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.

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.

Enhancing pediatric clinical trial feasibility through the use of Bayesian statistics.

PubMed

Huff, Robin A; Maca, Jeff D; Puri, Mala; Seltzer, Earl W

2017-11-01

BackgroundPediatric clinical trials commonly experience recruitment challenges including limited number of patients and investigators, inclusion/exclusion criteria that further reduce the patient pool, and a competitive research landscape created by pediatric regulatory commitments. To overcome these challenges, innovative approaches are needed.MethodsThis article explores the use of Bayesian statistics to improve pediatric trial feasibility, using pediatric Type-2 diabetes as an example. Data for six therapies approved for adults were used to perform simulations to determine the impact on pediatric trial size.ResultsWhen the number of adult patients contributing to the simulation was assumed to be the same as the number of patients to be enrolled in the pediatric trial, the pediatric trial size was reduced by 75-78% when compared with a frequentist statistical approach, but was associated with a 34-45% false-positive rate. In subsequent simulations, greater control was exerted over the false-positive rate by decreasing the contribution of the adult data. A 30-33% reduction in trial size was achieved when false-positives were held to less than 10%.ConclusionReducing the trial size through the use of Bayesian statistics would facilitate completion of pediatric trials, enabling drugs to be labeled appropriately for children.

Fully Bayesian inference for structural MRI: application to segmentation and statistical analysis of T2-hypointensities.

PubMed

Schmidt, Paul; Schmid, Volker J; Gaser, Christian; Buck, Dorothea; Bührlen, Susanne; Förschler, Annette; Mühlau, Mark

2013-01-01

Aiming at iron-related T2-hypointensity, which is related to normal aging and neurodegenerative processes, we here present two practicable approaches, based on Bayesian inference, for preprocessing and statistical analysis of a complex set of structural MRI data. In particular, Markov Chain Monte Carlo methods were used to simulate posterior distributions. First, we rendered a segmentation algorithm that uses outlier detection based on model checking techniques within a Bayesian mixture model. Second, we rendered an analytical tool comprising a Bayesian regression model with smoothness priors (in the form of Gaussian Markov random fields) mitigating the necessity to smooth data prior to statistical analysis. For validation, we used simulated data and MRI data of 27 healthy controls (age: [Formula: see text]; range, [Formula: see text]). We first observed robust segmentation of both simulated T2-hypointensities and gray-matter regions known to be T2-hypointense. Second, simulated data and images of segmented T2-hypointensity were analyzed. We found not only robust identification of simulated effects but also a biologically plausible age-related increase of T2-hypointensity primarily within the dentate nucleus but also within the globus pallidus, substantia nigra, and red nucleus. Our results indicate that fully Bayesian inference can successfully be applied for preprocessing and statistical analysis of structural MRI data.

A Hierarchical Multivariate Bayesian Approach to Ensemble Model output Statistics in Atmospheric Prediction

DTIC Science & Technology

2017-09-01

efficacy of statistical post-processing methods downstream of these dynamical model components with a hierarchical multivariate Bayesian approach to...Bayesian hierarchical modeling, Markov chain Monte Carlo methods , Metropolis algorithm, machine learning, atmospheric prediction 15. NUMBER OF PAGES...scale processes. However, this dissertation explores the efficacy of statistical post-processing methods downstream of these dynamical model components

Bayesian modeling of flexible cognitive control

PubMed Central

Jiang, Jiefeng; Heller, Katherine; Egner, Tobias

2014-01-01

“Cognitive control” describes endogenous guidance of behavior in situations where routine stimulus-response associations are suboptimal for achieving a desired goal. The computational and neural mechanisms underlying this capacity remain poorly understood. We examine recent advances stemming from the application of a Bayesian learner perspective that provides optimal prediction for control processes. In reviewing the application of Bayesian models to cognitive control, we note that an important limitation in current models is a lack of a plausible mechanism for the flexible adjustment of control over conflict levels changing at varying temporal scales. We then show that flexible cognitive control can be achieved by a Bayesian model with a volatility-driven learning mechanism that modulates dynamically the relative dependence on recent and remote experiences in its prediction of future control demand. We conclude that the emergent Bayesian perspective on computational mechanisms of cognitive control holds considerable promise, especially if future studies can identify neural substrates of the variables encoded by these models, and determine the nature (Bayesian or otherwise) of their neural implementation. PMID:24929218

Nonparametric Bayesian predictive distributions for future order statistics

Treesearch

Richard A. Johnson; James W. Evans; David W. Green

1999-01-01

We derive the predictive distribution for a specified order statistic, determined from a future random sample, under a Dirichlet process prior. Two variants of the approach are treated and some limiting cases studied. A practical application to monitoring the strength of lumber is discussed including choices of prior expectation and comparisons made to a Bayesian...

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

NASA Astrophysics Data System (ADS)

Al Sobhi, Mashail M.

2015-02-01

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

A BAYESIAN STATISTICAL APPROACH FOR THE EVALUATION OF CMAQ

EPA Science Inventory

Bayesian statistical methods are used to evaluate Community Multiscale Air Quality (CMAQ) model simulations of sulfate aerosol over a section of the eastern US for 4-week periods in summer and winter 2001. The observed data come from two U.S. Environmental Protection Agency data ...

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

PubMed

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

2012-01-01

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

New applications of maximum likelihood and Bayesian statistics in macromolecular crystallography.

PubMed

McCoy, Airlie J

2002-10-01

Maximum likelihood methods are well known to macromolecular crystallographers as the methods of choice for isomorphous phasing and structure refinement. Recently, the use of maximum likelihood and Bayesian statistics has extended to the areas of molecular replacement and density modification, placing these methods on a stronger statistical foundation and making them more accurate and effective.

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 Sensitivity Analysis of Statistical Models with Missing Data

PubMed Central

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

2013-01-01

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

Statistical Surrogate Modeling of Atmospheric Dispersion Events Using Bayesian Adaptive Splines

NASA Astrophysics Data System (ADS)

Francom, D.; Sansó, B.; Bulaevskaya, V.; Lucas, D. D.

2016-12-01

Uncertainty in the inputs of complex computer models, including atmospheric dispersion and transport codes, is often assessed via statistical surrogate models. Surrogate models are computationally efficient statistical approximations of expensive computer models that enable uncertainty analysis. We introduce Bayesian adaptive spline methods for producing surrogate models that capture the major spatiotemporal patterns of the parent model, while satisfying all the necessities of flexibility, accuracy and computational feasibility. We present novel methodological and computational approaches motivated by a controlled atmospheric tracer release experiment conducted at the Diablo Canyon nuclear power plant in California. Traditional methods for building statistical surrogate models often do not scale well to experiments with large amounts of data. Our approach is well suited to experiments involving large numbers of model inputs, large numbers of simulations, and functional output for each simulation. Our approach allows us to perform global sensitivity analysis with ease. We also present an approach to calibration of simulators using field data.

Technical Topic 3.2.2.d Bayesian and Non-Parametric Statistics: Integration of Neural Networks with Bayesian Networks for Data Fusion and Predictive Modeling

DTIC Science & Technology

2016-05-31

and included explosives such as TATP, HMTD, RDX, RDX, ammonium nitrate , potassium perchlorate, potassium nitrate , sugar, and TNT. The approach...Distribution Unlimited UU UU UU UU 31-05-2016 15-Apr-2014 14-Jan-2015 Final Report: Technical Topic 3.2.2. d Bayesian and Non- parametric Statistics...of Papers published in non peer-reviewed journals: Final Report: Technical Topic 3.2.2. d Bayesian and Non-parametric Statistics: Integration of Neural

Online Dectection and Modeling of Safety Boundaries for Aerospace Application Using Bayesian Statistics

NASA Technical Reports Server (NTRS)

He, Yuning

2015-01-01

The behavior of complex aerospace systems is governed by numerous parameters. For safety analysis it is important to understand how the system behaves with respect to these parameter values. In particular, understanding the boundaries between safe and unsafe regions is of major importance. In this paper, we describe a hierarchical Bayesian statistical modeling approach for the online detection and characterization of such boundaries. Our method for classification with active learning uses a particle filter-based model and a boundary-aware metric for best performance. From a library of candidate shapes incorporated with domain expert knowledge, the location and parameters of the boundaries are estimated using advanced Bayesian modeling techniques. The results of our boundary analysis are then provided in a form understandable by the domain expert. We illustrate our approach using a simulation model of a NASA neuro-adaptive flight control system, as well as a system for the detection of separation violations in the terminal airspace.

Fully Bayesian tests of neutrality using genealogical summary statistics.

PubMed

Drummond, Alexei J; Suchard, Marc A

2008-10-31

Many data summary statistics have been developed to detect departures from neutral expectations of evolutionary models. However questions about the neutrality of the evolution of genetic loci within natural populations remain difficult to assess. One critical cause of this difficulty is that most methods for testing neutrality make simplifying assumptions simultaneously about the mutational model and the population size model. Consequentially, rejecting the null hypothesis of neutrality under these methods could result from violations of either or both assumptions, making interpretation troublesome. Here we harness posterior predictive simulation to exploit summary statistics of both the data and model parameters to test the goodness-of-fit of standard models of evolution. We apply the method to test the selective neutrality of molecular evolution in non-recombining gene genealogies and we demonstrate the utility of our method on four real data sets, identifying significant departures of neutrality in human influenza A virus, even after controlling for variation in population size. Importantly, by employing a full model-based Bayesian analysis, our method separates the effects of demography from the effects of selection. The method also allows multiple summary statistics to be used in concert, thus potentially increasing sensitivity. Furthermore, our method remains useful in situations where analytical expectations and variances of summary statistics are not available. This aspect has great potential for the analysis of temporally spaced data, an expanding area previously ignored for limited availability of theory and methods.

Fine Mapping Causal Variants with an Approximate Bayesian Method Using Marginal Test Statistics

PubMed Central

Chen, Wenan; Larrabee, Beth R.; Ovsyannikova, Inna G.; Kennedy, Richard B.; Haralambieva, Iana H.; Poland, Gregory A.; Schaid, Daniel J.

2015-01-01

Two recently developed fine-mapping methods, CAVIAR and PAINTOR, demonstrate better performance over other fine-mapping methods. They also have the advantage of using only the marginal test statistics and the correlation among SNPs. Both methods leverage the fact that the marginal test statistics asymptotically follow a multivariate normal distribution and are likelihood based. However, their relationship with Bayesian fine mapping, such as BIMBAM, is not clear. In this study, we first show that CAVIAR and BIMBAM are actually approximately equivalent to each other. This leads to a fine-mapping method using marginal test statistics in the Bayesian framework, which we call CAVIAR Bayes factor (CAVIARBF). Another advantage of the Bayesian framework is that it can answer both association and fine-mapping questions. We also used simulations to compare CAVIARBF with other methods under different numbers of causal variants. The results showed that both CAVIARBF and BIMBAM have better performance than PAINTOR and other methods. Compared to BIMBAM, CAVIARBF has the advantage of using only marginal test statistics and takes about one-quarter to one-fifth of the running time. We applied different methods on two independent cohorts of the same phenotype. Results showed that CAVIARBF, BIMBAM, and PAINTOR selected the same top 3 SNPs; however, CAVIARBF and BIMBAM had better consistency in selecting the top 10 ranked SNPs between the two cohorts. Software is available at https://bitbucket.org/Wenan/caviarbf. PMID:25948564

Fine Mapping Causal Variants with an Approximate Bayesian Method Using Marginal Test Statistics.

PubMed

Chen, Wenan; Larrabee, Beth R; Ovsyannikova, Inna G; Kennedy, Richard B; Haralambieva, Iana H; Poland, Gregory A; Schaid, Daniel J

2015-07-01

Two recently developed fine-mapping methods, CAVIAR and PAINTOR, demonstrate better performance over other fine-mapping methods. They also have the advantage of using only the marginal test statistics and the correlation among SNPs. Both methods leverage the fact that the marginal test statistics asymptotically follow a multivariate normal distribution and are likelihood based. However, their relationship with Bayesian fine mapping, such as BIMBAM, is not clear. In this study, we first show that CAVIAR and BIMBAM are actually approximately equivalent to each other. This leads to a fine-mapping method using marginal test statistics in the Bayesian framework, which we call CAVIAR Bayes factor (CAVIARBF). Another advantage of the Bayesian framework is that it can answer both association and fine-mapping questions. We also used simulations to compare CAVIARBF with other methods under different numbers of causal variants. The results showed that both CAVIARBF and BIMBAM have better performance than PAINTOR and other methods. Compared to BIMBAM, CAVIARBF has the advantage of using only marginal test statistics and takes about one-quarter to one-fifth of the running time. We applied different methods on two independent cohorts of the same phenotype. Results showed that CAVIARBF, BIMBAM, and PAINTOR selected the same top 3 SNPs; however, CAVIARBF and BIMBAM had better consistency in selecting the top 10 ranked SNPs between the two cohorts. Software is available at https://bitbucket.org/Wenan/caviarbf. Copyright © 2015 by the Genetics Society of America.

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.

Bayesian selective response-adaptive design using the historical control.

PubMed

Kim, Mi-Ok; Harun, Nusrat; Liu, Chunyan; Khoury, Jane C; Broderick, Joseph P

2018-06-13

High quality historical control data, if incorporated, may reduce sample size, trial cost, and duration. A too optimistic use of the data, however, may result in bias under prior-data conflict. Motivated by well-publicized two-arm comparative trials in stroke, we propose a Bayesian design that both adaptively incorporates historical control data and selectively adapt the treatment allocation ratios within an ongoing trial responsively to the relative treatment effects. The proposed design differs from existing designs that borrow from historical controls. As opposed to reducing the number of subjects assigned to the control arm blindly, this design does so adaptively to the relative treatment effects only if evaluation of cumulated current trial data combined with the historical control suggests the superiority of the intervention arm. We used the effective historical sample size approach to quantify borrowed information on the control arm and modified the treatment allocation rules of the doubly adaptive biased coin design to incorporate the quantity. The modified allocation rules were then implemented under the Bayesian framework with commensurate priors addressing prior-data conflict. Trials were also more frequently concluded earlier in line with the underlying truth, reducing trial cost, and duration and yielded parameter estimates with smaller standard errors. © 2018 The Authors. Statistics in Medicine Published by John Wiley & Sons, Ltd.

Statistical modeling for Bayesian extrapolation of adult clinical trial information in pediatric drug evaluation.

PubMed

Gamalo-Siebers, Margaret; Savic, Jasmina; Basu, Cynthia; Zhao, Xin; Gopalakrishnan, Mathangi; Gao, Aijun; Song, Guochen; Baygani, Simin; Thompson, Laura; Xia, H Amy; Price, Karen; Tiwari, Ram; Carlin, Bradley P

2017-07-01

Children represent a large underserved population of "therapeutic orphans," as an estimated 80% of children are treated off-label. However, pediatric drug development often faces substantial challenges, including economic, logistical, technical, and ethical barriers, among others. Among many efforts trying to remove these barriers, increased recent attention has been paid to extrapolation; that is, the leveraging of available data from adults or older age groups to draw conclusions for the pediatric population. The Bayesian statistical paradigm is natural in this setting, as it permits the combining (or "borrowing") of information across disparate sources, such as the adult and pediatric data. In this paper, authored by the pediatric subteam of the Drug Information Association Bayesian Scientific Working Group and Adaptive Design Working Group, we develop, illustrate, and provide suggestions on Bayesian statistical methods that could be used to design improved pediatric development programs that use all available information in the most efficient manner. A variety of relevant Bayesian approaches are described, several of which are illustrated through 2 case studies: extrapolating adult efficacy data to expand the labeling for Remicade to include pediatric ulcerative colitis and extrapolating adult exposure-response information for antiepileptic drugs to pediatrics. Copyright © 2017 John Wiley & Sons, Ltd.

Structural mapping in statistical word problems: A relational reasoning approach to Bayesian inference.

PubMed

Johnson, Eric D; Tubau, Elisabet

2017-06-01

Presenting natural frequencies facilitates Bayesian inferences relative to using percentages. Nevertheless, many people, including highly educated and skilled reasoners, still fail to provide Bayesian responses to these computationally simple problems. We show that the complexity of relational reasoning (e.g., the structural mapping between the presented and requested relations) can help explain the remaining difficulties. With a non-Bayesian inference that required identical arithmetic but afforded a more direct structural mapping, performance was universally high. Furthermore, reducing the relational demands of the task through questions that directed reasoners to use the presented statistics, as compared with questions that prompted the representation of a second, similar sample, also significantly improved reasoning. Distinct error patterns were also observed between these presented- and similar-sample scenarios, which suggested differences in relational-reasoning strategies. On the other hand, while higher numeracy was associated with better Bayesian reasoning, higher-numerate reasoners were not immune to the relational complexity of the task. Together, these findings validate the relational-reasoning view of Bayesian problem solving and highlight the importance of considering not only the presented task structure, but also the complexity of the structural alignment between the presented and requested relations.

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.

Bayesian networks and statistical analysis application to analyze the diagnostic test accuracy

NASA Astrophysics Data System (ADS)

Orzechowski, P.; Makal, Jaroslaw; Onisko, A.

2005-02-01

The computer aided BPH diagnosis system based on Bayesian network is described in the paper. First result are compared to a given statistical method. Different statistical methods are used successfully in medicine for years. However, the undoubted advantages of probabilistic methods make them useful in application in newly created systems which are frequent in medicine, but do not have full and competent knowledge. The article presents advantages of the computer aided BPH diagnosis system in clinical practice for urologists.

How to interpret the results of medical time series data analysis: Classical statistical approaches versus dynamic Bayesian network modeling.

PubMed

Onisko, Agnieszka; Druzdzel, Marek J; Austin, R Marshall

2016-01-01

Classical statistics is a well-established approach in the analysis of medical data. While the medical community seems to be familiar with the concept of a statistical analysis and its interpretation, the Bayesian approach, argued by many of its proponents to be superior to the classical frequentist approach, is still not well-recognized in the analysis of medical data. The goal of this study is to encourage data analysts to use the Bayesian approach, such as modeling with graphical probabilistic networks, as an insightful alternative to classical statistical analysis of medical data. This paper offers a comparison of two approaches to analysis of medical time series data: (1) classical statistical approach, such as the Kaplan-Meier estimator and the Cox proportional hazards regression model, and (2) dynamic Bayesian network modeling. Our comparison is based on time series cervical cancer screening data collected at Magee-Womens Hospital, University of Pittsburgh Medical Center over 10 years. The main outcomes of our comparison are cervical cancer risk assessments produced by the three approaches. However, our analysis discusses also several aspects of the comparison, such as modeling assumptions, model building, dealing with incomplete data, individualized risk assessment, results interpretation, and model validation. Our study shows that the Bayesian approach is (1) much more flexible in terms of modeling effort, and (2) it offers an individualized risk assessment, which is more cumbersome for classical statistical approaches.

Bayesian Statistics in Educational Research: A Look at the Current State of Affairs

ERIC Educational Resources Information Center

König, Christoph; van de Schoot, Rens

2018-01-01

The ability of a scientific discipline to build cumulative knowledge depends on its predominant method of data analysis. A steady accumulation of knowledge requires approaches which allow researchers to consider results from comparable prior research. Bayesian statistics is especially relevant for establishing a cumulative scientific discipline,…

Bayesian Tracking of Emerging Epidemics Using Ensemble Optimal Statistical Interpolation

PubMed Central

Cobb, Loren; Krishnamurthy, Ashok; Mandel, Jan; Beezley, Jonathan D.

2014-01-01

We present a preliminary test of the Ensemble Optimal Statistical Interpolation (EnOSI) method for the statistical tracking of an emerging epidemic, with a comparison to its popular relative for Bayesian data assimilation, the Ensemble Kalman Filter (EnKF). The spatial data for this test was generated by a spatial susceptible-infectious-removed (S-I-R) epidemic model of an airborne infectious disease. Both tracking methods in this test employed Poisson rather than Gaussian noise, so as to handle epidemic data more accurately. The EnOSI and EnKF tracking methods worked well on the main body of the simulated spatial epidemic, but the EnOSI was able to detect and track a distant secondary focus of infection that the EnKF missed entirely. PMID:25113590

Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics

NASA Astrophysics Data System (ADS)

Abe, Sumiyoshi

2014-11-01

The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach to systems governed by dynamics with largely separated time scales and is based on three key concepts: conjugate pairs of variables, dimensionless integration measures with coarse-graining factors and partial maximization of the joint entropy. The method enables one to calculate a prior purely from a likelihood in a simple way. It is shown, in particular, how it not only yields Jeffreys's rules but also reveals new structures hidden behind them.

Boosting Bayesian parameter inference of stochastic differential equation models with methods from statistical physics

NASA Astrophysics Data System (ADS)

Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

2016-04-01

Measured time-series of both precipitation and runoff are known to exhibit highly non-trivial statistical properties. For making reliable probabilistic predictions in hydrology, it is therefore desirable to have stochastic models with output distributions that share these properties. When parameters of such models have to be inferred from data, we also need to quantify the associated parametric uncertainty. For non-trivial stochastic models, however, this latter step is typically very demanding, both conceptually and numerically, and always never done in hydrology. Here, we demonstrate that methods developed in statistical physics make a large class of stochastic differential equation (SDE) models amenable to a full-fledged Bayesian parameter inference. For concreteness we demonstrate these methods by means of a simple yet non-trivial toy SDE model. We consider a natural catchment that can be described by a linear reservoir, at the scale of observation. All the neglected processes are assumed to happen at much shorter time-scales and are therefore modeled with a Gaussian white noise term, the standard deviation of which is assumed to scale linearly with the system state (water volume in the catchment). Even for constant input, the outputs of this simple non-linear SDE model show a wealth of desirable statistical properties, such as fat-tailed distributions and long-range correlations. Standard algorithms for Bayesian inference fail, for models of this kind, because their likelihood functions are extremely high-dimensional intractable integrals over all possible model realizations. The use of Kalman filters is illegitimate due to the non-linearity of the model. Particle filters could be used but become increasingly inefficient with growing number of data points. Hamiltonian Monte Carlo algorithms allow us to translate this inference problem to the problem of simulating the dynamics of a statistical mechanics system and give us access to most sophisticated methods

Selecting summary statistics in approximate Bayesian computation for calibrating stochastic models.

PubMed

Burr, Tom; Skurikhin, Alexei

2013-01-01

Approximate Bayesian computation (ABC) is an approach for using measurement data to calibrate stochastic computer models, which are common in biology applications. ABC is becoming the "go-to" option when the data and/or parameter dimension is large because it relies on user-chosen summary statistics rather than the full data and is therefore computationally feasible. One technical challenge with ABC is that the quality of the approximation to the posterior distribution of model parameters depends on the user-chosen summary statistics. In this paper, the user requirement to choose effective summary statistics in order to accurately estimate the posterior distribution of model parameters is investigated and illustrated by example, using a model and corresponding real data of mitochondrial DNA population dynamics. We show that for some choices of summary statistics, the posterior distribution of model parameters is closely approximated and for other choices of summary statistics, the posterior distribution is not closely approximated. A strategy to choose effective summary statistics is suggested in cases where the stochastic computer model can be run at many trial parameter settings, as in the example.

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

Teaching Bayesian Statistics in a Health Research Methodology Program

ERIC Educational Resources Information Center

Pullenayegum, Eleanor M.; Thabane, Lehana

2009-01-01

Despite the appeal of Bayesian methods in health research, they are not widely used. This is partly due to a lack of courses in Bayesian methods at an appropriate level for non-statisticians in health research. Teaching such a course can be challenging because most statisticians have been taught Bayesian methods using a mathematical approach, and…

Dissolution curve comparisons through the F(2) parameter, a Bayesian extension of the f(2) statistic.

PubMed

Novick, Steven; Shen, Yan; Yang, Harry; Peterson, John; LeBlond, Dave; Altan, Stan

2015-01-01

Dissolution (or in vitro release) studies constitute an important aspect of pharmaceutical drug development. One important use of such studies is for justifying a biowaiver for post-approval changes which requires establishing equivalence between the new and old product. We propose a statistically rigorous modeling approach for this purpose based on the estimation of what we refer to as the F2 parameter, an extension of the commonly used f2 statistic. A Bayesian test procedure is proposed in relation to a set of composite hypotheses that capture the similarity requirement on the absolute mean differences between test and reference dissolution profiles. Several examples are provided to illustrate the application. Results of our simulation study comparing the performance of f2 and the proposed method show that our Bayesian approach is comparable to or in many cases superior to the f2 statistic as a decision rule. Further useful extensions of the method, such as the use of continuous-time dissolution modeling, are considered.

Selecting Summary Statistics in Approximate Bayesian Computation for Calibrating Stochastic Models

PubMed Central

Burr, Tom

2013-01-01

Approximate Bayesian computation (ABC) is an approach for using measurement data to calibrate stochastic computer models, which are common in biology applications. ABC is becoming the “go-to” option when the data and/or parameter dimension is large because it relies on user-chosen summary statistics rather than the full data and is therefore computationally feasible. One technical challenge with ABC is that the quality of the approximation to the posterior distribution of model parameters depends on the user-chosen summary statistics. In this paper, the user requirement to choose effective summary statistics in order to accurately estimate the posterior distribution of model parameters is investigated and illustrated by example, using a model and corresponding real data of mitochondrial DNA population dynamics. We show that for some choices of summary statistics, the posterior distribution of model parameters is closely approximated and for other choices of summary statistics, the posterior distribution is not closely approximated. A strategy to choose effective summary statistics is suggested in cases where the stochastic computer model can be run at many trial parameter settings, as in the example. PMID:24288668

Intelligent Condition Diagnosis Method Based on Adaptive Statistic Test Filter and Diagnostic Bayesian Network

PubMed Central

Li, Ke; Zhang, Qiuju; Wang, Kun; Chen, Peng; Wang, Huaqing

2016-01-01

A new fault diagnosis method for rotating machinery based on adaptive statistic test filter (ASTF) and Diagnostic Bayesian Network (DBN) is presented in this paper. ASTF is proposed to obtain weak fault features under background noise, ASTF is based on statistic hypothesis testing in the frequency domain to evaluate similarity between reference signal (noise signal) and original signal, and remove the component of high similarity. The optimal level of significance α is obtained using particle swarm optimization (PSO). To evaluate the performance of the ASTF, evaluation factor Ipq is also defined. In addition, a simulation experiment is designed to verify the effectiveness and robustness of ASTF. A sensitive evaluation method using principal component analysis (PCA) is proposed to evaluate the sensitiveness of symptom parameters (SPs) for condition diagnosis. By this way, the good SPs that have high sensitiveness for condition diagnosis can be selected. A three-layer DBN is developed to identify condition of rotation machinery based on the Bayesian Belief Network (BBN) theory. Condition diagnosis experiment for rolling element bearings demonstrates the effectiveness of the proposed method. PMID:26761006

Intelligent Condition Diagnosis Method Based on Adaptive Statistic Test Filter and Diagnostic Bayesian Network.

PubMed

Li, Ke; Zhang, Qiuju; Wang, Kun; Chen, Peng; Wang, Huaqing

2016-01-08

A new fault diagnosis method for rotating machinery based on adaptive statistic test filter (ASTF) and Diagnostic Bayesian Network (DBN) is presented in this paper. ASTF is proposed to obtain weak fault features under background noise, ASTF is based on statistic hypothesis testing in the frequency domain to evaluate similarity between reference signal (noise signal) and original signal, and remove the component of high similarity. The optimal level of significance α is obtained using particle swarm optimization (PSO). To evaluate the performance of the ASTF, evaluation factor Ipq is also defined. In addition, a simulation experiment is designed to verify the effectiveness and robustness of ASTF. A sensitive evaluation method using principal component analysis (PCA) is proposed to evaluate the sensitiveness of symptom parameters (SPs) for condition diagnosis. By this way, the good SPs that have high sensitiveness for condition diagnosis can be selected. A three-layer DBN is developed to identify condition of rotation machinery based on the Bayesian Belief Network (BBN) theory. Condition diagnosis experiment for rolling element bearings demonstrates the effectiveness of the proposed method.

Spectral Analysis of B Stars: An Application of Bayesian Statistics

NASA Astrophysics Data System (ADS)

Mugnes, J.-M.; Robert, C.

2012-12-01

To better understand the processes involved in stellar physics, it is necessary to obtain accurate stellar parameters (effective temperature, surface gravity, abundances…). Spectral analysis is a powerful tool for investigating stars, but it is also vital to reduce uncertainties at a decent computational cost. Here we present a spectral analysis method based on a combination of Bayesian statistics and grids of synthetic spectra obtained with TLUSTY. This method simultaneously constrains the stellar parameters by using all the lines accessible in observed spectra and thus greatly reduces uncertainties and improves the overall spectrum fitting. Preliminary results are shown using spectra from the Observatoire du Mont-Mégantic.

The Development of Bayesian Theory and Its Applications in Business and Bioinformatics

NASA Astrophysics Data System (ADS)

Zhang, Yifei

2018-03-01

Bayesian Theory originated from an Essay of a British mathematician named Thomas Bayes in 1763, and after its development in 20th century, Bayesian Statistics has been taking a significant part in statistical study of all fields. Due to the recent breakthrough of high-dimensional integral, Bayesian Statistics has been improved and perfected, and now it can be used to solve problems that Classical Statistics failed to solve. This paper summarizes Bayesian Statistics’ history, concepts and applications, which are illustrated in five parts: the history of Bayesian Statistics, the weakness of Classical Statistics, Bayesian Theory and its development and applications. The first two parts make a comparison between Bayesian Statistics and Classical Statistics in a macroscopic aspect. And the last three parts focus on Bayesian Theory in specific -- from introducing some particular Bayesian Statistics’ concepts to listing their development and finally their applications.

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.

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

PubMed

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

2011-08-01

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

An application of Bayesian statistics to the extragalactic Cepheid distance scale

NASA Astrophysics Data System (ADS)

Barnes, Thomas G., III; Moffett, Thomas J.; Jefferys, W. H.; Forestell, Amy D.

2004-05-01

We have determined quasi-geometric distances to the Magellanic Clouds, M31 and M33. Our analysis uses a Bayesian statistical method to provide mathematically rigorous and objective solutions for individual Cepheids. We combine the individual distances with a hierarchial Bayesian model to determine the galactic distances. We obtain distance moduli 18.87 ± 0.07 mag (LMC, 12 stars), 19.14 ± 0.10 (SMC, 8 stars), 23.83 ± 0.35 mag (M33, 1 star) and 25.2 ± 0.6 mag (M31, 1 star) - all uncorrected for metallicity. The M31 and M33 distances are very preliminary. If the Pl relations of the LMC, SMC, and Galaxy are identical, our results exclude the metallicity effect in the V, (V - R) surface brightness method predicted by Hindsley and Bell (1989) at the 5σ level. Alternately, if Hindsley & Bell's prediction is adopted as true, we find a metallicity effect intrinsic to the Cepheid PL relation requiring a correction Δ(V - Mv) = (0.36 ± 0.07)Δ[A/H] mag. The latter has the opposite sign to other observational estimates of the Cepheid metallicity effect.

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

NASA Technical Reports Server (NTRS)

Pohorille, Andrew

2006-01-01

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described

Spatial heterogeneity and risk factors for stunting among children under age five in Ethiopia: A Bayesian geo-statistical model.

PubMed

Hagos, Seifu; Hailemariam, Damen; WoldeHanna, Tasew; Lindtjørn, Bernt

2017-01-01

Understanding the spatial distribution of stunting and underlying factors operating at meso-scale is of paramount importance for intervention designing and implementations. Yet, little is known about the spatial distribution of stunting and some discrepancies are documented on the relative importance of reported risk factors. Therefore, the present study aims at exploring the spatial distribution of stunting at meso- (district) scale, and evaluates the effect of spatial dependency on the identification of risk factors and their relative contribution to the occurrence of stunting and severe stunting in a rural area of Ethiopia. A community based cross sectional study was conducted to measure the occurrence of stunting and severe stunting among children aged 0-59 months. Additionally, we collected relevant information on anthropometric measures, dietary habits, parent and child-related demographic and socio-economic status. Latitude and longitude of surveyed households were also recorded. Local Anselin Moran's I was calculated to investigate the spatial variation of stunting prevalence and identify potential local pockets (hotspots) of high prevalence. Finally, we employed a Bayesian geo-statistical model, which accounted for spatial dependency structure in the data, to identify potential risk factors for stunting in the study area. Overall, the prevalence of stunting and severe stunting in the district was 43.7% [95%CI: 40.9, 46.4] and 21.3% [95%CI: 19.5, 23.3] respectively. We identified statistically significant clusters of high prevalence of stunting (hotspots) in the eastern part of the district and clusters of low prevalence (cold spots) in the western. We found out that the inclusion of spatial structure of the data into the Bayesian model has shown to improve the fit for stunting model. The Bayesian geo-statistical model indicated that the risk of stunting increased as the child's age increased (OR 4.74; 95% Bayesian credible interval [BCI]:3.35-6.58) and

Bayesian statistics: estimating plant demographic parameters

Treesearch

James S. Clark; Michael Lavine

2001-01-01

There are times when external information should be brought tobear on an ecological analysis. experiments are never conducted in a knowledge-free context. The inference we draw from an observation may depend on everything else we know about the process. Bayesian analysis is a method that brings outside evidence into the analysis of experimental and observational data...

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.

UNITY: Confronting Supernova Cosmology's Statistical and Systematic Uncertainties in a Unified Bayesian Framework

NASA Astrophysics Data System (ADS)

Rubin, D.; Aldering, G.; Barbary, K.; Boone, K.; Chappell, G.; Currie, M.; Deustua, S.; Fagrelius, P.; Fruchter, A.; Hayden, B.; Lidman, C.; Nordin, J.; Perlmutter, S.; Saunders, C.; Sofiatti, C.; Supernova Cosmology Project, The

2015-11-01

While recent supernova (SN) cosmology research has benefited from improved measurements, current analysis approaches are not statistically optimal and will prove insufficient for future surveys. This paper discusses the limitations of current SN cosmological analyses in treating outliers, selection effects, shape- and color-standardization relations, unexplained dispersion, and heterogeneous observations. We present a new Bayesian framework, called UNITY (Unified Nonlinear Inference for Type-Ia cosmologY), that incorporates significant improvements in our ability to confront these effects. We apply the framework to real SN observations and demonstrate smaller statistical and systematic uncertainties. We verify earlier results that SNe Ia require nonlinear shape and color standardizations, but we now include these nonlinear relations in a statistically well-justified way. This analysis was primarily performed blinded, in that the basic framework was first validated on simulated data before transitioning to real data. We also discuss possible extensions of the method.

A Gentle Introduction to Bayesian Analysis: Applications to Developmental Research

PubMed Central

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

2014-01-01

Bayesian statistical methods are becoming ever more popular in applied and fundamental research. In this study a gentle introduction to Bayesian analysis is provided. It is shown under what circumstances it is attractive to use Bayesian estimation, and how to interpret properly the results. First, the ingredients underlying Bayesian methods are introduced using a simplified example. Thereafter, the advantages and pitfalls of the specification of prior knowledge are discussed. To illustrate Bayesian methods explained in this study, in a second example a series of studies that examine the theoretical framework of dynamic interactionism are considered. In the Discussion the advantages and disadvantages of using Bayesian statistics are reviewed, and guidelines on how to report on Bayesian statistics are provided. PMID:24116396

A Primer on Bayesian Analysis for Experimental Psychopathologists

PubMed Central

Krypotos, Angelos-Miltiadis; Blanken, Tessa F.; Arnaudova, Inna; Matzke, Dora; Beckers, Tom

2016-01-01

The principal goals of experimental psychopathology (EPP) research are to offer insights into the pathogenic mechanisms of mental disorders and to provide a stable ground for the development of clinical interventions. The main message of the present article is that those goals are better served by the adoption of Bayesian statistics than by the continued use of null-hypothesis significance testing (NHST). In the first part of the article we list the main disadvantages of NHST and explain why those disadvantages limit the conclusions that can be drawn from EPP research. Next, we highlight the advantages of Bayesian statistics. To illustrate, we then pit NHST and Bayesian analysis against each other using an experimental data set from our lab. Finally, we discuss some challenges when adopting Bayesian statistics. We hope that the present article will encourage experimental psychopathologists to embrace Bayesian statistics, which could strengthen the conclusions drawn from EPP research. PMID:28748068

Bayesian methods in reliability

NASA Astrophysics Data System (ADS)

Sander, P.; Badoux, R.

1991-11-01

The present proceedings from a course on Bayesian methods in reliability encompasses Bayesian statistical methods and their computational implementation, models for analyzing censored data from nonrepairable systems, the traits of repairable systems and growth models, the use of expert judgment, and a review of the problem of forecasting software reliability. Specific issues addressed include the use of Bayesian methods to estimate the leak rate of a gas pipeline, approximate analyses under great prior uncertainty, reliability estimation techniques, and a nonhomogeneous Poisson process. Also addressed are the calibration sets and seed variables of expert judgment systems for risk assessment, experimental illustrations of the use of expert judgment for reliability testing, and analyses of the predictive quality of software-reliability growth models such as the Weibull order statistics.

Bayesian Decision Support

NASA Astrophysics Data System (ADS)

Berliner, M.

2017-12-01

Bayesian statistical decision theory offers a natural framework for decision-policy making in the presence of uncertainty. Key advantages of the approach include efficient incorporation of information and observations. However, in complicated settings it is very difficult, perhaps essentially impossible, to formalize the mathematical inputs needed in the approach. Nevertheless, using the approach as a template is useful for decision support; that is, organizing and communicating our analyses. Bayesian hierarchical modeling is valuable in quantifying and managing uncertainty such cases. I review some aspects of the idea emphasizing statistical model development and use in the context of sea-level rise.

Advances in Bayesian Modeling in Educational Research

ERIC Educational Resources Information Center

Levy, Roy

2016-01-01

In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling…

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

Key variables that quantify the time scales over which atmospheric signals penetrate into the oceanic interior and their uncertainties are computed using Bayesian methods and transient tracers from both models and observations. First, the mean residence times, subduction rates, and formation rates of Subtropical Mode Water (STMW) and Subpolar Mode Water (SPMW) in the North Atlantic and Subantarctic Mode Water (SAMW) in the Southern Ocean are estimated by combining a model and observations of chlorofluorocarbon-11 (CFC-11) via Bayesian Model Averaging (BMA), statistical technique that weights model estimates according to how close they agree with observations. Second, a Bayesian method is presented to find two oceanic transport parameters associated with the age distribution of ocean waters, the transit-time distribution (TTD), by combining an eddying global ocean model's estimate of the TTD with hydrographic observations of CFC-11, temperature, and salinity. Uncertainties associated with objectively mapping irregularly spaced bottle data are quantified by making use of a thin-plate spline and then propagated via the two Bayesian techniques. It is found that the subduction of STMW, SPMW, and SAMW is mostly an advective process, but up to about one-third of STMW subduction likely owes to non-advective processes. Also, while the formation of STMW is mostly due to subduction, the formation of SPMW is mostly due to other processes. About half of the formation of SAMW is due to subduction and half is due to other processes. A combination of air-sea flux, acting on relatively short time scales, and turbulent mixing, acting on a wide range of time scales, is likely the dominant SPMW erosion mechanism. Air-sea flux is likely responsible for most STMW erosion, and turbulent mixing is likely responsible for most SAMW erosion. Two oceanic transport parameters, the mean age of a water parcel and the half-variance associated with the TTD, estimated using the model's tracers as

A novel approach for choosing summary statistics in approximate Bayesian computation.

PubMed

Aeschbacher, Simon; Beaumont, Mark A; Futschik, Andreas

2012-11-01

The choice of summary statistics is a crucial step in approximate Bayesian computation (ABC). Since statistics are often not sufficient, this choice involves a trade-off between loss of information and reduction of dimensionality. The latter may increase the efficiency of ABC. Here, we propose an approach for choosing summary statistics based on boosting, a technique from the machine-learning literature. We consider different types of boosting and compare them to partial least-squares regression as an alternative. To mitigate the lack of sufficiency, we also propose an approach for choosing summary statistics locally, in the putative neighborhood of the true parameter value. We study a demographic model motivated by the reintroduction of Alpine ibex (Capra ibex) into the Swiss Alps. The parameters of interest are the mean and standard deviation across microsatellites of the scaled ancestral mutation rate (θ(anc) = 4N(e)u) and the proportion of males obtaining access to matings per breeding season (ω). By simulation, we assess the properties of the posterior distribution obtained with the various methods. According to our criteria, ABC with summary statistics chosen locally via boosting with the L(2)-loss performs best. Applying that method to the ibex data, we estimate θ(anc)≈ 1.288 and find that most of the variation across loci of the ancestral mutation rate u is between 7.7 × 10(-4) and 3.5 × 10(-3) per locus per generation. The proportion of males with access to matings is estimated as ω≈ 0.21, which is in good agreement with recent independent estimates.

A Novel Approach for Choosing Summary Statistics in Approximate Bayesian Computation

PubMed Central

Aeschbacher, Simon; Beaumont, Mark A.; Futschik, Andreas

2012-01-01

The choice of summary statistics is a crucial step in approximate Bayesian computation (ABC). Since statistics are often not sufficient, this choice involves a trade-off between loss of information and reduction of dimensionality. The latter may increase the efficiency of ABC. Here, we propose an approach for choosing summary statistics based on boosting, a technique from the machine-learning literature. We consider different types of boosting and compare them to partial least-squares regression as an alternative. To mitigate the lack of sufficiency, we also propose an approach for choosing summary statistics locally, in the putative neighborhood of the true parameter value. We study a demographic model motivated by the reintroduction of Alpine ibex (Capra ibex) into the Swiss Alps. The parameters of interest are the mean and standard deviation across microsatellites of the scaled ancestral mutation rate (θanc = 4Neu) and the proportion of males obtaining access to matings per breeding season (ω). By simulation, we assess the properties of the posterior distribution obtained with the various methods. According to our criteria, ABC with summary statistics chosen locally via boosting with the L2-loss performs best. Applying that method to the ibex data, we estimate θ^anc≈1.288 and find that most of the variation across loci of the ancestral mutation rate u is between 7.7 × 10−4 and 3.5 × 10−3 per locus per generation. The proportion of males with access to matings is estimated as ω^≈0.21, which is in good agreement with recent independent estimates. PMID:22960215

Bayesian Nonparametric Prediction and Statistical Inference

DTIC Science & Technology

1989-09-07

Kadane, J. (1980), "Bayesian decision theory and the sim- plification of models," in Evaluation of Econometric Models, J. Kmenta and J. Ramsey , eds...the random model and weighted least squares regression," in Evaluation of Econometric Models, ed. by J. Kmenta and J. Ramsey , Academic Press, 197-217...likelihood function. On the other hand, H. Jeffreys’s theory of hypothesis testing covers the most important situations in which the prior is not diffuse. See

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 nonparametric adaptive control using Gaussian processes.

PubMed

Chowdhary, Girish; Kingravi, Hassan A; How, Jonathan P; Vela, Patricio A

2015-03-01

Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element is radial basis function networks (RBFNs), with RBF centers preallocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become noneffective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semiglobal in nature. This paper investigates a Gaussian process-based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. The GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed-loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.

Structure Learning in Bayesian Sensorimotor Integration

PubMed Central

Genewein, Tim; Hez, Eduard; Razzaghpanah, Zeynab; Braun, Daniel A.

2015-01-01

Previous studies have shown that sensorimotor processing can often be described by Bayesian learning, in particular the integration of prior and feedback information depending on its degree of reliability. Here we test the hypothesis that the integration process itself can be tuned to the statistical structure of the environment. We exposed human participants to a reaching task in a three-dimensional virtual reality environment where we could displace the visual feedback of their hand position in a two dimensional plane. When introducing statistical structure between the two dimensions of the displacement, we found that over the course of several days participants adapted their feedback integration process in order to exploit this structure for performance improvement. In control experiments we found that this adaptation process critically depended on performance feedback and could not be induced by verbal instructions. Our results suggest that structural learning is an important meta-learning component of Bayesian sensorimotor integration. PMID:26305797

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 pleiotropy-informed Bayesian false discovery rate adapted to a shared control design finds new disease associations from GWAS summary statistics.

