Expectation propagation for large scale Bayesian inference of non-linear molecular networks from perturbation data.

PubMed

Narimani, Zahra; Beigy, Hamid; Ahmad, Ashar; Masoudi-Nejad, Ali; Fröhlich, Holger

2017-01-01

Inferring the structure of molecular networks from time series protein or gene expression data provides valuable information about the complex biological processes of the cell. Causal network structure inference has been approached using different methods in the past. Most causal network inference techniques, such as Dynamic Bayesian Networks and ordinary differential equations, are limited by their computational complexity and thus make large scale inference infeasible. This is specifically true if a Bayesian framework is applied in order to deal with the unavoidable uncertainty about the correct model. We devise a novel Bayesian network reverse engineering approach using ordinary differential equations with the ability to include non-linearity. Besides modeling arbitrary, possibly combinatorial and time dependent perturbations with unknown targets, one of our main contributions is the use of Expectation Propagation, an algorithm for approximate Bayesian inference over large scale network structures in short computation time. We further explore the possibility of integrating prior knowledge into network inference. We evaluate the proposed model on DREAM4 and DREAM8 data and find it competitive against several state-of-the-art existing network inference methods.

Past and present cosmic structure in the SDSS DR7 main sample

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

Jasche, J.; Leclercq, F.; Wandelt, B.D., E-mail: jasche@iap.fr, E-mail: florent.leclercq@polytechnique.org, E-mail: wandelt@iap.fr

2015-01-01

We present a chrono-cosmography project, aiming at the inference of the four dimensional formation history of the observed large scale structure from its origin to the present epoch. To do so, we perform a full-scale Bayesian analysis of the northern galactic cap of the Sloan Digital Sky Survey (SDSS) Data Release 7 main galaxy sample, relying on a fully probabilistic, physical model of the non-linearly evolved density field. Besides inferring initial conditions from observations, our methodology naturally and accurately reconstructs non-linear features at the present epoch, such as walls and filaments, corresponding to high-order correlation functions generated by late-time structuremore » formation. Our inference framework self-consistently accounts for typical observational systematic and statistical uncertainties such as noise, survey geometry and selection effects. We further account for luminosity dependent galaxy biases and automatic noise calibration within a fully Bayesian approach. As a result, this analysis provides highly-detailed and accurate reconstructions of the present density field on scales larger than ∼ 3 Mpc/h, constrained by SDSS observations. This approach also leads to the first quantitative inference of plausible formation histories of the dynamic large scale structure underlying the observed galaxy distribution. The results described in this work constitute the first full Bayesian non-linear analysis of the cosmic large scale structure with the demonstrated capability of uncertainty quantification. Some of these results will be made publicly available along with this work. The level of detail of inferred results and the high degree of control on observational uncertainties pave the path towards high precision chrono-cosmography, the subject of simultaneously studying the dynamics and the morphology of the inhomogeneous Universe.« less

Win-Stay, Lose-Sample: a simple sequential algorithm for approximating Bayesian inference.

PubMed

Bonawitz, Elizabeth; Denison, Stephanie; Gopnik, Alison; Griffiths, Thomas L

2014-11-01

People can behave in a way that is consistent with Bayesian models of cognition, despite the fact that performing exact Bayesian inference is computationally challenging. What algorithms could people be using to make this possible? We show that a simple sequential algorithm "Win-Stay, Lose-Sample", inspired by the Win-Stay, Lose-Shift (WSLS) principle, can be used to approximate Bayesian inference. We investigate the behavior of adults and preschoolers on two causal learning tasks to test whether people might use a similar algorithm. These studies use a "mini-microgenetic method", investigating how people sequentially update their beliefs as they encounter new evidence. Experiment 1 investigates a deterministic causal learning scenario and Experiments 2 and 3 examine how people make inferences in a stochastic scenario. The behavior of adults and preschoolers in these experiments is consistent with our Bayesian version of the WSLS principle. This algorithm provides both a practical method for performing Bayesian inference and a new way to understand people's judgments. Copyright © 2014 Elsevier Inc. All rights reserved.

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.

Universal Darwinism As a Process of Bayesian Inference

PubMed Central

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. PMID:27375438

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.

Heuristics as Bayesian inference under extreme priors.

