and describe what this approach can do and when it works (or fails to work). Over the past decade, Bayesian networks have been formulated to analyze the multi-variate structure and evolution of coastal morphology and associated human and ecological impacts. The approach relates observable system variables to each other by estimating discrete correlations. The resulting Bayesian-networks make predictions that propagate errors, conduct inference via Bayes rule, or both. In scientific applications, the model results are useful for hypothesis testing, using confidence estimates to gage the strength of tests while applications to coastal resource management are aimed at decision-support, where the probabilities of desired ecosystems outcomes are evaluated. The range of Bayesian-network applications to coastal morphology includes emulation of high-resolution wave transformation models to make oceanographic predictions, morphologic response to storms and/or sea-level rise, groundwater response to sea-level rise and morphologic variability, habitat suitability for endangered species, and assessment of monetary or human-life risk associated with storms. All of these examples are based on vast observational data sets, numerical model output, or both. We will discuss the progression of our experiments, which has included testing whether the Bayesian-network approach can be implemented and is appropriate for addressing basic and applied scientific problems and evaluating the hindcast and forecast skill of these implementations. We will present and discuss calibration/validation tests that are used to assess the robustness of Bayesian-network models and we will compare these results to tests of other models. This will demonstrate how Bayesian networks are used to extract new insights about coastal morphologic behavior, assess impacts to societal and ecological systems, and communicate probabilistic predictions to decision makers.

Bayesian Inference on Proportional Elections

PubMed Central

Brunello, Gabriel Hideki Vatanabe; Nakano, Eduardo Yoshio

2015-01-01

Polls for majoritarian voting systems usually show estimates of the percentage of votes for each candidate. However, proportional vote systems do not necessarily guarantee the candidate with the most percentage of votes will be elected. Thus, traditional methods used in majoritarian elections cannot be applied on proportional elections. In this context, the purpose of this paper was to perform a Bayesian inference on proportional elections considering the Brazilian system of seats distribution. More specifically, a methodology to answer the probability that a given party will have representation on the chamber of deputies was developed. Inferences were made on a Bayesian scenario using the Monte Carlo simulation technique, and the developed methodology was applied on data from the Brazilian elections for Members of the Legislative Assembly and Federal Chamber of Deputies in 2010. A performance rate was also presented to evaluate the efficiency of the methodology. Calculations and simulations were carried out using the free R statistical software. PMID:25786259

Bayesian models based on test statistics for multiple hypothesis testing problems.

PubMed

Ji, Yuan; Lu, Yiling; Mills, Gordon B

2008-04-01

We propose a Bayesian method for the problem of multiple hypothesis testing that is routinely encountered in bioinformatics research, such as the differential gene expression analysis. Our algorithm is based on modeling the distributions of test statistics under both null and alternative hypotheses. We substantially reduce the complexity of the process of defining posterior model probabilities by modeling the test statistics directly instead of modeling the full data. Computationally, we apply a Bayesian FDR approach to control the number of rejections of null hypotheses. To check if our model assumptions for the test statistics are valid for various bioinformatics experiments, we also propose a simple graphical model-assessment tool. Using extensive simulations, we demonstrate the performance of our models and the utility of the model-assessment tool. In the end, we apply the proposed methodology to an siRNA screening and a gene expression experiment.