PubMed

Liley, James; Wallace, Chris

2015-02-01

Genome-wide association studies (GWAS) have been successful in identifying single nucleotide polymorphisms (SNPs) associated with many traits and diseases. However, at existing sample sizes, these variants explain only part of the estimated heritability. Leverage of GWAS results from related phenotypes may improve detection without the need for larger datasets. The Bayesian conditional false discovery rate (cFDR) constitutes an upper bound on the expected false discovery rate (FDR) across a set of SNPs whose p values for two diseases are both less than two disease-specific thresholds. Calculation of the cFDR requires only summary statistics and have several advantages over traditional GWAS analysis. However, existing methods require distinct control samples between studies. Here, we extend the technique to allow for some or all controls to be shared, increasing applicability. Several different SNP sets can be defined with the same cFDR value, and we show that the expected FDR across the union of these sets may exceed expected FDR in any single set. We describe a procedure to establish an upper bound for the expected FDR among the union of such sets of SNPs. We apply our technique to pairwise analysis of p values from ten autoimmune diseases with variable sharing of controls, enabling discovery of 59 SNP-disease associations which do not reach GWAS significance after genomic control in individual datasets. Most of the SNPs we highlight have previously been confirmed using replication studies or larger GWAS, a useful validation of our technique; we report eight SNP-disease associations across five diseases not previously declared. Our technique extends and strengthens the previous algorithm, and establishes robust limits on the expected FDR. This approach can improve SNP detection in GWAS, and give insight into shared aetiology between phenotypically related conditions.

The image recognition based on neural network and Bayesian decision

NASA Astrophysics Data System (ADS)

Wang, Chugege

2018-04-01

The artificial neural network began in 1940, which is an important part of artificial intelligence. At present, it has become a hot topic in the fields of neuroscience, computer science, brain science, mathematics, and psychology. Thomas Bayes firstly reported the Bayesian theory in 1763. After the development in the twentieth century, it has been widespread in all areas of statistics. In recent years, due to the solution of the problem of high-dimensional integral calculation, Bayesian Statistics has been improved theoretically, which solved many problems that cannot be solved by classical statistics and is also applied to the interdisciplinary fields. In this paper, the related concepts and principles of the artificial neural network are introduced. It also summarizes the basic content and principle of Bayesian Statistics, and combines the artificial neural network technology and Bayesian decision theory and implement them in all aspects of image recognition, such as enhanced face detection method based on neural network and Bayesian decision, as well as the image classification based on the Bayesian decision. It can be seen that the combination of artificial intelligence and statistical algorithms has always been the hot research topic.

BAYESIAN ESTIMATION OF THERMONUCLEAR REACTION RATES

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

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

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

Assessing compositional variability through graphical analysis and Bayesian statistical approaches: case studies on transgenic crops.

PubMed

Harrigan, George G; Harrison, Jay M

2012-01-01

New transgenic (GM) crops are subjected to extensive safety assessments that include compositional comparisons with conventional counterparts as a cornerstone of the process. The influence of germplasm, location, environment, and agronomic treatments on compositional variability is, however, often obscured in these pair-wise comparisons. Furthermore, classical statistical significance testing can often provide an incomplete and over-simplified summary of highly responsive variables such as crop composition. In order to more clearly describe the influence of the numerous sources of compositional variation we present an introduction to two alternative but complementary approaches to data analysis and interpretation. These include i) exploratory data analysis (EDA) with its emphasis on visualization and graphics-based approaches and ii) Bayesian statistical methodology that provides easily interpretable and meaningful evaluations of data in terms of probability distributions. The EDA case-studies include analyses of herbicide-tolerant GM soybean and insect-protected GM maize and soybean. Bayesian approaches are presented in an analysis of herbicide-tolerant GM soybean. Advantages of these approaches over classical frequentist significance testing include the more direct interpretation of results in terms of probabilities pertaining to quantities of interest and no confusion over the application of corrections for multiple comparisons. It is concluded that a standardized framework for these methodologies could provide specific advantages through enhanced clarity of presentation and interpretation in comparative assessments of crop composition.

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…

Nonlinear and non-Gaussian Bayesian based handwriting beautification

NASA Astrophysics Data System (ADS)

Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua

2013-03-01

A framework is proposed in this paper to effectively and efficiently beautify handwriting by means of a novel nonlinear and non-Gaussian Bayesian algorithm. In the proposed framework, format and size of handwriting image are firstly normalized, and then typeface in computer system is applied to optimize vision effect of handwriting. The Bayesian statistics is exploited to characterize the handwriting beautification process as a Bayesian dynamic model. The model parameters to translate, rotate and scale typeface in computer system are controlled by state equation, and the matching optimization between handwriting and transformed typeface is employed by measurement equation. Finally, the new typeface, which is transformed from the original one and gains the best nonlinear and non-Gaussian optimization, is the beautification result of handwriting. Experimental results demonstrate the proposed framework provides a creative handwriting beautification methodology to improve visual acceptance.

Bayesian statistical ionospheric tomography improved by incorporating ionosonde measurements

NASA Astrophysics Data System (ADS)

Norberg, Johannes; Virtanen, Ilkka I.; Roininen, Lassi; Vierinen, Juha; Orispää, Mikko; Kauristie, Kirsti; Lehtinen, Markku S.

2016-04-01

We validate two-dimensional ionospheric tomography reconstructions against EISCAT incoherent scatter radar measurements. Our tomography method is based on Bayesian statistical inversion with prior distribution given by its mean and covariance. We employ ionosonde measurements for the choice of the prior mean and covariance parameters and use the Gaussian Markov random fields as a sparse matrix approximation for the numerical computations. This results in a computationally efficient tomographic inversion algorithm with clear probabilistic interpretation. We demonstrate how this method works with simultaneous beacon satellite and ionosonde measurements obtained in northern Scandinavia. The performance is compared with results obtained with a zero-mean prior and with the prior mean taken from the International Reference Ionosphere 2007 model. In validating the results, we use EISCAT ultra-high-frequency incoherent scatter radar measurements as the ground truth for the ionization profile shape. We find that in comparison to the alternative prior information sources, ionosonde measurements improve the reconstruction by adding accurate information about the absolute value and the altitude distribution of electron density. With an ionosonde at continuous disposal, the presented method enhances stand-alone near-real-time ionospheric tomography for the given conditions significantly.

Practical Bayesian tomography

NASA Astrophysics Data System (ADS)

Granade, Christopher; Combes, Joshua; Cory, D. G.

2016-03-01

In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of-the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a lack of informative prior distributions, and an inability to track time-dependent processes. Here, we address all three problems. First, we use modern statistical methods, as pioneered by Huszár and Houlsby (2012 Phys. Rev. A 85 052120) and by Ferrie (2014 New J. Phys. 16 093035), to make Bayesian tomography numerically tractable. Our approach allows for practical computation of Bayesian point and region estimators for quantum states and channels. Second, we propose the first priors on quantum states and channels that allow for including useful experimental insight. Finally, we develop a method that allows tracking of time-dependent states and estimates the drift and diffusion processes affecting a state. We provide source code and animated visual examples for our methods.

Analysis of Feature Intervisibility and Cumulative Visibility Using GIS, Bayesian and Spatial Statistics: A Study from the Mandara Mountains, Northern Cameroon

PubMed Central

Wright, David K.; MacEachern, Scott; Lee, Jaeyong

2014-01-01

The locations of diy-geδ-bay (DGB) sites in the Mandara Mountains, northern Cameroon are hypothesized to occur as a function of their ability to see and be seen from points on the surrounding landscape. A series of geostatistical, two-way and Bayesian logistic regression analyses were performed to test two hypotheses related to the intervisibility of the sites to one another and their visual prominence on the landscape. We determine that the intervisibility of the sites to one another is highly statistically significant when compared to 10 stratified-random permutations of DGB sites. Bayesian logistic regression additionally demonstrates that the visibility of the sites to points on the surrounding landscape is statistically significant. The location of sites appears to have also been selected on the basis of lower slope than random permutations of sites. Using statistical measures, many of which are not commonly employed in archaeological research, to evaluate aspects of visibility on the landscape, we conclude that the placement of DGB sites improved their conspicuousness for enhanced ritual, social cooperation and/or competition purposes. PMID:25383883

Optimal speech motor control and token-to-token variability: a Bayesian modeling approach.

PubMed

Patri, Jean-François; Diard, Julien; Perrier, Pascal

2015-12-01

The remarkable capacity of the speech motor system to adapt to various speech conditions is due to an excess of degrees of freedom, which enables producing similar acoustical properties with different sets of control strategies. To explain how the central nervous system selects one of the possible strategies, a common approach, in line with optimal motor control theories, is to model speech motor planning as the solution of an optimality problem based on cost functions. Despite the success of this approach, one of its drawbacks is the intrinsic contradiction between the concept of optimality and the observed experimental intra-speaker token-to-token variability. The present paper proposes an alternative approach by formulating feedforward optimal control in a probabilistic Bayesian modeling framework. This is illustrated by controlling a biomechanical model of the vocal tract for speech production and by comparing it with an existing optimal control model (GEPPETO). The essential elements of this optimal control model are presented first. From them the Bayesian model is constructed in a progressive way. Performance of the Bayesian model is evaluated based on computer simulations and compared to the optimal control model. This approach is shown to be appropriate for solving the speech planning problem while accounting for variability in a principled way.

A systematic review of Bayesian articles in psychology: The last 25 years.

PubMed

van de Schoot, Rens; Winter, Sonja D; Ryan, Oisín; Zondervan-Zwijnenburg, Mariëlle; Depaoli, Sarah

2017-06-01

Although the statistical tools most often used by researchers in the field of psychology over the last 25 years are based on frequentist statistics, it is often claimed that the alternative Bayesian approach to statistics is gaining in popularity. In the current article, we investigated this claim by performing the very first systematic review of Bayesian psychological articles published between 1990 and 2015 (n = 1,579). We aim to provide a thorough presentation of the role Bayesian statistics plays in psychology. This historical assessment allows us to identify trends and see how Bayesian methods have been integrated into psychological research in the context of different statistical frameworks (e.g., hypothesis testing, cognitive models, IRT, SEM, etc.). We also describe take-home messages and provide "big-picture" recommendations to the field as Bayesian statistics becomes more popular. Our review indicated that Bayesian statistics is used in a variety of contexts across subfields of psychology and related disciplines. There are many different reasons why one might choose to use Bayes (e.g., the use of priors, estimating otherwise intractable models, modeling uncertainty, etc.). We found in this review that the use of Bayes has increased and broadened in the sense that this methodology can be used in a flexible manner to tackle many different forms of questions. We hope this presentation opens the door for a larger discussion regarding the current state of Bayesian statistics, as well as future trends. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Mapping malaria risk among children in Côte d'Ivoire using Bayesian geo-statistical models.

PubMed

Raso, Giovanna; Schur, Nadine; Utzinger, Jürg; Koudou, Benjamin G; Tchicaya, Emile S; Rohner, Fabian; N'goran, Eliézer K; Silué, Kigbafori D; Matthys, Barbara; Assi, Serge; Tanner, Marcel; Vounatsou, Penelope

2012-05-09

In Côte d'Ivoire, an estimated 767,000 disability-adjusted life years are due to malaria, placing the country at position number 14 with regard to the global burden of malaria. Risk maps are important to guide control interventions, and hence, the aim of this study was to predict the geographical distribution of malaria infection risk in children aged <16 years in Côte d'Ivoire at high spatial resolution. Using different data sources, a systematic review was carried out to compile and geo-reference survey data on Plasmodium spp. infection prevalence in Côte d'Ivoire, focusing on children aged <16 years. The period from 1988 to 2007 was covered. A suite of Bayesian geo-statistical logistic regression models was fitted to analyse malaria risk. Non-spatial models with and without exchangeable random effect parameters were compared to stationary and non-stationary spatial models. Non-stationarity was modelled assuming that the underlying spatial process is a mixture of separate stationary processes in each ecological zone. The best fitting model based on the deviance information criterion was used to predict Plasmodium spp. infection risk for entire Côte d'Ivoire, including uncertainty. Overall, 235 data points at 170 unique survey locations with malaria prevalence data for individuals aged <16 years were extracted. Most data points (n = 182, 77.4%) were collected between 2000 and 2007. A Bayesian non-stationary regression model showed the best fit with annualized rainfall and maximum land surface temperature identified as significant environmental covariates. This model was used to predict malaria infection risk at non-sampled locations. High-risk areas were mainly found in the north-central and western area, while relatively low-risk areas were located in the north at the country border, in the north-east, in the south-east around Abidjan, and in the central-west between two high prevalence areas. The malaria risk map at high spatial resolution gives an

Mapping malaria risk among children in Côte d’Ivoire using Bayesian geo-statistical models

PubMed Central

2012-01-01

Background In Côte d’Ivoire, an estimated 767,000 disability-adjusted life years are due to malaria, placing the country at position number 14 with regard to the global burden of malaria. Risk maps are important to guide control interventions, and hence, the aim of this study was to predict the geographical distribution of malaria infection risk in children aged <16 years in Côte d’Ivoire at high spatial resolution. Methods Using different data sources, a systematic review was carried out to compile and geo-reference survey data on Plasmodium spp. infection prevalence in Côte d’Ivoire, focusing on children aged <16 years. The period from 1988 to 2007 was covered. A suite of Bayesian geo-statistical logistic regression models was fitted to analyse malaria risk. Non-spatial models with and without exchangeable random effect parameters were compared to stationary and non-stationary spatial models. Non-stationarity was modelled assuming that the underlying spatial process is a mixture of separate stationary processes in each ecological zone. The best fitting model based on the deviance information criterion was used to predict Plasmodium spp. infection risk for entire Côte d’Ivoire, including uncertainty. Results Overall, 235 data points at 170 unique survey locations with malaria prevalence data for individuals aged <16 years were extracted. Most data points (n = 182, 77.4%) were collected between 2000 and 2007. A Bayesian non-stationary regression model showed the best fit with annualized rainfall and maximum land surface temperature identified as significant environmental covariates. This model was used to predict malaria infection risk at non-sampled locations. High-risk areas were mainly found in the north-central and western area, while relatively low-risk areas were located in the north at the country border, in the north-east, in the south-east around Abidjan, and in the central-west between two high prevalence areas. Conclusion The

Bayesian B-spline mapping for dynamic quantitative traits.

PubMed

Xing, Jun; Li, Jiahan; Yang, Runqing; Zhou, Xiaojing; Xu, Shizhong

2012-04-01

Owing to their ability and flexibility to describe individual gene expression at different time points, random regression (RR) analyses have become a popular procedure for the genetic analysis of dynamic traits whose phenotypes are collected over time. Specifically, when modelling the dynamic patterns of gene expressions in the RR framework, B-splines have been proved successful as an alternative to orthogonal polynomials. In the so-called Bayesian B-spline quantitative trait locus (QTL) mapping, B-splines are used to characterize the patterns of QTL effects and individual-specific time-dependent environmental errors over time, and the Bayesian shrinkage estimation method is employed to estimate model parameters. Extensive simulations demonstrate that (1) in terms of statistical power, Bayesian B-spline mapping outperforms the interval mapping based on the maximum likelihood; (2) for the simulated dataset with complicated growth curve simulated by B-splines, Legendre polynomial-based Bayesian mapping is not capable of identifying the designed QTLs accurately, even when higher-order Legendre polynomials are considered and (3) for the simulated dataset using Legendre polynomials, the Bayesian B-spline mapping can find the same QTLs as those identified by Legendre polynomial analysis. All simulation results support the necessity and flexibility of B-spline in Bayesian mapping of dynamic traits. The proposed method is also applied to a real dataset, where QTLs controlling the growth trajectory of stem diameters in Populus are located.

A Gentle Introduction to Bayesian Analysis: Applications to Developmental Research

ERIC Educational Resources Information Center

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

2014-01-01

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

Evaluation of a Partial Genome Screening of Two Asthma Susceptibility Regions Using Bayesian Network Based Bayesian Multilevel Analysis of Relevance

PubMed Central

Antal, Péter; Kiszel, Petra Sz.; Gézsi, András; Hadadi, Éva; Virág, Viktor; Hajós, Gergely; Millinghoffer, András; Nagy, Adrienne; Kiss, András; Semsei, Ágnes F.; Temesi, Gergely; Melegh, Béla; Kisfali, Péter; Széll, Márta; Bikov, András; Gálffy, Gabriella; Tamási, Lilla; Falus, András; Szalai, Csaba

2012-01-01

Genetic studies indicate high number of potential factors related to asthma. Based on earlier linkage analyses we selected the 11q13 and 14q22 asthma susceptibility regions, for which we designed a partial genome screening study using 145 SNPs in 1201 individuals (436 asthmatic children and 765 controls). The results were evaluated with traditional frequentist methods and we applied a new statistical method, called Bayesian network based Bayesian multilevel analysis of relevance (BN-BMLA). This method uses Bayesian network representation to provide detailed characterization of the relevance of factors, such as joint significance, the type of dependency, and multi-target aspects. We estimated posteriors for these relations within the Bayesian statistical framework, in order to estimate the posteriors whether a variable is directly relevant or its association is only mediated. With frequentist methods one SNP (rs3751464 in the FRMD6 gene) provided evidence for an association with asthma (OR = 1.43(1.2–1.8); p = 3×10−4). The possible role of the FRMD6 gene in asthma was also confirmed in an animal model and human asthmatics. In the BN-BMLA analysis altogether 5 SNPs in 4 genes were found relevant in connection with asthma phenotype: PRPF19 on chromosome 11, and FRMD6, PTGER2 and PTGDR on chromosome 14. In a subsequent step a partial dataset containing rhinitis and further clinical parameters was used, which allowed the analysis of relevance of SNPs for asthma and multiple targets. These analyses suggested that SNPs in the AHNAK and MS4A2 genes were indirectly associated with asthma. This paper indicates that BN-BMLA explores the relevant factors more comprehensively than traditional statistical methods and extends the scope of strong relevance based methods to include partial relevance, global characterization of relevance and multi-target relevance. PMID:22432035

Prior approval: the growth of Bayesian methods in psychology.

PubMed

Andrews, Mark; Baguley, Thom

2013-02-01

Within the last few years, Bayesian methods of data analysis in psychology have proliferated. In this paper, we briefly review the history or the Bayesian approach to statistics, and consider the implications that Bayesian methods have for the theory and practice of data analysis in psychology.

Statistical analysis of modal parameters of a suspension bridge based on Bayesian spectral density approach and SHM data

NASA Astrophysics Data System (ADS)

Li, Zhijun; Feng, Maria Q.; Luo, Longxi; Feng, Dongming; Xu, Xiuli

2018-01-01

Uncertainty of modal parameters estimation appear in structural health monitoring (SHM) practice of civil engineering to quite some significant extent due to environmental influences and modeling errors. Reasonable methodologies are needed for processing the uncertainty. Bayesian inference can provide a promising and feasible identification solution for the purpose of SHM. However, there are relatively few researches on the application of Bayesian spectral method in the modal identification using SHM data sets. To extract modal parameters from large data sets collected by SHM system, the Bayesian spectral density algorithm was applied to address the uncertainty of mode extraction from output-only response of a long-span suspension bridge. The posterior most possible values of modal parameters and their uncertainties were estimated through Bayesian inference. A long-term variation and statistical analysis was performed using the sensor data sets collected from the SHM system of the suspension bridge over a one-year period. The t location-scale distribution was shown to be a better candidate function for frequencies of lower modes. On the other hand, the burr distribution provided the best fitting to the higher modes which are sensitive to the temperature. In addition, wind-induced variation of modal parameters was also investigated. It was observed that both the damping ratios and modal forces increased during the period of typhoon excitations. Meanwhile, the modal damping ratios exhibit significant correlation with the spectral intensities of the corresponding modal forces.

Bayesian Inference: with ecological applications

USGS Publications Warehouse

Link, William A.; Barker, Richard J.

2010-01-01

This text provides a mathematically rigorous yet accessible and engaging introduction to Bayesian inference with relevant examples that will be of interest to biologists working in the fields of ecology, wildlife management and environmental studies as well as students in advanced undergraduate statistics.. This text opens the door to Bayesian inference, taking advantage of modern computational efficiencies and easily accessible software to evaluate complex hierarchical models.

Bayesian adjustment for measurement error in continuous exposures in an individually matched case-control study.

PubMed

Espino-Hernandez, Gabriela; Gustafson, Paul; Burstyn, Igor

2011-05-14

In epidemiological studies explanatory variables are frequently subject to measurement error. The aim of this paper is to develop a Bayesian method to correct for measurement error in multiple continuous exposures in individually matched case-control studies. This is a topic that has not been widely investigated. The new method is illustrated using data from an individually matched case-control study of the association between thyroid hormone levels during pregnancy and exposure to perfluorinated acids. The objective of the motivating study was to examine the risk of maternal hypothyroxinemia due to exposure to three perfluorinated acids measured on a continuous scale. Results from the proposed method are compared with those obtained from a naive analysis. Using a Bayesian approach, the developed method considers a classical measurement error model for the exposures, as well as the conditional logistic regression likelihood as the disease model, together with a random-effect exposure model. Proper and diffuse prior distributions are assigned, and results from a quality control experiment are used to estimate the perfluorinated acids' measurement error variability. As a result, posterior distributions and 95% credible intervals of the odds ratios are computed. A sensitivity analysis of method's performance in this particular application with different measurement error variability was performed. The proposed Bayesian method to correct for measurement error is feasible and can be implemented using statistical software. For the study on perfluorinated acids, a comparison of the inferences which are corrected for measurement error to those which ignore it indicates that little adjustment is manifested for the level of measurement error actually exhibited in the exposures. Nevertheless, a sensitivity analysis shows that more substantial adjustments arise if larger measurement errors are assumed. In individually matched case-control studies, the use of conditional

Probabilistic models in human sensorimotor control

PubMed Central

Wolpert, Daniel M.

2009-01-01

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

Back to BaySICS: a user-friendly program for Bayesian Statistical Inference from Coalescent Simulations.

PubMed

Sandoval-Castellanos, Edson; Palkopoulou, Eleftheria; Dalén, Love

2014-01-01

Inference of population demographic history has vastly improved in recent years due to a number of technological and theoretical advances including the use of ancient DNA. Approximate Bayesian computation (ABC) stands among the most promising methods due to its simple theoretical fundament and exceptional flexibility. However, limited availability of user-friendly programs that perform ABC analysis renders it difficult to implement, and hence programming skills are frequently required. In addition, there is limited availability of programs able to deal with heterochronous data. Here we present the software BaySICS: Bayesian Statistical Inference of Coalescent Simulations. BaySICS provides an integrated and user-friendly platform that performs ABC analyses by means of coalescent simulations from DNA sequence data. It estimates historical demographic population parameters and performs hypothesis testing by means of Bayes factors obtained from model comparisons. Although providing specific features that improve inference from datasets with heterochronous data, BaySICS also has several capabilities making it a suitable tool for analysing contemporary genetic datasets. Those capabilities include joint analysis of independent tables, a graphical interface and the implementation of Markov-chain Monte Carlo without likelihoods.

Integrating quantitative PCR and Bayesian statistics in quantifying human adenoviruses in small volumes of source water.

PubMed

Wu, Jianyong; Gronewold, Andrew D; Rodriguez, Roberto A; Stewart, Jill R; Sobsey, Mark D

2014-02-01

Rapid quantification of viral pathogens in drinking and recreational water can help reduce waterborne disease risks. For this purpose, samples in small volume (e.g. 1L) are favored because of the convenience of collection, transportation and processing. However, the results of viral analysis are often subject to uncertainty. To overcome this limitation, we propose an approach that integrates Bayesian statistics, efficient concentration methods, and quantitative PCR (qPCR) to quantify viral pathogens in water. Using this approach, we quantified human adenoviruses (HAdVs) in eighteen samples of source water collected from six drinking water treatment plants. HAdVs were found in seven samples. In the other eleven samples, HAdVs were not detected by qPCR, but might have existed based on Bayesian inference. Our integrated approach that quantifies uncertainty provides a better understanding than conventional assessments of potential risks to public health, particularly in cases when pathogens may present a threat but cannot be detected by traditional methods. © 2013 Elsevier B.V. All rights reserved.

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.

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

When mechanism matters: Bayesian forecasting using models of ecological diffusion

USGS Publications Warehouse

Hefley, Trevor J.; Hooten, Mevin B.; Russell, Robin E.; Walsh, Daniel P.; Powell, James A.

2017-01-01

Ecological diffusion is a theory that can be used to understand and forecast spatio-temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white-tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression-based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.

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.

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.

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

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.

Additive Genetic Variability and the Bayesian Alphabet

PubMed Central

Gianola, Daniel; de los Campos, Gustavo; Hill, William G.; Manfredi, Eduardo; Fernando, Rohan

2009-01-01

The use of all available molecular markers in statistical models for prediction of quantitative traits has led to what could be termed a genomic-assisted selection paradigm in animal and plant breeding. This article provides a critical review of some theoretical and statistical concepts in the context of genomic-assisted genetic evaluation of animals and crops. First, relationships between the (Bayesian) variance of marker effects in some regression models and additive genetic variance are examined under standard assumptions. Second, the connection between marker genotypes and resemblance between relatives is explored, and linkages between a marker-based model and the infinitesimal model are reviewed. Third, issues associated with the use of Bayesian models for marker-assisted selection, with a focus on the role of the priors, are examined from a theoretical angle. The sensitivity of a Bayesian specification that has been proposed (called “Bayes A”) with respect to priors is illustrated with a simulation. Methods that can solve potential shortcomings of some of these Bayesian regression procedures are discussed briefly. PMID:19620397

Toward evidence-based medical statistics: a Bayesian analysis of double-blind placebo-controlled antidepressant trials in the treatment of anxiety disorders.

PubMed

Monden, Rei; de Vos, Stijn; Morey, Richard; Wagenmakers, Eric-Jan; de Jonge, Peter; Roest, Annelieke M

2016-12-01

The Food and Drug Administration (FDA) uses a p < 0.05 null-hypothesis significance testing framework to evaluate "substantial evidence" for drug efficacy. This framework only allows dichotomous conclusions and does not quantify the strength of evidence supporting efficacy. The efficacy of FDA-approved antidepressants for the treatment of anxiety disorders was re-evaluated in a Bayesian framework that quantifies the strength of the evidence. Data from 58 double-blind placebo-controlled trials were retrieved from the FDA for the second-generation antidepressants for the treatment of anxiety disorders. Bayes factors (BFs) were calculated for all treatment arms compared to placebo and were compared with the corresponding p-values and the FDA conclusion categories. BFs ranged from 0.07 to 131,400, indicating a range of no support of evidence to strong evidence for the efficacy. Results also indicate a varying strength of evidence between the trials with p < 0.05. In sum, there were large differences in BFs across trials. Among trials providing "substantial evidence" according to the FDA, only 27 out of 59 dose groups obtained strong support for efficacy according to the typically used cutoff of BF ≥ 20. The Bayesian framework can provide valuable information on the strength of the evidence for drug efficacy. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Bayesian inference for psychology. Part II: Example applications with JASP.

PubMed

Wagenmakers, Eric-Jan; Love, Jonathon; Marsman, Maarten; Jamil, Tahira; Ly, Alexander; Verhagen, Josine; Selker, Ravi; Gronau, Quentin F; Dropmann, Damian; Boutin, Bruno; Meerhoff, Frans; Knight, Patrick; Raj, Akash; van Kesteren, Erik-Jan; van Doorn, Johnny; Šmíra, Martin; Epskamp, Sacha; Etz, Alexander; Matzke, Dora; de Jong, Tim; van den Bergh, Don; Sarafoglou, Alexandra; Steingroever, Helen; Derks, Koen; Rouder, Jeffrey N; Morey, Richard D

2018-02-01

Bayesian hypothesis testing presents an attractive alternative to p value hypothesis testing. Part I of this series outlined several advantages of Bayesian hypothesis testing, including the ability to quantify evidence and the ability to monitor and update this evidence as data come in, without the need to know the intention with which the data were collected. Despite these and other practical advantages, Bayesian hypothesis tests are still reported relatively rarely. An important impediment to the widespread adoption of Bayesian tests is arguably the lack of user-friendly software for the run-of-the-mill statistical problems that confront psychologists for the analysis of almost every experiment: the t-test, ANOVA, correlation, regression, and contingency tables. In Part II of this series we introduce JASP ( http://www.jasp-stats.org ), an open-source, cross-platform, user-friendly graphical software package that allows users to carry out Bayesian hypothesis tests for standard statistical problems. JASP is based in part on the Bayesian analyses implemented in Morey and Rouder's BayesFactor package for R. Armed with JASP, the practical advantages of Bayesian hypothesis testing are only a mouse click away.

A Bayesian test for Hardy–Weinberg equilibrium of biallelic X-chromosomal markers

PubMed Central

Puig, X; Ginebra, J; Graffelman, J

2017-01-01

The X chromosome is a relatively large chromosome, harboring a lot of genetic information. Much of the statistical analysis of X-chromosomal information is complicated by the fact that males only have one copy. Recently, frequentist statistical tests for Hardy–Weinberg equilibrium have been proposed specifically for dealing with markers on the X chromosome. Bayesian test procedures for Hardy–Weinberg equilibrium for the autosomes have been described, but Bayesian work on the X chromosome in this context is lacking. This paper gives the first Bayesian approach for testing Hardy–Weinberg equilibrium with biallelic markers at the X chromosome. Marginal and joint posterior distributions for the inbreeding coefficient in females and the male to female allele frequency ratio are computed, and used for statistical inference. The paper gives a detailed account of the proposed Bayesian test, and illustrates it with data from the 1000 Genomes project. In that implementation, a novel approach to tackle multiple testing from a Bayesian perspective through posterior predictive checks is used. PMID:28900292

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.

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

Bayesian multimodel inference for dose-response studies

USGS Publications Warehouse

Link, W.A.; Albers, P.H.

2007-01-01

Statistical inference in dose?response studies is model-based: The analyst posits a mathematical model of the relation between exposure and response, estimates parameters of the model, and reports conclusions conditional on the model. Such analyses rarely include any accounting for the uncertainties associated with model selection. The Bayesian inferential system provides a convenient framework for model selection and multimodel inference. In this paper we briefly describe the Bayesian paradigm and Bayesian multimodel inference. We then present a family of models for multinomial dose?response data and apply Bayesian multimodel inferential methods to the analysis of data on the reproductive success of American kestrels (Falco sparveriuss) exposed to various sublethal dietary concentrations of methylmercury.

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.

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.

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.

Bayesian structural equation modeling in sport and exercise psychology.

PubMed

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

2015-08-01

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

Bayesian integration and non-linear feedback control in a full-body motor task.

PubMed

Stevenson, Ian H; Fernandes, Hugo L; Vilares, Iris; Wei, Kunlin; Körding, Konrad P

2009-12-01

A large number of experiments have asked to what degree human reaching movements can be understood as being close to optimal in a statistical sense. However, little is known about whether these principles are relevant for other classes of movements. Here we analyzed movement in a task that is similar to surfing or snowboarding. Human subjects stand on a force plate that measures their center of pressure. This center of pressure affects the acceleration of a cursor that is displayed in a noisy fashion (as a cloud of dots) on a projection screen while the subject is incentivized to keep the cursor close to a fixed position. We find that salient aspects of observed behavior are well-described by optimal control models where a Bayesian estimation model (Kalman filter) is combined with an optimal controller (either a Linear-Quadratic-Regulator or Bang-bang controller). We find evidence that subjects integrate information over time taking into account uncertainty. However, behavior in this continuous steering task appears to be a highly non-linear function of the visual feedback. While the nervous system appears to implement Bayes-like mechanisms for a full-body, dynamic task, it may additionally take into account the specific costs and constraints of the task.

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.

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.

Understanding Short-Term Nonmigrating Tidal Variability in the Ionospheric Dynamo Region from SABER Using Information Theory and Bayesian Statistics

NASA Astrophysics Data System (ADS)

Kumari, K.; Oberheide, J.

2017-12-01

Nonmigrating tidal diagnostics of SABER temperature observations in the ionospheric dynamo region reveal a large amount of variability on time-scales of a few days to weeks. In this paper, we discuss the physical reasons for the observed short-term tidal variability using a novel approach based on Information theory and Bayesian statistics. We diagnose short-term tidal variability as a function of season, QBO, ENSO, and solar cycle and other drivers using time dependent probability density functions, Shannon entropy and Kullback-Leibler divergence. The statistical significance of the approach and its predictive capability is exemplified using SABER tidal diagnostics with emphasis on the responses to the QBO and solar cycle. Implications for F-region plasma density will be discussed.

A Bayesian sequential design using alpha spending function to control type I error.

PubMed

Zhu, Han; Yu, Qingzhao

2017-10-01

We propose in this article a Bayesian sequential design using alpha spending functions to control the overall type I error in phase III clinical trials. We provide algorithms to calculate critical values, power, and sample sizes for the proposed design. Sensitivity analysis is implemented to check the effects from different prior distributions, and conservative priors are recommended. We compare the power and actual sample sizes of the proposed Bayesian sequential design with different alpha spending functions through simulations. We also compare the power of the proposed method with frequentist sequential design using the same alpha spending function. Simulations show that, at the same sample size, the proposed method provides larger power than the corresponding frequentist sequential design. It also has larger power than traditional Bayesian sequential design which sets equal critical values for all interim analyses. When compared with other alpha spending functions, O'Brien-Fleming alpha spending function has the largest power and is the most conservative in terms that at the same sample size, the null hypothesis is the least likely to be rejected at early stage of clinical trials. And finally, we show that adding a step of stop for futility in the Bayesian sequential design can reduce the overall type I error and reduce the actual sample sizes.

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.

Bayesian theories of conditioning in a changing world.

PubMed

Courville, Aaron C; Daw, Nathaniel D; Touretzky, David S

2006-07-01

The recent flowering of Bayesian approaches invites the re-examination of classic issues in behavior, even in areas as venerable as Pavlovian conditioning. A statistical account can offer a new, principled interpretation of behavior, and previous experiments and theories can inform many unexplored aspects of the Bayesian enterprise. Here we consider one such issue: the finding that surprising events provoke animals to learn faster. We suggest that, in a statistical account of conditioning, surprise signals change and therefore uncertainty and the need for new learning. We discuss inference in a world that changes and show how experimental results involving surprise can be interpreted from this perspective, and also how, thus understood, these phenomena help constrain statistical theories of animal and human learning.

A study of finite mixture model: Bayesian approach on financial time series data

NASA Astrophysics Data System (ADS)

Phoong, Seuk-Yen; Ismail, Mohd Tahir

2014-07-01

Recently, statistician have emphasized on the fitting finite mixture model by using Bayesian method. Finite mixture model is a mixture of distributions in modeling a statistical distribution meanwhile Bayesian method is a statistical method that use to fit the mixture model. Bayesian method is being used widely because it has asymptotic properties which provide remarkable result. In addition, Bayesian method also shows consistency characteristic which means the parameter estimates are close to the predictive distributions. In the present paper, the number of components for mixture model is studied by using Bayesian Information Criterion. Identify the number of component is important because it may lead to an invalid result. Later, the Bayesian method is utilized to fit the k-component mixture model in order to explore the relationship between rubber price and stock market price for Malaysia, Thailand, Philippines and Indonesia. Lastly, the results showed that there is a negative effect among rubber price and stock market price for all selected countries.

Is probabilistic bias analysis approximately Bayesian?

PubMed Central

MacLehose, Richard F.; Gustafson, Paul

2011-01-01

Case-control studies are particularly susceptible to differential exposure misclassification when exposure status is determined following incident case status. Probabilistic bias analysis methods have been developed as ways to adjust standard effect estimates based on the sensitivity and specificity of exposure misclassification. The iterative sampling method advocated in probabilistic bias analysis bears a distinct resemblance to a Bayesian adjustment; however, it is not identical. Furthermore, without a formal theoretical framework (Bayesian or frequentist), the results of a probabilistic bias analysis remain somewhat difficult to interpret. We describe, both theoretically and empirically, the extent to which probabilistic bias analysis can be viewed as approximately Bayesian. While the differences between probabilistic bias analysis and Bayesian approaches to misclassification can be substantial, these situations often involve unrealistic prior specifications and are relatively easy to detect. Outside of these special cases, probabilistic bias analysis and Bayesian approaches to exposure misclassification in case-control studies appear to perform equally well. PMID:22157311

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.

Towards Validation of an Adaptive Flight Control Simulation Using Statistical Emulation

NASA Technical Reports Server (NTRS)

He, Yuning; Lee, Herbert K. H.; Davies, Misty D.

2012-01-01

Traditional validation of flight control systems is based primarily upon empirical testing. Empirical testing is sufficient for simple systems in which a.) the behavior is approximately linear and b.) humans are in-the-loop and responsible for off-nominal flight regimes. A different possible concept of operation is to use adaptive flight control systems with online learning neural networks (OLNNs) in combination with a human pilot for off-nominal flight behavior (such as when a plane has been damaged). Validating these systems is difficult because the controller is changing during the flight in a nonlinear way, and because the pilot and the control system have the potential to co-adapt in adverse ways traditional empirical methods are unlikely to provide any guarantees in this case. Additionally, the time it takes to find unsafe regions within the flight envelope using empirical testing means that the time between adaptive controller design iterations is large. This paper describes a new concept for validating adaptive control systems using methods based on Bayesian statistics. This validation framework allows the analyst to build nonlinear models with modal behavior, and to have an uncertainty estimate for the difference between the behaviors of the model and system under test.

The Application of Bayesian Analysis to Issues in Developmental Research

ERIC Educational Resources Information Center

Walker, Lawrence J.; Gustafson, Paul; Frimer, Jeremy A.

2007-01-01

This article reviews the concepts and methods of Bayesian statistical analysis, which can offer innovative and powerful solutions to some challenging analytical problems that characterize developmental research. In this article, we demonstrate the utility of Bayesian analysis, explain its unique adeptness in some circumstances, address some…

Moving beyond qualitative evaluations of Bayesian models of cognition.

PubMed

Hemmer, Pernille; Tauber, Sean; Steyvers, Mark

2015-06-01

Bayesian models of cognition provide a powerful way to understand the behavior and goals of individuals from a computational point of view. Much of the focus in the Bayesian cognitive modeling approach has been on qualitative model evaluations, where predictions from the models are compared to data that is often averaged over individuals. In many cognitive tasks, however, there are pervasive individual differences. We introduce an approach to directly infer individual differences related to subjective mental representations within the framework of Bayesian models of cognition. In this approach, Bayesian data analysis methods are used to estimate cognitive parameters and motivate the inference process within a Bayesian cognitive model. We illustrate this integrative Bayesian approach on a model of memory. We apply the model to behavioral data from a memory experiment involving the recall of heights of people. A cross-validation analysis shows that the Bayesian memory model with inferred subjective priors predicts withheld data better than a Bayesian model where the priors are based on environmental statistics. In addition, the model with inferred priors at the individual subject level led to the best overall generalization performance, suggesting that individual differences are important to consider in Bayesian models of cognition.

Bayesian correction for covariate measurement error: A frequentist evaluation and comparison with regression calibration.

PubMed

Bartlett, Jonathan W; Keogh, Ruth H

2018-06-01

Bayesian approaches for handling covariate measurement error are well established and yet arguably are still relatively little used by researchers. For some this is likely due to unfamiliarity or disagreement with the Bayesian inferential paradigm. For others a contributory factor is the inability of standard statistical packages to perform such Bayesian analyses. In this paper, we first give an overview of the Bayesian approach to handling covariate measurement error, and contrast it with regression calibration, arguably the most commonly adopted approach. We then argue why the Bayesian approach has a number of statistical advantages compared to regression calibration and demonstrate that implementing the Bayesian approach is usually quite feasible for the analyst. Next, we describe the closely related maximum likelihood and multiple imputation approaches and explain why we believe the Bayesian approach to generally be preferable. We then empirically compare the frequentist properties of regression calibration and the Bayesian approach through simulation studies. The flexibility of the Bayesian approach to handle both measurement error and missing data is then illustrated through an analysis of data from the Third National Health and Nutrition Examination Survey.

Bayesian stable isotope mixing models

EPA Science Inventory

In this paper we review recent advances in Stable Isotope Mixing Models (SIMMs) and place them into an over-arching Bayesian statistical framework which allows for several useful extensions. SIMMs are used to quantify the proportional contributions of various sources to a mixtur...

Bayesian Statistical Inference in Ion-Channel Models with Exact Missed Event Correction.

PubMed

Epstein, Michael; Calderhead, Ben; Girolami, Mark A; Sivilotti, Lucia G

2016-07-26

The stochastic behavior of single ion channels is most often described as an aggregated continuous-time Markov process with discrete states. For ligand-gated channels each state can represent a different conformation of the channel protein or a different number of bound ligands. Single-channel recordings show only whether the channel is open or shut: states of equal conductance are aggregated, so transitions between them have to be inferred indirectly. The requirement to filter noise from the raw signal further complicates the modeling process, as it limits the time resolution of the data. The consequence of the reduced bandwidth is that openings or shuttings that are shorter than the resolution cannot be observed; these are known as missed events. Postulated models fitted using filtered data must therefore explicitly account for missed events to avoid bias in the estimation of rate parameters and therefore assess parameter identifiability accurately. In this article, we present the first, to our knowledge, Bayesian modeling of ion-channels with exact missed events correction. Bayesian analysis represents uncertain knowledge of the true value of model parameters by considering these parameters as random variables. This allows us to gain a full appreciation of parameter identifiability and uncertainty when estimating values for model parameters. However, Bayesian inference is particularly challenging in this context as the correction for missed events increases the computational complexity of the model likelihood. Nonetheless, we successfully implemented a two-step Markov chain Monte Carlo method that we called "BICME", which performs Bayesian inference in models of realistic complexity. The method is demonstrated on synthetic and real single-channel data from muscle nicotinic acetylcholine channels. We show that parameter uncertainty can be characterized more accurately than with maximum-likelihood methods. Our code for performing inference in these ion channel

Using Alien Coins to Test Whether Simple Inference Is Bayesian

ERIC Educational Resources Information Center

Cassey, Peter; Hawkins, Guy E.; Donkin, Chris; Brown, Scott D.

2016-01-01

Reasoning and inference are well-studied aspects of basic cognition that have been explained as statistically optimal Bayesian inference. Using a simplified experimental design, we conducted quantitative comparisons between Bayesian inference and human inference at the level of individuals. In 3 experiments, with more than 13,000 participants, we…

Bayesian analysis of CCDM models

NASA Astrophysics Data System (ADS)

Jesus, J. F.; Valentim, R.; Andrade-Oliveira, F.

2017-09-01

Creation of Cold Dark Matter (CCDM), in the context of Einstein Field Equations, produces a negative pressure term which can be used to explain the accelerated expansion of the Universe. In this work we tested six different spatially flat models for matter creation using statistical criteria, in light of SNe Ia data: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Bayesian Evidence (BE). These criteria allow to compare models considering goodness of fit and number of free parameters, penalizing excess of complexity. We find that JO model is slightly favoured over LJO/ΛCDM model, however, neither of these, nor Γ = 3αH0 model can be discarded from the current analysis. Three other scenarios are discarded either because poor fitting or because of the excess of free parameters. A method of increasing Bayesian evidence through reparameterization in order to reducing parameter degeneracy is also developed.

Beyond P Values and Hypothesis Testing: Using the Minimum Bayes Factor to Teach Statistical Inference in Undergraduate Introductory Statistics Courses

ERIC Educational Resources Information Center

Page, Robert; Satake, Eiki

2017-01-01

While interest in Bayesian statistics has been growing in statistics education, the treatment of the topic is still inadequate in both textbooks and the classroom. Because so many fields of study lead to careers that involve a decision-making process requiring an understanding of Bayesian methods, it is becoming increasingly clear that Bayesian…

The current state of Bayesian methods in medical product development: survey results and recommendations from the DIA Bayesian Scientific Working Group.

PubMed

Natanegara, Fanni; Neuenschwander, Beat; Seaman, John W; Kinnersley, Nelson; Heilmann, Cory R; Ohlssen, David; Rochester, George

2014-01-01

Bayesian applications in medical product development have recently gained popularity. Despite many advances in Bayesian methodology and computations, increase in application across the various areas of medical product development has been modest. The DIA Bayesian Scientific Working Group (BSWG), which includes representatives from industry, regulatory agencies, and academia, has adopted the vision to ensure Bayesian methods are well understood, accepted more broadly, and appropriately utilized to improve decision making and enhance patient outcomes. As Bayesian applications in medical product development are wide ranging, several sub-teams were formed to focus on various topics such as patient safety, non-inferiority, prior specification, comparative effectiveness, joint modeling, program-wide decision making, analytical tools, and education. The focus of this paper is on the recent effort of the BSWG Education sub-team to administer a Bayesian survey to statisticians across 17 organizations involved in medical product development. We summarize results of this survey, from which we provide recommendations on how to accelerate progress in Bayesian applications throughout medical product development. The survey results support findings from the literature and provide additional insight on regulatory acceptance of Bayesian methods and information on the need for a Bayesian infrastructure within an organization. The survey findings support the claim that only modest progress in areas of education and implementation has been made recently, despite substantial progress in Bayesian statistical research and software availability. Copyright © 2013 John Wiley & Sons, Ltd.

BATSE gamma-ray burst line search. 2: Bayesian consistency methodology

NASA Technical Reports Server (NTRS)

Band, D. L.; Ford, L. A.; Matteson, J. L.; Briggs, M.; Paciesas, W.; Pendleton, G.; Preece, R.; Palmer, D.; Teegarden, B.; Schaefer, B.

1994-01-01

We describe a Bayesian methodology to evaluate the consistency between the reported Ginga and Burst and Transient Source Experiment (BATSE) detections of absorption features in gamma-ray burst spectra. Currently no features have been detected by BATSE, but this methodology will still be applicable if and when such features are discovered. The Bayesian methodology permits the comparison of hypotheses regarding the two detectors' observations and makes explicit the subjective aspects of our analysis (e.g., the quantification of our confidence in detector performance). We also present non-Bayesian consistency statistics. Based on preliminary calculations of line detectability, we find that both the Bayesian and non-Bayesian techniques show that the BATSE and Ginga observations are consistent given our understanding of these detectors.

Bayesian truthing and experimental validation in homeland security and defense

NASA Astrophysics Data System (ADS)

Jannson, Tomasz; Forrester, Thomas; Wang, Wenjian; Kostrzewski, Andrew; Pradhan, Ranjit

2014-05-01

In this paper we discuss relations between Bayesian Truthing (experimental validation), Bayesian statistics, and Binary Sensing in the context of selected Homeland Security and Intelligence, Surveillance, Reconnaissance (ISR) optical and nonoptical application scenarios. The basic Figure of Merit (FoM) is Positive Predictive Value (PPV), as well as false positives and false negatives. By using these simple binary statistics, we can analyze, classify, and evaluate a broad variety of events including: ISR; natural disasters; QC; and terrorism-related, GIS-related, law enforcement-related, and other C3I events.

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.

Quantifying Trace Amounts of Aggregates in Biopharmaceuticals Using Analytical Ultracentrifugation Sedimentation Velocity: Bayesian Analyses and F Statistics.

PubMed

Wafer, Lucas; Kloczewiak, Marek; Luo, Yin

2016-07-01

Analytical ultracentrifugation-sedimentation velocity (AUC-SV) is often used to quantify high molar mass species (HMMS) present in biopharmaceuticals. Although these species are often present in trace quantities, they have received significant attention due to their potential immunogenicity. Commonly, AUC-SV data is analyzed as a diffusion-corrected, sedimentation coefficient distribution, or c(s), using SEDFIT to numerically solve Lamm-type equations. SEDFIT also utilizes maximum entropy or Tikhonov-Phillips regularization to further allow the user to determine relevant sample information, including the number of species present, their sedimentation coefficients, and their relative abundance. However, this methodology has several, often unstated, limitations, which may impact the final analysis of protein therapeutics. These include regularization-specific effects, artificial "ripple peaks," and spurious shifts in the sedimentation coefficients. In this investigation, we experimentally verified that an explicit Bayesian approach, as implemented in SEDFIT, can largely correct for these effects. Clear guidelines on how to implement this technique and interpret the resulting data, especially for samples containing micro-heterogeneity (e.g., differential glycosylation), are also provided. In addition, we demonstrated how the Bayesian approach can be combined with F statistics to draw more accurate conclusions and rigorously exclude artifactual peaks. Numerous examples with an antibody and an antibody-drug conjugate were used to illustrate the strengths and drawbacks of each technique.

Statistical Bayesian method for reliability evaluation based on ADT data

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Bayesian 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.

Bayesian inference of physiologically meaningful parameters from body sway measurements.

PubMed

Tietäväinen, A; Gutmann, M U; Keski-Vakkuri, E; Corander, J; Hæggström, E

2017-06-19

The control of the human body sway by the central nervous system, muscles, and conscious brain is of interest since body sway carries information about the physiological status of a person. Several models have been proposed to describe body sway in an upright standing position, however, due to the statistical intractability of the more realistic models, no formal parameter inference has previously been conducted and the expressive power of such models for real human subjects remains unknown. Using the latest advances in Bayesian statistical inference for intractable models, we fitted a nonlinear control model to posturographic measurements, and we showed that it can accurately predict the sway characteristics of both simulated and real subjects. Our method provides a full statistical characterization of the uncertainty related to all model parameters as quantified by posterior probability density functions, which is useful for comparisons across subjects and test settings. The ability to infer intractable control models from sensor data opens new possibilities for monitoring and predicting body status in health applications.

An introduction to using Bayesian linear regression with clinical data.

PubMed

Baldwin, Scott A; Larson, Michael J

2017-11-01

Statistical training psychology focuses on frequentist methods. Bayesian methods are an alternative to standard frequentist methods. This article provides researchers with an introduction to fundamental ideas in Bayesian modeling. We use data from an electroencephalogram (EEG) and anxiety study to illustrate Bayesian models. Specifically, the models examine the relationship between error-related negativity (ERN), a particular event-related potential, and trait anxiety. Methodological topics covered include: how to set up a regression model in a Bayesian framework, specifying priors, examining convergence of the model, visualizing and interpreting posterior distributions, interval estimates, expected and predicted values, and model comparison tools. We also discuss situations where Bayesian methods can outperform frequentist methods as well has how to specify more complicated regression models. Finally, we conclude with recommendations about reporting guidelines for those using Bayesian methods in their own research. We provide data and R code for replicating our analyses. Copyright © 2017 Elsevier Ltd. 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

Bayesian Inference for Functional Dynamics Exploring in fMRI Data.

PubMed

Guo, Xuan; Liu, Bing; Chen, Le; Chen, Guantao; Pan, Yi; Zhang, Jing

2016-01-01

This paper aims to review state-of-the-art Bayesian-inference-based methods applied to functional magnetic resonance imaging (fMRI) data. Particularly, we focus on one specific long-standing challenge in the computational modeling of fMRI datasets: how to effectively explore typical functional interactions from fMRI time series and the corresponding boundaries of temporal segments. Bayesian inference is a method of statistical inference which has been shown to be a powerful tool to encode dependence relationships among the variables with uncertainty. Here we provide an introduction to a group of Bayesian-inference-based methods for fMRI data analysis, which were designed to detect magnitude or functional connectivity change points and to infer their functional interaction patterns based on corresponding temporal boundaries. We also provide a comparison of three popular Bayesian models, that is, Bayesian Magnitude Change Point Model (BMCPM), Bayesian Connectivity Change Point Model (BCCPM), and Dynamic Bayesian Variable Partition Model (DBVPM), and give a summary of their applications. We envision that more delicate Bayesian inference models will be emerging and play increasingly important roles in modeling brain functions in the years to come.

Advances in statistics

Treesearch

Howard Stauffer; Nadav Nur

2005-01-01

The papers included in the Advances in Statistics section of the Partners in Flight (PIF) 2002 Proceedings represent a small sample of statistical topics of current importance to Partners In Flight research scientists: hierarchical modeling, estimation of detection probabilities, and Bayesian applications. Sauer et al. (this volume) examines a hierarchical model...

Theory-based Bayesian Models of Inductive Inference

DTIC Science & Technology

2010-07-19

Subjective randomness and natural scene statistics. Psychonomic Bulletin & Review . http://cocosci.berkeley.edu/tom/papers/randscenes.pdf Page 1...in press). Exemplar models as a mechanism for performing Bayesian inference. Psychonomic Bulletin & Review . http://cocosci.berkeley.edu/tom

Bayesian networks in neuroscience: a survey.

PubMed

Bielza, Concha; Larrañaga, Pedro

2014-01-01

Bayesian networks are a type of probabilistic graphical models lie at the intersection between statistics and machine learning. They have been shown to be powerful tools to encode dependence relationships among the variables of a domain under uncertainty. Thanks to their generality, Bayesian networks can accommodate continuous and discrete variables, as well as temporal processes. In this paper we review Bayesian networks and how they can be learned automatically from data by means of structure learning algorithms. Also, we examine how a user can take advantage of these networks for reasoning by exact or approximate inference algorithms that propagate the given evidence through the graphical structure. Despite their applicability in many fields, they have been little used in neuroscience, where they have focused on specific problems, like functional connectivity analysis from neuroimaging data. Here we survey key research in neuroscience where Bayesian networks have been used with different aims: discover associations between variables, perform probabilistic reasoning over the model, and classify new observations with and without supervision. The networks are learned from data of any kind-morphological, electrophysiological, -omics and neuroimaging-, thereby broadening the scope-molecular, cellular, structural, functional, cognitive and medical- of the brain aspects to be studied.

[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.

Bayesian depth estimation from monocular natural images.

PubMed

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

2017-05-01

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

A Bayesian approach to meta-analysis of plant pathology studies.

PubMed

Mila, A L; Ngugi, H K

2011-01-01

Bayesian statistical methods are used for meta-analysis in many disciplines, including medicine, molecular biology, and engineering, but have not yet been applied for quantitative synthesis of plant pathology studies. In this paper, we illustrate the key concepts of Bayesian statistics and outline the differences between Bayesian and classical (frequentist) methods in the way parameters describing population attributes are considered. We then describe a Bayesian approach to meta-analysis and present a plant pathological example based on studies evaluating the efficacy of plant protection products that induce systemic acquired resistance for the management of fire blight of apple. In a simple random-effects model assuming a normal distribution of effect sizes and no prior information (i.e., a noninformative prior), the results of the Bayesian meta-analysis are similar to those obtained with classical methods. Implementing the same model with a Student's t distribution and a noninformative prior for the effect sizes, instead of a normal distribution, yields similar results for all but acibenzolar-S-methyl (Actigard) which was evaluated only in seven studies in this example. Whereas both the classical (P = 0.28) and the Bayesian analysis with a noninformative prior (95% credibility interval [CRI] for the log response ratio: -0.63 to 0.08) indicate a nonsignificant effect for Actigard, specifying a t distribution resulted in a significant, albeit variable, effect for this product (CRI: -0.73 to -0.10). These results confirm the sensitivity of the analytical outcome (i.e., the posterior distribution) to the choice of prior in Bayesian meta-analyses involving a limited number of studies. We review some pertinent literature on more advanced topics, including modeling of among-study heterogeneity, publication bias, analyses involving a limited number of studies, and methods for dealing with missing data, and show how these issues can be approached in a Bayesian framework

Rating locomotive crew diesel emission exposure profiles using statistics and Bayesian Decision Analysis.

PubMed

Hewett, Paul; Bullock, William H

2014-01-01

For more than 20 years CSX Transportation (CSXT) has collected exposure measurements from locomotive engineers and conductors who are potentially exposed to diesel emissions. The database included measurements for elemental and total carbon, polycyclic aromatic hydrocarbons, aromatics, aldehydes, carbon monoxide, and nitrogen dioxide. This database was statistically analyzed and summarized, and the resulting statistics and exposure profiles were compared to relevant occupational exposure limits (OELs) using both parametric and non-parametric descriptive and compliance statistics. Exposure ratings, using the American Industrial Health Association (AIHA) exposure categorization scheme, were determined using both the compliance statistics and Bayesian Decision Analysis (BDA). The statistical analysis of the elemental carbon data (a marker for diesel particulate) strongly suggests that the majority of levels in the cabs of the lead locomotives (n = 156) were less than the California guideline of 0.020 mg/m(3). The sample 95th percentile was roughly half the guideline; resulting in an AIHA exposure rating of category 2/3 (determined using BDA). The elemental carbon (EC) levels in the trailing locomotives tended to be greater than those in the lead locomotive; however, locomotive crews rarely ride in the trailing locomotive. Lead locomotive EC levels were similar to those reported by other investigators studying locomotive crew exposures and to levels measured in urban areas. Lastly, both the EC sample mean and 95%UCL were less than the Environmental Protection Agency (EPA) reference concentration of 0.005 mg/m(3). With the exception of nitrogen dioxide, the overwhelming majority of the measurements for total carbon, polycyclic aromatic hydrocarbons, aromatics, aldehydes, and combustion gases in the cabs of CSXT locomotives were either non-detects or considerably less than the working OELs for the years represented in the database. When compared to the previous American

Bayesian survival analysis in clinical trials: What methods are used in practice?

PubMed

Brard, Caroline; Le Teuff, Gwénaël; Le Deley, Marie-Cécile; Hampson, Lisa V

2017-02-01

Background Bayesian statistics are an appealing alternative to the traditional frequentist approach to designing, analysing, and reporting of clinical trials, especially in rare diseases. Time-to-event endpoints are widely used in many medical fields. There are additional complexities to designing Bayesian survival trials which arise from the need to specify a model for the survival distribution. The objective of this article was to critically review the use and reporting of Bayesian methods in survival trials. Methods A systematic review of clinical trials using Bayesian survival analyses was performed through PubMed and Web of Science databases. This was complemented by a full text search of the online repositories of pre-selected journals. Cost-effectiveness, dose-finding studies, meta-analyses, and methodological papers using clinical trials were excluded. Results In total, 28 articles met the inclusion criteria, 25 were original reports of clinical trials and 3 were re-analyses of a clinical trial. Most trials were in oncology (n = 25), were randomised controlled (n = 21) phase III trials (n = 13), and half considered a rare disease (n = 13). Bayesian approaches were used for monitoring in 14 trials and for the final analysis only in 14 trials. In the latter case, Bayesian survival analyses were used for the primary analysis in four cases, for the secondary analysis in seven cases, and for the trial re-analysis in three cases. Overall, 12 articles reported fitting Bayesian regression models (semi-parametric, n = 3; parametric, n = 9). Prior distributions were often incompletely reported: 20 articles did not define the prior distribution used for the parameter of interest. Over half of the trials used only non-informative priors for monitoring and the final analysis (n = 12) when it was specified. Indeed, no articles fitting Bayesian regression models placed informative priors on the parameter of interest. The prior for the treatment

A Bayesian Approach to Interactive Retrieval

ERIC Educational Resources Information Center

Tague, Jean M.

1973-01-01

A probabilistic model for interactive retrieval is presented. Bayesian statistical decision theory principles are applied: use of prior and sample information about the relationship of document descriptions to query relevance; maximization of expected value of a utility function, to the problem of optimally restructuring search strategies in an…

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.

Development of uncertainty-based work injury model using Bayesian structural equation modelling.

PubMed

Chatterjee, Snehamoy

2014-01-01

This paper proposed a Bayesian method-based structural equation model (SEM) of miners' work injury for an underground coal mine in India. The environmental and behavioural variables for work injury were identified and causal relationships were developed. For Bayesian modelling, prior distributions of SEM parameters are necessary to develop the model. In this paper, two approaches were adopted to obtain prior distribution for factor loading parameters and structural parameters of SEM. In the first approach, the prior distributions were considered as a fixed distribution function with specific parameter values, whereas, in the second approach, prior distributions of the parameters were generated from experts' opinions. The posterior distributions of these parameters were obtained by applying Bayesian rule. The Markov Chain Monte Carlo sampling in the form Gibbs sampling was applied for sampling from the posterior distribution. The results revealed that all coefficients of structural and measurement model parameters are statistically significant in experts' opinion-based priors, whereas, two coefficients are not statistically significant when fixed prior-based distributions are applied. The error statistics reveals that Bayesian structural model provides reasonably good fit of work injury with high coefficient of determination (0.91) and less mean squared error as compared to traditional SEM.

Bayesian Statistical Analysis of Historical and Late Holocene Rates of Sea-Level Change

NASA Astrophysics Data System (ADS)

Cahill, Niamh; Parnell, Andrew; Kemp, Andrew; Horton, Benjamin

2014-05-01

A fundamental concern associated with climate change is the rate at which sea levels are rising. Studies of past sea level (particularly beyond the instrumental data range) allow modern sea-level rise to be placed in a more complete context. Considering this, we perform a Bayesian statistical analysis on historical and late Holocene rates of sea-level change. The data that form the input to the statistical model are tide-gauge measurements and proxy reconstructions from cores of coastal sediment. The aims are to estimate rates of sea-level rise, to determine when modern rates of sea-level rise began and to observe how these rates have been changing over time. Many of the current methods for doing this use simple linear regression to estimate rates. This is often inappropriate as it is too rigid and it can ignore uncertainties that arise as part of the data collection exercise. This can lead to over confidence in the sea-level trends being characterized. The proposed Bayesian model places a Gaussian process prior on the rate process (i.e. the process that determines how rates of sea-level are changing over time). The likelihood of the observed data is the integral of this process. When dealing with proxy reconstructions, this is set in an errors-in-variables framework so as to take account of age uncertainty. It is also necessary, in this case, for the model to account for glacio-isostatic adjustment, which introduces a covariance between individual age and sea-level observations. This method provides a flexible fit and it allows for the direct estimation of the rate process with full consideration of all sources of uncertainty. Analysis of tide-gauge datasets and proxy reconstructions in this way means that changing rates of sea level can be estimated more comprehensively and accurately than previously possible. The model captures the continuous and dynamic evolution of sea-level change and results show that not only are modern sea levels rising but that the rates

Bayesian Parameter Inference and Model Selection by Population Annealing in Systems Biology

PubMed Central

Murakami, Yohei

2014-01-01

Parameter inference and model selection are very important for mathematical modeling in systems biology. Bayesian statistics can be used to conduct both parameter inference and model selection. Especially, the framework named approximate Bayesian computation is often used for parameter inference and model selection in systems biology. However, Monte Carlo methods needs to be used to compute Bayesian posterior distributions. In addition, the posterior distributions of parameters are sometimes almost uniform or very similar to their prior distributions. In such cases, it is difficult to choose one specific value of parameter with high credibility as the representative value of the distribution. To overcome the problems, we introduced one of the population Monte Carlo algorithms, population annealing. Although population annealing is usually used in statistical mechanics, we showed that population annealing can be used to compute Bayesian posterior distributions in the approximate Bayesian computation framework. To deal with un-identifiability of the representative values of parameters, we proposed to run the simulations with the parameter ensemble sampled from the posterior distribution, named “posterior parameter ensemble”. We showed that population annealing is an efficient and convenient algorithm to generate posterior parameter ensemble. We also showed that the simulations with the posterior parameter ensemble can, not only reproduce the data used for parameter inference, but also capture and predict the data which was not used for parameter inference. Lastly, we introduced the marginal likelihood in the approximate Bayesian computation framework for Bayesian model selection. We showed that population annealing enables us to compute the marginal likelihood in the approximate Bayesian computation framework and conduct model selection depending on the Bayes factor. PMID:25089832

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 Software Health Management for Aircraft Guidance, Navigation, and Control

NASA Technical Reports Server (NTRS)

Schumann, Johann; Mbaya, Timmy; Menghoel, Ole

2011-01-01

Modern aircraft, both piloted fly-by-wire commercial aircraft as well as UAVs, more and more depend on highly complex safety critical software systems with many sensors and computer-controlled actuators. Despite careful design and V&V of the software, severe incidents have happened due to malfunctioning software. In this paper, we discuss the use of Bayesian networks (BNs) to monitor the health of the on-board software and sensor system, and to perform advanced on-board diagnostic reasoning. We will focus on the approach to develop reliable and robust health models for the combined software and sensor systems.

Statistical Inference at Work: Statistical Process Control as an Example

ERIC Educational Resources Information Center

Bakker, Arthur; Kent, Phillip; Derry, Jan; Noss, Richard; Hoyles, Celia

2008-01-01

To characterise statistical inference in the workplace this paper compares a prototypical type of statistical inference at work, statistical process control (SPC), with a type of statistical inference that is better known in educational settings, hypothesis testing. Although there are some similarities between the reasoning structure involved in…

Quantification and propagation of disciplinary uncertainty via Bayesian statistics

NASA Astrophysics Data System (ADS)

Mantis, George Constantine

2002-08-01

Several needs exist in the military, commercial, and civil sectors for new hypersonic systems. These needs remain unfulfilled, due in part to the uncertainty encountered in designing these systems. This uncertainty takes a number of forms, including disciplinary uncertainty, that which is inherent in the analytical tools utilized during the design process. Yet, few efforts to date empower the designer with the means to account for this uncertainty within the disciplinary analyses. In the current state-of-the-art in design, the effects of this unquantifiable uncertainty significantly increase the risks associated with new design efforts. Typically, the risk proves too great to allow a given design to proceed beyond the conceptual stage. To that end, the research encompasses the formulation and validation of a new design method, a systematic process for probabilistically assessing the impact of disciplinary uncertainty. The method implements Bayesian Statistics theory to quantify this source of uncertainty, and propagate its effects to the vehicle system level. Comparison of analytical and physical data for existing systems, modeled a priori in the given analysis tools, leads to quantification of uncertainty in those tools' calculation of discipline-level metrics. Then, after exploration of the new vehicle's design space, the quantified uncertainty is propagated probabilistically through the design space. This ultimately results in the assessment of the impact of disciplinary uncertainty on the confidence in the design solution: the final shape and variability of the probability functions defining the vehicle's system-level metrics. Although motivated by the hypersonic regime, the proposed treatment of uncertainty applies to any class of aerospace vehicle, just as the problem itself affects the design process of any vehicle. A number of computer programs comprise the environment constructed for the implementation of this work. Application to a single

Why Bayesian Psychologists Should Change the Way They Use the Bayes Factor.

PubMed

Hoijtink, Herbert; van Kooten, Pascal; Hulsker, Koenraad

2016-01-01

The discussion following Bem's ( 2011 ) psi research highlights that applications of the Bayes factor in psychological research are not without problems. The first problem is the omission to translate subjective prior knowledge into subjective prior distributions. In the words of Savage ( 1961 ): "they make the Bayesian omelet without breaking the Bayesian egg." The second problem occurs if the Bayesian egg is not broken: the omission to choose default prior distributions such that the ensuing inferences are well calibrated. The third problem is the adherence to inadequate rules for the interpretation of the size of the Bayes factor. The current paper will elaborate these problems and show how to avoid them using the basic hypotheses and statistical model used in the first experiment described in Bem ( 2011 ). It will be argued that a thorough investigation of these problems in the context of more encompassing hypotheses and statistical models is called for if Bayesian psychologists want to add a well-founded Bayes factor to the tool kit of psychological researchers.

On a full Bayesian inference for force reconstruction problems

NASA Astrophysics Data System (ADS)

Aucejo, M.; De Smet, O.

2018-05-01

In a previous paper, the authors introduced a flexible methodology for reconstructing mechanical sources in the frequency domain from prior local information on both their nature and location over a linear and time invariant structure. The proposed approach was derived from Bayesian statistics, because of its ability in mathematically accounting for experimenter's prior knowledge. However, since only the Maximum a Posteriori estimate was computed, the posterior uncertainty about the regularized solution given the measured vibration field, the mechanical model and the regularization parameter was not assessed. To answer this legitimate question, this paper fully exploits the Bayesian framework to provide, from a Markov Chain Monte Carlo algorithm, credible intervals and other statistical measures (mean, median, mode) for all the parameters of the force reconstruction problem.

Population forecasts for Bangladesh, using a Bayesian methodology.

PubMed

Mahsin, Md; Hossain, Syed Shahadat

2012-12-01

Population projection for many developing countries could be quite a challenging task for the demographers mostly due to lack of availability of enough reliable data. The objective of this paper is to present an overview of the existing methods for population forecasting and to propose an alternative based on the Bayesian statistics, combining the formality of inference. The analysis has been made using Markov Chain Monte Carlo (MCMC) technique for Bayesian methodology available with the software WinBUGS. Convergence diagnostic techniques available with the WinBUGS software have been applied to ensure the convergence of the chains necessary for the implementation of MCMC. The Bayesian approach allows for the use of observed data and expert judgements by means of appropriate priors, and a more realistic population forecasts, along with associated uncertainty, has been possible.

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.

Bayesian networks in neuroscience: a survey

PubMed Central

Bielza, Concha; Larrañaga, Pedro

2014-01-01

Bayesian networks are a type of probabilistic graphical models lie at the intersection between statistics and machine learning. They have been shown to be powerful tools to encode dependence relationships among the variables of a domain under uncertainty. Thanks to their generality, Bayesian networks can accommodate continuous and discrete variables, as well as temporal processes. In this paper we review Bayesian networks and how they can be learned automatically from data by means of structure learning algorithms. Also, we examine how a user can take advantage of these networks for reasoning by exact or approximate inference algorithms that propagate the given evidence through the graphical structure. Despite their applicability in many fields, they have been little used in neuroscience, where they have focused on specific problems, like functional connectivity analysis from neuroimaging data. Here we survey key research in neuroscience where Bayesian networks have been used with different aims: discover associations between variables, perform probabilistic reasoning over the model, and classify new observations with and without supervision. The networks are learned from data of any kind–morphological, electrophysiological, -omics and neuroimaging–, thereby broadening the scope–molecular, cellular, structural, functional, cognitive and medical– of the brain aspects to be studied. PMID:25360109

Characterization of a Saccharomyces cerevisiae fermentation process for production of a therapeutic recombinant protein using a multivariate Bayesian approach.

PubMed

Fu, Zhibiao; Baker, Daniel; Cheng, Aili; Leighton, Julie; Appelbaum, Edward; Aon, Juan

2016-05-01

The principle of quality by design (QbD) has been widely applied to biopharmaceutical manufacturing processes. Process characterization is an essential step to implement the QbD concept to establish the design space and to define the proven acceptable ranges (PAR) for critical process parameters (CPPs). In this study, we present characterization of a Saccharomyces cerevisiae fermentation process using risk assessment analysis, statistical design of experiments (DoE), and the multivariate Bayesian predictive approach. The critical quality attributes (CQAs) and CPPs were identified with a risk assessment. The statistical model for each attribute was established using the results from the DoE study with consideration given to interactions between CPPs. Both the conventional overlapping contour plot and the multivariate Bayesian predictive approaches were used to establish the region of process operating conditions where all attributes met their specifications simultaneously. The quantitative Bayesian predictive approach was chosen to define the PARs for the CPPs, which apply to the manufacturing control strategy. Experience from the 10,000 L manufacturing scale process validation, including 64 continued process verification batches, indicates that the CPPs remain under a state of control and within the established PARs. The end product quality attributes were within their drug substance specifications. The probability generated with the Bayesian approach was also used as a tool to assess CPP deviations. This approach can be extended to develop other production process characterization and quantify a reliable operating region. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:799-812, 2016. © 2016 American Institute of Chemical Engineers.

Bayesian Atmospheric Radiative Transfer (BART): Model, Statistics Driver, and Application to HD 209458b

NASA Astrophysics Data System (ADS)

Cubillos, Patricio; Harrington, Joseph; Blecic, Jasmina; Stemm, Madison M.; Lust, Nate B.; Foster, Andrew S.; Rojo, Patricio M.; Loredo, Thomas J.

2014-11-01

Multi-wavelength secondary-eclipse and transit depths probe the thermo-chemical properties of exoplanets. In recent years, several research groups have developed retrieval codes to analyze the existing data and study the prospects of future facilities. However, the scientific community has limited access to these packages. Here we premiere the open-source Bayesian Atmospheric Radiative Transfer (BART) code. We discuss the key aspects of the radiative-transfer algorithm and the statistical package. The radiation code includes line databases for all HITRAN molecules, high-temperature H2O, TiO, and VO, and includes a preprocessor for adding additional line databases without recompiling the radiation code. Collision-induced absorption lines are available for H2-H2 and H2-He. The parameterized thermal and molecular abundance profiles can be modified arbitrarily without recompilation. The generated spectra are integrated over arbitrary bandpasses for comparison to data. BART's statistical package, Multi-core Markov-chain Monte Carlo (MC3), is a general-purpose MCMC module. MC3 implements the Differental-evolution Markov-chain Monte Carlo algorithm (ter Braak 2006, 2009). MC3 converges 20-400 times faster than the usual Metropolis-Hastings MCMC algorithm, and in addition uses the Message Passing Interface (MPI) to parallelize the MCMC chains. We apply the BART retrieval code to the HD 209458b data set to estimate the planet's temperature profile and molecular abundances. This work was supported by NASA Planetary Atmospheres grant NNX12AI69G and NASA Astrophysics Data Analysis Program grant NNX13AF38G. JB holds a NASA Earth and Space Science Fellowship.

Preferential sampling and Bayesian geostatistics: Statistical modeling and examples.

PubMed

Cecconi, Lorenzo; Grisotto, Laura; Catelan, Dolores; Lagazio, Corrado; Berrocal, Veronica; Biggeri, Annibale

2016-08-01

Preferential sampling refers to any situation in which the spatial process and the sampling locations are not stochastically independent. In this paper, we present two examples of geostatistical analysis in which the usual assumption of stochastic independence between the point process and the measurement process is violated. To account for preferential sampling, we specify a flexible and general Bayesian geostatistical model that includes a shared spatial random component. We apply the proposed model to two different case studies that allow us to highlight three different modeling and inferential aspects of geostatistical modeling under preferential sampling: (1) continuous or finite spatial sampling frame; (2) underlying causal model and relevant covariates; and (3) inferential goals related to mean prediction surface or prediction uncertainty. © The Author(s) 2016.

Incorporating Functional Annotations for Fine-Mapping Causal Variants in a Bayesian Framework Using Summary Statistics.

PubMed

Chen, Wenan; McDonnell, Shannon K; Thibodeau, Stephen N; Tillmans, Lori S; Schaid, Daniel J

2016-11-01

Functional annotations have been shown to improve both the discovery power and fine-mapping accuracy in genome-wide association studies. However, the optimal strategy to incorporate the large number of existing annotations is still not clear. In this study, we propose a Bayesian framework to incorporate functional annotations in a systematic manner. We compute the maximum a posteriori solution and use cross validation to find the optimal penalty parameters. By extending our previous fine-mapping method CAVIARBF into this framework, we require only summary statistics as input. We also derived an exact calculation of Bayes factors using summary statistics for quantitative traits, which is necessary when a large proportion of trait variance is explained by the variants of interest, such as in fine mapping expression quantitative trait loci (eQTL). We compared the proposed method with PAINTOR using different strategies to combine annotations. Simulation results show that the proposed method achieves the best accuracy in identifying causal variants among the different strategies and methods compared. We also find that for annotations with moderate effects from a large annotation pool, screening annotations individually and then combining the top annotations can produce overly optimistic results. We applied these methods on two real data sets: a meta-analysis result of lipid traits and a cis-eQTL study of normal prostate tissues. For the eQTL data, incorporating annotations significantly increased the number of potential causal variants with high probabilities. Copyright © 2016 by the Genetics Society of America.

Estimating size and scope economies in the Portuguese water sector using the Bayesian stochastic frontier analysis.

PubMed

Carvalho, Pedro; Marques, Rui Cunha

2016-02-15

This study aims to search for economies of size and scope in the Portuguese water sector applying Bayesian and classical statistics to make inference in stochastic frontier analysis (SFA). This study proves the usefulness and advantages of the application of Bayesian statistics for making inference in SFA over traditional SFA which just uses classical statistics. The resulting Bayesian methods allow overcoming some problems that arise in the application of the traditional SFA, such as the bias in small samples and skewness of residuals. In the present case study of the water sector in Portugal, these Bayesian methods provide more plausible and acceptable results. Based on the results obtained we found that there are important economies of output density, economies of size, economies of vertical integration and economies of scope in the Portuguese water sector, pointing out to the huge advantages in undertaking mergers by joining the retail and wholesale components and by joining the drinking water and wastewater services. Copyright © 2015 Elsevier B.V. All rights reserved.

Bayesian generalized linear mixed modeling of Tuberculosis using informative priors.

PubMed

Ojo, Oluwatobi Blessing; Lougue, Siaka; Woldegerima, Woldegebriel Assefa

2017-01-01

TB is rated as one of the world's deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014.

Bayesian generalized linear mixed modeling of Tuberculosis using informative priors

PubMed Central

Woldegerima, Woldegebriel Assefa

2017-01-01

TB is rated as one of the world’s deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014. PMID:28257437

The Misidentified Identifiability Problem of Bayesian Knowledge Tracing

ERIC Educational Resources Information Center

Doroudi, Shayan; Brunskill, Emma

2017-01-01

In this paper, we investigate two purported problems with Bayesian Knowledge Tracing (BKT), a popular statistical model of student learning: "identifiability" and "semantic model degeneracy." In 2007, Beck and Chang stated that BKT is susceptible to an "identifiability problem"--various models with different…

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.

Uncertainty analysis of depth predictions from seismic reflection data using Bayesian statistics

NASA Astrophysics Data System (ADS)

Michelioudakis, Dimitrios G.; Hobbs, Richard W.; Caiado, Camila C. S.

2018-03-01

Estimating the depths of target horizons from seismic reflection data is an important task in exploration geophysics. To constrain these depths we need a reliable and accurate velocity model. Here, we build an optimum 2D seismic reflection data processing flow focused on pre - stack deghosting filters and velocity model building and apply Bayesian methods, including Gaussian process emulation and Bayesian History Matching (BHM), to estimate the uncertainties of the depths of key horizons near the borehole DSDP-258 located in the Mentelle Basin, south west of Australia, and compare the results with the drilled core from that well. Following this strategy, the tie between the modelled and observed depths from DSDP-258 core was in accordance with the ± 2σ posterior credibility intervals and predictions for depths to key horizons were made for the two new drill sites, adjacent the existing borehole of the area. The probabilistic analysis allowed us to generate multiple realizations of pre-stack depth migrated images, these can be directly used to better constrain interpretation and identify potential risk at drill sites. The method will be applied to constrain the drilling targets for the upcoming International Ocean Discovery Program (IODP), leg 369.

Using Bayesian statistics for modeling PTSD through Latent Growth Mixture Modeling: implementation and discussion.

PubMed

Depaoli, Sarah; van de Schoot, Rens; van Loey, Nancy; Sijbrandij, Marit

2015-01-01

After traumatic events, such as disaster, war trauma, and injuries including burns (which is the focus here), the risk to develop posttraumatic stress disorder (PTSD) is approximately 10% (Breslau & Davis, 1992). Latent Growth Mixture Modeling can be used to classify individuals into distinct groups exhibiting different patterns of PTSD (Galatzer-Levy, 2015). Currently, empirical evidence points to four distinct trajectories of PTSD patterns in those who have experienced burn trauma. These trajectories are labeled as: resilient, recovery, chronic, and delayed onset trajectories (e.g., Bonanno, 2004; Bonanno, Brewin, Kaniasty, & Greca, 2010; Maercker, Gäbler, O'Neil, Schützwohl, & Müller, 2013; Pietrzak et al., 2013). The delayed onset trajectory affects only a small group of individuals, that is, about 4-5% (O'Donnell, Elliott, Lau, & Creamer, 2007). In addition to its low frequency, the later onset of this trajectory may contribute to the fact that these individuals can be easily overlooked by professionals. In this special symposium on Estimating PTSD trajectories (Van de Schoot, 2015a), we illustrate how to properly identify this small group of individuals through the Bayesian estimation framework using previous knowledge through priors (see, e.g., Depaoli & Boyajian, 2014; Van de Schoot, Broere, Perryck, Zondervan-Zwijnenburg, & Van Loey, 2015). We used latent growth mixture modeling (LGMM) (Van de Schoot, 2015b) to estimate PTSD trajectories across 4 years that followed a traumatic burn. We demonstrate and compare results from traditional (maximum likelihood) and Bayesian estimation using priors (see, Depaoli, 2012, 2013). Further, we discuss where priors come from and how to define them in the estimation process. We demonstrate that only the Bayesian approach results in the desired theory-driven solution of PTSD trajectories. Since the priors are chosen subjectively, we also present a sensitivity analysis of the Bayesian results to illustrate how to check

Embedding the results of focussed Bayesian fusion into a global context

NASA Astrophysics Data System (ADS)

Sander, Jennifer; Heizmann, Michael

2014-05-01

Bayesian statistics offers a well-founded and powerful fusion methodology also for the fusion of heterogeneous information sources. However, except in special cases, the needed posterior distribution is not analytically derivable. As consequence, Bayesian fusion may cause unacceptably high computational and storage costs in practice. Local Bayesian fusion approaches aim at reducing the complexity of the Bayesian fusion methodology significantly. This is done by concentrating the actual Bayesian fusion on the potentially most task relevant parts of the domain of the Properties of Interest. Our research on these approaches is motivated by an analogy to criminal investigations where criminalists pursue clues also only locally. This publication follows previous publications on a special local Bayesian fusion technique called focussed Bayesian fusion. Here, the actual calculation of the posterior distribution gets completely restricted to a suitably chosen local context. By this, the global posterior distribution is not completely determined. Strategies for using the results of a focussed Bayesian analysis appropriately are needed. In this publication, we primarily contrast different ways of embedding the results of focussed Bayesian fusion explicitly into a global context. To obtain a unique global posterior distribution, we analyze the application of the Maximum Entropy Principle that has been shown to be successfully applicable in metrology and in different other areas. To address the special need for making further decisions subsequently to the actual fusion task, we further analyze criteria for decision making under partial information.

Bayesian Group Bridge for Bi-level Variable Selection.

PubMed

Mallick, Himel; Yi, Nengjun

2017-06-01

A Bayesian bi-level variable selection method (BAGB: Bayesian Analysis of Group Bridge) is developed for regularized regression and classification. This new development is motivated by grouped data, where generic variables can be divided into multiple groups, with variables in the same group being mechanistically related or statistically correlated. As an alternative to frequentist group variable selection methods, BAGB incorporates structural information among predictors through a group-wise shrinkage prior. Posterior computation proceeds via an efficient MCMC algorithm. In addition to the usual ease-of-interpretation of hierarchical linear models, the Bayesian formulation produces valid standard errors, a feature that is notably absent in the frequentist framework. Empirical evidence of the attractiveness of the method is illustrated by extensive Monte Carlo simulations and real data analysis. Finally, several extensions of this new approach are presented, providing a unified framework for bi-level variable selection in general models with flexible penalties.

Predicting uncertainty in future marine ice sheet volume using Bayesian statistical methods

NASA Astrophysics Data System (ADS)

Davis, A. D.

2015-12-01

The marine ice instability can trigger rapid retreat of marine ice streams. Recent observations suggest that marine ice systems in West Antarctica have begun retreating. However, unknown ice dynamics, computationally intensive mathematical models, and uncertain parameters in these models make predicting retreat rate and ice volume difficult. In this work, we fuse current observational data with ice stream/shelf models to develop probabilistic predictions of future grounded ice sheet volume. Given observational data (e.g., thickness, surface elevation, and velocity) and a forward model that relates uncertain parameters (e.g., basal friction and basal topography) to these observations, we use a Bayesian framework to define a posterior distribution over the parameters. A stochastic predictive model then propagates uncertainties in these parameters to uncertainty in a particular quantity of interest (QoI)---here, the volume of grounded ice at a specified future time. While the Bayesian approach can in principle characterize the posterior predictive distribution of the QoI, the computational cost of both the forward and predictive models makes this effort prohibitively expensive. To tackle this challenge, we introduce a new Markov chain Monte Carlo method that constructs convergent approximations of the QoI target density in an online fashion, yielding accurate characterizations of future ice sheet volume at significantly reduced computational cost.Our second goal is to attribute uncertainty in these Bayesian predictions to uncertainties in particular parameters. Doing so can help target data collection, for the purpose of constraining the parameters that contribute most strongly to uncertainty in the future volume of grounded ice. For instance, smaller uncertainties in parameters to which the QoI is highly sensitive may account for more variability in the prediction than larger uncertainties in parameters to which the QoI is less sensitive. We use global sensitivity

Refining calibration and predictions of a Bayesian statistical-dynamical model for long term avalanche forecasting using dendrochronological reconstructions

NASA Astrophysics Data System (ADS)

Eckert, Nicolas; Schläppy, Romain; Jomelli, Vincent; Naaim, Mohamed

2013-04-01

A crucial step for proposing relevant long-term mitigation measures in long term avalanche forecasting is the accurate definition of high return period avalanches. Recently, "statistical-dynamical" approach combining a numerical model with stochastic operators describing the variability of its inputs-outputs have emerged. Their main interests is to take into account the topographic dependency of snow avalanche runout distances, and to constrain the correlation structure between model's variables by physical rules, so as to simulate the different marginal distributions of interest (pressure, flow depth, etc.) with a reasonable realism. Bayesian methods have been shown to be well adapted to achieve model inference, getting rid of identifiability problems thanks to prior information. An important problem which has virtually never been considered before is the validation of the predictions resulting from a statistical-dynamical approach (or from any other engineering method for computing extreme avalanches). In hydrology, independent "fossil" data such as flood deposits in caves are sometimes confronted to design discharges corresponding to high return periods. Hence, the aim of this work is to implement a similar comparison between high return period avalanches obtained with a statistical-dynamical approach and independent validation data resulting from careful dendrogeomorphological reconstructions. To do so, an up-to-date statistical model based on the depth-averaged equations and the classical Voellmy friction law is used on a well-documented case study. First, parameter values resulting from another path are applied, and the dendrological validation sample shows that this approach fails in providing realistic prediction for the case study. This may be due to the strongly bounded behaviour of runouts in this case (the extreme of their distribution is identified as belonging to the Weibull attraction domain). Second, local calibration on the available avalanche

Sequential Inverse Problems Bayesian Principles and the Logistic Map Example

NASA Astrophysics Data System (ADS)

Duan, Lian; Farmer, Chris L.; Moroz, Irene M.

2010-09-01

Bayesian statistics provides a general framework for solving inverse problems, but is not without interpretation and implementation problems. This paper discusses difficulties arising from the fact that forward models are always in error to some extent. Using a simple example based on the one-dimensional logistic map, we argue that, when implementation problems are minimal, the Bayesian framework is quite adequate. In this paper the Bayesian Filter is shown to be able to recover excellent state estimates in the perfect model scenario (PMS) and to distinguish the PMS from the imperfect model scenario (IMS). Through a quantitative comparison of the way in which the observations are assimilated in both the PMS and the IMS scenarios, we suggest that one can, sometimes, measure the degree of imperfection.

Personalized Multi-Student Improvement Based on Bayesian Cybernetics

ERIC Educational Resources Information Center

Kaburlasos, Vassilis G.; Marinagi, Catherine C.; Tsoukalas, Vassilis Th.

2008-01-01

This work presents innovative cybernetics (feedback) techniques based on Bayesian statistics for drawing questions from an Item Bank towards personalized multi-student improvement. A novel software tool, namely "Module for Adaptive Assessment of Students" (or, "MAAS" for short), implements the proposed (feedback) techniques. In conclusion, a pilot…

Planetary micro-rover operations on Mars using a Bayesian framework for inference and control

NASA Astrophysics Data System (ADS)

Post, Mark A.; Li, Junquan; Quine, Brendan M.

2016-03-01

With the recent progress toward the application of commercially-available hardware to small-scale space missions, it is now becoming feasible for groups of small, efficient robots based on low-power embedded hardware to perform simple tasks on other planets in the place of large-scale, heavy and expensive robots. In this paper, we describe design and programming of the Beaver micro-rover developed for Northern Light, a Canadian initiative to send a small lander and rover to Mars to study the Martian surface and subsurface. For a small, hardware-limited rover to handle an uncertain and mostly unknown environment without constant management by human operators, we use a Bayesian network of discrete random variables as an abstraction of expert knowledge about the rover and its environment, and inference operations for control. A framework for efficient construction and inference into a Bayesian network using only the C language and fixed-point mathematics on embedded hardware has been developed for the Beaver to make intelligent decisions with minimal sensor data. We study the performance of the Beaver as it probabilistically maps a simple outdoor environment with sensor models that include uncertainty. Results indicate that the Beaver and other small and simple robotic platforms can make use of a Bayesian network to make intelligent decisions in uncertain planetary environments.

Quantitative trait nucleotide analysis using Bayesian model selection.

PubMed

Blangero, John; Goring, Harald H H; Kent, Jack W; Williams, Jeff T; Peterson, Charles P; Almasy, Laura; Dyer, Thomas D

2005-10-01

Although much attention has been given to statistical genetic methods for the initial localization and fine mapping of quantitative trait loci (QTLs), little methodological work has been done to date on the problem of statistically identifying the most likely functional polymorphisms using sequence data. In this paper we provide a general statistical genetic framework, called Bayesian quantitative trait nucleotide (BQTN) analysis, for assessing the likely functional status of genetic variants. The approach requires the initial enumeration of all genetic variants in a set of resequenced individuals. These polymorphisms are then typed in a large number of individuals (potentially in families), and marker variation is related to quantitative phenotypic variation using Bayesian model selection and averaging. For each sequence variant a posterior probability of effect is obtained and can be used to prioritize additional molecular functional experiments. An example of this quantitative nucleotide analysis is provided using the GAW12 simulated data. The results show that the BQTN method may be useful for choosing the most likely functional variants within a gene (or set of genes). We also include instructions on how to use our computer program, SOLAR, for association analysis and BQTN analysis.

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.

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.

Statistical estimation via convex optimization for trending and performance monitoring

NASA Astrophysics Data System (ADS)

Samar, Sikandar

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

Bayesian Regression with Network Prior: Optimal Bayesian Filtering Perspective

PubMed Central

Qian, Xiaoning; Dougherty, Edward R.

2017-01-01

The recently introduced intrinsically Bayesian robust filter (IBRF) provides fully optimal filtering relative to a prior distribution over an uncertainty class ofjoint random process models, whereas formerly the theory was limited to model-constrained Bayesian robust filters, for which optimization was limited to the filters that are optimal for models in the uncertainty class. This paper extends the IBRF theory to the situation where there are both a prior on the uncertainty class and sample data. The result is optimal Bayesian filtering (OBF), where optimality is relative to the posterior distribution derived from the prior and the data. The IBRF theories for effective characteristics and canonical expansions extend to the OBF setting. A salient focus of the present work is to demonstrate the advantages of Bayesian regression within the OBF setting over the classical Bayesian approach in the context otlinear Gaussian models. PMID:28824268

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

PubMed

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

2017-01-01

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

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

PubMed Central

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

2017-01-01

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

Bayesian Networks for Modeling Dredging Decisions

DTIC Science & Technology

2011-10-01

change scenarios. Arctic Expert elicitation Netica Bacon et al . 2002 Identify factors that might lead to a change in land use from farming to...tree) algorithms developed by Lauritzen and Spiegelhalter (1988) and Jensen et al . (1990). Statistical inference is simply the process of...causality when constructing a Bayesian network (Kjaerulff and Madsen 2008, Darwiche 2009, Marcot et al . 2006). A knowledge representation approach is the

How Reliable is Bayesian Model Averaging Under Noisy Data? Statistical Assessment and Implications for Robust Model Selection

NASA Astrophysics Data System (ADS)

Schöniger, Anneli; Wöhling, Thomas; Nowak, Wolfgang

2014-05-01

Bayesian model averaging ranks the predictive capabilities of alternative conceptual models based on Bayes' theorem. The individual models are weighted with their posterior probability to be the best one in the considered set of models. Finally, their predictions are combined into a robust weighted average and the predictive uncertainty can be quantified. This rigorous procedure does, however, not yet account for possible instabilities due to measurement noise in the calibration data set. This is a major drawback, since posterior model weights may suffer a lack of robustness related to the uncertainty in noisy data, which may compromise the reliability of model ranking. We present a new statistical concept to account for measurement noise as source of uncertainty for the weights in Bayesian model averaging. Our suggested upgrade reflects the limited information content of data for the purpose of model selection. It allows us to assess the significance of the determined posterior model weights, the confidence in model selection, and the accuracy of the quantified predictive uncertainty. Our approach rests on a brute-force Monte Carlo framework. We determine the robustness of model weights against measurement noise by repeatedly perturbing the observed data with random realizations of measurement error. Then, we analyze the induced variability in posterior model weights and introduce this "weighting variance" as an additional term into the overall prediction uncertainty analysis scheme. We further determine the theoretical upper limit in performance of the model set which is imposed by measurement noise. As an extension to the merely relative model ranking, this analysis provides a measure of absolute model performance. To finally decide, whether better data or longer time series are needed to ensure a robust basis for model selection, we resample the measurement time series and assess the convergence of model weights for increasing time series length. We illustrate

Uncertainty analysis of depth predictions from seismic reflection data using Bayesian statistics

NASA Astrophysics Data System (ADS)

Michelioudakis, Dimitrios G.; Hobbs, Richard W.; Caiado, Camila C. S.

2018-06-01

Estimating the depths of target horizons from seismic reflection data is an important task in exploration geophysics. To constrain these depths we need a reliable and accurate velocity model. Here, we build an optimum 2-D seismic reflection data processing flow focused on pre-stack deghosting filters and velocity model building and apply Bayesian methods, including Gaussian process emulation and Bayesian History Matching, to estimate the uncertainties of the depths of key horizons near the Deep Sea Drilling Project (DSDP) borehole 258 (DSDP-258) located in the Mentelle Basin, southwest of Australia, and compare the results with the drilled core from that well. Following this strategy, the tie between the modelled and observed depths from DSDP-258 core was in accordance with the ±2σ posterior credibility intervals and predictions for depths to key horizons were made for the two new drill sites, adjacent to the existing borehole of the area. The probabilistic analysis allowed us to generate multiple realizations of pre-stack depth migrated images, these can be directly used to better constrain interpretation and identify potential risk at drill sites. The method will be applied to constrain the drilling targets for the upcoming International Ocean Discovery Program, leg 369.

Bayesian learning of visual chunks by human observers

PubMed Central

Orbán, Gergő; Fiser, József; Aslin, Richard N.; Lengyel, Máté

2008-01-01

Efficient and versatile processing of any hierarchically structured information requires a learning mechanism that combines lower-level features into higher-level chunks. We investigated this chunking mechanism in humans with a visual pattern-learning paradigm. We developed an ideal learner based on Bayesian model comparison that extracts and stores only those chunks of information that are minimally sufficient to encode a set of visual scenes. Our ideal Bayesian chunk learner not only reproduced the results of a large set of previous empirical findings in the domain of human pattern learning but also made a key prediction that we confirmed experimentally. In accordance with Bayesian learning but contrary to associative learning, human performance was well above chance when pair-wise statistics in the exemplars contained no relevant information. Thus, humans extract chunks from complex visual patterns by generating accurate yet economical representations and not by encoding the full correlational structure of the input. PMID:18268353

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 Correlation Analysis for Sequence Count Data

PubMed Central

Lau, Nelson; Perkins, Theodore J.

2016-01-01

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

A Bayesian statistical analysis of mouse dermal tumor promotion assay data for evaluating cigarette smoke condensate.

PubMed

Kathman, Steven J; Potts, Ryan J; Ayres, Paul H; Harp, Paul R; Wilson, Cody L; Garner, Charles D

2010-10-01

The mouse dermal assay has long been used to assess the dermal tumorigenicity of cigarette smoke condensate (CSC). This mouse skin model has been developed for use in carcinogenicity testing utilizing the SENCAR mouse as the standard strain. Though the model has limitations, it remains as the most relevant method available to study the dermal tumor promoting potential of mainstream cigarette smoke. In the typical SENCAR mouse CSC bioassay, CSC is applied for 29 weeks following the application of a tumor initiator such as 7,12-dimethylbenz[a]anthracene (DMBA). Several endpoints are considered for analysis including: the percentage of animals with at least one mass, latency, and number of masses per animal. In this paper, a relatively straightforward analytic model and procedure is presented for analyzing the time course of the incidence of masses. The procedure considered here takes advantage of Bayesian statistical techniques, which provide powerful methods for model fitting and simulation. Two datasets are analyzed to illustrate how the model fits the data, how well the model may perform in predicting data from such trials, and how the model may be used as a decision tool when comparing the dermal tumorigenicity of cigarette smoke condensate from multiple cigarette types. The analysis presented here was developed as a statistical decision tool for differentiating between two or more prototype products based on the dermal tumorigenicity. Copyright (c) 2010 Elsevier Inc. All rights reserved.

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

ANUBIS: artificial neuromodulation using a Bayesian inference system.

PubMed

Smith, Benjamin J H; Saaj, Chakravarthini M; Allouis, Elie

2013-01-01

Gain tuning is a crucial part of controller design and depends not only on an accurate understanding of the system in question, but also on the designer's ability to predict what disturbances and other perturbations the system will encounter throughout its operation. This letter presents ANUBIS (artificial neuromodulation using a Bayesian inference system), a novel biologically inspired technique for automatically tuning controller parameters in real time. ANUBIS is based on the Bayesian brain concept and modifies it by incorporating a model of the neuromodulatory system comprising four artificial neuromodulators. It has been applied to the controller of EchinoBot, a prototype walking rover for Martian exploration. ANUBIS has been implemented at three levels of the controller; gait generation, foot trajectory planning using Bézier curves, and foot trajectory tracking using a terminal sliding mode controller. We compare the results to a similar system that has been tuned using a multilayer perceptron. The use of Bayesian inference means that the system retains mathematical interpretability, unlike other intelligent tuning techniques, which use neural networks, fuzzy logic, or evolutionary algorithms. The simulation results show that ANUBIS provides significant improvements in efficiency and adaptability of the three controller components; it allows the robot to react to obstacles and uncertainties faster than the system tuned with the MLP, while maintaining stability and accuracy. As well as advancing rover autonomy, ANUBIS could also be applied to other situations where operating conditions are likely to change or cannot be accurately modeled in advance, such as process control. In addition, it demonstrates one way in which neuromodulation could fit into the Bayesian brain framework.

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 inference on proportional elections.

PubMed

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.

Analysis of statistical and standard algorithms for detecting muscle onset with surface electromyography

PubMed Central

Tweedell, Andrew J.; Haynes, Courtney A.

2017-01-01

The timing of muscle activity is a commonly applied analytic method to understand how the nervous system controls movement. This study systematically evaluates six classes of standard and statistical algorithms to determine muscle onset in both experimental surface electromyography (EMG) and simulated EMG with a known onset time. Eighteen participants had EMG collected from the biceps brachii and vastus lateralis while performing a biceps curl or knee extension, respectively. Three established methods and three statistical methods for EMG onset were evaluated. Linear envelope, Teager-Kaiser energy operator + linear envelope and sample entropy were the established methods evaluated while general time series mean/variance, sequential and batch processing of parametric and nonparametric tools, and Bayesian changepoint analysis were the statistical techniques used. Visual EMG onset (experimental data) and objective EMG onset (simulated data) were compared with algorithmic EMG onset via root mean square error and linear regression models for stepwise elimination of inferior algorithms. The top algorithms for both data types were analyzed for their mean agreement with the gold standard onset and evaluation of 95% confidence intervals. The top algorithms were all Bayesian changepoint analysis iterations where the parameter of the prior (p0) was zero. The best performing Bayesian algorithms were p0 = 0 and a posterior probability for onset determination at 60–90%. While existing algorithms performed reasonably, the Bayesian changepoint analysis methodology provides greater reliability and accuracy when determining the singular onset of EMG activity in a time series. Further research is needed to determine if this class of algorithms perform equally well when the time series has multiple bursts of muscle activity. PMID:28489897

Analysis of statistical and standard algorithms for detecting muscle onset with surface electromyography.

PubMed

Tenan, Matthew S; Tweedell, Andrew J; Haynes, Courtney A

2017-01-01

The timing of muscle activity is a commonly applied analytic method to understand how the nervous system controls movement. This study systematically evaluates six classes of standard and statistical algorithms to determine muscle onset in both experimental surface electromyography (EMG) and simulated EMG with a known onset time. Eighteen participants had EMG collected from the biceps brachii and vastus lateralis while performing a biceps curl or knee extension, respectively. Three established methods and three statistical methods for EMG onset were evaluated. Linear envelope, Teager-Kaiser energy operator + linear envelope and sample entropy were the established methods evaluated while general time series mean/variance, sequential and batch processing of parametric and nonparametric tools, and Bayesian changepoint analysis were the statistical techniques used. Visual EMG onset (experimental data) and objective EMG onset (simulated data) were compared with algorithmic EMG onset via root mean square error and linear regression models for stepwise elimination of inferior algorithms. The top algorithms for both data types were analyzed for their mean agreement with the gold standard onset and evaluation of 95% confidence intervals. The top algorithms were all Bayesian changepoint analysis iterations where the parameter of the prior (p0) was zero. The best performing Bayesian algorithms were p0 = 0 and a posterior probability for onset determination at 60-90%. While existing algorithms performed reasonably, the Bayesian changepoint analysis methodology provides greater reliability and accuracy when determining the singular onset of EMG activity in a time series. Further research is needed to determine if this class of algorithms perform equally well when the time series has multiple bursts of muscle activity.

Bayesian model selection techniques as decision support for shaping a statistical analysis plan of a clinical trial: An example from a vertigo phase III study with longitudinal count data as primary endpoint

PubMed Central

2012-01-01

Background A statistical analysis plan (SAP) is a critical link between how a clinical trial is conducted and the clinical study report. To secure objective study results, regulatory bodies expect that the SAP will meet requirements in pre-specifying inferential analyses and other important statistical techniques. To write a good SAP for model-based sensitivity and ancillary analyses involves non-trivial decisions on and justification of many aspects of the chosen setting. In particular, trials with longitudinal count data as primary endpoints pose challenges for model choice and model validation. In the random effects setting, frequentist strategies for model assessment and model diagnosis are complex and not easily implemented and have several limitations. Therefore, it is of interest to explore Bayesian alternatives which provide the needed decision support to finalize a SAP. Methods We focus on generalized linear mixed models (GLMMs) for the analysis of longitudinal count data. A series of distributions with over- and under-dispersion is considered. Additionally, the structure of the variance components is modified. We perform a simulation study to investigate the discriminatory power of Bayesian tools for model criticism in different scenarios derived from the model setting. We apply the findings to the data from an open clinical trial on vertigo attacks. These data are seen as pilot data for an ongoing phase III trial. To fit GLMMs we use a novel Bayesian computational approach based on integrated nested Laplace approximations (INLAs). The INLA methodology enables the direct computation of leave-one-out predictive distributions. These distributions are crucial for Bayesian model assessment. We evaluate competing GLMMs for longitudinal count data according to the deviance information criterion (DIC) or probability integral transform (PIT), and by using proper scoring rules (e.g. the logarithmic score). Results The instruments under study provide excellent

Bayesian model selection techniques as decision support for shaping a statistical analysis plan of a clinical trial: an example from a vertigo phase III study with longitudinal count data as primary endpoint.

PubMed

Adrion, Christine; Mansmann, Ulrich

2012-09-10

A statistical analysis plan (SAP) is a critical link between how a clinical trial is conducted and the clinical study report. To secure objective study results, regulatory bodies expect that the SAP will meet requirements in pre-specifying inferential analyses and other important statistical techniques. To write a good SAP for model-based sensitivity and ancillary analyses involves non-trivial decisions on and justification of many aspects of the chosen setting. In particular, trials with longitudinal count data as primary endpoints pose challenges for model choice and model validation. In the random effects setting, frequentist strategies for model assessment and model diagnosis are complex and not easily implemented and have several limitations. Therefore, it is of interest to explore Bayesian alternatives which provide the needed decision support to finalize a SAP. We focus on generalized linear mixed models (GLMMs) for the analysis of longitudinal count data. A series of distributions with over- and under-dispersion is considered. Additionally, the structure of the variance components is modified. We perform a simulation study to investigate the discriminatory power of Bayesian tools for model criticism in different scenarios derived from the model setting. We apply the findings to the data from an open clinical trial on vertigo attacks. These data are seen as pilot data for an ongoing phase III trial. To fit GLMMs we use a novel Bayesian computational approach based on integrated nested Laplace approximations (INLAs). The INLA methodology enables the direct computation of leave-one-out predictive distributions. These distributions are crucial for Bayesian model assessment. We evaluate competing GLMMs for longitudinal count data according to the deviance information criterion (DIC) or probability integral transform (PIT), and by using proper scoring rules (e.g. the logarithmic score). The instruments under study provide excellent tools for preparing decisions

Distinguishing between statistical significance and practical/clinical meaningfulness using statistical inference.

PubMed

Wilkinson, Michael

2014-03-01

Decisions about support for predictions of theories in light of data are made using statistical inference. The dominant approach in sport and exercise science is the Neyman-Pearson (N-P) significance-testing approach. When applied correctly it provides a reliable procedure for making dichotomous decisions for accepting or rejecting zero-effect null hypotheses with known and controlled long-run error rates. Type I and type II error rates must be specified in advance and the latter controlled by conducting an a priori sample size calculation. The N-P approach does not provide the probability of hypotheses or indicate the strength of support for hypotheses in light of data, yet many scientists believe it does. Outcomes of analyses allow conclusions only about the existence of non-zero effects, and provide no information about the likely size of true effects or their practical/clinical value. Bayesian inference can show how much support data provide for different hypotheses, and how personal convictions should be altered in light of data, but the approach is complicated by formulating probability distributions about prior subjective estimates of population effects. A pragmatic solution is magnitude-based inference, which allows scientists to estimate the true magnitude of population effects and how likely they are to exceed an effect magnitude of practical/clinical importance, thereby integrating elements of subjective Bayesian-style thinking. While this approach is gaining acceptance, progress might be hastened if scientists appreciate the shortcomings of traditional N-P null hypothesis significance testing.

Online Variational Bayesian Filtering-Based Mobile Target Tracking in Wireless Sensor Networks

PubMed Central

Zhou, Bingpeng; Chen, Qingchun; Li, Tiffany Jing; Xiao, Pei

2014-01-01

The received signal strength (RSS)-based online tracking for a mobile node in wireless sensor networks (WSNs) is investigated in this paper. Firstly, a multi-layer dynamic Bayesian network (MDBN) is introduced to characterize the target mobility with either directional or undirected movement. In particular, it is proposed to employ the Wishart distribution to approximate the time-varying RSS measurement precision's randomness due to the target movement. It is shown that the proposed MDBN offers a more general analysis model via incorporating the underlying statistical information of both the target movement and observations, which can be utilized to improve the online tracking capability by exploiting the Bayesian statistics. Secondly, based on the MDBN model, a mean-field variational Bayesian filtering (VBF) algorithm is developed to realize the online tracking of a mobile target in the presence of nonlinear observations and time-varying RSS precision, wherein the traditional Bayesian filtering scheme cannot be directly employed. Thirdly, a joint optimization between the real-time velocity and its prior expectation is proposed to enable online velocity tracking in the proposed online tacking scheme. Finally, the associated Bayesian Cramer–Rao Lower Bound (BCRLB) analysis and numerical simulations are conducted. Our analysis unveils that, by exploiting the potential state information via the general MDBN model, the proposed VBF algorithm provides a promising solution to the online tracking of a mobile node in WSNs. In addition, it is shown that the final tracking accuracy linearly scales with its expectation when the RSS measurement precision is time-varying. PMID:25393784

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.

Application of a data-mining method based on Bayesian networks to lesion-deficit analysis

NASA Technical Reports Server (NTRS)

Herskovits, Edward H.; Gerring, Joan P.

2003-01-01

Although lesion-deficit analysis (LDA) has provided extensive information about structure-function associations in the human brain, LDA has suffered from the difficulties inherent to the analysis of spatial data, i.e., there are many more variables than subjects, and data may be difficult to model using standard distributions, such as the normal distribution. We herein describe a Bayesian method for LDA; this method is based on data-mining techniques that employ Bayesian networks to represent structure-function associations. These methods are computationally tractable, and can represent complex, nonlinear structure-function associations. When applied to the evaluation of data obtained from a study of the psychiatric sequelae of traumatic brain injury in children, this method generates a Bayesian network that demonstrates complex, nonlinear associations among lesions in the left caudate, right globus pallidus, right side of the corpus callosum, right caudate, and left thalamus, and subsequent development of attention-deficit hyperactivity disorder, confirming and extending our previous statistical analysis of these data. Furthermore, analysis of simulated data indicates that methods based on Bayesian networks may be more sensitive and specific for detecting associations among categorical variables than methods based on chi-square and Fisher exact statistics.

TOWARDS A BAYESIAN PERSPECTIVE ON STATISTICAL DISCLOSURE LIMITATION

EPA Science Inventory

National statistical offices and other organizations collect data on individual subjects (person, businesses, organizations), typically while assuring the subject that data pertaining to them will be held confidential. These data provide the raw material for statistical data pro...

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.

Case studies in Bayesian microbial risk assessments.

PubMed

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

2009-12-21

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

Bayesian data analysis for newcomers.

PubMed

Kruschke, John K; Liddell, Torrin M

2018-02-01

This article explains the foundational concepts of Bayesian data analysis using virtually no mathematical notation. Bayesian ideas already match your intuitions from everyday reasoning and from traditional data analysis. Simple examples of Bayesian data analysis are presented that illustrate how the information delivered by a Bayesian analysis can be directly interpreted. Bayesian approaches to null-value assessment are discussed. The article clarifies misconceptions about Bayesian methods that newcomers might have acquired elsewhere. We discuss prior distributions and explain how they are not a liability but an important asset. We discuss the relation of Bayesian data analysis to Bayesian models of mind, and we briefly discuss what methodological problems Bayesian data analysis is not meant to solve. After you have read this article, you should have a clear sense of how Bayesian data analysis works and the sort of information it delivers, and why that information is so intuitive and useful for drawing conclusions from data.

Free will in Bayesian and inverse Bayesian inference-driven endo-consciousness.

PubMed

Gunji, Yukio-Pegio; Minoura, Mai; Kojima, Kei; Horry, Yoichi

2017-12-01

How can we link challenging issues related to consciousness and/or qualia with natural science? The introduction of endo-perspective, instead of exo-perspective, as proposed by Matsuno, Rössler, and Gunji, is considered one of the most promising candidate approaches. Here, we distinguish the endo-from the exo-perspective in terms of whether the external is or is not directly operated. In the endo-perspective, the external can be neither perceived nor recognized directly; rather, one can only indirectly summon something outside of the perspective, which can be illustrated by a causation-reversal pair. On one hand, causation logically proceeds from the cause to the effect. On the other hand, a reversal from the effect to the cause is non-logical and is equipped with a metaphorical structure. We argue that the differences in exo- and endo-perspectives result not from the difference between Western and Eastern cultures, but from differences between modernism and animism. Here, a causation-reversal pair described using a pair of upward (from premise to consequence) and downward (from consequence to premise) causation and a pair of Bayesian and inverse Bayesian inference (BIB inference). Accordingly, the notion of endo-consciousness is proposed as an agent equipped with BIB inference. We also argue that BIB inference can yield both highly efficient computations through Bayesian interference and robust computations through inverse Bayesian inference. By adapting a logical model of the free will theorem to the BIB inference, we show that endo-consciousness can explain free will as a regression of the controllability of voluntary action. Copyright © 2017. Published by Elsevier Ltd.

BATMAN: Bayesian Technique for Multi-image Analysis

NASA Astrophysics Data System (ADS)

Casado, J.; Ascasibar, Y.; García-Benito, R.; Guidi, G.; Choudhury, O. S.; Bellocchi, E.; Sánchez, S. F.; Díaz, A. I.

2017-04-01

This paper describes the Bayesian Technique for Multi-image Analysis (BATMAN), a novel image-segmentation technique based on Bayesian statistics that characterizes any astronomical data set containing spatial information and performs a tessellation based on the measurements and errors provided as input. The algorithm iteratively merges spatial elements as long as they are statistically consistent with carrying the same information (I.e. identical signal within the errors). We illustrate its operation and performance with a set of test cases including both synthetic and real integral-field spectroscopic data. The output segmentations adapt to the underlying spatial structure, regardless of its morphology and/or the statistical properties of the noise. The quality of the recovered signal represents an improvement with respect to the input, especially in regions with low signal-to-noise ratio. However, the algorithm may be sensitive to small-scale random fluctuations, and its performance in presence of spatial gradients is limited. Due to these effects, errors may be underestimated by as much as a factor of 2. Our analysis reveals that the algorithm prioritizes conservation of all the statistically significant information over noise reduction, and that the precise choice of the input data has a crucial impact on the results. Hence, the philosophy of BaTMAn is not to be used as a 'black box' to improve the signal-to-noise ratio, but as a new approach to characterize spatially resolved data prior to its analysis. The source code is publicly available at http://astro.ft.uam.es/SELGIFS/BaTMAn.

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.

Confidence of compliance: a Bayesian approach for percentile standards.

PubMed

McBride, G B; Ellis, J C

2001-04-01

Rules for assessing compliance with percentile standards commonly limit the number of exceedances permitted in a batch of samples taken over a defined assessment period. Such rules are commonly developed using classical statistical methods. Results from alternative Bayesian methods are presented (using beta-distributed prior information and a binomial likelihood), resulting in "confidence of compliance" graphs. These allow simple reading of the consumer's risk and the supplier's risks for any proposed rule. The influence of the prior assumptions required by the Bayesian technique on the confidence results is demonstrated, using two reference priors (uniform and Jeffreys') and also using optimistic and pessimistic user-defined priors. All four give less pessimistic results than does the classical technique, because interpreting classical results as "confidence of compliance" actually invokes a Bayesian approach with an extreme prior distribution. Jeffreys' prior is shown to be the most generally appropriate choice of prior distribution. Cost savings can be expected using rules based on this approach.

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.

A Bayesian nonparametric method for prediction in EST analysis

PubMed Central

Lijoi, Antonio; Mena, Ramsés H; Prünster, Igor

2007-01-01

Background Expressed sequence tags (ESTs) analyses are a fundamental tool for gene identification in organisms. Given a preliminary EST sample from a certain library, several statistical prediction problems arise. In particular, it is of interest to estimate how many new genes can be detected in a future EST sample of given size and also to determine the gene discovery rate: these estimates represent the basis for deciding whether to proceed sequencing the library and, in case of a positive decision, a guideline for selecting the size of the new sample. Such information is also useful for establishing sequencing efficiency in experimental design and for measuring the degree of redundancy of an EST library. Results In this work we propose a Bayesian nonparametric approach for tackling statistical problems related to EST surveys. In particular, we provide estimates for: a) the coverage, defined as the proportion of unique genes in the library represented in the given sample of reads; b) the number of new unique genes to be observed in a future sample; c) the discovery rate of new genes as a function of the future sample size. The Bayesian nonparametric model we adopt conveys, in a statistically rigorous way, the available information into prediction. Our proposal has appealing properties over frequentist nonparametric methods, which become unstable when prediction is required for large future samples. EST libraries, previously studied with frequentist methods, are analyzed in detail. Conclusion The Bayesian nonparametric approach we undertake yields valuable tools for gene capture and prediction in EST libraries. The estimators we obtain do not feature the kind of drawbacks associated with frequentist estimators and are reliable for any size of the additional sample. PMID:17868445

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 estimates of the incidence of rare cancers in Europe.

PubMed

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

2018-04-21

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

Investigating the collision energy dependence of η /s in the beam energy scan at the BNL Relativistic Heavy Ion Collider using Bayesian statistics

NASA Astrophysics Data System (ADS)

Auvinen, Jussi; Bernhard, Jonah E.; Bass, Steffen A.; Karpenko, Iurii

2018-04-01

We determine the probability distributions of the shear viscosity over the entropy density ratio η /s in the quark-gluon plasma formed in Au + Au collisions at √{sN N}=19.6 ,39 , and 62.4 GeV , using Bayesian inference and Gaussian process emulators for a model-to-data statistical analysis that probes the full input parameter space of a transport + viscous hydrodynamics hybrid model. We find the most likely value of η /s to be larger at smaller √{sN N}, although the uncertainties still allow for a constant value between 0.10 and 0.15 for the investigated collision energy range.

Topics in Computational Bayesian Statistics With Applications to Hierarchical Models in Astronomy and Sociology

NASA Astrophysics Data System (ADS)

Sahai, Swupnil

This thesis includes three parts. The overarching theme is how to analyze structured hierarchical data, with applications to astronomy and sociology. The first part discusses how expectation propagation can be used to parallelize the computation when fitting big hierarchical bayesian models. This methodology is then used to fit a novel, nonlinear mixture model to ultraviolet radiation from various regions of the observable universe. The second part discusses how the Stan probabilistic programming language can be used to numerically integrate terms in a hierarchical bayesian model. This technique is demonstrated on supernovae data to significantly speed up convergence to the posterior distribution compared to a previous study that used a Gibbs-type sampler. The third part builds a formal latent kernel representation for aggregate relational data as a way to more robustly estimate the mixing characteristics of agents in a network. In particular, the framework is applied to sociology surveys to estimate, as a function of ego age, the age and sex composition of the personal networks of individuals in the United States.

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

Cortical Hierarchies Perform Bayesian Causal Inference in Multisensory Perception

PubMed Central

Rohe, Tim; Noppeney, Uta

2015-01-01

To form a veridical percept of the environment, the brain needs to integrate sensory signals from a common source but segregate those from independent sources. Thus, perception inherently relies on solving the “causal inference problem.” Behaviorally, humans solve this problem optimally as predicted by Bayesian Causal Inference; yet, the underlying neural mechanisms are unexplored. Combining psychophysics, Bayesian modeling, functional magnetic resonance imaging (fMRI), and multivariate decoding in an audiovisual spatial localization task, we demonstrate that Bayesian Causal Inference is performed by a hierarchy of multisensory processes in the human brain. At the bottom of the hierarchy, in auditory and visual areas, location is represented on the basis that the two signals are generated by independent sources (= segregation). At the next stage, in posterior intraparietal sulcus, location is estimated under the assumption that the two signals are from a common source (= forced fusion). Only at the top of the hierarchy, in anterior intraparietal sulcus, the uncertainty about the causal structure of the world is taken into account and sensory signals are combined as predicted by Bayesian Causal Inference. Characterizing the computational operations of signal interactions reveals the hierarchical nature of multisensory perception in human neocortex. It unravels how the brain accomplishes Bayesian Causal Inference, a statistical computation fundamental for perception and cognition. Our results demonstrate how the brain combines information in the face of uncertainty about the underlying causal structure of the world. PMID:25710328

Control Theory and Statistical Generalizations.

ERIC Educational Resources Information Center

Powers, William T.

1990-01-01

Contrasts modeling methods in control theory to the methods of statistical generalizations in empirical studies of human or animal behavior. Presents a computer simulation that predicts behavior based on variables (effort and rewards) determined by the invariable (desired reward). Argues that control theory methods better reflect relationships to…

Numerical study on the sequential Bayesian approach for radioactive materials detection

NASA Astrophysics Data System (ADS)

Qingpei, Xiang; Dongfeng, Tian; Jianyu, Zhu; Fanhua, Hao; Ge, Ding; Jun, Zeng

2013-01-01

A new detection method, based on the sequential Bayesian approach proposed by Candy et al., offers new horizons for the research of radioactive detection. Compared with the commonly adopted detection methods incorporated with statistical theory, the sequential Bayesian approach offers the advantages of shorter verification time during the analysis of spectra that contain low total counts, especially in complex radionuclide components. In this paper, a simulation experiment platform implanted with the methodology of sequential Bayesian approach was developed. Events sequences of γ-rays associating with the true parameters of a LaBr3(Ce) detector were obtained based on an events sequence generator using Monte Carlo sampling theory to study the performance of the sequential Bayesian approach. The numerical experimental results are in accordance with those of Candy. Moreover, the relationship between the detection model and the event generator, respectively represented by the expected detection rate (Am) and the tested detection rate (Gm) parameters, is investigated. To achieve an optimal performance for this processor, the interval of the tested detection rate as a function of the expected detection rate is also presented.

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.

Analyzing Genome-Wide Association Studies with an FDR Controlling Modification of the Bayesian Information Criterion

PubMed Central

Dolejsi, Erich; Bodenstorfer, Bernhard; Frommlet, Florian

2014-01-01

The prevailing method of analyzing GWAS data is still to test each marker individually, although from a statistical point of view it is quite obvious that in case of complex traits such single marker tests are not ideal. Recently several model selection approaches for GWAS have been suggested, most of them based on LASSO-type procedures. Here we will discuss an alternative model selection approach which is based on a modification of the Bayesian Information Criterion (mBIC2) which was previously shown to have certain asymptotic optimality properties in terms of minimizing the misclassification error. Heuristic search strategies are introduced which attempt to find the model which minimizes mBIC2, and which are efficient enough to allow the analysis of GWAS data. Our approach is implemented in a software package called MOSGWA. Its performance in case control GWAS is compared with the two algorithms HLASSO and d-GWASelect, as well as with single marker tests, where we performed a simulation study based on real SNP data from the POPRES sample. Our results show that MOSGWA performs slightly better than HLASSO, where specifically for more complex models MOSGWA is more powerful with only a slight increase in Type I error. On the other hand according to our simulations GWASelect does not at all control the type I error when used to automatically determine the number of important SNPs. We also reanalyze the GWAS data from the Wellcome Trust Case-Control Consortium and compare the findings of the different procedures, where MOSGWA detects for complex diseases a number of interesting SNPs which are not found by other methods. PMID:25061809

Bayesian component separation: The Planck experience

NASA Astrophysics Data System (ADS)

Wehus, Ingunn Kathrine; Eriksen, Hans Kristian

2018-05-01

Bayesian component separation techniques have played a central role in the data reduction process of Planck. The most important strength of this approach is its global nature, in which a parametric and physical model is fitted to the data. Such physical modeling allows the user to constrain very general data models, and jointly probe cosmological, astrophysical and instrumental parameters. This approach also supports statistically robust goodness-of-fit tests in terms of data-minus-model residual maps, which are essential for identifying residual systematic effects in the data. The main challenges are high code complexity and computational cost. Whether or not these costs are justified for a given experiment depends on its final uncertainty budget. We therefore predict that the importance of Bayesian component separation techniques is likely to increase with time for intensity mapping experiments, similar to what has happened in the CMB field, as observational techniques mature, and their overall sensitivity improves.

Bayesian Inference on the Radio-quietness of Gamma-ray Pulsars

NASA Astrophysics Data System (ADS)

Yu, Hoi-Fung; Hui, Chung Yue; Kong, Albert K. H.; Takata, Jumpei

2018-04-01

For the first time we demonstrate using a robust Bayesian approach to analyze the populations of radio-quiet (RQ) and radio-loud (RL) gamma-ray pulsars. We quantify their differences and obtain their distributions of the radio-cone opening half-angle δ and the magnetic inclination angle α by Bayesian inference. In contrast to the conventional frequentist point estimations that might be non-representative when the distribution is highly skewed or multi-modal, which is often the case when data points are scarce, Bayesian statistics displays the complete posterior distribution that the uncertainties can be readily obtained regardless of the skewness and modality. We found that the spin period, the magnetic field strength at the light cylinder, the spin-down power, the gamma-ray-to-X-ray flux ratio, and the spectral curvature significance of the two groups of pulsars exhibit significant differences at the 99% level. Using Bayesian inference, we are able to infer the values and uncertainties of δ and α from the distribution of RQ and RL pulsars. We found that δ is between 10° and 35° and the distribution of α is skewed toward large values.

Nonlinear Bayesian filtering and learning: a neuronal dynamics for perception.

PubMed

Kutschireiter, Anna; Surace, Simone Carlo; Sprekeler, Henning; Pfister, Jean-Pascal

2017-08-18

The robust estimation of dynamical hidden features, such as the position of prey, based on sensory inputs is one of the hallmarks of perception. This dynamical estimation can be rigorously formulated by nonlinear Bayesian filtering theory. Recent experimental and behavioral studies have shown that animals' performance in many tasks is consistent with such a Bayesian statistical interpretation. However, it is presently unclear how a nonlinear Bayesian filter can be efficiently implemented in a network of neurons that satisfies some minimum constraints of biological plausibility. Here, we propose the Neural Particle Filter (NPF), a sampling-based nonlinear Bayesian filter, which does not rely on importance weights. We show that this filter can be interpreted as the neuronal dynamics of a recurrently connected rate-based neural network receiving feed-forward input from sensory neurons. Further, it captures properties of temporal and multi-sensory integration that are crucial for perception, and it allows for online parameter learning with a maximum likelihood approach. The NPF holds the promise to avoid the 'curse of dimensionality', and we demonstrate numerically its capability to outperform weighted particle filters in higher dimensions and when the number of particles is limited.

Model Comparison of Bayesian Semiparametric and Parametric Structural Equation Models

ERIC Educational Resources Information Center

Song, Xin-Yuan; Xia, Ye-Mao; Pan, Jun-Hao; Lee, Sik-Yum

2011-01-01

Structural equation models have wide applications. One of the most important issues in analyzing structural equation models is model comparison. This article proposes a Bayesian model comparison statistic, namely the "L[subscript nu]"-measure for both semiparametric and parametric structural equation models. For illustration purposes, we consider…

Bayesian Networks to Compare Pest Control Interventions on Commodities Along Agricultural Production Chains.

PubMed

Holt, J; Leach, A W; Johnson, S; Tu, D M; Nhu, D T; Anh, N T; Quinlan, M M; Whittle, P J L; Mengersen, K; Mumford, J D

2018-02-01

The production of an agricultural commodity involves a sequence of processes: planting/growing, harvesting, sorting/grading, postharvest treatment, packing, and exporting. A Bayesian network has been developed to represent the level of potential infestation of an agricultural commodity by a specified pest along an agricultural production chain. It reflects the dependency of this infestation on the predicted level of pest challenge, the anticipated susceptibility of the commodity to the pest, the level of impact from pest control measures as designed, and any variation from that due to uncertainty in measure efficacy. The objective of this Bayesian network is to facilitate agreement between national governments of the exporters and importers on a set of phytosanitary measures to meet specific phytosanitary measure requirements to achieve target levels of protection against regulated pests. The model can be used to compare the performance of different combinations of measures under different scenarios of pest challenge, making use of available measure performance data. A case study is presented using a model developed for a fruit fly pest on dragon fruit in Vietnam; the model parameters and results are illustrative and do not imply a particular level of fruit fly infestation of these exports; rather, they provide the most likely, alternative, or worst-case scenarios of the impact of measures. As a means to facilitate agreement for trade, the model provides a framework to support communication between exporters and importers about any differences in perceptions of the risk reduction achieved by pest control measures deployed during the commodity production chain. © 2017 Society for Risk Analysis.

A program for the Bayesian Neural Network in the ROOT framework

NASA Astrophysics Data System (ADS)

Zhong, Jiahang; Huang, Run-Sheng; Lee, Shih-Chang

2011-12-01

We present a Bayesian Neural Network algorithm implemented in the TMVA package (Hoecker et al., 2007 [1]), within the ROOT framework (Brun and Rademakers, 1997 [2]). Comparing to the conventional utilization of Neural Network as discriminator, this new implementation has more advantages as a non-parametric regression tool, particularly for fitting probabilities. It provides functionalities including cost function selection, complexity control and uncertainty estimation. An example of such application in High Energy Physics is shown. The algorithm is available with ROOT release later than 5.29. Program summaryProgram title: TMVA-BNN Catalogue identifier: AEJX_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJX_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: BSD license No. of lines in distributed program, including test data, etc.: 5094 No. of bytes in distributed program, including test data, etc.: 1,320,987 Distribution format: tar.gz Programming language: C++ Computer: Any computer system or cluster with C++ compiler and UNIX-like operating system Operating system: Most UNIX/Linux systems. The application programs were thoroughly tested under Fedora and Scientific Linux CERN. Classification: 11.9 External routines: ROOT package version 5.29 or higher ( http://root.cern.ch) Nature of problem: Non-parametric fitting of multivariate distributions Solution method: An implementation of Neural Network following the Bayesian statistical interpretation. Uses Laplace approximation for the Bayesian marginalizations. Provides the functionalities of automatic complexity control and uncertainty estimation. Running time: Time consumption for the training depends substantially on the size of input sample, the NN topology, the number of training iterations, etc. For the example in this manuscript, about 7 min was used on a PC/Linux with 2.0 GHz processors.

Statistical Physics for Adaptive Distributed Control

NASA Technical Reports Server (NTRS)

Wolpert, David H.

2005-01-01

A viewgraph presentation on statistical physics for distributed adaptive control is shown. The topics include: 1) The Golden Rule; 2) Advantages; 3) Roadmap; 4) What is Distributed Control? 5) Review of Information Theory; 6) Iterative Distributed Control; 7) Minimizing L(q) Via Gradient Descent; and 8) Adaptive Distributed Control.

Bayesian networks for evaluation of evidence from forensic entomology.

PubMed

Andersson, M Gunnar; Sundström, Anders; Lindström, Anders

2013-09-01

In the aftermath of a CBRN incident, there is an urgent need to reconstruct events in order to bring the perpetrators to court and to take preventive actions for the future. The challenge is to discriminate, based on available information, between alternative scenarios. Forensic interpretation is used to evaluate to what extent results from the forensic investigation favor the prosecutors' or the defendants' arguments, using the framework of Bayesian hypothesis testing. Recently, several new scientific disciplines have been used in a forensic context. In the AniBioThreat project, the framework was applied to veterinary forensic pathology, tracing of pathogenic microorganisms, and forensic entomology. Forensic entomology is an important tool for estimating the postmortem interval in, for example, homicide investigations as a complement to more traditional methods. In this article we demonstrate the applicability of the Bayesian framework for evaluating entomological evidence in a forensic investigation through the analysis of a hypothetical scenario involving suspect movement of carcasses from a clandestine laboratory. Probabilities of different findings under the alternative hypotheses were estimated using a combination of statistical analysis of data, expert knowledge, and simulation, and entomological findings are used to update the beliefs about the prosecutors' and defendants' hypotheses and to calculate the value of evidence. The Bayesian framework proved useful for evaluating complex hypotheses using findings from several insect species, accounting for uncertainty about development rate, temperature, and precolonization. The applicability of the forensic statistic approach to evaluating forensic results from a CBRN incident is discussed.

Lead isotope ratios for bullets, forensic evaluation in a Bayesian paradigm.

PubMed

Sjåstad, Knut-Endre; Lucy, David; Andersen, Tom

2016-01-01

Forensic science is a discipline concerned with collection, examination and evaluation of physical evidence related to criminal cases. The results from the activities of the forensic scientist may ultimately be presented to the court in such a way that the triers of fact understand the implications of the data. Forensic science has been, and still is, driven by development of new technology, and in the last two decades evaluation of evidence based on logical reasoning and Bayesian statistic has reached some level of general acceptance within the forensic community. Tracing of lead fragments of unknown origin to a given source of ammunition is a task that might be of interest for the Court. Use of data from lead isotope ratios analysis interpreted within a Bayesian framework has shown to be suitable method to guide the Court to draw their conclusion for such task. In this work we have used isotopic composition of lead from small arms projectiles (cal. .22) and developed an approach based on Bayesian statistics and likelihood ratio calculation. The likelihood ratio is a single quantity that provides a measure of the value of evidence that can be used in the deliberation of the court. Copyright © 2015 Elsevier B.V. All rights reserved.

Model-based Bayesian inference for ROC data analysis

NASA Astrophysics Data System (ADS)

Lei, Tianhu; Bae, K. Ty

2013-03-01

This paper presents a study of model-based Bayesian inference to Receiver Operating Characteristics (ROC) data. The model is a simple version of general non-linear regression model. Different from Dorfman model, it uses a probit link function with a covariate variable having zero-one two values to express binormal distributions in a single formula. Model also includes a scale parameter. Bayesian inference is implemented by Markov Chain Monte Carlo (MCMC) method carried out by Bayesian analysis Using Gibbs Sampling (BUGS). Contrast to the classical statistical theory, Bayesian approach considers model parameters as random variables characterized by prior distributions. With substantial amount of simulated samples generated by sampling algorithm, posterior distributions of parameters as well as parameters themselves can be accurately estimated. MCMC-based BUGS adopts Adaptive Rejection Sampling (ARS) protocol which requires the probability density function (pdf) which samples are drawing from be log concave with respect to the targeted parameters. Our study corrects a common misconception and proves that pdf of this regression model is log concave with respect to its scale parameter. Therefore, ARS's requirement is satisfied and a Gaussian prior which is conjugate and possesses many analytic and computational advantages is assigned to the scale parameter. A cohort of 20 simulated data sets and 20 simulations from each data set are used in our study. Output analysis and convergence diagnostics for MCMC method are assessed by CODA package. Models and methods by using continuous Gaussian prior and discrete categorical prior are compared. Intensive simulations and performance measures are given to illustrate our practice in the framework of model-based Bayesian inference using MCMC method.

Statistical process control in nursing research.

PubMed

Polit, Denise F; Chaboyer, Wendy

2012-02-01

In intervention studies in which randomization to groups is not possible, researchers typically use quasi-experimental designs. Time series designs are strong quasi-experimental designs but are seldom used, perhaps because of technical and analytic hurdles. Statistical process control (SPC) is an alternative analytic approach to testing hypotheses about intervention effects using data collected over time. SPC, like traditional statistical methods, is a tool for understanding variation and involves the construction of control charts that distinguish between normal, random fluctuations (common cause variation), and statistically significant special cause variation that can result from an innovation. The purpose of this article is to provide an overview of SPC and to illustrate its use in a study of a nursing practice improvement intervention. Copyright © 2011 Wiley Periodicals, Inc.

Bayesian posterior distributions without Markov chains.

PubMed

Cole, Stephen R; Chu, Haitao; Greenland, Sander; Hamra, Ghassan; Richardson, David B

2012-03-01

Bayesian posterior parameter distributions are often simulated using Markov chain Monte Carlo (MCMC) methods. However, MCMC methods are not always necessary and do not help the uninitiated understand Bayesian inference. As a bridge to understanding Bayesian inference, the authors illustrate a transparent rejection sampling method. In example 1, they illustrate rejection sampling using 36 cases and 198 controls from a case-control study (1976-1983) assessing the relation between residential exposure to magnetic fields and the development of childhood cancer. Results from rejection sampling (odds ratio (OR) = 1.69, 95% posterior interval (PI): 0.57, 5.00) were similar to MCMC results (OR = 1.69, 95% PI: 0.58, 4.95) and approximations from data-augmentation priors (OR = 1.74, 95% PI: 0.60, 5.06). In example 2, the authors apply rejection sampling to a cohort study of 315 human immunodeficiency virus seroconverters (1984-1998) to assess the relation between viral load after infection and 5-year incidence of acquired immunodeficiency syndrome, adjusting for (continuous) age at seroconversion and race. In this more complex example, rejection sampling required a notably longer run time than MCMC sampling but remained feasible and again yielded similar results. The transparency of the proposed approach comes at a price of being less broadly applicable than MCMC.

Bayesian conditional-independence modeling of the AIDS epidemic in England and Wales

NASA Astrophysics Data System (ADS)

Gilks, Walter R.; De Angelis, Daniela; Day, Nicholas E.

We describe the use of conditional-independence modeling, Bayesian inference and Markov chain Monte Carlo, to model and project the HIV-AIDS epidemic in homosexual/bisexual males in England and Wales. Complexity in this analysis arises through selectively missing data, indirectly observed underlying processes, and measurement error. Our emphasis is on presentation and discussion of the concepts, not on the technicalities of this analysis, which can be found elsewhere [D. De Angelis, W.R. Gilks, N.E. Day, Bayesian projection of the the acquired immune deficiency syndrome epidemic (with discussion), Applied Statistics, in press].

BaTMAn: Bayesian Technique for Multi-image Analysis

NASA Astrophysics Data System (ADS)

Casado, J.; Ascasibar, Y.; García-Benito, R.; Guidi, G.; Choudhury, O. S.; Bellocchi, E.; Sánchez, S. F.; Díaz, A. I.

2016-12-01

Bayesian Technique for Multi-image Analysis (BaTMAn) characterizes any astronomical dataset containing spatial information and performs a tessellation based on the measurements and errors provided as input. The algorithm iteratively merges spatial elements as long as they are statistically consistent with carrying the same information (i.e. identical signal within the errors). The output segmentations successfully adapt to the underlying spatial structure, regardless of its morphology and/or the statistical properties of the noise. BaTMAn identifies (and keeps) all the statistically-significant information contained in the input multi-image (e.g. an IFS datacube). The main aim of the algorithm is to characterize spatially-resolved data prior to their analysis.

Model Diagnostics for Bayesian Networks

ERIC Educational Resources Information Center

Sinharay, Sandip

2006-01-01

Bayesian networks are frequently used in educational assessments primarily for learning about students' knowledge and skills. There is a lack of works on assessing fit of Bayesian networks. This article employs the posterior predictive model checking method, a popular Bayesian model checking tool, to assess fit of simple Bayesian networks. A…

Order priors for Bayesian network discovery with an application to malware phylogeny

DOE PAGES

Oyen, Diane; Anderson, Blake; Sentz, Kari; ...

2017-09-15

Here, Bayesian networks have been used extensively to model and discover dependency relationships among sets of random variables. We learn Bayesian network structure with a combination of human knowledge about the partial ordering of variables and statistical inference of conditional dependencies from observed data. Our approach leverages complementary information from human knowledge and inference from observed data to produce networks that reflect human beliefs about the system as well as to fit the observed data. Applying prior beliefs about partial orderings of variables is an approach distinctly different from existing methods that incorporate prior beliefs about direct dependencies (or edges)more » in a Bayesian network. We provide an efficient implementation of the partial-order prior in a Bayesian structure discovery learning algorithm, as well as an edge prior, showing that both priors meet the local modularity requirement necessary for an efficient Bayesian discovery algorithm. In benchmark studies, the partial-order prior improves the accuracy of Bayesian network structure learning as well as the edge prior, even though order priors are more general. Our primary motivation is in characterizing the evolution of families of malware to aid cyber security analysts. For the problem of malware phylogeny discovery, we find that our algorithm, compared to existing malware phylogeny algorithms, more accurately discovers true dependencies that are missed by other algorithms.« less

Order priors for Bayesian network discovery with an application to malware phylogeny

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

Oyen, Diane; Anderson, Blake; Sentz, Kari

Here, Bayesian networks have been used extensively to model and discover dependency relationships among sets of random variables. We learn Bayesian network structure with a combination of human knowledge about the partial ordering of variables and statistical inference of conditional dependencies from observed data. Our approach leverages complementary information from human knowledge and inference from observed data to produce networks that reflect human beliefs about the system as well as to fit the observed data. Applying prior beliefs about partial orderings of variables is an approach distinctly different from existing methods that incorporate prior beliefs about direct dependencies (or edges)more » in a Bayesian network. We provide an efficient implementation of the partial-order prior in a Bayesian structure discovery learning algorithm, as well as an edge prior, showing that both priors meet the local modularity requirement necessary for an efficient Bayesian discovery algorithm. In benchmark studies, the partial-order prior improves the accuracy of Bayesian network structure learning as well as the edge prior, even though order priors are more general. Our primary motivation is in characterizing the evolution of families of malware to aid cyber security analysts. For the problem of malware phylogeny discovery, we find that our algorithm, compared to existing malware phylogeny algorithms, more accurately discovers true dependencies that are missed by other algorithms.« less

Quantification of downscaled precipitation uncertainties via Bayesian inference

NASA Astrophysics Data System (ADS)

Nury, A. H.; Sharma, A.; Marshall, L. A.

2017-12-01

Prediction of precipitation from global climate model (GCM) outputs remains critical to decision-making in water-stressed regions. In this regard, downscaling of GCM output has been a useful tool for analysing future hydro-climatological states. Several downscaling approaches have been developed for precipitation downscaling, including those using dynamical or statistical downscaling methods. Frequently, outputs from dynamical downscaling are not readily transferable across regions for significant methodical and computational difficulties. Statistical downscaling approaches provide a flexible and efficient alternative, providing hydro-climatological outputs across multiple temporal and spatial scales in many locations. However these approaches are subject to significant uncertainty, arising due to uncertainty in the downscaled model parameters and in the use of different reanalysis products for inferring appropriate model parameters. Consequently, these will affect the performance of simulation in catchment scale. This study develops a Bayesian framework for modelling downscaled daily precipitation from GCM outputs. This study aims to introduce uncertainties in downscaling evaluating reanalysis datasets against observational rainfall data over Australia. In this research a consistent technique for quantifying downscaling uncertainties by means of Bayesian downscaling frame work has been proposed. The results suggest that there are differences in downscaled precipitation occurrences and extremes.

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.

Bayesian Integrated Microbial Forensics

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

Jarman, Kristin H.; Kreuzer-Martin, Helen W.; Wunschel, David S.

2008-06-01

In the aftermath of the 2001 anthrax letters, researchers have been exploring ways to predict the production environment of unknown source microorganisms. Different mass spectral techniques are being developed to characterize components of a microbe’s culture medium including water, carbon and nitrogen sources, metal ions added, and the presence of agar. Individually, each technique has the potential to identify one or two ingredients in a culture medium recipe. However, by integrating data from multiple mass spectral techniques, a more complete characterization is possible. We present a Bayesian statistical approach to integrated microbial forensics and illustrate its application on spores grownmore » in different culture media.« less

Inference on the Genetic Basis of Eye and Skin Color in an Admixed Population via Bayesian Linear Mixed Models.

PubMed

Lloyd-Jones, Luke R; Robinson, Matthew R; Moser, Gerhard; Zeng, Jian; Beleza, Sandra; Barsh, Gregory S; Tang, Hua; Visscher, Peter M

2017-06-01

Genetic association studies in admixed populations are underrepresented in the genomics literature, with a key concern for researchers being the adequate control of spurious associations due to population structure. Linear mixed models (LMMs) are well suited for genome-wide association studies (GWAS) because they account for both population stratification and cryptic relatedness and achieve increased statistical power by jointly modeling all genotyped markers. Additionally, Bayesian LMMs allow for more flexible assumptions about the underlying distribution of genetic effects, and can concurrently estimate the proportion of phenotypic variance explained by genetic markers. Using three recently published Bayesian LMMs, Bayes R, BSLMM, and BOLT-LMM, we investigate an existing data set on eye ( n = 625) and skin ( n = 684) color from Cape Verde, an island nation off West Africa that is home to individuals with a broad range of phenotypic values for eye and skin color due to the mix of West African and European ancestry. We use simulations to demonstrate the utility of Bayesian LMMs for mapping loci and studying the genetic architecture of quantitative traits in admixed populations. The Bayesian LMMs provide evidence for two new pigmentation loci: one for eye color ( AHRR ) and one for skin color ( DDB1 ). Copyright © 2017 by the Genetics Society of America.

Uncovering robust patterns of microRNA co-expression across cancers using Bayesian Relevance Networks

PubMed Central

2017-01-01

Co-expression networks have long been used as a tool for investigating the molecular circuitry governing biological systems. However, most algorithms for constructing co-expression networks were developed in the microarray era, before high-throughput sequencing—with its unique statistical properties—became the norm for expression measurement. Here we develop Bayesian Relevance Networks, an algorithm that uses Bayesian reasoning about expression levels to account for the differing levels of uncertainty in expression measurements between highly- and lowly-expressed entities, and between samples with different sequencing depths. It combines data from groups of samples (e.g., replicates) to estimate group expression levels and confidence ranges. It then computes uncertainty-moderated estimates of cross-group correlations between entities, and uses permutation testing to assess their statistical significance. Using large scale miRNA data from The Cancer Genome Atlas, we show that our Bayesian update of the classical Relevance Networks algorithm provides improved reproducibility in co-expression estimates and lower false discovery rates in the resulting co-expression networks. Software is available at www.perkinslab.ca. PMID:28817636

Uncovering robust patterns of microRNA co-expression across cancers using Bayesian Relevance Networks.

PubMed

Ramachandran, Parameswaran; Sánchez-Taltavull, Daniel; Perkins, Theodore J

2017-01-01

Co-expression networks have long been used as a tool for investigating the molecular circuitry governing biological systems. However, most algorithms for constructing co-expression networks were developed in the microarray era, before high-throughput sequencing-with its unique statistical properties-became the norm for expression measurement. Here we develop Bayesian Relevance Networks, an algorithm that uses Bayesian reasoning about expression levels to account for the differing levels of uncertainty in expression measurements between highly- and lowly-expressed entities, and between samples with different sequencing depths. It combines data from groups of samples (e.g., replicates) to estimate group expression levels and confidence ranges. It then computes uncertainty-moderated estimates of cross-group correlations between entities, and uses permutation testing to assess their statistical significance. Using large scale miRNA data from The Cancer Genome Atlas, we show that our Bayesian update of the classical Relevance Networks algorithm provides improved reproducibility in co-expression estimates and lower false discovery rates in the resulting co-expression networks. Software is available at www.perkinslab.ca.

Bayesian classification theory

NASA Technical Reports Server (NTRS)

Hanson, Robin; Stutz, John; Cheeseman, Peter

1991-01-01

The task of inferring a set of classes and class descriptions most likely to explain a given data set can be placed on a firm theoretical foundation using Bayesian statistics. Within this framework and using various mathematical and algorithmic approximations, the AutoClass system searches for the most probable classifications, automatically choosing the number of classes and complexity of class descriptions. A simpler version of AutoClass has been applied to many large real data sets, has discovered new independently-verified phenomena, and has been released as a robust software package. Recent extensions allow attributes to be selectively correlated within particular classes, and allow classes to inherit or share model parameters though a class hierarchy. We summarize the mathematical foundations of AutoClass.

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…

A Comparison of Imputation Methods for Bayesian Factor Analysis Models

ERIC Educational Resources Information Center

Merkle, Edgar C.

2011-01-01

Imputation methods are popular for the handling of missing data in psychology. The methods generally consist of predicting missing data based on observed data, yielding a complete data set that is amiable to standard statistical analyses. In the context of Bayesian factor analysis, this article compares imputation under an unrestricted…

Application of Bayesian Methods for Detecting Fraudulent Behavior on Tests

ERIC Educational Resources Information Center

Sinharay, Sandip

2018-01-01

Producers and consumers of test scores are increasingly concerned about fraudulent behavior before and during the test. There exist several statistical or psychometric methods for detecting fraudulent behavior on tests. This paper provides a review of the Bayesian approaches among them. Four hitherto-unpublished real data examples are provided to…

Flood quantile estimation at ungauged sites by Bayesian networks

NASA Astrophysics Data System (ADS)

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

2012-04-01

stochastic generator of synthetic data was developed. Synthetic basin characteristics were randomised, keeping the statistical properties of observed physical and climatic variables in the homogeneous region. The synthetic flood quantiles were stochastically generated taking the regression equation as basis. The learnt Bayesian network was validated by the reliability diagram, the Brier Score and the ROC diagram, which are common measures used in the validation of probabilistic forecasts. Summarising, the flood quantile estimations through Bayesian networks supply information about the prediction uncertainty as a probability distribution function of discharges is given as result. Therefore, the Bayesian network model has application as a decision support for water resources and planning management.

Bayesian Methods for Effective Field Theories

NASA Astrophysics Data System (ADS)

Wesolowski, Sarah

Microscopic predictions of the properties of atomic nuclei have reached a high level of precision in the past decade. This progress mandates improved uncertainty quantification (UQ) for a robust comparison of experiment with theory. With the uncertainty from many-body methods under control, calculations are now sensitive to the input inter-nucleon interactions. These interactions include parameters that must be fit to experiment, inducing both uncertainty from the fit and from missing physics in the operator structure of the Hamiltonian. Furthermore, the implementation of the inter-nucleon interactions is not unique, which presents the additional problem of assessing results using different interactions. Effective field theories (EFTs) take advantage of a separation of high- and low-energy scales in the problem to form a power-counting scheme that allows the organization of terms in the Hamiltonian based on their expected contribution to observable predictions. This scheme gives a natural framework for quantification of uncertainty due to missing physics. The free parameters of the EFT, called the low-energy constants (LECs), must be fit to data, but in a properly constructed EFT these constants will be natural-sized, i.e., of order unity. The constraints provided by the EFT, namely the size of the systematic uncertainty from truncation of the theory and the natural size of the LECs, are assumed information even before a calculation is performed or a fit is done. Bayesian statistical methods provide a framework for treating uncertainties that naturally incorporates prior information as well as putting stochastic and systematic uncertainties on an equal footing. For EFT UQ Bayesian methods allow the relevant EFT properties to be incorporated quantitatively as prior probability distribution functions (pdfs). Following the logic of probability theory, observable quantities and underlying physical parameters such as the EFT breakdown scale may be expressed as pdfs that

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

NASA Astrophysics Data System (ADS)

Takiyama, Ken

2016-05-01

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

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.

Statistical Symbolic Execution with Informed Sampling

NASA Technical Reports Server (NTRS)

Filieri, Antonio; Pasareanu, Corina S.; Visser, Willem; Geldenhuys, Jaco

2014-01-01

Symbolic execution techniques have been proposed recently for the probabilistic analysis of programs. These techniques seek to quantify the likelihood of reaching program events of interest, e.g., assert violations. They have many promising applications but have scalability issues due to high computational demand. To address this challenge, we propose a statistical symbolic execution technique that performs Monte Carlo sampling of the symbolic program paths and uses the obtained information for Bayesian estimation and hypothesis testing with respect to the probability of reaching the target events. To speed up the convergence of the statistical analysis, we propose Informed Sampling, an iterative symbolic execution that first explores the paths that have high statistical significance, prunes them from the state space and guides the execution towards less likely paths. The technique combines Bayesian estimation with a partial exact analysis for the pruned paths leading to provably improved convergence of the statistical analysis. We have implemented statistical symbolic execution with in- formed sampling in the Symbolic PathFinder tool. We show experimentally that the informed sampling obtains more precise results and converges faster than a purely statistical analysis and may also be more efficient than an exact symbolic analysis. When the latter does not terminate symbolic execution with informed sampling can give meaningful results under the same time and memory limits.

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

NASA Astrophysics Data System (ADS)

Rajabi, Mohammad Mahdi; Ataie-Ashtiani, Behzad

2016-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

Theory-based Bayesian models of inductive learning and reasoning.

PubMed

Tenenbaum, Joshua B; Griffiths, Thomas L; Kemp, Charles

2006-07-01

Inductive inference allows humans to make powerful generalizations from sparse data when learning about word meanings, unobserved properties, causal relationships, and many other aspects of the world. Traditional accounts of induction emphasize either the power of statistical learning, or the importance of strong constraints from structured domain knowledge, intuitive theories or schemas. We argue that both components are necessary to explain the nature, use and acquisition of human knowledge, and we introduce a theory-based Bayesian framework for modeling inductive learning and reasoning as statistical inferences over structured knowledge representations.

On Some Assumptions of the Null Hypothesis Statistical Testing

ERIC Educational Resources Information Center

Patriota, Alexandre Galvão

2017-01-01

Bayesian and classical statistical approaches are based on different types of logical principles. In order to avoid mistaken inferences and misguided interpretations, the practitioner must respect the inference rules embedded into each statistical method. Ignoring these principles leads to the paradoxical conclusions that the hypothesis…

A fully Bayesian before-after analysis of permeable friction course (PFC) pavement wet weather safety.

PubMed

Buddhavarapu, Prasad; Smit, Andre F; Prozzi, Jorge A

2015-07-01

Permeable friction course (PFC), a porous hot-mix asphalt, is typically applied to improve wet weather safety on high-speed roadways in Texas. In order to warrant expensive PFC construction, a statistical evaluation of its safety benefits is essential. Generally, the literature on the effectiveness of porous mixes in reducing wet-weather crashes is limited and often inconclusive. In this study, the safety effectiveness of PFC was evaluated using a fully Bayesian before-after safety analysis. First, two groups of road segments overlaid with PFC and non-PFC material were identified across Texas; the non-PFC or reference road segments selected were similar to their PFC counterparts in terms of site specific features. Second, a negative binomial data generating process was assumed to model the underlying distribution of crash counts of PFC and reference road segments to perform Bayesian inference on the safety effectiveness. A data-augmentation based computationally efficient algorithm was employed for a fully Bayesian estimation. The statistical analysis shows that PFC is not effective in reducing wet weather crashes. It should be noted that the findings of this study are in agreement with the existing literature, although these studies were not based on a fully Bayesian statistical analysis. Our study suggests that the safety effectiveness of PFC road surfaces, or any other safety infrastructure, largely relies on its interrelationship with the road user. The results suggest that the safety infrastructure must be properly used to reap the benefits of the substantial investments. Copyright © 2015 Elsevier Ltd. All rights reserved.

Modeling Error Distributions of Growth Curve Models through Bayesian Methods

ERIC Educational Resources Information Center

Zhang, Zhiyong

2016-01-01

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is…

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

PubMed

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

2006-07-01

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

Neural network approaches versus statistical methods in classification of multisource remote sensing data

NASA Technical Reports Server (NTRS)

Benediktsson, Jon A.; Swain, Philip H.; Ersoy, Okan K.

1990-01-01

Neural network learning procedures and statistical classificaiton methods are applied and compared empirically in classification of multisource remote sensing and geographic data. Statistical multisource classification by means of a method based on Bayesian classification theory is also investigated and modified. The modifications permit control of the influence of the data sources involved in the classification process. Reliability measures are introduced to rank the quality of the data sources. The data sources are then weighted according to these rankings in the statistical multisource classification. Four data sources are used in experiments: Landsat MSS data and three forms of topographic data (elevation, slope, and aspect). Experimental results show that two different approaches have unique advantages and disadvantages in this classification application.

Combining statistical inference and decisions in ecology

USGS Publications Warehouse

Williams, Perry J.; Hooten, Mevin B.

2016-01-01

Statistical decision theory (SDT) is a sub-field of decision theory that formally incorporates statistical investigation into a decision-theoretic framework to account for uncertainties in a decision problem. SDT provides a unifying analysis of three types of information: statistical results from a data set, knowledge of the consequences of potential choices (i.e., loss), and prior beliefs about a system. SDT links the theoretical development of a large body of statistical methods including point estimation, hypothesis testing, and confidence interval estimation. The theory and application of SDT have mainly been developed and published in the fields of mathematics, statistics, operations research, and other decision sciences, but have had limited exposure in ecology. Thus, we provide an introduction to SDT for ecologists and describe its utility for linking the conventionally separate tasks of statistical investigation and decision making in a single framework. We describe the basic framework of both Bayesian and frequentist SDT, its traditional use in statistics, and discuss its application to decision problems that occur in ecology. We demonstrate SDT with two types of decisions: Bayesian point estimation, and an applied management problem of selecting a prescribed fire rotation for managing a grassland bird species. Central to SDT, and decision theory in general, are loss functions. Thus, we also provide basic guidance and references for constructing loss functions for an SDT problem.

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.

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.

Mean Field Variational Bayesian Data Assimilation

NASA Astrophysics Data System (ADS)

Vrettas, M.; Cornford, D.; Opper, M.

2012-04-01

Current data assimilation schemes propose a range of approximate solutions to the classical data assimilation problem, particularly state estimation. Broadly there are three main active research areas: ensemble Kalman filter methods which rely on statistical linearization of the model evolution equations, particle filters which provide a discrete point representation of the posterior filtering or smoothing distribution and 4DVAR methods which seek the most likely posterior smoothing solution. In this paper we present a recent extension to our variational Bayesian algorithm which seeks the most probably posterior distribution over the states, within the family of non-stationary Gaussian processes. Our original work on variational Bayesian approaches to data assimilation sought the best approximating time varying Gaussian process to the posterior smoothing distribution for stochastic dynamical systems. This approach was based on minimising the Kullback-Leibler divergence between the true posterior over paths, and our Gaussian process approximation. So long as the observation density was sufficiently high to bring the posterior smoothing density close to Gaussian the algorithm proved very effective, on lower dimensional systems. However for higher dimensional systems, the algorithm was computationally very demanding. We have been developing a mean field version of the algorithm which treats the state variables at a given time as being independent in the posterior approximation, but still accounts for their relationships between each other in the mean solution arising from the original dynamical system. In this work we present the new mean field variational Bayesian approach, illustrating its performance on a range of classical data assimilation problems. We discuss the potential and limitations of the new approach. We emphasise that the variational Bayesian approach we adopt, in contrast to other variational approaches, provides a bound on the marginal likelihood of

A Bayesian perspective on Markovian dynamics and the fluctuation theorem

NASA Astrophysics Data System (ADS)

Virgo, Nathaniel

2013-08-01

One of E. T. Jaynes' most important achievements was to derive statistical mechanics from the maximum entropy (MaxEnt) method. I re-examine a relatively new result in statistical mechanics, the Evans-Searles fluctuation theorem, from a MaxEnt perspective. This is done in the belief that interpreting such results in Bayesian terms will lead to new advances in statistical physics. The version of the fluctuation theorem that I will discuss applies to discrete, stochastic systems that begin in a non-equilibrium state and relax toward equilibrium. I will show that for such systems the fluctuation theorem can be seen as a consequence of the fact that the equilibrium distribution must obey the property of detailed balance. Although the principle of detailed balance applies only to equilibrium ensembles, it puts constraints on the form of non-equilibrium trajectories. This will be made clear by taking a novel kind of Bayesian perspective, in which the equilibrium distribution is seen as a prior over the system's set of possible trajectories. Non-equilibrium ensembles are calculated from this prior using Bayes' theorem, with the initial conditions playing the role of the data. I will also comment on the implications of this perspective for the question of how to derive the second law.

Comparison between the basic least squares and the Bayesian approach for elastic constants identification

NASA Astrophysics Data System (ADS)

Gogu, C.; Haftka, R.; LeRiche, R.; Molimard, J.; Vautrin, A.; Sankar, B.

2008-11-01

The basic formulation of the least squares method, based on the L2 norm of the misfit, is still widely used today for identifying elastic material properties from experimental data. An alternative statistical approach is the Bayesian method. We seek here situations with significant difference between the material properties found by the two methods. For a simple three bar truss example we illustrate three such situations in which the Bayesian approach leads to more accurate results: different magnitude of the measurements, different uncertainty in the measurements and correlation among measurements. When all three effects add up, the Bayesian approach can have a large advantage. We then compared the two methods for identification of elastic constants from plate vibration natural frequencies.

pyblocxs: Bayesian Low-Counts X-ray Spectral Analysis in Sherpa

NASA Astrophysics Data System (ADS)

Siemiginowska, A.; Kashyap, V.; Refsdal, B.; van Dyk, D.; Connors, A.; Park, T.

2011-07-01

Typical X-ray spectra have low counts and should be modeled using the Poisson distribution. However, χ2 statistic is often applied as an alternative and the data are assumed to follow the Gaussian distribution. A variety of weights to the statistic or a binning of the data is performed to overcome the low counts issues. However, such modifications introduce biases or/and a loss of information. Standard modeling packages such as XSPEC and Sherpa provide the Poisson likelihood and allow computation of rudimentary MCMC chains, but so far do not allow for setting a full Bayesian model. We have implemented a sophisticated Bayesian MCMC-based algorithm to carry out spectral fitting of low counts sources in the Sherpa environment. The code is a Python extension to Sherpa and allows to fit a predefined Sherpa model to high-energy X-ray spectral data and other generic data. We present the algorithm and discuss several issues related to the implementation, including flexible definition of priors and allowing for variations in the calibration information.

Bayesian Estimation of Thermonuclear Reaction Rates for Deuterium+Deuterium Reactions

NASA Astrophysics Data System (ADS)

Gómez Iñesta, Á.; Iliadis, C.; Coc, A.

2017-11-01

The study of d+d reactions is of major interest since their reaction rates affect the predicted abundances of D, 3He, and 7Li. In particular, recent measurements of primordial D/H ratios call for reduced uncertainties in the theoretical abundances predicted by Big Bang nucleosynthesis (BBN). Different authors have studied reactions involved in BBN by incorporating new experimental data and a careful treatment of systematic and probabilistic uncertainties. To analyze the experimental data, Coc et al. used results of ab initio models for the theoretical calculation of the energy dependence of S-factors in conjunction with traditional statistical methods based on χ 2 minimization. Bayesian methods have now spread to many scientific fields and provide numerous advantages in data analysis. Astrophysical S-factors and reaction rates using Bayesian statistics were calculated by Iliadis et al. Here we present a similar analysis for two d+d reactions, d(d, n)3He and d(d, p)3H, that has been translated into a total decrease of the predicted D/H value by 0.16%.

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

A statistical assessment of seismic models of the U.S. continental crust using Bayesian inversion of ambient noise surface wave dispersion data

NASA Astrophysics Data System (ADS)

Olugboji, T. M.; Lekic, V.; McDonough, W.

2017-07-01

We present a new approach for evaluating existing crustal models using ambient noise data sets and its associated uncertainties. We use a transdimensional hierarchical Bayesian inversion approach to invert ambient noise surface wave phase dispersion maps for Love and Rayleigh waves using measurements obtained from Ekström (2014). Spatiospectral analysis shows that our results are comparable to a linear least squares inverse approach (except at higher harmonic degrees), but the procedure has additional advantages: (1) it yields an autoadaptive parameterization that follows Earth structure without making restricting assumptions on model resolution (regularization or damping) and data errors; (2) it can recover non-Gaussian phase velocity probability distributions while quantifying the sources of uncertainties in the data measurements and modeling procedure; and (3) it enables statistical assessments of different crustal models (e.g., CRUST1.0, LITHO1.0, and NACr14) using variable resolution residual and standard deviation maps estimated from the ensemble. These assessments show that in the stable old crust of the Archean, the misfits are statistically negligible, requiring no significant update to crustal models from the ambient noise data set. In other regions of the U.S., significant updates to regionalization and crustal structure are expected especially in the shallow sedimentary basins and the tectonically active regions, where the differences between model predictions and data are statistically significant.

Using Statistical Process Control to Enhance Student Progression

ERIC Educational Resources Information Center

Hanna, Mark D.; Raichura, Nilesh; Bernardes, Ednilson

2012-01-01

Public interest in educational outcomes has markedly increased in the most recent decade; however, quality management and statistical process control have not deeply penetrated the management of academic institutions. This paper presents results of an attempt to use Statistical Process Control (SPC) to identify a key impediment to continuous…

Bayesian Mediation Analysis

ERIC Educational Resources Information Center

Yuan, Ying; MacKinnon, David P.

2009-01-01

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

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

PubMed Central

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

2014-01-01

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

Quantum-Like Bayesian Networks for Modeling Decision Making

PubMed Central

Moreira, Catarina; Wichert, Andreas

2016-01-01

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

Bayesian Monte Carlo and Maximum Likelihood Approach for ...

EPA Pesticide Factsheets

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

A Bayesian Missing Data Framework for Generalized Multiple Outcome Mixed Treatment Comparisons

ERIC Educational Resources Information Center

Hong, Hwanhee; Chu, Haitao; Zhang, Jing; Carlin, Bradley P.

2016-01-01

Bayesian statistical approaches to mixed treatment comparisons (MTCs) are becoming more popular because of their flexibility and interpretability. Many randomized clinical trials report multiple outcomes with possible inherent correlations. Moreover, MTC data are typically sparse (although richer than standard meta-analysis, comparing only two…

Stan: A Probabilistic Programming Language for Bayesian Inference and Optimization

ERIC Educational Resources Information Center

Gelman, Andrew; Lee, Daniel; Guo, Jiqiang

2015-01-01

Stan is a free and open-source C++ program that performs Bayesian inference or optimization for arbitrary user-specified models and can be called from the command line, R, Python, Matlab, or Julia and has great promise for fitting large and complex statistical models in many areas of application. We discuss Stan from users' and developers'…

Factors contributing to academic achievement: a Bayesian structure equation modelling study

NASA Astrophysics Data System (ADS)

Payandeh Najafabadi, Amir T.; Omidi Najafabadi, Maryam; Farid-Rohani, Mohammad Reza

2013-06-01

In Iran, high school graduates enter university after taking a very difficult entrance exam called the Konkoor. Therefore, only the top-performing students are admitted by universities to continue their bachelor's education in statistics. Surprisingly, statistically, most of such students fall into the following categories: (1) do not succeed in their education despite their excellent performance on the Konkoor and in high school; (2) graduate with a grade point average (GPA) that is considerably lower than their high school GPA; (3) continue their master's education in majors other than statistics and (4) try to find jobs unrelated to statistics. This article employs the well-known and powerful statistical technique, the Bayesian structural equation modelling (SEM), to study the academic success of recent graduates who have studied statistics at Shahid Beheshti University in Iran. This research: (i) considered academic success as a latent variable, which was measured by GPA and other academic success (see below) of students in the target population; (ii) employed the Bayesian SEM, which works properly for small sample sizes and ordinal variables; (iii), which is taken from the literature, developed five main factors that affected academic success and (iv) considered several standard psychological tests and measured characteristics such as 'self-esteem' and 'anxiety'. We then study the impact of such factors on the academic success of the target population. Six factors that positively impact student academic success were identified in the following order of relative impact (from greatest to least): 'Teaching-Evaluation', 'Learner', 'Environment', 'Family', 'Curriculum' and 'Teaching Knowledge'. Particularly, influential variables within each factor have also been noted.

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.

Bayesian Image Segmentations by Potts Prior and Loopy Belief Propagation

NASA Astrophysics Data System (ADS)

Tanaka, Kazuyuki; Kataoka, Shun; Yasuda, Muneki; Waizumi, Yuji; Hsu, Chiou-Ting

2014-12-01

This paper presents a Bayesian image segmentation model based on Potts prior and loopy belief propagation. The proposed Bayesian model involves several terms, including the pairwise interactions of Potts models, and the average vectors and covariant matrices of Gauss distributions in color image modeling. These terms are often referred to as hyperparameters in statistical machine learning theory. In order to determine these hyperparameters, we propose a new scheme for hyperparameter estimation based on conditional maximization of entropy in the Potts prior. The algorithm is given based on loopy belief propagation. In addition, we compare our conditional maximum entropy framework with the conventional maximum likelihood framework, and also clarify how the first order phase transitions in loopy belief propagations for Potts models influence our hyperparameter estimation procedures.

Statistical Control Paradigm for Aerospace Structures Under Impulsive Disturbances

DTIC Science & Technology

2006-08-03

attitude control system with an innovative and robust statistical controller design shows significant promise for use in attitude hold mode operation...indicate that the existing attitude control system with an innovative and robust statistical controller design shows significant promise for use in...and three thrusters are for use in controlling the attitude of the satellite. Then the angular momentum of the satellite with three thrusters and a

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

PubMed Central

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

2016-01-01

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

Hierarchical Bayesian Logistic Regression to forecast metabolic control in type 2 DM patients.

PubMed

Dagliati, Arianna; Malovini, Alberto; Decata, Pasquale; Cogni, Giulia; Teliti, Marsida; Sacchi, Lucia; Cerra, Carlo; Chiovato, Luca; Bellazzi, Riccardo

2016-01-01

In this work we present our efforts in building a model able to forecast patients' changes in clinical conditions when repeated measurements are available. In this case the available risk calculators are typically not applicable. We propose a Hierarchical Bayesian Logistic Regression model, which allows taking into account individual and population variability in model parameters estimate. The model is used to predict metabolic control and its variation in type 2 diabetes mellitus. In particular we have analyzed a population of more than 1000 Italian type 2 diabetic patients, collected within the European project Mosaic. The results obtained in terms of Matthews Correlation Coefficient are significantly better than the ones gathered with standard logistic regression model, based on data pooling.

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

A Bayesian Approach for Summarizing and Modeling Time-Series Exposure Data with Left Censoring.

PubMed

Houseman, E Andres; Virji, M Abbas

2017-08-01

Direct reading instruments are valuable tools for measuring exposure as they provide real-time measurements for rapid decision making. However, their use is limited to general survey applications in part due to issues related to their performance. Moreover, statistical analysis of real-time data is complicated by autocorrelation among successive measurements, non-stationary time series, and the presence of left-censoring due to limit-of-detection (LOD). A Bayesian framework is proposed that accounts for non-stationary autocorrelation and LOD issues in exposure time-series data in order to model workplace factors that affect exposure and estimate summary statistics for tasks or other covariates of interest. A spline-based approach is used to model non-stationary autocorrelation with relatively few assumptions about autocorrelation structure. Left-censoring is addressed by integrating over the left tail of the distribution. The model is fit using Markov-Chain Monte Carlo within a Bayesian paradigm. The method can flexibly account for hierarchical relationships, random effects and fixed effects of covariates. The method is implemented using the rjags package in R, and is illustrated by applying it to real-time exposure data. Estimates for task means and covariates from the Bayesian model are compared to those from conventional frequentist models including linear regression, mixed-effects, and time-series models with different autocorrelation structures. Simulations studies are also conducted to evaluate method performance. Simulation studies with percent of measurements below the LOD ranging from 0 to 50% showed lowest root mean squared errors for task means and the least biased standard deviations from the Bayesian model compared to the frequentist models across all levels of LOD. In the application, task means from the Bayesian model were similar to means from the frequentist models, while the standard deviations were different. Parameter estimates for covariates

Using Bayesian analysis in repeated preclinical in vivo studies for a more effective use of animals.

PubMed

Walley, Rosalind; Sherington, John; Rastrick, Joe; Detrait, Eric; Hanon, Etienne; Watt, Gillian

2016-05-01

Whilst innovative Bayesian approaches are increasingly used in clinical studies, in the preclinical area Bayesian methods appear to be rarely used in the reporting of pharmacology data. This is particularly surprising in the context of regularly repeated in vivo studies where there is a considerable amount of data from historical control groups, which has potential value. This paper describes our experience with introducing Bayesian analysis for such studies using a Bayesian meta-analytic predictive approach. This leads naturally either to an informative prior for a control group as part of a full Bayesian analysis of the next study or using a predictive distribution to replace a control group entirely. We use quality control charts to illustrate study-to-study variation to the scientists and describe informative priors in terms of their approximate effective numbers of animals. We describe two case studies of animal models: the lipopolysaccharide-induced cytokine release model used in inflammation and the novel object recognition model used to screen cognitive enhancers, both of which show the advantage of a Bayesian approach over the standard frequentist analysis. We conclude that using Bayesian methods in stable repeated in vivo studies can result in a more effective use of animals, either by reducing the total number of animals used or by increasing the precision of key treatment differences. This will lead to clearer results and supports the "3Rs initiative" to Refine, Reduce and Replace animals in research. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

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

Estimation of Lithological Classification in Taipei Basin: A Bayesian Maximum Entropy Method

NASA Astrophysics Data System (ADS)

Wu, Meng-Ting; Lin, Yuan-Chien; Yu, Hwa-Lung

2015-04-01

In environmental or other scientific applications, we must have a certain understanding of geological lithological composition. Because of restrictions of real conditions, only limited amount of data can be acquired. To find out the lithological distribution in the study area, many spatial statistical methods used to estimate the lithological composition on unsampled points or grids. This study applied the Bayesian Maximum Entropy (BME method), which is an emerging method of the geological spatiotemporal statistics field. The BME method can identify the spatiotemporal correlation of the data, and combine not only the hard data but the soft data to improve estimation. The data of lithological classification is discrete categorical data. Therefore, this research applied Categorical BME to establish a complete three-dimensional Lithological estimation model. Apply the limited hard data from the cores and the soft data generated from the geological dating data and the virtual wells to estimate the three-dimensional lithological classification in Taipei Basin. Keywords: Categorical Bayesian Maximum Entropy method, Lithological Classification, Hydrogeological Setting

Applying Statistical Process Control to Clinical Data: An Illustration.

ERIC Educational Resources Information Center

Pfadt, Al; And Others

1992-01-01

Principles of statistical process control are applied to a clinical setting through the use of control charts to detect changes, as part of treatment planning and clinical decision-making processes. The logic of control chart analysis is derived from principles of statistical inference. Sample charts offer examples of evaluating baselines and…

The Bayesian reader: explaining word recognition as an optimal Bayesian decision process.

PubMed

Norris, Dennis

2006-04-01

This article presents a theory of visual word recognition that assumes that, in the tasks of word identification, lexical decision, and semantic categorization, human readers behave as optimal Bayesian decision makers. This leads to the development of a computational model of word recognition, the Bayesian reader. The Bayesian reader successfully simulates some of the most significant data on human reading. The model accounts for the nature of the function relating word frequency to reaction time and identification threshold, the effects of neighborhood density and its interaction with frequency, and the variation in the pattern of neighborhood density effects seen in different experimental tasks. Both the general behavior of the model and the way the model predicts different patterns of results in different tasks follow entirely from the assumption that human readers approximate optimal Bayesian decision makers. ((c) 2006 APA, all rights reserved).

Informative Bayesian Type A uncertainty evaluation, especially applicable to a small number of observations

NASA Astrophysics Data System (ADS)

Cox, M.; Shirono, K.

2017-10-01

A criticism levelled at the Guide to the Expression of Uncertainty in Measurement (GUM) is that it is based on a mixture of frequentist and Bayesian thinking. In particular, the GUM’s Type A (statistical) uncertainty evaluations are frequentist, whereas the Type B evaluations, using state-of-knowledge distributions, are Bayesian. In contrast, making the GUM fully Bayesian implies, among other things, that a conventional objective Bayesian approach to Type A uncertainty evaluation for a number n of observations leads to the impractical consequence that n must be at least equal to 4, thus presenting a difficulty for many metrologists. This paper presents a Bayesian analysis of Type A uncertainty evaluation that applies for all n ≥slant 2 , as in the frequentist analysis in the current GUM. The analysis is based on assuming that the observations are drawn from a normal distribution (as in the conventional objective Bayesian analysis), but uses an informative prior based on lower and upper bounds for the standard deviation of the sampling distribution for the quantity under consideration. The main outcome of the analysis is a closed-form mathematical expression for the factor by which the standard deviation of the mean observation should be multiplied to calculate the required standard uncertainty. Metrological examples are used to illustrate the approach, which is straightforward to apply using a formula or look-up table.

Combining statistical inference and decisions in ecology.

PubMed

Williams, Perry J; Hooten, Mevin B

2016-09-01

Statistical decision theory (SDT) is a sub-field of decision theory that formally incorporates statistical investigation into a decision-theoretic framework to account for uncertainties in a decision problem. SDT provides a unifying analysis of three types of information: statistical results from a data set, knowledge of the consequences of potential choices (i.e., loss), and prior beliefs about a system. SDT links the theoretical development of a large body of statistical methods, including point estimation, hypothesis testing, and confidence interval estimation. The theory and application of SDT have mainly been developed and published in the fields of mathematics, statistics, operations research, and other decision sciences, but have had limited exposure in ecology. Thus, we provide an introduction to SDT for ecologists and describe its utility for linking the conventionally separate tasks of statistical investigation and decision making in a single framework. We describe the basic framework of both Bayesian and frequentist SDT, its traditional use in statistics, and discuss its application to decision problems that occur in ecology. We demonstrate SDT with two types of decisions: Bayesian point estimation and an applied management problem of selecting a prescribed fire rotation for managing a grassland bird species. Central to SDT, and decision theory in general, are loss functions. Thus, we also provide basic guidance and references for constructing loss functions for an SDT problem. © 2016 by the Ecological Society of America.

Applying Statistical Process Quality Control Methodology to Educational Settings.

ERIC Educational Resources Information Center

Blumberg, Carol Joyce

A subset of Statistical Process Control (SPC) methodology known as Control Charting is introduced. SPC methodology is a collection of graphical and inferential statistics techniques used to study the progress of phenomena over time. The types of control charts covered are the null X (mean), R (Range), X (individual observations), MR (moving…

Hydrological modelling of the Chaohe Basin in China: Statistical model formulation and Bayesian inference

NASA Astrophysics Data System (ADS)

Yang, Jing; Reichert, Peter; Abbaspour, Karim C.; Yang, Hong

2007-07-01

SummaryCalibration of hydrologic models is very difficult because of measurement errors in input and response, errors in model structure, and the large number of non-identifiable parameters of distributed models. The difficulties even increase in arid regions with high seasonal variation of precipitation, where the modelled residuals often exhibit high heteroscedasticity and autocorrelation. On the other hand, support of water management by hydrologic models is important in arid regions, particularly if there is increasing water demand due to urbanization. The use and assessment of model results for this purpose require a careful calibration and uncertainty analysis. Extending earlier work in this field, we developed a procedure to overcome (i) the problem of non-identifiability of distributed parameters by introducing aggregate parameters and using Bayesian inference, (ii) the problem of heteroscedasticity of errors by combining a Box-Cox transformation of results and data with seasonally dependent error variances, (iii) the problems of autocorrelated errors, missing data and outlier omission with a continuous-time autoregressive error model, and (iv) the problem of the seasonal variation of error correlations with seasonally dependent characteristic correlation times. The technique was tested with the calibration of the hydrologic sub-model of the Soil and Water Assessment Tool (SWAT) in the Chaohe Basin in North China. The results demonstrated the good performance of this approach to uncertainty analysis, particularly with respect to the fulfilment of statistical assumptions of the error model. A comparison with an independent error model and with error models that only considered a subset of the suggested techniques clearly showed the superiority of the approach based on all the features (i)-(iv) mentioned above.

[Statistical process control applied to intensity modulated radiotherapy pretreatment controls with portal dosimetry].

PubMed

Villani, N; Gérard, K; Marchesi, V; Huger, S; François, P; Noël, A

2010-06-01

The first purpose of this study was to illustrate the contribution of statistical process control for a better security in intensity modulated radiotherapy (IMRT) treatments. This improvement is possible by controlling the dose delivery process, characterized by pretreatment quality control results. So, it is necessary to put under control portal dosimetry measurements (currently, the ionisation chamber measurements were already monitored by statistical process control thanks to statistical process control tools). The second objective was to state whether it is possible to substitute ionisation chamber with portal dosimetry in order to optimize time devoted to pretreatment quality control. At Alexis-Vautrin center, pretreatment quality controls in IMRT for prostate and head and neck treatments were performed for each beam of each patient. These controls were made with an ionisation chamber, which is the reference detector for the absolute dose measurement, and with portal dosimetry for the verification of dose distribution. Statistical process control is a statistical analysis method, coming from industry, used to control and improve the studied process quality. It uses graphic tools as control maps to follow-up process, warning the operator in case of failure, and quantitative tools to evaluate the process toward its ability to respect guidelines: this is the capability study. The study was performed on 450 head and neck beams and on 100 prostate beams. Control charts, showing drifts, both slow and weak, and also both strong and fast, of mean and standard deviation have been established and have shown special cause introduced (manual shift of the leaf gap of the multileaf collimator). Correlation between dose measured at one point, given with the EPID and the ionisation chamber has been evaluated at more than 97% and disagreement cases between the two measurements were identified. The study allowed to demonstrate the feasibility to reduce the time devoted to

Prediction of Individual Serum Infliximab Concentrations in Inflammatory Bowel Disease by a Bayesian Dashboard System.

PubMed

Eser, Alexander; Primas, Christian; Reinisch, Sieglinde; Vogelsang, Harald; Novacek, Gottfried; Mould, Diane R; Reinisch, Walter

2018-01-30

Despite a robust exposure-response relationship of infliximab in inflammatory bowel disease (IBD), attempts to adjust dosing to individually predicted serum concentrations of infliximab (SICs) are lacking. Compared with labor-intensive conventional software for pharmacokinetic (PK) modeling (eg, NONMEM) dashboards are easy-to-use programs incorporating complex Bayesian statistics to determine individual pharmacokinetics. We evaluated various infliximab detection assays and the number of samples needed to precisely forecast individual SICs using a Bayesian dashboard. We assessed long-term infliximab retention in patients being dosed concordantly versus discordantly with Bayesian dashboard recommendations. Three hundred eighty-two serum samples from 117 adult IBD patients on infliximab maintenance therapy were analyzed by 3 commercially available assays. Data from each assay was modeled using NONMEM and a Bayesian dashboard. PK parameter precision and residual variability were assessed. Forecast concentrations from both systems were compared with observed concentrations. Infliximab retention was assessed by prediction for dose intensification via Bayesian dashboard versus real-life practice. Forecast precision of SICs varied between detection assays. At least 3 SICs from a reliable assay are needed for an accurate forecast. The Bayesian dashboard performed similarly to NONMEM to predict SICs. Patients dosed concordantly with Bayesian dashboard recommendations had a significantly longer median drug survival than those dosed discordantly (51.5 versus 4.6 months, P < .0001). The Bayesian dashboard helps to assess the diagnostic performance of infliximab detection assays. Three, not single, SICs provide sufficient information for individualized dose adjustment when incorporated into the Bayesian dashboard. Treatment adjusted to forecasted SICs is associated with longer drug retention of infliximab. © 2018, The American College of Clinical Pharmacology.

Decision generation tools and Bayesian inference

NASA Astrophysics Data System (ADS)

Jannson, Tomasz; Wang, Wenjian; Forrester, Thomas; Kostrzewski, Andrew; Veeris, Christian; Nielsen, Thomas

2014-05-01

Digital Decision Generation (DDG) tools are important software sub-systems of Command and Control (C2) systems and technologies. In this paper, we present a special type of DDGs based on Bayesian Inference, related to adverse (hostile) networks, including such important applications as terrorism-related networks and organized crime ones.

Bayesian Dose-Response Modeling in Sparse Data

NASA Astrophysics Data System (ADS)

Kim, Steven B.

This book discusses Bayesian dose-response modeling in small samples applied to two different settings. The first setting is early phase clinical trials, and the second setting is toxicology studies in cancer risk assessment. In early phase clinical trials, experimental units are humans who are actual patients. Prior to a clinical trial, opinions from multiple subject area experts are generally more informative than the opinion of a single expert, but we may face a dilemma when they have disagreeing prior opinions. In this regard, we consider compromising the disagreement and compare two different approaches for making a decision. In addition to combining multiple opinions, we also address balancing two levels of ethics in early phase clinical trials. The first level is individual-level ethics which reflects the perspective of trial participants. The second level is population-level ethics which reflects the perspective of future patients. We extensively compare two existing statistical methods which focus on each perspective and propose a new method which balances the two conflicting perspectives. In toxicology studies, experimental units are living animals. Here we focus on a potential non-monotonic dose-response relationship which is known as hormesis. Briefly, hormesis is a phenomenon which can be characterized by a beneficial effect at low doses and a harmful effect at high doses. In cancer risk assessments, the estimation of a parameter, which is known as a benchmark dose, can be highly sensitive to a class of assumptions, monotonicity or hormesis. In this regard, we propose a robust approach which considers both monotonicity and hormesis as a possibility. In addition, We discuss statistical hypothesis testing for hormesis and consider various experimental designs for detecting hormesis based on Bayesian decision theory. Past experiments have not been optimally designed for testing for hormesis, and some Bayesian optimal designs may not be optimal under a

Estimability and simple dynamical analyses of range (range-rate range-difference) observations to artificial satellites. [laser range observations to LAGEOS using non-Bayesian statistics

NASA Technical Reports Server (NTRS)

Vangelder, B. H. W.

1978-01-01

Non-Bayesian statistics were used in simulation studies centered around laser range observations to LAGEOS. The capabilities of satellite laser ranging especially in connection with relative station positioning are evaluated. The satellite measurement system under investigation may fall short in precise determinations of the earth's orientation (precession and nutation) and earth's rotation as opposed to systems as very long baseline interferometry (VLBI) and lunar laser ranging (LLR). Relative station positioning, determination of (differential) polar motion, positioning of stations with respect to the earth's center of mass and determination of the earth's gravity field should be easily realized by satellite laser ranging (SLR). The last two features should be considered as best (or solely) determinable by SLR in contrast to VLBI and LLR.

Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring

Treesearch

Carlos Carroll; Devin S. Johnson; Jeffrey R. Dunk; William J. Zielinski

2010-01-01

Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data’s spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and...

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

Statistical Design Model (SDM) of satellite thermal control subsystem

NASA Astrophysics Data System (ADS)

Mirshams, Mehran; Zabihian, Ehsan; Aarabi Chamalishahi, Mahdi

2016-07-01

Satellites thermal control, is a satellite subsystem that its main task is keeping the satellite components at its own survival and activity temperatures. Ability of satellite thermal control plays a key role in satisfying satellite's operational requirements and designing this subsystem is a part of satellite design. In the other hand due to the lack of information provided by companies and designers still doesn't have a specific design process while it is one of the fundamental subsystems. The aim of this paper, is to identify and extract statistical design models of spacecraft thermal control subsystem by using SDM design method. This method analyses statistical data with a particular procedure. To implement SDM method, a complete database is required. Therefore, we first collect spacecraft data and create a database, and then we extract statistical graphs using Microsoft Excel, from which we further extract mathematical models. Inputs parameters of the method are mass, mission, and life time of the satellite. For this purpose at first thermal control subsystem has been introduced and hardware using in the this subsystem and its variants has been investigated. In the next part different statistical models has been mentioned and a brief compare will be between them. Finally, this paper particular statistical model is extracted from collected statistical data. Process of testing the accuracy and verifying the method use a case study. Which by the comparisons between the specifications of thermal control subsystem of a fabricated satellite and the analyses results, the methodology in this paper was proved to be effective. Key Words: Thermal control subsystem design, Statistical design model (SDM), Satellite conceptual design, Thermal hardware

Statistical learning and adaptive decision-making underlie human response time variability in inhibitory control.

PubMed

Ma, Ning; Yu, Angela J

2015-01-01

Response time (RT) is an oft-reported behavioral measure in psychological and neurocognitive experiments, but the high level of observed trial-to-trial variability in this measure has often limited its usefulness. Here, we combine computational modeling and psychophysics to examine the hypothesis that fluctuations in this noisy measure reflect dynamic computations in human statistical learning and corresponding cognitive adjustments. We present data from the stop-signal task (SST), in which subjects respond to a go stimulus on each trial, unless instructed not to by a subsequent, infrequently presented stop signal. We model across-trial learning of stop signal frequency, P(stop), and stop-signal onset time, SSD (stop-signal delay), with a Bayesian hidden Markov model, and within-trial decision-making with an optimal stochastic control model. The combined model predicts that RT should increase with both expected P(stop) and SSD. The human behavioral data (n = 20) bear out this prediction, showing P(stop) and SSD both to be significant, independent predictors of RT, with P(stop) being a more prominent predictor in 75% of the subjects, and SSD being more prominent in the remaining 25%. The results demonstrate that humans indeed readily internalize environmental statistics and adjust their cognitive/behavioral strategy accordingly, and that subtle patterns in RT variability can serve as a valuable tool for validating models of statistical learning and decision-making. More broadly, the modeling tools presented in this work can be generalized to a large body of behavioral paradigms, in order to extract insights about cognitive and neural processing from apparently quite noisy behavioral measures. We also discuss how this behaviorally validated model can then be used to conduct model-based analysis of neural data, in order to help identify specific brain areas for representing and encoding key computational quantities in learning and decision-making.

A Bayesian approach for parameter estimation and prediction using a computationally intensive model

DOE PAGES

Higdon, Dave; McDonnell, Jordan D.; Schunck, Nicolas; ...

2015-02-05

Bayesian methods have been successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based modelmore » $$\\eta (\\theta )$$, where θ denotes the uncertain, best input setting. Hence the statistical model is of the form $$y=\\eta (\\theta )+\\epsilon ,$$ where $$\\epsilon $$ accounts for measurement, and possibly other, error sources. When nonlinearity is present in $$\\eta (\\cdot )$$, the resulting posterior distribution for the unknown parameters in the Bayesian formulation is typically complex and nonstandard, requiring computationally demanding computational approaches such as Markov chain Monte Carlo (MCMC) to produce multivariate draws from the posterior. Although generally applicable, MCMC requires thousands (or even millions) of evaluations of the physics model $$\\eta (\\cdot )$$. This requirement is problematic if the model takes hours or days to evaluate. To overcome this computational bottleneck, we present an approach adapted from Bayesian model calibration. This approach combines output from an ensemble of computational model runs with physical measurements, within a statistical formulation, to carry out inference. A key component of this approach is a statistical response surface, or emulator, estimated from the ensemble of model runs. We demonstrate this approach with a case study in estimating parameters for a density functional theory model, using experimental mass/binding energy measurements from a collection of atomic nuclei. Lastly, we also demonstrate how this approach produces uncertainties in predictions for recent mass measurements obtained at Argonne National Laboratory.« less

Bayesian evaluation of budgets for endemic disease control: An example using management changes to reduce milk somatic cell count early in the first lactation of Irish dairy cows.

PubMed

Archer, S C; Mc Coy, F; Wapenaar, W; Green, M J

2014-01-01

The aim of this research was to determine budgets for specific management interventions to control heifer mastitis in Irish dairy herds as an example of evidence synthesis and 1-step Bayesian micro-simulation in a veterinary context. Budgets were determined for different decision makers based on their willingness to pay. Reducing the prevalence of heifers with a high milk somatic cell count (SCC) early in the first lactation could be achieved through herd level management interventions for pre- and peri-partum heifers, however the cost effectiveness of these interventions is unknown. A synthesis of multiple sources of evidence, accounting for variability and uncertainty in the available data is invaluable to inform decision makers around likely economic outcomes of investing in disease control measures. One analytical approach to this is Bayesian micro-simulation, where the trajectory of different individuals undergoing specific interventions is simulated. The classic micro-simulation framework was extended to encompass synthesis of evidence from 2 separate statistical models and previous research, with the outcome for an individual cow or herd assessed in terms of changes in lifetime milk yield, disposal risk, and likely financial returns conditional on the interventions being simultaneously applied. The 3 interventions tested were storage of bedding inside, decreasing transition yard stocking density, and spreading of bedding evenly in the calving area. Budgets for the interventions were determined based on the minimum expected return on investment, and the probability of the desired outcome. Budgets for interventions to control heifer mastitis were highly dependent on the decision maker's willingness to pay, and hence minimum expected return on investment. Understanding the requirements of decision makers and their rational spending limits would be useful for the development of specific interventions for particular farms to control heifer mastitis, and other

The frequentist implications of optional stopping on Bayesian hypothesis tests.

PubMed

Sanborn, Adam N; Hills, Thomas T

2014-04-01

Null hypothesis significance testing (NHST) is the most commonly used statistical methodology in psychology. The probability of achieving a value as extreme or more extreme than the statistic obtained from the data is evaluated, and if it is low enough, the null hypothesis is rejected. However, because common experimental practice often clashes with the assumptions underlying NHST, these calculated probabilities are often incorrect. Most commonly, experimenters use tests that assume that sample sizes are fixed in advance of data collection but then use the data to determine when to stop; in the limit, experimenters can use data monitoring to guarantee that the null hypothesis will be rejected. Bayesian hypothesis testing (BHT) provides a solution to these ills because the stopping rule used is irrelevant to the calculation of a Bayes factor. In addition, there are strong mathematical guarantees on the frequentist properties of BHT that are comforting for researchers concerned that stopping rules could influence the Bayes factors produced. Here, we show that these guaranteed bounds have limited scope and often do not apply in psychological research. Specifically, we quantitatively demonstrate the impact of optional stopping on the resulting Bayes factors in two common situations: (1) when the truth is a combination of the hypotheses, such as in a heterogeneous population, and (2) when a hypothesis is composite-taking multiple parameter values-such as the alternative hypothesis in a t-test. We found that, for these situations, while the Bayesian interpretation remains correct regardless of the stopping rule used, the choice of stopping rule can, in some situations, greatly increase the chance of experimenters finding evidence in the direction they desire. We suggest ways to control these frequentist implications of stopping rules on BHT.

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 Preliminary Bayesian Analysis of Incomplete Longitudinal Data from a Small Sample: Methodological Advances in an International Comparative Study of Educational Inequality

ERIC Educational Resources Information Center

Hsieh, Chueh-An; Maier, Kimberly S.

2009-01-01

The capacity of Bayesian methods in estimating complex statistical models is undeniable. Bayesian data analysis is seen as having a range of advantages, such as an intuitive probabilistic interpretation of the parameters of interest, the efficient incorporation of prior information to empirical data analysis, model averaging and model selection.…

Improved head direction command classification using an optimised Bayesian neural network.

PubMed

Nguyen, Son T; Nguyen, Hung T; Taylor, Philip B; Middleton, James

2006-01-01

Assistive technologies have recently emerged to improve the quality of life of severely disabled people by enhancing their independence in daily activities. Since many of those individuals have limited or non-existing control from the neck downward, alternative hands-free input modalities have become very important for these people to access assistive devices. In hands-free control, head movement has been proved to be a very effective user interface as it can provide a comfortable, reliable and natural way to access the device. Recently, neural networks have been shown to be useful not only for real-time pattern recognition but also for creating user-adaptive models. Since multi-layer perceptron neural networks trained using standard back-propagation may cause poor generalisation, the Bayesian technique has been proposed to improve the generalisation and robustness of these networks. This paper describes the use of Bayesian neural networks in developing a hands-free wheelchair control system. The experimental results show that with the optimised architecture, classification Bayesian neural networks can detect head commands of wheelchair users accurately irrespective to their levels of injuries.

77 FR 46096 - Statistical Process Controls for Blood Establishments; Public Workshop

Federal Register 2010, 2011, 2012, 2013, 2014

2012-08-02

...] Statistical Process Controls for Blood Establishments; Public Workshop AGENCY: Food and Drug Administration... workshop entitled: ``Statistical Process Controls for Blood Establishments.'' The purpose of this public workshop is to discuss the implementation of statistical process controls to validate and monitor...

Predicting Drug Safety and Communicating Risk: Benefits of a Bayesian Approach.

PubMed

Lazic, Stanley E; Edmunds, Nicholas; Pollard, Christopher E

2018-03-01

Drug toxicity is a major source of attrition in drug discovery and development. Pharmaceutical companies routinely use preclinical data to predict clinical outcomes and continue to invest in new assays to improve predictions. However, there are many open questions about how to make the best use of available data, combine diverse data, quantify risk, and communicate risk and uncertainty to enable good decisions. The costs of suboptimal decisions are clear: resources are wasted and patients may be put at risk. We argue that Bayesian methods provide answers to all of these problems and use hERG-mediated QT prolongation as a case study. Benefits of Bayesian machine learning models include intuitive probabilistic statements of risk that incorporate all sources of uncertainty, the option to include diverse data and external information, and visualizations that have a clear link between the output from a statistical model and what this means for risk. Furthermore, Bayesian methods are easy to use with modern software, making their adoption for safety screening straightforward. We include R and Python code to encourage the adoption of these methods.

A Bayesian Measurment Error Model for Misaligned Radiographic Data

DOE PAGES

Lennox, Kristin P.; Glascoe, Lee G.

2013-09-06

An understanding of the inherent variability in micro-computed tomography (micro-CT) data is essential to tasks such as statistical process control and the validation of radiographic simulation tools. The data present unique challenges to variability analysis due to the relatively low resolution of radiographs, and also due to minor variations from run to run which can result in misalignment or magnification changes between repeated measurements of a sample. Positioning changes artificially inflate the variability of the data in ways that mask true physical phenomena. We present a novel Bayesian nonparametric regression model that incorporates both additive and multiplicative measurement error inmore » addition to heteroscedasticity to address this problem. We also use this model to assess the effects of sample thickness and sample position on measurement variability for an aluminum specimen. Supplementary materials for this article are available online.« less

Statistics based sampling for controller and estimator design

NASA Astrophysics Data System (ADS)

Tenne, Dirk

The purpose of this research is the development of statistical design tools for robust feed-forward/feedback controllers and nonlinear estimators. This dissertation is threefold and addresses the aforementioned topics nonlinear estimation, target tracking and robust control. To develop statistically robust controllers and nonlinear estimation algorithms, research has been performed to extend existing techniques, which propagate the statistics of the state, to achieve higher order accuracy. The so-called unscented transformation has been extended to capture higher order moments. Furthermore, higher order moment update algorithms based on a truncated power series have been developed. The proposed techniques are tested on various benchmark examples. Furthermore, the unscented transformation has been utilized to develop a three dimensional geometrically constrained target tracker. The proposed planar circular prediction algorithm has been developed in a local coordinate framework, which is amenable to extension of the tracking algorithm to three dimensional space. This tracker combines the predictions of a circular prediction algorithm and a constant velocity filter by utilizing the Covariance Intersection. This combined prediction can be updated with the subsequent measurement using a linear estimator. The proposed technique is illustrated on a 3D benchmark trajectory, which includes coordinated turns and straight line maneuvers. The third part of this dissertation addresses the design of controller which include knowledge of parametric uncertainties and their distributions. The parameter distributions are approximated by a finite set of points which are calculated by the unscented transformation. This set of points is used to design robust controllers which minimize a statistical performance of the plant over the domain of uncertainty consisting of a combination of the mean and variance. The proposed technique is illustrated on three benchmark problems. The first

BAYESIAN LARGE-SCALE MULTIPLE REGRESSION WITH SUMMARY STATISTICS FROM GENOME-WIDE ASSOCIATION STUDIES1

PubMed Central

Zhu, Xiang; Stephens, Matthew

2017-01-01

Bayesian methods for large-scale multiple regression provide attractive approaches to the analysis of genome-wide association studies (GWAS). For example, they can estimate heritability of complex traits, allowing for both polygenic and sparse models; and by incorporating external genomic data into the priors, they can increase power and yield new biological insights. However, these methods require access to individual genotypes and phenotypes, which are often not easily available. Here we provide a framework for performing these analyses without individual-level data. Specifically, we introduce a “Regression with Summary Statistics” (RSS) likelihood, which relates the multiple regression coefficients to univariate regression results that are often easily available. The RSS likelihood requires estimates of correlations among covariates (SNPs), which also can be obtained from public databases. We perform Bayesian multiple regression analysis by combining the RSS likelihood with previously proposed prior distributions, sampling posteriors by Markov chain Monte Carlo. In a wide range of simulations RSS performs similarly to analyses using the individual data, both for estimating heritability and detecting associations. We apply RSS to a GWAS of human height that contains 253,288 individuals typed at 1.06 million SNPs, for which analyses of individual-level data are practically impossible. Estimates of heritability (52%) are consistent with, but more precise, than previous results using subsets of these data. We also identify many previously unreported loci that show evidence for association with height in our analyses. Software is available at https://github.com/stephenslab/rss. PMID:29399241

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.

Improving Instruction Using Statistical Process Control.

ERIC Educational Resources Information Center

Higgins, Ronald C.; Messer, George H.

1990-01-01

Two applications of statistical process control to the process of education are described. Discussed are the use of prompt feedback to teachers and prompt feedback to students. A sample feedback form is provided. (CW)

A Monte Carlo–Based Bayesian Approach for Measuring Agreement in a Qualitative Scale

PubMed Central

Pérez Sánchez, Carlos Javier

2014-01-01

Agreement analysis has been an active research area whose techniques have been widely applied in psychology and other fields. However, statistical agreement among raters has been mainly considered from a classical statistics point of view. Bayesian methodology is a viable alternative that allows the inclusion of subjective initial information coming from expert opinions, personal judgments, or historical data. A Bayesian approach is proposed by providing a unified Monte Carlo–based framework to estimate all types of measures of agreement in a qualitative scale of response. The approach is conceptually simple and it has a low computational cost. Both informative and non-informative scenarios are considered. In case no initial information is available, the results are in line with the classical methodology, but providing more information on the measures of agreement. For the informative case, some guidelines are presented to elicitate the prior distribution. The approach has been applied to two applications related to schizophrenia diagnosis and sensory analysis. PMID:29881002

CRAFT (complete reduction to amplitude frequency table)--robust and time-efficient Bayesian approach for quantitative mixture analysis by NMR.

PubMed

Krishnamurthy, Krish

2013-12-01

The intrinsic quantitative nature of NMR is increasingly exploited in areas ranging from complex mixture analysis (as in metabolomics and reaction monitoring) to quality assurance/control. Complex NMR spectra are more common than not, and therefore, extraction of quantitative information generally involves significant prior knowledge and/or operator interaction to characterize resonances of interest. Moreover, in most NMR-based metabolomic experiments, the signals from metabolites are normally present as a mixture of overlapping resonances, making quantification difficult. Time-domain Bayesian approaches have been reported to be better than conventional frequency-domain analysis at identifying subtle changes in signal amplitude. We discuss an approach that exploits Bayesian analysis to achieve a complete reduction to amplitude frequency table (CRAFT) in an automated and time-efficient fashion - thus converting the time-domain FID to a frequency-amplitude table. CRAFT uses a two-step approach to FID analysis. First, the FID is digitally filtered and downsampled to several sub FIDs, and secondly, these sub FIDs are then modeled as sums of decaying sinusoids using the Bayesian approach. CRAFT tables can be used for further data mining of quantitative information using fingerprint chemical shifts of compounds of interest and/or statistical analysis of modulation of chemical quantity in a biological study (metabolomics) or process study (reaction monitoring) or quality assurance/control. The basic principles behind this approach as well as results to evaluate the effectiveness of this approach in mixture analysis are presented. Copyright © 2013 John Wiley & Sons, Ltd.

A Bayesian sequential design with adaptive randomization for 2-sided hypothesis test.

PubMed

Yu, Qingzhao; Zhu, Lin; Zhu, Han

2017-11-01

Bayesian sequential and adaptive randomization designs are gaining popularity in clinical trials thanks to their potentials to reduce the number of required participants and save resources. We propose a Bayesian sequential design with adaptive randomization rates so as to more efficiently attribute newly recruited patients to different treatment arms. In this paper, we consider 2-arm clinical trials. Patients are allocated to the 2 arms with a randomization rate to achieve minimum variance for the test statistic. Algorithms are presented to calculate the optimal randomization rate, critical values, and power for the proposed design. Sensitivity analysis is implemented to check the influence on design by changing the prior distributions. Simulation studies are applied to compare the proposed method and traditional methods in terms of power and actual sample sizes. Simulations show that, when total sample size is fixed, the proposed design can obtain greater power and/or cost smaller actual sample size than the traditional Bayesian sequential design. Finally, we apply the proposed method to a real data set and compare the results with the Bayesian sequential design without adaptive randomization in terms of sample sizes. The proposed method can further reduce required sample size. Copyright © 2017 John Wiley & Sons, Ltd.

Bayesian flood forecasting methods: A review

NASA Astrophysics Data System (ADS)

Han, Shasha; Coulibaly, Paulin

2017-08-01

Over the past few decades, floods have been seen as one of the most common and largely distributed natural disasters in the world. If floods could be accurately forecasted in advance, then their negative impacts could be greatly minimized. It is widely recognized that quantification and reduction of uncertainty associated with the hydrologic forecast is of great importance for flood estimation and rational decision making. Bayesian forecasting system (BFS) offers an ideal theoretic framework for uncertainty quantification that can be developed for probabilistic flood forecasting via any deterministic hydrologic model. It provides suitable theoretical structure, empirically validated models and reasonable analytic-numerical computation method, and can be developed into various Bayesian forecasting approaches. This paper presents a comprehensive review on Bayesian forecasting approaches applied in flood forecasting from 1999 till now. The review starts with an overview of fundamentals of BFS and recent advances in BFS, followed with BFS application in river stage forecasting and real-time flood forecasting, then move to a critical analysis by evaluating advantages and limitations of Bayesian forecasting methods and other predictive uncertainty assessment approaches in flood forecasting, and finally discusses the future research direction in Bayesian flood forecasting. Results show that the Bayesian flood forecasting approach is an effective and advanced way for flood estimation, it considers all sources of uncertainties and produces a predictive distribution of the river stage, river discharge or runoff, thus gives more accurate and reliable flood forecasts. Some emerging Bayesian forecasting methods (e.g. ensemble Bayesian forecasting system, Bayesian multi-model combination) were shown to overcome limitations of single model or fixed model weight and effectively reduce predictive uncertainty. In recent years, various Bayesian flood forecasting approaches have been

Bayesian statistics as a new tool for spectral analysis - I. Application for the determination of basic parameters of massive stars

NASA Astrophysics Data System (ADS)

Mugnes, J.-M.; Robert, C.

2015-11-01

Spectral analysis is a powerful tool to investigate stellar properties and it has been widely used for decades now. However, the methods considered to perform this kind of analysis are mostly based on iteration among a few diagnostic lines to determine the stellar parameters. While these methods are often simple and fast, they can lead to errors and large uncertainties due to the required assumptions. Here, we present a method based on Bayesian statistics to find simultaneously the best combination of effective temperature, surface gravity, projected rotational velocity, and microturbulence velocity, using all the available spectral lines. Different tests are discussed to demonstrate the strength of our method, which we apply to 54 mid-resolution spectra of field and cluster B stars obtained at the Observatoire du Mont-Mégantic. We compare our results with those found in the literature. Differences are seen which are well explained by the different methods used. We conclude that the B-star microturbulence velocities are often underestimated. We also confirm the trend that B stars in clusters are on average faster rotators than field B stars.

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

PubMed

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

2014-03-01

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

An absolute chronology for early Egypt using radiocarbon dating and Bayesian statistical modelling

PubMed Central

Dee, Michael; Wengrow, David; Shortland, Andrew; Stevenson, Alice; Brock, Fiona; Girdland Flink, Linus; Bronk Ramsey, Christopher

2013-01-01

The Egyptian state was formed prior to the existence of verifiable historical records. Conventional dates for its formation are based on the relative ordering of artefacts. This approach is no longer considered sufficient for cogent historical analysis. Here, we produce an absolute chronology for Early Egypt by combining radiocarbon and archaeological evidence within a Bayesian paradigm. Our data cover the full trajectory of Egyptian state formation and indicate that the process occurred more rapidly than previously thought. We provide a timeline for the First Dynasty of Egypt of generational-scale resolution that concurs with prevailing archaeological analysis and produce a chronometric date for the foundation of Egypt that distinguishes between historical estimates. PMID:24204188

Why Are People Bad at Detecting Randomness? A Statistical Argument

ERIC Educational Resources Information Center

Williams, Joseph J.; Griffiths, Thomas L.

2013-01-01

Errors in detecting randomness are often explained in terms of biases and misconceptions. We propose and provide evidence for an account that characterizes the contribution of the inherent statistical difficulty of the task. Our account is based on a Bayesian statistical analysis, focusing on the fact that a random process is a special case of…

Artificial Intelligence Approach to Support Statistical Quality Control Teaching

ERIC Educational Resources Information Center

Reis, Marcelo Menezes; Paladini, Edson Pacheco; Khator, Suresh; Sommer, Willy Arno

2006-01-01

Statistical quality control--SQC (consisting of Statistical Process Control, Process Capability Studies, Acceptance Sampling and Design of Experiments) is a very important tool to obtain, maintain and improve the Quality level of goods and services produced by an organization. Despite its importance, and the fact that it is taught in technical and…

Efficient Dependency Computation for Dynamic Hybrid Bayesian Network in On-line System Health Management Applications

DTIC Science & Technology

2014-10-02

intervals (Neil, Tailor, Marquez, Fenton , & Hear, 2007). This is cumbersome, error prone and usually inaccurate. Even though a universal framework...Science. Neil, M., Tailor, M., Marquez, D., Fenton , N., & Hear. (2007). Inference in Bayesian networks using dynamic discretisation. Statistics

Three Insights from a Bayesian Interpretation of the One-Sided "P" Value

ERIC Educational Resources Information Center

Marsman, Maarten; Wagenmakers, Eric-Jan

2017-01-01

P values have been critiqued on several grounds but remain entrenched as the dominant inferential method in the empirical sciences. In this article, we elaborate on the fact that in many statistical models, the one-sided "P" value has a direct Bayesian interpretation as the approximate posterior mass for values lower than zero. The…

A Bayesian sequential processor approach to spectroscopic portal system decisions

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

Sale, K; Candy, J; Breitfeller, E

The development of faster more reliable techniques to detect radioactive contraband in a portal type scenario is an extremely important problem especially in this era of constant terrorist threats. Towards this goal the development of a model-based, Bayesian sequential data processor for the detection problem is discussed. In the sequential processor each datum (detector energy deposit and pulse arrival time) is used to update the posterior probability distribution over the space of model parameters. The nature of the sequential processor approach is that a detection is produced as soon as it is statistically justified by the data rather than waitingmore » for a fixed counting interval before any analysis is performed. In this paper the Bayesian model-based approach, physics and signal processing models and decision functions are discussed along with the first results of our research.« less

Search for transient ultralight dark matter signatures with networks of precision measurement devices using a Bayesian statistics method

NASA Astrophysics Data System (ADS)

Roberts, B. M.; Blewitt, G.; Dailey, C.; Derevianko, A.

2018-04-01

We analyze the prospects of employing a distributed global network of precision measurement devices as a dark matter and exotic physics observatory. In particular, we consider the atomic clocks of the global positioning system (GPS), consisting of a constellation of 32 medium-Earth orbit satellites equipped with either Cs or Rb microwave clocks and a number of Earth-based receiver stations, some of which employ highly-stable H-maser atomic clocks. High-accuracy timing data is available for almost two decades. By analyzing the satellite and terrestrial atomic clock data, it is possible to search for transient signatures of exotic physics, such as "clumpy" dark matter and dark energy, effectively transforming the GPS constellation into a 50 000 km aperture sensor array. Here we characterize the noise of the GPS satellite atomic clocks, describe the search method based on Bayesian statistics, and test the method using simulated clock data. We present the projected discovery reach using our method, and demonstrate that it can surpass the existing constrains by several order of magnitude for certain models. Our method is not limited in scope to GPS or atomic clock networks, and can also be applied to other networks of precision measurement devices.

Modeling Statistical Insensitivity: Sources of Suboptimal Behavior

ERIC Educational Resources Information Center

Gagliardi, Annie; Feldman, Naomi H.; Lidz, Jeffrey

2017-01-01

Children acquiring languages with noun classes (grammatical gender) have ample statistical information available that characterizes the distribution of nouns into these classes, but their use of this information to classify novel nouns differs from the predictions made by an optimal Bayesian classifier. We use rational analysis to investigate the…

Bayesian inference for the spatio-temporal invasion of alien species.

PubMed

Cook, Alex; Marion, Glenn; Butler, Adam; Gibson, Gavin

2007-08-01

In this paper we develop a Bayesian approach to parameter estimation in a stochastic spatio-temporal model of the spread of invasive species across a landscape. To date, statistical techniques, such as logistic and autologistic regression, have outstripped stochastic spatio-temporal models in their ability to handle large numbers of covariates. Here we seek to address this problem by making use of a range of covariates describing the bio-geographical features of the landscape. Relative to regression techniques, stochastic spatio-temporal models are more transparent in their representation of biological processes. They also explicitly model temporal change, and therefore do not require the assumption that the species' distribution (or other spatial pattern) has already reached equilibrium as is often the case with standard statistical approaches. In order to illustrate the use of such techniques we apply them to the analysis of data detailing the spread of an invasive plant, Heracleum mantegazzianum, across Britain in the 20th Century using geo-referenced covariate information describing local temperature, elevation and habitat type. The use of Markov chain Monte Carlo sampling within a Bayesian framework facilitates statistical assessments of differences in the suitability of different habitat classes for H. mantegazzianum, and enables predictions of future spread to account for parametric uncertainty and system variability. Our results show that ignoring such covariate information may lead to biased estimates of key processes and implausible predictions of future distributions.

Bayesian hypothesis testing for human threat conditioning research: an introduction and the condir R package

PubMed Central

Krypotos, Angelos-Miltiadis; Klugkist, Irene; Engelhard, Iris M.

2017-01-01

ABSTRACT Threat conditioning procedures have allowed the experimental investigation of the pathogenesis of Post-Traumatic Stress Disorder. The findings of these procedures have also provided stable foundations for the development of relevant intervention programs (e.g. exposure therapy). Statistical inference of threat conditioning procedures is commonly based on p-values and Null Hypothesis Significance Testing (NHST). Nowadays, however, there is a growing concern about this statistical approach, as many scientists point to the various limitations of p-values and NHST. As an alternative, the use of Bayes factors and Bayesian hypothesis testing has been suggested. In this article, we apply this statistical approach to threat conditioning data. In order to enable the easy computation of Bayes factors for threat conditioning data we present a new R package named condir, which can be used either via the R console or via a Shiny application. This article provides both a non-technical introduction to Bayesian analysis for researchers using the threat conditioning paradigm, and the necessary tools for computing Bayes factors easily. PMID:29038683

The effect of iconicity of visual displays on statistical reasoning: evidence in favor of the null hypothesis.

PubMed

Sirota, Miroslav; Kostovičová, Lenka; Juanchich, Marie

2014-08-01

Knowing which properties of visual displays facilitate statistical reasoning bears practical and theoretical implications. Therefore, we studied the effect of one property of visual diplays - iconicity (i.e., the resemblance of a visual sign to its referent) - on Bayesian reasoning. Two main accounts of statistical reasoning predict different effect of iconicity on Bayesian reasoning. The ecological-rationality account predicts a positive iconicity effect, because more highly iconic signs resemble more individuated objects, which tap better into an evolutionary-designed frequency-coding mechanism that, in turn, facilitates Bayesian reasoning. The nested-sets account predicts a null iconicity effect, because iconicity does not affect the salience of a nested-sets structure-the factor facilitating Bayesian reasoning processed by a general reasoning mechanism. In two well-powered experiments (N = 577), we found no support for a positive iconicity effect across different iconicity levels that were manipulated in different visual displays (meta-analytical overall effect: log OR = -0.13, 95% CI [-0.53, 0.28]). A Bayes factor analysis provided strong evidence in favor of the null hypothesis-the null iconicity effect. Thus, these findings corroborate the nested-sets rather than the ecological-rationality account of statistical reasoning.

Development of a Bayesian response-adaptive trial design for the Dexamethasone for Excessive Menstruation study.

PubMed

Holm Hansen, Christian; Warner, Pamela; Parker, Richard A; Walker, Brian R; Critchley, Hilary Od; Weir, Christopher J

2017-12-01

It is often unclear what specific adaptive trial design features lead to an efficient design which is also feasible to implement. This article describes the preparatory simulation study for a Bayesian response-adaptive dose-finding trial design. Dexamethasone for Excessive Menstruation aims to assess the efficacy of Dexamethasone in reducing excessive menstrual bleeding and to determine the best dose for further study. To maximise learning about the dose response, patients receive placebo or an active dose with randomisation probabilities adapting based on evidence from patients already recruited. The dose-response relationship is estimated using a flexible Bayesian Normal Dynamic Linear Model. Several competing design options were considered including: number of doses, proportion assigned to placebo, adaptation criterion, and number and timing of adaptations. We performed a fractional factorial study using SAS software to simulate virtual trial data for candidate adaptive designs under a variety of scenarios and to invoke WinBUGS for Bayesian model estimation. We analysed the simulated trial results using Normal linear models to estimate the effects of each design feature on empirical type I error and statistical power. Our readily-implemented approach using widely available statistical software identified a final design which performed robustly across a range of potential trial scenarios.

Truth, models, model sets, AIC, and multimodel inference: a Bayesian perspective

USGS Publications Warehouse

Barker, Richard J.; Link, William A.

2015-01-01

Statistical inference begins with viewing data as realizations of stochastic processes. Mathematical models provide partial descriptions of these processes; inference is the process of using the data to obtain a more complete description of the stochastic processes. Wildlife and ecological scientists have become increasingly concerned with the conditional nature of model-based inference: what if the model is wrong? Over the last 2 decades, Akaike's Information Criterion (AIC) has been widely and increasingly used in wildlife statistics for 2 related purposes, first for model choice and second to quantify model uncertainty. We argue that for the second of these purposes, the Bayesian paradigm provides the natural framework for describing uncertainty associated with model choice and provides the most easily communicated basis for model weighting. Moreover, Bayesian arguments provide the sole justification for interpreting model weights (including AIC weights) as coherent (mathematically self consistent) model probabilities. This interpretation requires treating the model as an exact description of the data-generating mechanism. We discuss the implications of this assumption, and conclude that more emphasis is needed on model checking to provide confidence in the quality of inference.

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

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.

Bayesian Fundamentalism or Enlightenment? On the explanatory status and theoretical contributions of Bayesian models of cognition.

PubMed

Jones, Matt; Love, Bradley C

2011-08-01

The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology - namely, Behaviorism and evolutionary psychology - that set aside mechanistic explanations or make use of optimality assumptions. Through these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls

Alveolar ridge preservation after tooth extraction: a Bayesian Network meta-analysis of grafting materials efficacy on prevention of bone height and width reduction.

PubMed

Iocca, Oreste; Farcomeni, Alessio; Pardiñas Lopez, Simon; Talib, Huzefa S

2017-01-01

To conduct a traditional meta-analysis and a Bayesian Network meta-analysis to synthesize the information coming from randomized controlled trials on different socket grafting materials and combine the resulting indirect evidence in order to make inferences on treatments that have not been compared directly. RCTs were identified for inclusion in the systematic review and subsequent statistical analysis. Bone height and width remodelling were selected as the chosen summary measures for comparison. First, a series of pairwise meta-analyses were performed and overall mean difference (MD) in mm with 95% CI was calculated between grafted versus non-grafted sockets. Then, a Bayesian Network meta-analysis was performed to draw indirect conclusions on which grafting materials can be considered most likely the best compared to the others. From the six included studies, seven comparisons were obtained. Traditional meta-analysis showed statistically significant results in favour of grafting the socket compared to no-graft both for height (MD 1.02, 95% CI 0.44-1.59, p value < 0.001) than for width (MD 1.52 95% CI 1.18-1.86, p value <0.000001) remodelling. Bayesian Network meta-analysis allowed to obtain a rank of intervention efficacy. On the basis of the results of the present analysis, socket grafting seems to be more favourable than unassisted socket healing. Moreover, Bayesian Network meta-analysis indicates that freeze-dried bone graft plus membrane is the most likely effective in the reduction of bone height remodelling. Autologous bone marrow resulted the most likely effective when width remodelling was considered. Studies with larger samples and less risk of bias should be conducted in the future in order to further strengthen the results of this analysis. © 2016 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Organism-level models: When mechanisms and statistics fail us

NASA Astrophysics Data System (ADS)

Phillips, M. H.; Meyer, J.; Smith, W. P.; Rockhill, J. K.

2014-03-01

Purpose: To describe the unique characteristics of models that represent the entire course of radiation therapy at the organism level and to highlight the uses to which such models can be put. Methods: At the level of an organism, traditional model-building runs into severe difficulties. We do not have sufficient knowledge to devise a complete biochemistry-based model. Statistical model-building fails due to the vast number of variables and the inability to control many of them in any meaningful way. Finally, building surrogate models, such as animal-based models, can result in excluding some of the most critical variables. Bayesian probabilistic models (Bayesian networks) provide a useful alternative that have the advantages of being mathematically rigorous, incorporating the knowledge that we do have, and being practical. Results: Bayesian networks representing radiation therapy pathways for prostate cancer and head & neck cancer were used to highlight the important aspects of such models and some techniques of model-building. A more specific model representing the treatment of occult lymph nodes in head & neck cancer were provided as an example of how such a model can inform clinical decisions. A model of the possible role of PET imaging in brain cancer was used to illustrate the means by which clinical trials can be modelled in order to come up with a trial design that will have meaningful outcomes. Conclusions: Probabilistic models are currently the most useful approach to representing the entire therapy outcome process.

A new Bayesian recursive technique for parameter estimation

NASA Astrophysics Data System (ADS)

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

2006-08-01

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

Collaborative autonomous sensing with Bayesians in the loop

NASA Astrophysics Data System (ADS)

Ahmed, Nisar

2016-10-01

There is a strong push to develop intelligent unmanned autonomy that complements human reasoning for applications as diverse as wilderness search and rescue, military surveillance, and robotic space exploration. More than just replacing humans for `dull, dirty and dangerous' work, autonomous agents are expected to cope with a whole host of uncertainties while working closely together with humans in new situations. The robotics revolution firmly established the primacy of Bayesian algorithms for tackling challenging perception, learning and decision-making problems. Since the next frontier of autonomy demands the ability to gather information across stretches of time and space that are beyond the reach of a single autonomous agent, the next generation of Bayesian algorithms must capitalize on opportunities to draw upon the sensing and perception abilities of humans-in/on-the-loop. This work summarizes our recent research toward harnessing `human sensors' for information gathering tasks. The basic idea behind is to allow human end users (i.e. non-experts in robotics, statistics, machine learning, etc.) to directly `talk to' the information fusion engine and perceptual processes aboard any autonomous agent. Our approach is grounded in rigorous Bayesian modeling and fusion of flexible semantic information derived from user-friendly interfaces, such as natural language chat and locative hand-drawn sketches. This naturally enables `plug and play' human sensing with existing probabilistic algorithms for planning and perception, and has been successfully demonstrated with human-robot teams in target localization applications.

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.

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

PubMed

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

2013-01-01

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

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.

Exploiting Data Missingness in Bayesian Network Modeling

NASA Astrophysics Data System (ADS)

Rodrigues de Morais, Sérgio; Aussem, Alex

This paper proposes a framework built on the use of Bayesian networks (BN) for representing statistical dependencies between the existing random variables and additional dummy boolean variables, which represent the presence/absence of the respective random variable value. We show how augmenting the BN with these additional variables helps pinpoint the mechanism through which missing data contributes to the classification task. The missing data mechanism is thus explicitly taken into account to predict the class variable using the data at hand. Extensive experiments on synthetic and real-world incomplete data sets reveals that the missingness information improves classification accuracy.

Statistical Modeling for Radiation Hardness Assurance

NASA Technical Reports Server (NTRS)

Ladbury, Raymond L.

2014-01-01

We cover the models and statistics associated with single event effects (and total ionizing dose), why we need them, and how to use them: What models are used, what errors exist in real test data, and what the model allows us to say about the DUT will be discussed. In addition, how to use other sources of data such as historical, heritage, and similar part and how to apply experience, physics, and expert opinion to the analysis will be covered. Also included will be concepts of Bayesian statistics, data fitting, and bounding rates.

A baker's dozen of new particle flows for nonlinear filters, Bayesian decisions and transport

NASA Astrophysics Data System (ADS)

Daum, Fred; Huang, Jim

2015-05-01

We describe a baker's dozen of new particle flows to compute Bayes' rule for nonlinear filters, Bayesian decisions and learning as well as transport. Several of these new flows were inspired by transport theory, but others were inspired by physics or statistics or Markov chain Monte Carlo methods.

Efficient Algorithms for Bayesian Network Parameter Learning from Incomplete Data

DTIC Science & Technology

2015-07-01

Efficient Algorithms for Bayesian Network Parameter Learning from Incomplete Data Guy Van den Broeck∗ and Karthika Mohan∗ and Arthur Choi and Adnan ...notwithstanding any other provision of law , no person shall be subject to a penalty for failing to comply with a collection of information if it does...Wasserman, L. (2011). All of Statistics. Springer Science & Business Media. Yaramakala, S., & Margaritis, D. (2005). Speculative markov blanket discovery for optimal feature selection. In Proceedings of ICDM.

Incorporating historical information in biosimilar trials: Challenges and a hybrid Bayesian-frequentist approach.

PubMed

Mielke, Johanna; Schmidli, Heinz; Jones, Byron

2018-05-01

For the approval of biosimilars, it is, in most cases, necessary to conduct large Phase III clinical trials in patients to convince the regulatory authorities that the product is comparable in terms of efficacy and safety to the originator product. As the originator product has already been studied in several trials beforehand, it seems natural to include this historical information into the showing of equivalent efficacy. Since all studies for the regulatory approval of biosimilars are confirmatory studies, it is required that the statistical approach has reasonable frequentist properties, most importantly, that the Type I error rate is controlled-at least in all scenarios that are realistic in practice. However, it is well known that the incorporation of historical information can lead to an inflation of the Type I error rate in the case of a conflict between the distribution of the historical data and the distribution of the trial data. We illustrate this issue and confirm, using the Bayesian robustified meta-analytic-predictive (MAP) approach as an example, that simultaneously controlling the Type I error rate over the complete parameter space and gaining power in comparison to a standard frequentist approach that only considers the data in the new study, is not possible. We propose a hybrid Bayesian-frequentist approach for binary endpoints that controls the Type I error rate in the neighborhood of the center of the prior distribution, while improving the power. We study the properties of this approach in an extensive simulation study and provide a real-world example. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Bayesian phylogenetic estimation of fossil ages.

PubMed

Drummond, Alexei J; Stadler, Tanja

2016-07-19

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

Bayesian phylogenetic estimation of fossil ages

PubMed Central

Drummond, Alexei J.; Stadler, Tanja

2016-01-01

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

Bayesian Model Selection under Time Constraints

NASA Astrophysics Data System (ADS)

Hoege, M.; Nowak, W.; Illman, W. A.

2017-12-01

Bayesian model selection (BMS) provides a consistent framework for rating and comparing models in multi-model inference. In cases where models of vastly different complexity compete with each other, we also face vastly different computational runtimes of such models. For instance, time series of a quantity of interest can be simulated by an autoregressive process model that takes even less than a second for one run, or by a partial differential equations-based model with runtimes up to several hours or even days. The classical BMS is based on a quantity called Bayesian model evidence (BME). It determines the model weights in the selection process and resembles a trade-off between bias of a model and its complexity. However, in practice, the runtime of models is another weight relevant factor for model selection. Hence, we believe that it should be included, leading to an overall trade-off problem between bias, variance and computing effort. We approach this triple trade-off from the viewpoint of our ability to generate realizations of the models under a given computational budget. One way to obtain BME values is through sampling-based integration techniques. We argue with the fact that more expensive models can be sampled much less under time constraints than faster models (in straight proportion to their runtime). The computed evidence in favor of a more expensive model is statistically less significant than the evidence computed in favor of a faster model, since sampling-based strategies are always subject to statistical sampling error. We present a straightforward way to include this misbalance into the model weights that are the basis for model selection. Our approach follows directly from the idea of insufficient significance. It is based on a computationally cheap bootstrapping error estimate of model evidence and is easy to implement. The approach is illustrated in a small synthetic modeling study.

Bayesian methods for the design and interpretation of clinical trials in very rare diseases

PubMed Central

Hampson, Lisa V; Whitehead, John; Eleftheriou, Despina; Brogan, Paul

2014-01-01

This paper considers the design and interpretation of clinical trials comparing treatments for conditions so rare that worldwide recruitment efforts are likely to yield total sample sizes of 50 or fewer, even when patients are recruited over several years. For such studies, the sample size needed to meet a conventional frequentist power requirement is clearly infeasible. Rather, the expectation of any such trial has to be limited to the generation of an improved understanding of treatment options. We propose a Bayesian approach for the conduct of rare-disease trials comparing an experimental treatment with a control where patient responses are classified as a success or failure. A systematic elicitation from clinicians of their beliefs concerning treatment efficacy is used to establish Bayesian priors for unknown model parameters. The process of determining the prior is described, including the possibility of formally considering results from related trials. As sample sizes are small, it is possible to compute all possible posterior distributions of the two success rates. A number of allocation ratios between the two treatment groups can be considered with a view to maximising the prior probability that the trial concludes recommending the new treatment when in fact it is non-inferior to control. Consideration of the extent to which opinion can be changed, even by data from the best feasible design, can help to determine whether such a trial is worthwhile. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24957522

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

Effective control of complex turbulent dynamical systems through statistical functionals.

PubMed

Majda, Andrew J; Qi, Di

2017-05-30

Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among complex systems in science and engineering, including climate, material, and neural science. Control of these complex systems is a grand challenge, for example, in mitigating the effects of climate change or safe design of technology with fully developed shear turbulence. Control of flows in the transition to turbulence, where there is a small dimension of instabilities about a basic mean state, is an important and successful discipline. In complex turbulent dynamical systems, it is impossible to track and control the large dimension of instabilities, which strongly interact and exchange energy, and new control strategies are needed. The goal of this paper is to propose an effective statistical control strategy for complex turbulent dynamical systems based on a recent statistical energy principle and statistical linear response theory. We illustrate the potential practical efficiency and verify this effective statistical control strategy on the 40D Lorenz 1996 model in forcing regimes with various types of fully turbulent dynamics with nearly one-half of the phase space unstable.

Using Statistical Process Control to Make Data-Based Clinical Decisions.

ERIC Educational Resources Information Center

Pfadt, Al; Wheeler, Donald J.

1995-01-01

Statistical process control (SPC), which employs simple statistical tools and problem-solving techniques such as histograms, control charts, flow charts, and Pareto charts to implement continual product improvement procedures, can be incorporated into human service organizations. Examples illustrate use of SPC procedures to analyze behavioral data…

Modelling maximum river flow by using Bayesian Markov Chain Monte Carlo

NASA Astrophysics Data System (ADS)

Cheong, R. Y.; Gabda, D.

2017-09-01

Analysis of flood trends is vital since flooding threatens human living in terms of financial, environment and security. The data of annual maximum river flows in Sabah were fitted into generalized extreme value (GEV) distribution. Maximum likelihood estimator (MLE) raised naturally when working with GEV distribution. However, previous researches showed that MLE provide unstable results especially in small sample size. In this study, we used different Bayesian Markov Chain Monte Carlo (MCMC) based on Metropolis-Hastings algorithm to estimate GEV parameters. Bayesian MCMC method is a statistical inference which studies the parameter estimation by using posterior distribution based on Bayes’ theorem. Metropolis-Hastings algorithm is used to overcome the high dimensional state space faced in Monte Carlo method. This approach also considers more uncertainty in parameter estimation which then presents a better prediction on maximum river flow in Sabah.

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

PubMed

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

2018-01-01

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

A robust bayesian estimate of the concordance correlation coefficient.

PubMed

Feng, Dai; Baumgartner, Richard; Svetnik, Vladimir

2015-01-01

A need for assessment of agreement arises in many situations including statistical biomarker qualification or assay or method validation. Concordance correlation coefficient (CCC) is one of the most popular scaled indices reported in evaluation of agreement. Robust methods for CCC estimation currently present an important statistical challenge. Here, we propose a novel Bayesian method of robust estimation of CCC based on multivariate Student's t-distribution and compare it with its alternatives. Furthermore, we extend the method to practically relevant settings, enabling incorporation of confounding covariates and replications. The superiority of the new approach is demonstrated using simulation as well as real datasets from biomarker application in electroencephalography (EEG). This biomarker is relevant in neuroscience for development of treatments for insomnia.

Bayesian Atmospheric Radiative Transfer (BART) Code and Application to WASP-43b

NASA Astrophysics Data System (ADS)

Blecic, Jasmina; Harrington, Joseph; Cubillos, Patricio; Bowman, Oliver; Rojo, Patricio; Stemm, Madison; Lust, Nathaniel B.; Challener, Ryan; Foster, Austin James; Foster, Andrew S.; Blumenthal, Sarah D.; Bruce, Dylan

2016-01-01

We present a new open-source Bayesian radiative-transfer framework, Bayesian Atmospheric Radiative Transfer (BART, https://github.com/exosports/BART), and its application to WASP-43b. BART initializes a model for the atmospheric retrieval calculation, generates thousands of theoretical model spectra using parametrized pressure and temperature profiles and line-by-line radiative-transfer calculation, and employs a statistical package to compare the models with the observations. It consists of three self-sufficient modules available to the community under the reproducible-research license, the Thermochemical Equilibrium Abundances module (TEA, https://github.com/dzesmin/TEA, Blecic et al. 2015}, the radiative-transfer module (Transit, https://github.com/exosports/transit), and the Multi-core Markov-chain Monte Carlo statistical module (MCcubed, https://github.com/pcubillos/MCcubed, Cubillos et al. 2015). We applied BART on all available WASP-43b secondary eclipse data from the space- and ground-based observations constraining the temperature-pressure profile and molecular abundances of the dayside atmosphere of WASP-43b. This work was supported by NASA Planetary Atmospheres grant NNX12AI69G and NASA Astrophysics Data Analysis Program grant NNX13AF38G. JB holds a NASA Earth and Space Science Fellowship.

Robust Bayesian clustering.

PubMed

Archambeau, Cédric; Verleysen, Michel

2007-01-01

A new variational Bayesian learning algorithm for Student-t mixture models is introduced. This algorithm leads to (i) robust density estimation, (ii) robust clustering and (iii) robust automatic model selection. Gaussian mixture models are learning machines which are based on a divide-and-conquer approach. They are commonly used for density estimation and clustering tasks, but are sensitive to outliers. The Student-t distribution has heavier tails than the Gaussian distribution and is therefore less sensitive to any departure of the empirical distribution from Gaussianity. As a consequence, the Student-t distribution is suitable for constructing robust mixture models. In this work, we formalize the Bayesian Student-t mixture model as a latent variable model in a different way from Svensén and Bishop [Svensén, M., & Bishop, C. M. (2005). Robust Bayesian mixture modelling. Neurocomputing, 64, 235-252]. The main difference resides in the fact that it is not necessary to assume a factorized approximation of the posterior distribution on the latent indicator variables and the latent scale variables in order to obtain a tractable solution. Not neglecting the correlations between these unobserved random variables leads to a Bayesian model having an increased robustness. Furthermore, it is expected that the lower bound on the log-evidence is tighter. Based on this bound, the model complexity, i.e. the number of components in the mixture, can be inferred with a higher confidence.

Using Bayesian neural networks to classify forest scenes

NASA Astrophysics Data System (ADS)

Vehtari, Aki; Heikkonen, Jukka; Lampinen, Jouko; Juujarvi, Jouni

1998-10-01

We present results that compare the performance of Bayesian learning methods for neural networks on the task of classifying forest scenes into trees and background. Classification task is demanding due to the texture richness of the trees, occlusions of the forest scene objects and diverse lighting conditions under operation. This makes it difficult to determine which are optimal image features for the classification. A natural way to proceed is to extract many different types of potentially suitable features, and to evaluate their usefulness in later processing stages. One approach to cope with large number of features is to use Bayesian methods to control the model complexity. Bayesian learning uses a prior on model parameters, combines this with evidence from a training data, and the integrates over the resulting posterior to make predictions. With this method, we can use large networks and many features without fear of overfitting. For this classification task we compare two Bayesian learning methods for multi-layer perceptron (MLP) neural networks: (1) The evidence framework of MacKay uses a Gaussian approximation to the posterior weight distribution and maximizes with respect to hyperparameters. (2) In a Markov Chain Monte Carlo (MCMC) method due to Neal, the posterior distribution of the network parameters is numerically integrated using the MCMC method. As baseline classifiers for comparison we use (3) MLP early stop committee, (4) K-nearest-neighbor and (5) Classification And Regression Tree.

Bayesian estimation of the transmissivity spatial structure from pumping test data

NASA Astrophysics Data System (ADS)

Demir, Mehmet Taner; Copty, Nadim K.; Trinchero, Paolo; Sanchez-Vila, Xavier

2017-06-01

Estimating the statistical parameters (mean, variance, and integral scale) that define the spatial structure of the transmissivity or hydraulic conductivity fields is a fundamental step for the accurate prediction of subsurface flow and contaminant transport. In practice, the determination of the spatial structure is a challenge because of spatial heterogeneity and data scarcity. In this paper, we describe a novel approach that uses time drawdown data from multiple pumping tests to determine the transmissivity statistical spatial structure. The method builds on the pumping test interpretation procedure of Copty et al. (2011) (Continuous Derivation method, CD), which uses the time-drawdown data and its time derivative to estimate apparent transmissivity values as a function of radial distance from the pumping well. A Bayesian approach is then used to infer the statistical parameters of the transmissivity field by combining prior information about the parameters and the likelihood function expressed in terms of radially-dependent apparent transmissivities determined from pumping tests. A major advantage of the proposed Bayesian approach is that the likelihood function is readily determined from randomly generated multiple realizations of the transmissivity field, without the need to solve the groundwater flow equation. Applying the method to synthetically-generated pumping test data, we demonstrate that, through a relatively simple procedure, information on the spatial structure of the transmissivity may be inferred from pumping tests data. It is also shown that the prior parameter distribution has a significant influence on the estimation procedure, given the non-uniqueness of the estimation procedure. Results also indicate that the reliability of the estimated transmissivity statistical parameters increases with the number of available pumping tests.

Bayesian analysis of a mastitis control plan to investigate the influence of veterinary prior beliefs on clinical interpretation.

PubMed

Green, M J; Browne, W J; Green, L E; Bradley, A J; Leach, K A; Breen, J E; Medley, G F

2009-10-01

The fundamental objective for health research is to determine whether changes should be made to clinical decisions. Decisions made by veterinary surgeons in the light of new research evidence are known to be influenced by their prior beliefs, especially their initial opinions about the plausibility of possible results. In this paper, clinical trial results for a bovine mastitis control plan were evaluated within a Bayesian context, to incorporate a community of prior distributions that represented a spectrum of clinical prior beliefs. The aim was to quantify the effect of veterinary surgeons' initial viewpoints on the interpretation of the trial results. A Bayesian analysis was conducted using Markov chain Monte Carlo procedures. Stochastic models included a financial cost attributed to a change in clinical mastitis following implementation of the control plan. Prior distributions were incorporated that covered a realistic range of possible clinical viewpoints, including scepticism, enthusiasm and uncertainty. Posterior distributions revealed important differences in the financial gain that clinicians with different starting viewpoints would anticipate from the mastitis control plan, given the actual research results. For example, a severe skeptic would ascribe a probability of 0.50 for a return of < 5 UK pounds per cow in an average herd that implemented the plan, whereas an enthusiast would ascribe this probability for a return of > 20 UK pounds per cow. Simulations using increased trial sizes indicated that if the original study was four times as large, an initial skeptic would be more convinced about the efficacy of the control plan but would still anticipate less financial return than an initial enthusiast would anticipate after the original study. In conclusion, it is possible to estimate how clinicians' prior beliefs influence their interpretation of research evidence. Further research on the extent to which different interpretations of evidence result in

Bayesian networks improve causal environmental ...

EPA Pesticide Factsheets

Rule-based weight of evidence approaches to ecological risk assessment may not account for uncertainties and generally lack probabilistic integration of lines of evidence. Bayesian networks allow causal inferences to be made from evidence by including causal knowledge about the problem, using this knowledge with probabilistic calculus to combine multiple lines of evidence, and minimizing biases in predicting or diagnosing causal relationships. Too often, sources of uncertainty in conventional weight of evidence approaches are ignored that can be accounted for with Bayesian networks. Specifying and propagating uncertainties improve the ability of models to incorporate strength of the evidence in the risk management phase of an assessment. Probabilistic inference from a Bayesian network allows evaluation of changes in uncertainty for variables from the evidence. The network structure and probabilistic framework of a Bayesian approach provide advantages over qualitative approaches in weight of evidence for capturing the impacts of multiple sources of quantifiable uncertainty on predictions of ecological risk. Bayesian networks can facilitate the development of evidence-based policy under conditions of uncertainty by incorporating analytical inaccuracies or the implications of imperfect information, structuring and communicating causal issues through qualitative directed graph formulations, and quantitatively comparing the causal power of multiple stressors on value

Predicting Football Matches Results using Bayesian Networks for English Premier League (EPL)

NASA Astrophysics Data System (ADS)

Razali, Nazim; Mustapha, Aida; Yatim, Faiz Ahmad; Aziz, Ruhaya Ab

2017-08-01

The issues of modeling asscoiation football prediction model has become increasingly popular in the last few years and many different approaches of prediction models have been proposed with the point of evaluating the attributes that lead a football team to lose, draw or win the match. There are three types of approaches has been considered for predicting football matches results which include statistical approaches, machine learning approaches and Bayesian approaches. Lately, many studies regarding football prediction models has been produced using Bayesian approaches. This paper proposes a Bayesian Networks (BNs) to predict the results of football matches in term of home win (H), away win (A) and draw (D). The English Premier League (EPL) for three seasons of 2010-2011, 2011-2012 and 2012-2013 has been selected and reviewed. K-fold cross validation has been used for testing the accuracy of prediction model. The required information about the football data is sourced from a legitimate site at http://www.football-data.co.uk. BNs achieved predictive accuracy of 75.09% in average across three seasons. It is hoped that the results could be used as the benchmark output for future research in predicting football matches results.

A BAYESIAN SPATIAL AND TEMPORAL MODELING APPROACH TO MAPPING GEOGRAPHIC VARIATION IN MORTALITY RATES FOR SUBNATIONAL AREAS WITH R-INLA.

PubMed

Khana, Diba; Rossen, Lauren M; Hedegaard, Holly; Warner, Margaret

2018-01-01

Hierarchical Bayes models have been used in disease mapping to examine small scale geographic variation. State level geographic variation for less common causes of mortality outcomes have been reported however county level variation is rarely examined. Due to concerns about statistical reliability and confidentiality, county-level mortality rates based on fewer than 20 deaths are suppressed based on Division of Vital Statistics, National Center for Health Statistics (NCHS) statistical reliability criteria, precluding an examination of spatio-temporal variation in less common causes of mortality outcomes such as suicide rates (SRs) at the county level using direct estimates. Existing Bayesian spatio-temporal modeling strategies can be applied via Integrated Nested Laplace Approximation (INLA) in R to a large number of rare causes of mortality outcomes to enable examination of spatio-temporal variations on smaller geographic scales such as counties. This method allows examination of spatiotemporal variation across the entire U.S., even where the data are sparse. We used mortality data from 2005-2015 to explore spatiotemporal variation in SRs, as one particular application of the Bayesian spatio-temporal modeling strategy in R-INLA to predict year and county-specific SRs. Specifically, hierarchical Bayesian spatio-temporal models were implemented with spatially structured and unstructured random effects, correlated time effects, time varying confounders and space-time interaction terms in the software R-INLA, borrowing strength across both counties and years to produce smoothed county level SRs. Model-based estimates of SRs were mapped to explore geographic variation.

A Bayesian Nonparametric Approach to Test Equating

ERIC Educational Resources Information Center

Karabatsos, George; Walker, Stephen G.

2009-01-01

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are…

Bayesian Model Averaging for Propensity Score Analysis

ERIC Educational Resources Information Center

Kaplan, David; Chen, Jianshen

2013-01-01

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

Perspectives on the Use of Null Hypothesis Statistical Testing. Part III: the Various Nuts and Bolts of Statistical and Hypothesis Testing

ERIC Educational Resources Information Center

Marmolejo-Ramos, Fernando; Cousineau, Denis

2017-01-01

The number of articles showing dissatisfaction with the null hypothesis statistical testing (NHST) framework has been progressively increasing over the years. Alternatives to NHST have been proposed and the Bayesian approach seems to have achieved the highest amount of visibility. In this last part of the special issue, a few alternative…

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

NASA Astrophysics Data System (ADS)

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

2005-10-01

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

HARMONIZATION OF HUMAN AND ECOLOGICAL HEALTH ASSESSMENT: DEVELOPMENT OF BAYESIAN UPDATING TECHNIQUES TO INCORPORATE MECHANISTIC INFORMATION ACROSS SPECIES

EPA Science Inventory

Bayesian statistical techniques have proven useful in clinical and environmental epidemiological applications to evaluate and integrate available information, and in regulatory applications such as the National Ambient Air Quality Assessment for Nitrogen Oxides. A recent special...

Effective Online Bayesian Phylogenetics via Sequential Monte Carlo with Guided Proposals

PubMed Central

Fourment, Mathieu; Claywell, Brian C; Dinh, Vu; McCoy, Connor; Matsen IV, Frederick A; Darling, Aaron E

2018-01-01

Abstract Modern infectious disease outbreak surveillance produces continuous streams of sequence data which require phylogenetic analysis as data arrives. Current software packages for Bayesian phylogenetic inference are unable to quickly incorporate new sequences as they become available, making them less useful for dynamically unfolding evolutionary stories. This limitation can be addressed by applying a class of Bayesian statistical inference algorithms called sequential Monte Carlo (SMC) to conduct online inference, wherein new data can be continuously incorporated to update the estimate of the posterior probability distribution. In this article, we describe and evaluate several different online phylogenetic sequential Monte Carlo (OPSMC) algorithms. We show that proposing new phylogenies with a density similar to the Bayesian prior suffers from poor performance, and we develop “guided” proposals that better match the proposal density to the posterior. Furthermore, we show that the simplest guided proposals can exhibit pathological behavior in some situations, leading to poor results, and that the situation can be resolved by heating the proposal density. The results demonstrate that relative to the widely used MCMC-based algorithm implemented in MrBayes, the total time required to compute a series of phylogenetic posteriors as sequences arrive can be significantly reduced by the use of OPSMC, without incurring a significant loss in accuracy. PMID:29186587

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

Bayesian Analysis of High Dimensional Classification

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Subhadeep; Liang, Faming

2009-12-01

Modern data mining and bioinformatics have presented an important playground for statistical learning techniques, where the number of input variables is possibly much larger than the sample size of the training data. In supervised learning, logistic regression or probit regression can be used to model a binary output and form perceptron classification rules based on Bayesian inference. In these cases , there is a lot of interest in searching for sparse model in High Dimensional regression(/classification) setup. we first discuss two common challenges for analyzing high dimensional data. The first one is the curse of dimensionality. The complexity of many existing algorithms scale exponentially with the dimensionality of the space and by virtue of that algorithms soon become computationally intractable and therefore inapplicable in many real applications. secondly, multicollinearities among the predictors which severely slowdown the algorithm. In order to make Bayesian analysis operational in high dimension we propose a novel 'Hierarchical stochastic approximation monte carlo algorithm' (HSAMC), which overcomes the curse of dimensionality, multicollinearity of predictors in high dimension and also it possesses the self-adjusting mechanism to avoid the local minima separated by high energy barriers. Models and methods are illustrated by simulation inspired from from the feild of genomics. Numerical results indicate that HSAMC can work as a general model selection sampler in high dimensional complex model space.

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

Bayesian neural adjustment of inhibitory control predicts emergence of problem stimulant use.

PubMed

Harlé, Katia M; Stewart, Jennifer L; Zhang, Shunan; Tapert, Susan F; Yu, Angela J; Paulus, Martin P

2015-11-01

Bayesian ideal observer models quantify individuals' context- and experience-dependent beliefs and expectations about their environment, which provides a powerful approach (i) to link basic behavioural mechanisms to neural processing; and (ii) to generate clinical predictors for patient populations. Here, we focus on (ii) and determine whether individual differences in the neural representation of the need to stop in an inhibitory task can predict the development of problem use (i.e. abuse or dependence) in individuals experimenting with stimulants. One hundred and fifty-seven non-dependent occasional stimulant users, aged 18-24, completed a stop-signal task while undergoing functional magnetic resonance imaging. These individuals were prospectively followed for 3 years and evaluated for stimulant use and abuse/dependence symptoms. At follow-up, 38 occasional stimulant users met criteria for a stimulant use disorder (problem stimulant users), while 50 had discontinued use (desisted stimulant users). We found that those individuals who showed greater neural responses associated with Bayesian prediction errors, i.e. the difference between actual and expected need to stop on a given trial, in right medial prefrontal cortex/anterior cingulate cortex, caudate, anterior insula, and thalamus were more likely to exhibit problem use 3 years later. Importantly, these computationally based neural predictors outperformed clinical measures and non-model based neural variables in predicting clinical status. In conclusion, young adults who show exaggerated brain processing underlying whether to 'stop' or to 'go' are more likely to develop stimulant abuse. Thus, Bayesian cognitive models provide both a computational explanation and potential predictive biomarkers of belief processing deficits in individuals at risk for stimulant addiction. © The Author (2015). Published by Oxford University Press on behalf of the Guarantors of Brain. All rights reserved. For Permissions, please

A review and comparison of Bayesian and likelihood-based inferences in beta regression and zero-or-one-inflated beta regression.

PubMed

Liu, Fang; Eugenio, Evercita C

2018-04-01

Beta regression is an increasingly popular statistical technique in medical research for modeling of outcomes that assume values in (0, 1), such as proportions and patient reported outcomes. When outcomes take values in the intervals [0,1), (0,1], or [0,1], zero-or-one-inflated beta (zoib) regression can be used. We provide a thorough review on beta regression and zoib regression in the modeling, inferential, and computational aspects via the likelihood-based and Bayesian approaches. We demonstrate the statistical and practical importance of correctly modeling the inflation at zero/one rather than ad hoc replacing them with values close to zero/one via simulation studies; the latter approach can lead to biased estimates and invalid inferences. We show via simulation studies that the likelihood-based approach is computationally faster in general than MCMC algorithms used in the Bayesian inferences, but runs the risk of non-convergence, large biases, and sensitivity to starting values in the optimization algorithm especially with clustered/correlated data, data with sparse inflation at zero and one, and data that warrant regularization of the likelihood. The disadvantages of the regular likelihood-based approach make the Bayesian approach an attractive alternative in these cases. Software packages and tools for fitting beta and zoib regressions in both the likelihood-based and Bayesian frameworks are also reviewed.

Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach.

PubMed

Chertkov, Michael; Chernyak, Vladimir

2017-08-17

Thermostatically controlled loads, e.g., air conditioners and heaters, are by far the most widespread consumers of electricity. Normally the devices are calibrated to provide the so-called bang-bang control - changing from on to off, and vice versa, depending on temperature. We considered aggregation of a large group of similar devices into a statistical ensemble, where the devices operate following the same dynamics, subject to stochastic perturbations and randomized, Poisson on/off switching policy. Using theoretical and computational tools of statistical physics, we analyzed how the ensemble relaxes to a stationary distribution and established a relationship between the relaxation and the statistics of the probability flux associated with devices' cycling in the mixed (discrete, switch on/off, and continuous temperature) phase space. This allowed us to derive the spectrum of the non-equilibrium (detailed balance broken) statistical system and uncover how switching policy affects oscillatory trends and the speed of the relaxation. Relaxation of the ensemble is of practical interest because it describes how the ensemble recovers from significant perturbations, e.g., forced temporary switching off aimed at utilizing the flexibility of the ensemble to provide "demand response" services to change consumption temporarily to balance a larger power grid. We discuss how the statistical analysis can guide further development of the emerging demand response technology.

Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach

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

Chertkov, Michael; Chernyak, Vladimir

Thermostatically Controlled Loads (TCL), e.g. air-conditioners and heaters, are by far the most wide-spread consumers of electricity. Normally the devices are calibrated to provide the so-called bang-bang control of temperature - changing from on to off , and vice versa, depending on temperature. Aggregation of a large group of similar devices into a statistical ensemble is considered, where the devices operate following the same dynamics subject to stochastic perturbations and randomized, Poisson on/off switching policy. We analyze, using theoretical and computational tools of statistical physics, how the ensemble relaxes to a stationary distribution and establish relation between the re- laxationmore » and statistics of the probability flux, associated with devices' cycling in the mixed (discrete, switch on/off , and continuous, temperature) phase space. This allowed us to derive and analyze spec- trum of the non-equilibrium (detailed balance broken) statistical system. and uncover how switching policy affects oscillatory trend and speed of the relaxation. Relaxation of the ensemble is of a practical interest because it describes how the ensemble recovers from significant perturbations, e.g. forceful temporary switching o aimed at utilizing flexibility of the ensemble in providing "demand response" services relieving consumption temporarily to balance larger power grid. We discuss how the statistical analysis can guide further development of the emerging demand response technology.« less

Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach

DOE PAGES

Chertkov, Michael; Chernyak, Vladimir

2017-01-17

Thermostatically Controlled Loads (TCL), e.g. air-conditioners and heaters, are by far the most wide-spread consumers of electricity. Normally the devices are calibrated to provide the so-called bang-bang control of temperature - changing from on to off , and vice versa, depending on temperature. Aggregation of a large group of similar devices into a statistical ensemble is considered, where the devices operate following the same dynamics subject to stochastic perturbations and randomized, Poisson on/off switching policy. We analyze, using theoretical and computational tools of statistical physics, how the ensemble relaxes to a stationary distribution and establish relation between the re- laxationmore » and statistics of the probability flux, associated with devices' cycling in the mixed (discrete, switch on/off , and continuous, temperature) phase space. This allowed us to derive and analyze spec- trum of the non-equilibrium (detailed balance broken) statistical system. and uncover how switching policy affects oscillatory trend and speed of the relaxation. Relaxation of the ensemble is of a practical interest because it describes how the ensemble recovers from significant perturbations, e.g. forceful temporary switching o aimed at utilizing flexibility of the ensemble in providing "demand response" services relieving consumption temporarily to balance larger power grid. We discuss how the statistical analysis can guide further development of the emerging demand response technology.« less

Bayesian Analysis for Risk Assessment of Selected Medical Events in Support of the Integrated Medical Model Effort

NASA Technical Reports Server (NTRS)

Gilkey, Kelly M.; Myers, Jerry G.; McRae, Michael P.; Griffin, Elise A.; Kallrui, Aditya S.

2012-01-01

The Exploration Medical Capability project is creating a catalog of risk assessments using the Integrated Medical Model (IMM). The IMM is a software-based system intended to assist mission planners in preparing for spaceflight missions by helping them to make informed decisions about medical preparations and supplies needed for combating and treating various medical events using Probabilistic Risk Assessment. The objective is to use statistical analyses to inform the IMM decision tool with estimated probabilities of medical events occurring during an exploration mission. Because data regarding astronaut health are limited, Bayesian statistical analysis is used. Bayesian inference combines prior knowledge, such as data from the general U.S. population, the U.S. Submarine Force, or the analog astronaut population located at the NASA Johnson Space Center, with observed data for the medical condition of interest. The posterior results reflect the best evidence for specific medical events occurring in flight. Bayes theorem provides a formal mechanism for combining available observed data with data from similar studies to support the quantification process. The IMM team performed Bayesian updates on the following medical events: angina, appendicitis, atrial fibrillation, atrial flutter, dental abscess, dental caries, dental periodontal disease, gallstone disease, herpes zoster, renal stones, seizure, and stroke.

Bayesian analysis of U.S. hurricane climate

USGS Publications Warehouse

Elsner, James B.; Bossak, Brian H.

2001-01-01

Predictive climate distributions of U.S. landfalling hurricanes are estimated from observational records over the period 1851–2000. The approach is Bayesian, combining the reliable records of hurricane activity during the twentieth century with the less precise accounts of activity during the nineteenth century to produce a best estimate of the posterior distribution on the annual rates. The methodology provides a predictive distribution of future activity that serves as a climatological benchmark. Results are presented for the entire coast as well as for the Gulf Coast, Florida, and the East Coast. Statistics on the observed annual counts of U.S. hurricanes, both for the entire coast and by region, are similar within each of the three consecutive 50-yr periods beginning in 1851. However, evidence indicates that the records during the nineteenth century are less precise. Bayesian theory provides a rational approach for defining hurricane climate that uses all available information and that makes no assumption about whether the 150-yr record of hurricanes has been adequately or uniformly monitored. The analysis shows that the number of major hurricanes expected to reach the U.S. coast over the next 30 yr is 18 and the number of hurricanes expected to hit Florida is 20.

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.

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

PubMed

Karabatsos, George

2017-02-01

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

Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Cockayne, Jon; Oates, Chris; Sullivan, Tim; Girolami, Mark

2017-06-01

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model.

Environmental statistics and optimal regulation.

PubMed

Sivak, David A; Thomson, Matt

2014-09-01

Any organism is embedded in an environment that changes over time. The timescale for and statistics of environmental change, the precision with which the organism can detect its environment, and the costs and benefits of particular protein expression levels all will affect the suitability of different strategies--such as constitutive expression or graded response--for regulating protein levels in response to environmental inputs. We propose a general framework-here specifically applied to the enzymatic regulation of metabolism in response to changing concentrations of a basic nutrient-to predict the optimal regulatory strategy given the statistics of fluctuations in the environment and measurement apparatus, respectively, and the costs associated with enzyme production. We use this framework to address three fundamental questions: (i) when a cell should prefer thresholding to a graded response; (ii) when there is a fitness advantage to implementing a Bayesian decision rule; and (iii) when retaining memory of the past provides a selective advantage. We specifically find that: (i) relative convexity of enzyme expression cost and benefit influences the fitness of thresholding or graded responses; (ii) intermediate levels of measurement uncertainty call for a sophisticated Bayesian decision rule; and (iii) in dynamic contexts, intermediate levels of uncertainty call for retaining memory of the past. Statistical properties of the environment, such as variability and correlation times, set optimal biochemical parameters, such as thresholds and decay rates in signaling pathways. Our framework provides a theoretical basis for interpreting molecular signal processing algorithms and a classification scheme that organizes known regulatory strategies and may help conceptualize heretofore unknown ones.

Environmental Statistics and Optimal Regulation

PubMed Central

2014-01-01

Any organism is embedded in an environment that changes over time. The timescale for and statistics of environmental change, the precision with which the organism can detect its environment, and the costs and benefits of particular protein expression levels all will affect the suitability of different strategies–such as constitutive expression or graded response–for regulating protein levels in response to environmental inputs. We propose a general framework–here specifically applied to the enzymatic regulation of metabolism in response to changing concentrations of a basic nutrient–to predict the optimal regulatory strategy given the statistics of fluctuations in the environment and measurement apparatus, respectively, and the costs associated with enzyme production. We use this framework to address three fundamental questions: (i) when a cell should prefer thresholding to a graded response; (ii) when there is a fitness advantage to implementing a Bayesian decision rule; and (iii) when retaining memory of the past provides a selective advantage. We specifically find that: (i) relative convexity of enzyme expression cost and benefit influences the fitness of thresholding or graded responses; (ii) intermediate levels of measurement uncertainty call for a sophisticated Bayesian decision rule; and (iii) in dynamic contexts, intermediate levels of uncertainty call for retaining memory of the past. Statistical properties of the environment, such as variability and correlation times, set optimal biochemical parameters, such as thresholds and decay rates in signaling pathways. Our framework provides a theoretical basis for interpreting molecular signal processing algorithms and a classification scheme that organizes known regulatory strategies and may help conceptualize heretofore unknown ones. PMID:25254493

A BAYESIAN STATISTICAL APPROACHES FOR THE EVALUATION OF CMAQ

EPA Science Inventory

This research focuses on the application of spatial statistical techniques for the evaluation of the Community Multiscale Air Quality (CMAQ) model. The upcoming release version of the CMAQ model was run for the calendar year 2001 and is in the process of being evaluated by EPA an...

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

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

A Statistical Project Control Tool for Engineering Managers

NASA Technical Reports Server (NTRS)

Bauch, Garland T.

2001-01-01

This slide presentation reviews the use of a Statistical Project Control Tool (SPCT) for managing engineering projects. A literature review pointed to a definition of project success, (i.e., A project is successful when the cost, schedule, technical performance, and quality satisfy the customer.) The literature review also pointed to project success factors, and traditional project control tools, and performance measures that are detailed in the report. The essential problem is that with resources becoming more limited, and an increasing number or projects, project failure is increasing, there is a limitation of existing methods and systematic methods are required. The objective of the work is to provide a new statistical project control tool for project managers. Graphs using the SPCT method plotting results of 3 successful projects and 3 failed projects are reviewed, with success and failure being defined by the owner.

Application of Turchin's method of statistical regularization

NASA Astrophysics Data System (ADS)

Zelenyi, Mikhail; Poliakova, Mariia; Nozik, Alexander; Khudyakov, Alexey

2018-04-01

During analysis of experimental data, one usually needs to restore a signal after it has been convoluted with some kind of apparatus function. According to Hadamard's definition this problem is ill-posed and requires regularization to provide sensible results. In this article we describe an implementation of the Turchin's method of statistical regularization based on the Bayesian approach to the regularization strategy.

Statistical process control charts for monitoring military injuries.

PubMed

Schuh, Anna; Canham-Chervak, Michelle; Jones, Bruce H

2017-12-01

An essential aspect of an injury prevention process is surveillance, which quantifies and documents injury rates in populations of interest and enables monitoring of injury frequencies, rates and trends. To drive progress towards injury reduction goals, additional tools are needed. Statistical process control charts, a methodology that has not been previously applied to Army injury monitoring, capitalise on existing medical surveillance data to provide information to leadership about injury trends necessary for prevention planning and evaluation. Statistical process control Shewhart u-charts were created for 49 US Army installations using quarterly injury medical encounter rates, 2007-2015, for active duty soldiers obtained from the Defense Medical Surveillance System. Injuries were defined according to established military injury surveillance recommendations. Charts display control limits three standard deviations (SDs) above and below an installation-specific historical average rate determined using 28 data points, 2007-2013. Charts are available in Army strategic management dashboards. From 2007 to 2015, Army injury rates ranged from 1254 to 1494 unique injuries per 1000 person-years. Installation injury rates ranged from 610 to 2312 injuries per 1000 person-years. Control charts identified four installations with injury rates exceeding the upper control limits at least once during 2014-2015, rates at three installations exceeded the lower control limit at least once and 42 installations had rates that fluctuated around the historical mean. Control charts can be used to drive progress towards injury reduction goals by indicating statistically significant increases and decreases in injury rates. Future applications to military subpopulations, other health outcome metrics and chart enhancements are suggested. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/.

Automating approximate Bayesian computation by local linear regression.

PubMed

Thornton, Kevin R

2009-07-07

In several biological contexts, parameter inference often relies on computationally-intensive techniques. "Approximate Bayesian Computation", or ABC, methods based on summary statistics have become increasingly popular. A particular flavor of ABC based on using a linear regression to approximate the posterior distribution of the parameters, conditional on the summary statistics, is computationally appealing, yet no standalone tool exists to automate the procedure. Here, I describe a program to implement the method. The software package ABCreg implements the local linear-regression approach to ABC. The advantages are: 1. The code is standalone, and fully-documented. 2. The program will automatically process multiple data sets, and create unique output files for each (which may be processed immediately in R), facilitating the testing of inference procedures on simulated data, or the analysis of multiple data sets. 3. The program implements two different transformation methods for the regression step. 4. Analysis options are controlled on the command line by the user, and the program is designed to output warnings for cases where the regression fails. 5. The program does not depend on any particular simulation machinery (coalescent, forward-time, etc.), and therefore is a general tool for processing the results from any simulation. 6. The code is open-source, and modular.Examples of applying the software to empirical data from Drosophila melanogaster, and testing the procedure on simulated data, are shown. In practice, the ABCreg simplifies implementing ABC based on local-linear regression.

The meta-Gaussian Bayesian Processor of forecasts and associated preliminary experiments

NASA Astrophysics Data System (ADS)

Chen, Fajing; Jiao, Meiyan; Chen, Jing

2013-04-01

Public weather services are trending toward providing users with probabilistic weather forecasts, in place of traditional deterministic forecasts. Probabilistic forecasting techniques are continually being improved to optimize available forecasting information. The Bayesian Processor of Forecast (BPF), a new statistical method for probabilistic forecast, can transform a deterministic forecast into a probabilistic forecast according to the historical statistical relationship between observations and forecasts generated by that forecasting system. This technique accounts for the typical forecasting performance of a deterministic forecasting system in quantifying the forecast uncertainty. The meta-Gaussian likelihood model is suitable for a variety of stochastic dependence structures with monotone likelihood ratios. The meta-Gaussian BPF adopting this kind of likelihood model can therefore be applied across many fields, including meteorology and hydrology. The Bayes theorem with two continuous random variables and the normal-linear BPF are briefly introduced. The meta-Gaussian BPF for a continuous predictand using a single predictor is then presented and discussed. The performance of the meta-Gaussian BPF is tested in a preliminary experiment. Control forecasts of daily surface temperature at 0000 UTC at Changsha and Wuhan stations are used as the deterministic forecast data. These control forecasts are taken from ensemble predictions with a 96-h lead time generated by the National Meteorological Center of the China Meteorological Administration, the European Centre for Medium-Range Weather Forecasts, and the US National Centers for Environmental Prediction during January 2008. The results of the experiment show that the meta-Gaussian BPF can transform a deterministic control forecast of surface temperature from any one of the three ensemble predictions into a useful probabilistic forecast of surface temperature. These probabilistic forecasts quantify the uncertainty

Monte Carlo Bayesian inference on a statistical model of sub-gridcolumn moisture variability using high-resolution cloud observations. Part 1: Method.

PubMed

Norris, Peter M; da Silva, Arlindo M

2016-07-01

A method is presented to constrain a statistical model of sub-gridcolumn moisture variability using high-resolution satellite cloud data. The method can be used for large-scale model parameter estimation or cloud data assimilation. The gridcolumn model includes assumed probability density function (PDF) intra-layer horizontal variability and a copula-based inter-layer correlation model. The observables used in the current study are Moderate Resolution Imaging Spectroradiometer (MODIS) cloud-top pressure, brightness temperature and cloud optical thickness, but the method should be extensible to direct cloudy radiance assimilation for a small number of channels. The algorithm is a form of Bayesian inference with a Markov chain Monte Carlo (MCMC) approach to characterizing the posterior distribution. This approach is especially useful in cases where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach is not gradient-based and allows jumps into regions of non-zero cloud probability. The current study uses a skewed-triangle distribution for layer moisture. The article also includes a discussion of the Metropolis and multiple-try Metropolis versions of MCMC.

Monte Carlo Bayesian Inference on a Statistical Model of Sub-Gridcolumn Moisture Variability Using High-Resolution Cloud Observations. Part 1: Method

NASA Technical Reports Server (NTRS)

Norris, Peter M.; Da Silva, Arlindo M.

2016-01-01

A method is presented to constrain a statistical model of sub-gridcolumn moisture variability using high-resolution satellite cloud data. The method can be used for large-scale model parameter estimation or cloud data assimilation. The gridcolumn model includes assumed probability density function (PDF) intra-layer horizontal variability and a copula-based inter-layer correlation model. The observables used in the current study are Moderate Resolution Imaging Spectroradiometer (MODIS) cloud-top pressure, brightness temperature and cloud optical thickness, but the method should be extensible to direct cloudy radiance assimilation for a small number of channels. The algorithm is a form of Bayesian inference with a Markov chain Monte Carlo (MCMC) approach to characterizing the posterior distribution. This approach is especially useful in cases where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach is not gradient-based and allows jumps into regions of non-zero cloud probability. The current study uses a skewed-triangle distribution for layer moisture. The article also includes a discussion of the Metropolis and multiple-try Metropolis versions of MCMC.

Monte Carlo Bayesian inference on a statistical model of sub-gridcolumn moisture variability using high-resolution cloud observations. Part 1: Method

PubMed Central

Norris, Peter M.; da Silva, Arlindo M.

2018-01-01

A method is presented to constrain a statistical model of sub-gridcolumn moisture variability using high-resolution satellite cloud data. The method can be used for large-scale model parameter estimation or cloud data assimilation. The gridcolumn model includes assumed probability density function (PDF) intra-layer horizontal variability and a copula-based inter-layer correlation model. The observables used in the current study are Moderate Resolution Imaging Spectroradiometer (MODIS) cloud-top pressure, brightness temperature and cloud optical thickness, but the method should be extensible to direct cloudy radiance assimilation for a small number of channels. The algorithm is a form of Bayesian inference with a Markov chain Monte Carlo (MCMC) approach to characterizing the posterior distribution. This approach is especially useful in cases where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach is not gradient-based and allows jumps into regions of non-zero cloud probability. The current study uses a skewed-triangle distribution for layer moisture. The article also includes a discussion of the Metropolis and multiple-try Metropolis versions of MCMC. PMID:29618847

Construction of monitoring model and algorithm design on passenger security during shipping based on improved Bayesian network.

PubMed

Wang, Jiali; Zhang, Qingnian; Ji, Wenfeng

2014-01-01

A large number of data is needed by the computation of the objective Bayesian network, but the data is hard to get in actual computation. The calculation method of Bayesian network was improved in this paper, and the fuzzy-precise Bayesian network was obtained. Then, the fuzzy-precise Bayesian network was used to reason Bayesian network model when the data is limited. The security of passengers during shipping is affected by various factors, and it is hard to predict and control. The index system that has the impact on the passenger safety during shipping was established on basis of the multifield coupling theory in this paper. Meanwhile, the fuzzy-precise Bayesian network was applied to monitor the security of passengers in the shipping process. The model was applied to monitor the passenger safety during shipping of a shipping company in Hainan, and the effectiveness of this model was examined. This research work provides guidance for guaranteeing security of passengers during shipping.

Construction of Monitoring Model and Algorithm Design on Passenger Security during Shipping Based on Improved Bayesian Network

PubMed Central

Wang, Jiali; Zhang, Qingnian; Ji, Wenfeng

2014-01-01

A large number of data is needed by the computation of the objective Bayesian network, but the data is hard to get in actual computation. The calculation method of Bayesian network was improved in this paper, and the fuzzy-precise Bayesian network was obtained. Then, the fuzzy-precise Bayesian network was used to reason Bayesian network model when the data is limited. The security of passengers during shipping is affected by various factors, and it is hard to predict and control. The index system that has the impact on the passenger safety during shipping was established on basis of the multifield coupling theory in this paper. Meanwhile, the fuzzy-precise Bayesian network was applied to monitor the security of passengers in the shipping process. The model was applied to monitor the passenger safety during shipping of a shipping company in Hainan, and the effectiveness of this model was examined. This research work provides guidance for guaranteeing security of passengers during shipping. PMID:25254227

Use of limited data to construct Bayesian networks for probabilistic risk assessment.

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

Groth, Katrina M.; Swiler, Laura Painton

2013-03-01

Probabilistic Risk Assessment (PRA) is a fundamental part of safety/quality assurance for nuclear power and nuclear weapons. Traditional PRA very effectively models complex hardware system risks using binary probabilistic models. However, traditional PRA models are not flexible enough to accommodate non-binary soft-causal factors, such as digital instrumentation&control, passive components, aging, common cause failure, and human errors. Bayesian Networks offer the opportunity to incorporate these risks into the PRA framework. This report describes the results of an early career LDRD project titled %E2%80%9CUse of Limited Data to Construct Bayesian Networks for Probabilistic Risk Assessment%E2%80%9D. The goal of the work was tomore » establish the capability to develop Bayesian Networks from sparse data, and to demonstrate this capability by producing a data-informed Bayesian Network for use in Human Reliability Analysis (HRA) as part of nuclear power plant Probabilistic Risk Assessment (PRA). This report summarizes the research goal and major products of the research.« less

A practical Bayesian stepped wedge design for community-based cluster-randomized clinical trials: The British Columbia Telehealth Trial.

PubMed

Cunanan, Kristen M; Carlin, Bradley P; Peterson, Kevin A

2016-12-01

Many clinical trial designs are impractical for community-based clinical intervention trials. Stepped wedge trial designs provide practical advantages, but few descriptions exist of their clinical implementational features, statistical design efficiencies, and limitations. Enhance efficiency of stepped wedge trial designs by evaluating the impact of design characteristics on statistical power for the British Columbia Telehealth Trial. The British Columbia Telehealth Trial is a community-based, cluster-randomized, controlled clinical trial in rural and urban British Columbia. To determine the effect of an Internet-based telehealth intervention on healthcare utilization, 1000 subjects with an existing diagnosis of congestive heart failure or type 2 diabetes will be enrolled from 50 clinical practices. Hospital utilization is measured using a composite of disease-specific hospital admissions and emergency visits. The intervention comprises online telehealth data collection and counseling provided to support a disease-specific action plan developed by the primary care provider. The planned intervention is sequentially introduced across all participating practices. We adopt a fully Bayesian, Markov chain Monte Carlo-driven statistical approach, wherein we use simulation to determine the effect of cluster size, sample size, and crossover interval choice on type I error and power to evaluate differences in hospital utilization. For our Bayesian stepped wedge trial design, simulations suggest moderate decreases in power when crossover intervals from control to intervention are reduced from every 3 to 2 weeks, and dramatic decreases in power as the numbers of clusters decrease. Power and type I error performance were not notably affected by the addition of nonzero cluster effects or a temporal trend in hospitalization intensity. Stepped wedge trial designs that intervene in small clusters across longer periods can provide enhanced power to evaluate comparative

Manufacturing Squares: An Integrative Statistical Process Control Exercise

ERIC Educational Resources Information Center

Coy, Steven P.

2016-01-01

In the exercise, students in a junior-level operations management class are asked to manufacture a simple product. Given product specifications, they must design a production process, create roles and design jobs for each team member, and develop a statistical process control plan that efficiently and effectively controls quality during…

Statistical quality control through overall vibration analysis

NASA Astrophysics Data System (ADS)

Carnero, M. ^a. Carmen; González-Palma, Rafael; Almorza, David; Mayorga, Pedro; López-Escobar, Carlos

2010-05-01

The present study introduces the concept of statistical quality control in automotive wheel bearings manufacturing processes. Defects on products under analysis can have a direct influence on passengers' safety and comfort. At present, the use of vibration analysis on machine tools for quality control purposes is not very extensive in manufacturing facilities. Noise and vibration are common quality problems in bearings. These failure modes likely occur under certain operating conditions and do not require high vibration amplitudes but relate to certain vibration frequencies. The vibration frequencies are affected by the type of surface problems (chattering) of ball races that are generated through grinding processes. The purpose of this paper is to identify grinding process variables that affect the quality of bearings by using statistical principles in the field of machine tools. In addition, an evaluation of the quality results of the finished parts under different combinations of process variables is assessed. This paper intends to establish the foundations to predict the quality of the products through the analysis of self-induced vibrations during the contact between the grinding wheel and the parts. To achieve this goal, the overall self-induced vibration readings under different combinations of process variables are analysed using statistical tools. The analysis of data and design of experiments follows a classical approach, considering all potential interactions between variables. The analysis of data is conducted through analysis of variance (ANOVA) for data sets that meet normality and homoscedasticity criteria. This paper utilizes different statistical tools to support the conclusions such as chi squared, Shapiro-Wilks, symmetry, Kurtosis, Cochran, Hartlett, and Hartley and Krushal-Wallis. The analysis presented is the starting point to extend the use of predictive techniques (vibration analysis) for quality control. This paper demonstrates the existence

Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modeling.

PubMed

Strelioff, Christopher C; Crutchfield, James P; Hübler, Alfred W

2007-07-01

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer kth order Markov chains, for arbitrary k , from finite data by applying Bayesian methods to both parameter estimation and model-order selection. Extending existing results for multinomial models of discrete data, we connect inference to statistical mechanics through information-theoretic (type theory) techniques. We establish a direct relationship between Bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Finally, we introduce a method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes.

Searching Algorithm Using Bayesian Updates

ERIC Educational Resources Information Center

Caudle, Kyle

2010-01-01

In late October 1967, the USS Scorpion was lost at sea, somewhere between the Azores and Norfolk Virginia. Dr. Craven of the U.S. Navy's Special Projects Division is credited with using Bayesian Search Theory to locate the submarine. Bayesian Search Theory is a straightforward and interesting application of Bayes' theorem which involves searching…

Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring.

PubMed

Carroll, Carlos; Johnson, Devin S; Dunk, Jeffrey R; Zielinski, William J

2010-12-01

Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data's spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and invertebrate taxa of conservation concern (Church's sideband snails [Monadenia churchi], red tree voles [Arborimus longicaudus], and Pacific fishers [Martes pennanti pacifica]) that provide examples of a range of distributional extents and dispersal abilities. We used presence-absence data derived from regional monitoring programs to develop models with both landscape and site-level environmental covariates. We used Markov chain Monte Carlo algorithms and a conditional autoregressive or intrinsic conditional autoregressive model framework to fit spatial models. The fit of Bayesian spatial models was between 35 and 55% better than the fit of nonspatial analogue models. Bayesian spatial models outperformed analogous models developed with maximum entropy (Maxent) methods. Although the best spatial and nonspatial models included similar environmental variables, spatial models provided estimates of residual spatial effects that suggested how ecological processes might structure distribution patterns. Spatial models built from presence-absence data improved fit most for localized endemic species with ranges constrained by poorly known biogeographic factors and for widely distributed species suspected to be strongly affected by unmeasured environmental variables or population processes. By treating spatial effects as a variable of interest rather than a nuisance, hierarchical Bayesian spatial models, especially when they are based on a common broad-scale spatial lattice (here the national Forest Inventory and Analysis grid of 24 km(2) hexagons), can increase the relevance of habitat models to multispecies

Bayesian models for cost-effectiveness analysis in the presence of structural zero costs

PubMed Central

Baio, Gianluca

2014-01-01

Bayesian modelling for cost-effectiveness data has received much attention in both the health economics and the statistical literature, in recent years. Cost-effectiveness data are characterised by a relatively complex structure of relationships linking a suitable measure of clinical benefit (e.g. quality-adjusted life years) and the associated costs. Simplifying assumptions, such as (bivariate) normality of the underlying distributions, are usually not granted, particularly for the cost variable, which is characterised by markedly skewed distributions. In addition, individual-level data sets are often characterised by the presence of structural zeros in the cost variable. Hurdle models can be used to account for the presence of excess zeros in a distribution and have been applied in the context of cost data. We extend their application to cost-effectiveness data, defining a full Bayesian specification, which consists of a model for the individual probability of null costs, a marginal model for the costs and a conditional model for the measure of effectiveness (given the observed costs). We presented the model using a working example to describe its main features. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24343868

Bayesian models for cost-effectiveness analysis in the presence of structural zero costs.

PubMed

Baio, Gianluca

2014-05-20

Bayesian modelling for cost-effectiveness data has received much attention in both the health economics and the statistical literature, in recent years. Cost-effectiveness data are characterised by a relatively complex structure of relationships linking a suitable measure of clinical benefit (e.g. quality-adjusted life years) and the associated costs. Simplifying assumptions, such as (bivariate) normality of the underlying distributions, are usually not granted, particularly for the cost variable, which is characterised by markedly skewed distributions. In addition, individual-level data sets are often characterised by the presence of structural zeros in the cost variable. Hurdle models can be used to account for the presence of excess zeros in a distribution and have been applied in the context of cost data. We extend their application to cost-effectiveness data, defining a full Bayesian specification, which consists of a model for the individual probability of null costs, a marginal model for the costs and a conditional model for the measure of effectiveness (given the observed costs). We presented the model using a working example to describe its main features. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.

Statistical Process Control for KSC Processing

NASA Technical Reports Server (NTRS)

Ford, Roger G.; Delgado, Hector; Tilley, Randy

1996-01-01

The 1996 Summer Faculty Fellowship Program and Kennedy Space Center (KSC) served as the basis for a research effort into statistical process control for KSC processing. The effort entailed several tasks and goals. The first was to develop a customized statistical process control (SPC) course for the Safety and Mission Assurance Trends Analysis Group. The actual teaching of this course took place over several weeks. In addition, an Internet version of the same course complete with animation and video excerpts from the course when it was taught at KSC was developed. The application of SPC to shuttle processing took up the rest of the summer research project. This effort entailed the evaluation of SPC use at KSC, both present and potential, due to the change in roles for NASA and the Single Flight Operations Contractor (SFOC). Individual consulting on SPC use was accomplished as well as an evaluation of SPC software for KSC use in the future. A final accomplishment of the orientation of the author to NASA changes, terminology, data format, and new NASA task definitions will allow future consultation when the needs arise.

Climatic Models Ensemble-based Mid-21st Century Runoff Projections: A Bayesian Framework

NASA Astrophysics Data System (ADS)

Achieng, K. O.; Zhu, J.

2017-12-01

There are a number of North American Regional Climate Change Assessment Program (NARCCAP) climatic models that have been used to project surface runoff in the mid-21st century. Statistical model selection techniques are often used to select the model that best fits data. However, model selection techniques often lead to different conclusions. In this study, ten models are averaged in Bayesian paradigm to project runoff. Bayesian Model Averaging (BMA) is used to project and identify effect of model uncertainty on future runoff projections. Baseflow separation - a two-digital filter which is also called Eckhardt filter - is used to separate USGS streamflow (total runoff) into two components: baseflow and surface runoff. We use this surface runoff as the a priori runoff when conducting BMA of runoff simulated from the ten RCM models. The primary objective of this study is to evaluate how well RCM multi-model ensembles simulate surface runoff, in a Bayesian framework. Specifically, we investigate and discuss the following questions: How well do ten RCM models ensemble jointly simulate surface runoff by averaging over all the models using BMA, given a priori surface runoff? What are the effects of model uncertainty on surface runoff simulation?

Bayesian just-so stories in psychology and neuroscience.

PubMed

Bowers, Jeffrey S; Davis, Colin J

2012-05-01

According to Bayesian theories in psychology and neuroscience, minds and brains are (near) optimal in solving a wide range of tasks. We challenge this view and argue that more traditional, non-Bayesian approaches are more promising. We make 3 main arguments. First, we show that the empirical evidence for Bayesian theories in psychology is weak. This weakness relates to the many arbitrary ways that priors, likelihoods, and utility functions can be altered in order to account for the data that are obtained, making the models unfalsifiable. It further relates to the fact that Bayesian theories are rarely better at predicting data compared with alternative (and simpler) non-Bayesian theories. Second, we show that the empirical evidence for Bayesian theories in neuroscience is weaker still. There are impressive mathematical analyses showing how populations of neurons could compute in a Bayesian manner but little or no evidence that they do. Third, we challenge the general scientific approach that characterizes Bayesian theorizing in cognitive science. A common premise is that theories in psychology should largely be constrained by a rational analysis of what the mind ought to do. We question this claim and argue that many of the important constraints come from biological, evolutionary, and processing (algorithmic) considerations that have no adaptive relevance to the problem per se. In our view, these factors have contributed to the development of many Bayesian "just so" stories in psychology and neuroscience; that is, mathematical analyses of cognition that can be used to explain almost any behavior as optimal. 2012 APA, all rights reserved.

A surrogate-based sensitivity quantification and Bayesian inversion of a regional groundwater flow model

NASA Astrophysics Data System (ADS)

Chen, Mingjie; Izady, Azizallah; Abdalla, Osman A.; Amerjeed, Mansoor

2018-02-01

Bayesian inference using Markov Chain Monte Carlo (MCMC) provides an explicit framework for stochastic calibration of hydrogeologic models accounting for uncertainties; however, the MCMC sampling entails a large number of model calls, and could easily become computationally unwieldy if the high-fidelity hydrogeologic model simulation is time consuming. This study proposes a surrogate-based Bayesian framework to address this notorious issue, and illustrates the methodology by inverse modeling a regional MODFLOW model. The high-fidelity groundwater model is approximated by a fast statistical model using Bagging Multivariate Adaptive Regression Spline (BMARS) algorithm, and hence the MCMC sampling can be efficiently performed. In this study, the MODFLOW model is developed to simulate the groundwater flow in an arid region of Oman consisting of mountain-coast aquifers, and used to run representative simulations to generate training dataset for BMARS model construction. A BMARS-based Sobol' method is also employed to efficiently calculate input parameter sensitivities, which are used to evaluate and rank their importance for the groundwater flow model system. According to sensitivity analysis, insensitive parameters are screened out of Bayesian inversion of the MODFLOW model, further saving computing efforts. The posterior probability distribution of input parameters is efficiently inferred from the prescribed prior distribution using observed head data, demonstrating that the presented BMARS-based Bayesian framework is an efficient tool to reduce parameter uncertainties of a groundwater system.

Assessing noninferiority in a three-arm trial using the Bayesian approach.

PubMed

Ghosh, Pulak; Nathoo, Farouk; Gönen, Mithat; Tiwari, Ram C

2011-07-10

Non-inferiority trials, which aim to demonstrate that a test product is not worse than a competitor by more than a pre-specified small amount, are of great importance to the pharmaceutical community. As a result, methodology for designing and analyzing such trials is required, and developing new methods for such analysis is an important area of statistical research. The three-arm trial consists of a placebo, a reference and an experimental treatment, and simultaneously tests the superiority of the reference over the placebo along with comparing this reference to an experimental treatment. In this paper, we consider the analysis of non-inferiority trials using Bayesian methods which incorporate both parametric as well as semi-parametric models. The resulting testing approach is both flexible and robust. The benefit of the proposed Bayesian methods is assessed via simulation, based on a study examining home-based blood pressure interventions. Copyright © 2011 John Wiley & Sons, Ltd.

Statistical comparison of a hybrid approach with approximate and exact inference models for Fusion 2+

NASA Astrophysics Data System (ADS)

Lee, K. David; Wiesenfeld, Eric; Gelfand, Andrew

2007-04-01

One of the greatest challenges in modern combat is maintaining a high level of timely Situational Awareness (SA). In many situations, computational complexity and accuracy considerations make the development and deployment of real-time, high-level inference tools very difficult. An innovative hybrid framework that combines Bayesian inference, in the form of Bayesian Networks, and Possibility Theory, in the form of Fuzzy Logic systems, has recently been introduced to provide a rigorous framework for high-level inference. In previous research, the theoretical basis and benefits of the hybrid approach have been developed. However, lacking is a concrete experimental comparison of the hybrid framework with traditional fusion methods, to demonstrate and quantify this benefit. The goal of this research, therefore, is to provide a statistical analysis on the comparison of the accuracy and performance of hybrid network theory, with pure Bayesian and Fuzzy systems and an inexact Bayesian system approximated using Particle Filtering. To accomplish this task, domain specific models will be developed under these different theoretical approaches and then evaluated, via Monte Carlo Simulation, in comparison to situational ground truth to measure accuracy and fidelity. Following this, a rigorous statistical analysis of the performance results will be performed, to quantify the benefit of hybrid inference to other fusion tools.

"Magnitude-based inference": a statistical review.

PubMed

Welsh, Alan H; Knight, Emma J

2015-04-01

We consider "magnitude-based inference" and its interpretation by examining in detail its use in the problem of comparing two means. We extract from the spreadsheets, which are provided to users of the analysis (http://www.sportsci.org/), a precise description of how "magnitude-based inference" is implemented. We compare the implemented version of the method with general descriptions of it and interpret the method in familiar statistical terms. We show that "magnitude-based inference" is not a progressive improvement on modern statistics. The additional probabilities introduced are not directly related to the confidence interval but, rather, are interpretable either as P values for two different nonstandard tests (for different null hypotheses) or as approximate Bayesian calculations, which also lead to a type of test. We also discuss sample size calculations associated with "magnitude-based inference" and show that the substantial reduction in sample sizes claimed for the method (30% of the sample size obtained from standard frequentist calculations) is not justifiable so the sample size calculations should not be used. Rather than using "magnitude-based inference," a better solution is to be realistic about the limitations of the data and use either confidence intervals or a fully Bayesian analysis.

Using Paper Helicopters to Teach Statistical Process Control

ERIC Educational Resources Information Center

Johnson, Danny J.

2011-01-01

This hands-on project uses a paper helicopter to teach students how to distinguish between common and special causes of variability when developing and using statistical process control charts. It allows the student to experience a process that is out-of-control due to imprecise or incomplete product design specifications and to discover how the…

Using Bayesian networks to support decision-focused information retrieval

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

Lehner, P.; Elsaesser, C.; Seligman, L.

This paper has described an approach to controlling the process of pulling data/information from distributed data bases in a way that is specific to a persons specific decision making context. Our prototype implementation of this approach uses a knowledge-based planner to generate a plan, an automatically constructed Bayesian network to evaluate the plan, specialized processing of the network to derive key information items that would substantially impact the evaluation of the plan (e.g., determine that replanning is needed), automated construction of Standing Requests for Information (SRIs) which are automated functions that monitor changes and trends in distributed data base thatmore » are relevant to the key information items. This emphasis of this paper is on how Bayesian networks are used.« less

Applying dynamic Bayesian networks to perturbed gene expression data.

PubMed

Dojer, Norbert; Gambin, Anna; Mizera, Andrzej; Wilczyński, Bartek; Tiuryn, Jerzy

2006-05-08

A central goal of molecular biology is to understand the regulatory mechanisms of gene transcription and protein synthesis. Because of their solid basis in statistics, allowing to deal with the stochastic aspects of gene expressions and noisy measurements in a natural way, Bayesian networks appear attractive in the field of inferring gene interactions structure from microarray experiments data. However, the basic formalism has some disadvantages, e.g. it is sometimes hard to distinguish between the origin and the target of an interaction. Two kinds of microarray experiments yield data particularly rich in information regarding the direction of interactions: time series and perturbation experiments. In order to correctly handle them, the basic formalism must be modified. For example, dynamic Bayesian networks (DBN) apply to time series microarray data. To our knowledge the DBN technique has not been applied in the context of perturbation experiments. We extend the framework of dynamic Bayesian networks in order to incorporate perturbations. Moreover, an exact algorithm for inferring an optimal network is proposed and a discretization method specialized for time series data from perturbation experiments is introduced. We apply our procedure to realistic simulations data. The results are compared with those obtained by standard DBN learning techniques. Moreover, the advantages of using exact learning algorithm instead of heuristic methods are analyzed. We show that the quality of inferred networks dramatically improves when using data from perturbation experiments. We also conclude that the exact algorithm should be used when it is possible, i.e. when considered set of genes is small enough.

Wavelet-Bayesian inference of cosmic strings embedded in the cosmic microwave background

NASA Astrophysics Data System (ADS)

McEwen, J. D.; Feeney, S. M.; Peiris, H. V.; Wiaux, Y.; Ringeval, C.; Bouchet, F. R.

2017-12-01

Cosmic strings are a well-motivated extension to the standard cosmological model and could induce a subdominant component in the anisotropies of the cosmic microwave background (CMB), in addition to the standard inflationary component. The detection of strings, while observationally challenging, would provide a direct probe of physics at very high-energy scales. We develop a framework for cosmic string inference from observations of the CMB made over the celestial sphere, performing a Bayesian analysis in wavelet space where the string-induced CMB component has distinct statistical properties to the standard inflationary component. Our wavelet-Bayesian framework provides a principled approach to compute the posterior distribution of the string tension Gμ and the Bayesian evidence ratio comparing the string model to the standard inflationary model. Furthermore, we present a technique to recover an estimate of any string-induced CMB map embedded in observational data. Using Planck-like simulations, we demonstrate the application of our framework and evaluate its performance. The method is sensitive to Gμ ∼ 5 × 10-7 for Nambu-Goto string simulations that include an integrated Sachs-Wolfe contribution only and do not include any recombination effects, before any parameters of the analysis are optimized. The sensitivity of the method compares favourably with other techniques applied to the same simulations.

No Control Genes Required: Bayesian Analysis of qRT-PCR Data

PubMed Central

Matz, Mikhail V.; Wright, Rachel M.; Scott, James G.

2013-01-01

Background Model-based analysis of data from quantitative reverse-transcription PCR (qRT-PCR) is potentially more powerful and versatile than traditional methods. Yet existing model-based approaches cannot properly deal with the higher sampling variances associated with low-abundant targets, nor do they provide a natural way to incorporate assumptions about the stability of control genes directly into the model-fitting process. Results In our method, raw qPCR data are represented as molecule counts, and described using generalized linear mixed models under Poisson-lognormal error. A Markov Chain Monte Carlo (MCMC) algorithm is used to sample from the joint posterior distribution over all model parameters, thereby estimating the effects of all experimental factors on the expression of every gene. The Poisson-based model allows for the correct specification of the mean-variance relationship of the PCR amplification process, and can also glean information from instances of no amplification (zero counts). Our method is very flexible with respect to control genes: any prior knowledge about the expected degree of their stability can be directly incorporated into the model. Yet the method provides sensible answers without such assumptions, or even in the complete absence of control genes. We also present a natural Bayesian analogue of the “classic” analysis, which uses standard data pre-processing steps (logarithmic transformation and multi-gene normalization) but estimates all gene expression changes jointly within a single model. The new methods are considerably more flexible and powerful than the standard delta-delta Ct analysis based on pairwise t-tests. Conclusions Our methodology expands the applicability of the relative-quantification analysis protocol all the way to the lowest-abundance targets, and provides a novel opportunity to analyze qRT-PCR data without making any assumptions concerning target stability. These procedures have been implemented as the MCMC

No control genes required: Bayesian analysis of qRT-PCR data.

PubMed

Matz, Mikhail V; Wright, Rachel M; Scott, James G

2013-01-01

Model-based analysis of data from quantitative reverse-transcription PCR (qRT-PCR) is potentially more powerful and versatile than traditional methods. Yet existing model-based approaches cannot properly deal with the higher sampling variances associated with low-abundant targets, nor do they provide a natural way to incorporate assumptions about the stability of control genes directly into the model-fitting process. In our method, raw qPCR data are represented as molecule counts, and described using generalized linear mixed models under Poisson-lognormal error. A Markov Chain Monte Carlo (MCMC) algorithm is used to sample from the joint posterior distribution over all model parameters, thereby estimating the effects of all experimental factors on the expression of every gene. The Poisson-based model allows for the correct specification of the mean-variance relationship of the PCR amplification process, and can also glean information from instances of no amplification (zero counts). Our method is very flexible with respect to control genes: any prior knowledge about the expected degree of their stability can be directly incorporated into the model. Yet the method provides sensible answers without such assumptions, or even in the complete absence of control genes. We also present a natural Bayesian analogue of the "classic" analysis, which uses standard data pre-processing steps (logarithmic transformation and multi-gene normalization) but estimates all gene expression changes jointly within a single model. The new methods are considerably more flexible and powerful than the standard delta-delta Ct analysis based on pairwise t-tests. Our methodology expands the applicability of the relative-quantification analysis protocol all the way to the lowest-abundance targets, and provides a novel opportunity to analyze qRT-PCR data without making any assumptions concerning target stability. These procedures have been implemented as the MCMC.qpcr package in R.

A default Bayesian hypothesis test for mediation.

PubMed

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

2015-03-01

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

Experimentally Derived δ13C and δ15N Discrimination Factors for Gray Wolves and the Impact of Prior Information in Bayesian Mixing Models

PubMed Central

Bucci, Melanie E.; Callahan, Peggy; Koprowski, John L.; Polfus, Jean L.; Krausman, Paul R.

2015-01-01

Stable isotope analysis of diet has become a common tool in conservation research. However, the multiple sources of uncertainty inherent in this analysis framework involve consequences that have not been thoroughly addressed. Uncertainty arises from the choice of trophic discrimination factors, and for Bayesian stable isotope mixing models (SIMMs), the specification of prior information; the combined effect of these aspects has not been explicitly tested. We used a captive feeding study of gray wolves (Canis lupus) to determine the first experimentally-derived trophic discrimination factors of C and N for this large carnivore of broad conservation interest. Using the estimated diet in our controlled system and data from a published study on wild wolves and their prey in Montana, USA, we then investigated the simultaneous effect of discrimination factors and prior information on diet reconstruction with Bayesian SIMMs. Discrimination factors for gray wolves and their prey were 1.97‰ for δ13C and 3.04‰ for δ15N. Specifying wolf discrimination factors, as opposed to the commonly used red fox (Vulpes vulpes) factors, made little practical difference to estimates of wolf diet, but prior information had a strong effect on bias, precision, and accuracy of posterior estimates. Without specifying prior information in our Bayesian SIMM, it was not possible to produce SIMM posteriors statistically similar to the estimated diet in our controlled study or the diet of wild wolves. Our study demonstrates the critical effect of prior information on estimates of animal diets using Bayesian SIMMs, and suggests species-specific trophic discrimination factors are of secondary importance. When using stable isotope analysis to inform conservation decisions researchers should understand the limits of their data. It may be difficult to obtain useful information from SIMMs if informative priors are omitted and species-specific discrimination factors are unavailable. PMID:25803664

Noninformative prior in the quantum statistical model of pure states

NASA Astrophysics Data System (ADS)

Tanaka, Fuyuhiko

2012-06-01

In the present paper, we consider a suitable definition of a noninformative prior on the quantum statistical model of pure states. While the full pure-states model is invariant under unitary rotation and admits the Haar measure, restricted models, which we often see in quantum channel estimation and quantum process tomography, have less symmetry and no compelling rationale for any choice. We adopt a game-theoretic approach that is applicable to classical Bayesian statistics and yields a noninformative prior for a general class of probability distributions. We define the quantum detection game and show that there exist noninformative priors for a general class of a pure-states model. Theoretically, it gives one of the ways that we represent ignorance on the given quantum system with partial information. Practically, our method proposes a default distribution on the model in order to use the Bayesian technique in the quantum-state tomography with a small sample.

75 FR 6209 - Guidance for Industry and Food and Drug Administration; Guidance for the Use of Bayesian...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-02-08

... DEPARTMENT OF HEALTH AND HUMAN SERVICES Food and Drug Administration [Docket No. FDA-2006-D-0410] (formerly Docket No. 2006D-0191) Guidance for Industry and Food and Drug Administration; Guidance for the Use of Bayesian Statistics in Medical Device Clinical Trials; Availability AGENCY: Food and Drug...

Application of Bayesian Approach in Cancer Clinical Trial

PubMed Central

Bhattacharjee, Atanu

2014-01-01

The application of Bayesian approach in clinical trials becomes more useful over classical method. It is beneficial from design to analysis phase. The straight forward statement is possible to obtain through Bayesian about the drug treatment effect. Complex computational problems are simple to handle with Bayesian techniques. The technique is only feasible to performing presence of prior information of the data. The inference is possible to establish through posterior estimates. However, some limitations are present in this method. The objective of this work was to explore the several merits and demerits of Bayesian approach in cancer research. The review of the technique will be helpful for the clinical researcher involved in the oncology to explore the limitation and power of Bayesian techniques. PMID:29147387

Bayesian least squares deconvolution

NASA Astrophysics Data System (ADS)

Asensio Ramos, A.; Petit, P.

2015-11-01

Aims: We develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods: We consider LSD under the Bayesian framework and we introduce a flexible Gaussian process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results: We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.

A guide to Bayesian model selection for ecologists

USGS Publications Warehouse

Hooten, Mevin B.; Hobbs, N.T.

2015-01-01

The steady upward trend in the use of model selection and Bayesian methods in ecological research has made it clear that both approaches to inference are important for modern analysis of models and data. However, in teaching Bayesian methods and in working with our research colleagues, we have noticed a general dissatisfaction with the available literature on Bayesian model selection and multimodel inference. Students and researchers new to Bayesian methods quickly find that the published advice on model selection is often preferential in its treatment of options for analysis, frequently advocating one particular method above others. The recent appearance of many articles and textbooks on Bayesian modeling has provided welcome background on relevant approaches to model selection in the Bayesian framework, but most of these are either very narrowly focused in scope or inaccessible to ecologists. Moreover, the methodological details of Bayesian model selection approaches are spread thinly throughout the literature, appearing in journals from many different fields. Our aim with this guide is to condense the large body of literature on Bayesian approaches to model selection and multimodel inference and present it specifically for quantitative ecologists as neutrally as possible. We also bring to light a few important and fundamental concepts relating directly to model selection that seem to have gone unnoticed in the ecological literature. Throughout, we provide only a minimal discussion of philosophy, preferring instead to examine the breadth of approaches as well as their practical advantages and disadvantages. This guide serves as a reference for ecologists using Bayesian methods, so that they can better understand their options and can make an informed choice that is best aligned with their goals for inference.

Bayesian Computation for Log-Gaussian Cox Processes: A Comparative Analysis of Methods

PubMed Central

Teng, Ming; Nathoo, Farouk S.; Johnson, Timothy D.

2017-01-01

The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point pattern data. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Various methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulation studies as well as through two applications, the first examining ecological data and the second involving neuroimaging data. PMID:29200537

Model selection and parameter estimation in structural dynamics using approximate Bayesian computation

NASA Astrophysics Data System (ADS)

Ben Abdessalem, Anis; Dervilis, Nikolaos; Wagg, David; Worden, Keith

2018-01-01

This paper will introduce the use of the approximate Bayesian computation (ABC) algorithm for model selection and parameter estimation in structural dynamics. ABC is a likelihood-free method typically used when the likelihood function is either intractable or cannot be approached in a closed form. To circumvent the evaluation of the likelihood function, simulation from a forward model is at the core of the ABC algorithm. The algorithm offers the possibility to use different metrics and summary statistics representative of the data to carry out Bayesian inference. The efficacy of the algorithm in structural dynamics is demonstrated through three different illustrative examples of nonlinear system identification: cubic and cubic-quintic models, the Bouc-Wen model and the Duffing oscillator. The obtained results suggest that ABC is a promising alternative to deal with model selection and parameter estimation issues, specifically for systems with complex behaviours.

Bayesian Statistics and Uncertainty Quantification for Safety Boundary Analysis in Complex Systems

NASA Technical Reports Server (NTRS)

He, Yuning; Davies, Misty Dawn

2014-01-01

The analysis of a safety-critical system often requires detailed knowledge of safe regions and their highdimensional non-linear boundaries. We present a statistical approach to iteratively detect and characterize the boundaries, which are provided as parameterized shape candidates. Using methods from uncertainty quantification and active learning, we incrementally construct a statistical model from only few simulation runs and obtain statistically sound estimates of the shape parameters for safety boundaries.

Statistical detection of EEG synchrony using empirical bayesian inference.

PubMed

Singh, Archana K; Asoh, Hideki; Takeda, Yuji; Phillips, Steven

2015-01-01

There is growing interest in understanding how the brain utilizes synchronized oscillatory activity to integrate information across functionally connected regions. Computing phase-locking values (PLV) between EEG signals is a popular method for quantifying such synchronizations and elucidating their role in cognitive tasks. However, high-dimensionality in PLV data incurs a serious multiple testing problem. Standard multiple testing methods in neuroimaging research (e.g., false discovery rate, FDR) suffer severe loss of power, because they fail to exploit complex dependence structure between hypotheses that vary in spectral, temporal and spatial dimension. Previously, we showed that a hierarchical FDR and optimal discovery procedures could be effectively applied for PLV analysis to provide better power than FDR. In this article, we revisit the multiple comparison problem from a new Empirical Bayes perspective and propose the application of the local FDR method (locFDR; Efron, 2001) for PLV synchrony analysis to compute FDR as a posterior probability that an observed statistic belongs to a null hypothesis. We demonstrate the application of Efron's Empirical Bayes approach for PLV synchrony analysis for the first time. We use simulations to validate the specificity and sensitivity of locFDR and a real EEG dataset from a visual search study for experimental validation. We also compare locFDR with hierarchical FDR and optimal discovery procedures in both simulation and experimental analyses. Our simulation results showed that the locFDR can effectively control false positives without compromising on the power of PLV synchrony inference. Our results from the application locFDR on experiment data detected more significant discoveries than our previously proposed methods whereas the standard FDR method failed to detect any significant discoveries.

Human-in-the-loop Bayesian optimization of wearable device parameters

PubMed Central

Malcolm, Philippe; Speeckaert, Jozefien; Siviy, Christoper J.; Walsh, Conor J.; Kuindersma, Scott

2017-01-01

The increasing capabilities of exoskeletons and powered prosthetics for walking assistance have paved the way for more sophisticated and individualized control strategies. In response to this opportunity, recent work on human-in-the-loop optimization has considered the problem of automatically tuning control parameters based on realtime physiological measurements. However, the common use of metabolic cost as a performance metric creates significant experimental challenges due to its long measurement times and low signal-to-noise ratio. We evaluate the use of Bayesian optimization—a family of sample-efficient, noise-tolerant, and global optimization methods—for quickly identifying near-optimal control parameters. To manage experimental complexity and provide comparisons against related work, we consider the task of minimizing metabolic cost by optimizing walking step frequencies in unaided human subjects. Compared to an existing approach based on gradient descent, Bayesian optimization identified a near-optimal step frequency with a faster time to convergence (12 minutes, p < 0.01), smaller inter-subject variability in convergence time (± 2 minutes, p < 0.01), and lower overall energy expenditure (p < 0.01). PMID:28926613

Bayesian LASSO, scale space and decision making in association genetics.

PubMed

Pasanen, Leena; Holmström, Lasse; Sillanpää, Mikko J

2015-01-01

LASSO is a penalized regression method that facilitates model fitting in situations where there are as many, or even more explanatory variables than observations, and only a few variables are relevant in explaining the data. We focus on the Bayesian version of LASSO and consider four problems that need special attention: (i) controlling false positives, (ii) multiple comparisons, (iii) collinearity among explanatory variables, and (iv) the choice of the tuning parameter that controls the amount of shrinkage and the sparsity of the estimates. The particular application considered is association genetics, where LASSO regression can be used to find links between chromosome locations and phenotypic traits in a biological organism. However, the proposed techniques are relevant also in other contexts where LASSO is used for variable selection. We separate the true associations from false positives using the posterior distribution of the effects (regression coefficients) provided by Bayesian LASSO. We propose to solve the multiple comparisons problem by using simultaneous inference based on the joint posterior distribution of the effects. Bayesian LASSO also tends to distribute an effect among collinear variables, making detection of an association difficult. We propose to solve this problem by considering not only individual effects but also their functionals (i.e. sums and differences). Finally, whereas in Bayesian LASSO the tuning parameter is often regarded as a random variable, we adopt a scale space view and consider a whole range of fixed tuning parameters, instead. The effect estimates and the associated inference are considered for all tuning parameters in the selected range and the results are visualized with color maps that provide useful insights into data and the association problem considered. The methods are illustrated using two sets of artificial data and one real data set, all representing typical settings in association genetics.

Universal Darwinism As a Process of Bayesian Inference.

PubMed

Campbell, John O

2016-01-01

Many of the mathematical frameworks describing natural selection are equivalent to Bayes' Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus, natural selection serves as a counter example to a widely-held interpretation that restricts Bayesian Inference to human mental processes (including the endeavors of statisticians). As Bayesian inference can always be cast in terms of (variational) free energy minimization, natural selection can be viewed as comprising two components: a generative model of an "experiment" in the external world environment, and the results of that "experiment" or the "surprise" entailed by predicted and actual outcomes of the "experiment." Minimization of free energy implies that the implicit measure of "surprise" experienced serves to update the generative model in a Bayesian manner. This description closely accords with the mechanisms of generalized Darwinian process proposed both by Dawkins, in terms of replicators and vehicles, and Campbell, in terms of inferential systems. Bayesian inference is an algorithm for the accumulation of evidence-based knowledge. This algorithm is now seen to operate over a wide range of evolutionary processes, including natural selection, the evolution of mental models and cultural evolutionary processes, notably including science itself. The variational principle of free energy minimization may thus serve as a unifying mathematical framework for universal Darwinism, the study of evolutionary processes operating throughout nature.

A hierarchical Bayesian approach to adaptive vision testing: A case study with the contrast sensitivity function.

PubMed

Gu, Hairong; Kim, Woojae; Hou, Fang; Lesmes, Luis Andres; Pitt, Mark A; Lu, Zhong-Lin; Myung, Jay I

2016-01-01

Measurement efficiency is of concern when a large number of observations are required to obtain reliable estimates for parametric models of vision. The standard entropy-based Bayesian adaptive testing procedures addressed the issue by selecting the most informative stimulus in sequential experimental trials. Noninformative, diffuse priors were commonly used in those tests. Hierarchical adaptive design optimization (HADO; Kim, Pitt, Lu, Steyvers, & Myung, 2014) further improves the efficiency of the standard Bayesian adaptive testing procedures by constructing an informative prior using data from observers who have already participated in the experiment. The present study represents an empirical validation of HADO in estimating the human contrast sensitivity function. The results show that HADO significantly improves the accuracy and precision of parameter estimates, and therefore requires many fewer observations to obtain reliable inference about contrast sensitivity, compared to the method of quick contrast sensitivity function (Lesmes, Lu, Baek, & Albright, 2010), which uses the standard Bayesian procedure. The improvement with HADO was maintained even when the prior was constructed from heterogeneous populations or a relatively small number of observers. These results of this case study support the conclusion that HADO can be used in Bayesian adaptive testing by replacing noninformative, diffuse priors with statistically justified informative priors without introducing unwanted bias.

A hierarchical Bayesian approach to adaptive vision testing: A case study with the contrast sensitivity function

PubMed Central

Gu, Hairong; Kim, Woojae; Hou, Fang; Lesmes, Luis Andres; Pitt, Mark A.; Lu, Zhong-Lin; Myung, Jay I.