PubMed

Parpart, Paula; Jones, Matt; Love, Bradley C

2018-05-01

Simple heuristics are often regarded as tractable decision strategies because they ignore a great deal of information in the input data. One puzzle is why heuristics can outperform full-information models, such as linear regression, which make full use of the available information. These "less-is-more" effects, in which a relatively simpler model outperforms a more complex model, are prevalent throughout cognitive science, and are frequently argued to demonstrate an inherent advantage of simplifying computation or ignoring information. In contrast, we show at the computational level (where algorithmic restrictions are set aside) that it is never optimal to discard information. Through a formal Bayesian analysis, we prove that popular heuristics, such as tallying and take-the-best, are formally equivalent to Bayesian inference under the limit of infinitely strong priors. Varying the strength of the prior yields a continuum of Bayesian models with the heuristics at one end and ordinary regression at the other. Critically, intermediate models perform better across all our simulations, suggesting that down-weighting information with the appropriate prior is preferable to entirely ignoring it. Rather than because of their simplicity, our analyses suggest heuristics perform well because they implement strong priors that approximate the actual structure of the environment. We end by considering how new heuristics could be derived by infinitely strengthening the priors of other Bayesian models. These formal results have implications for work in psychology, machine learning and economics. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

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.

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 models is publicly available. Copyright © 2016 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Semisupervised learning using Bayesian interpretation: application to LS-SVM.

PubMed

Adankon, Mathias M; Cheriet, Mohamed; Biem, Alain

2011-04-01

Bayesian reasoning provides an ideal basis for representing and manipulating uncertain knowledge, with the result that many interesting algorithms in machine learning are based on Bayesian inference. In this paper, we use the Bayesian approach with one and two levels of inference to model the semisupervised learning problem and give its application to the successful kernel classifier support vector machine (SVM) and its variant least-squares SVM (LS-SVM). Taking advantage of Bayesian interpretation of LS-SVM, we develop a semisupervised learning algorithm for Bayesian LS-SVM using our approach based on two levels of inference. Experimental results on both artificial and real pattern recognition problems show the utility of our method.

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.

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

PubMed

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

2014-08-01

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

From Neutron Star Observables to the Equation of State. II. Bayesian Inference of Equation of State Pressures

NASA Astrophysics Data System (ADS)

Raithel, Carolyn A.; Özel, Feryal; Psaltis, Dimitrios

2017-08-01

One of the key goals of observing neutron stars is to infer the equation of state (EoS) of the cold, ultradense matter in their interiors. Here, we present a Bayesian statistical method of inferring the pressures at five fixed densities, from a sample of mock neutron star masses and radii. We show that while five polytropic segments are needed for maximum flexibility in the absence of any prior knowledge of the EoS, regularizers are also necessary to ensure that simple underlying EoS are not over-parameterized. For ideal data with small measurement uncertainties, we show that the pressure at roughly twice the nuclear saturation density, {ρ }{sat}, can be inferred to within 0.3 dex for many realizations of potential sources of uncertainties. The pressures of more complicated EoS with significant phase transitions can also be inferred to within ˜30%. We also find that marginalizing the multi-dimensional parameter space of pressure to infer a mass-radius relation can lead to biases of nearly 1 km in radius, toward larger radii. Using the full, five-dimensional posterior likelihoods avoids this bias.

Bayesian Inference and Online Learning in Poisson Neuronal Networks.

PubMed

Huang, Yanping; Rao, Rajesh P N

2016-08-01

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

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

PubMed Central

Weiss, Scott T.

2014-01-01

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

Markov Chain Monte Carlo Inference of Parametric Dictionaries for Sparse Bayesian Approximations

PubMed Central

Chaspari, Theodora; Tsiartas, Andreas; Tsilifis, Panagiotis; Narayanan, Shrikanth

2016-01-01

Parametric dictionaries can increase the ability of sparse representations to meaningfully capture and interpret the underlying signal information, such as encountered in biomedical problems. Given a mapping function from the atom parameter space to the actual atoms, we propose a sparse Bayesian framework for learning the atom parameters, because of its ability to provide full posterior estimates, take uncertainty into account and generalize on unseen data. Inference is performed with Markov Chain Monte Carlo, that uses block sampling to generate the variables of the Bayesian problem. Since the parameterization of dictionary atoms results in posteriors that cannot be analytically computed, we use a Metropolis-Hastings-within-Gibbs framework, according to which variables with closed-form posteriors are generated with the Gibbs sampler, while the remaining ones with the Metropolis Hastings from appropriate candidate-generating densities. We further show that the corresponding Markov Chain is uniformly ergodic ensuring its convergence to a stationary distribution independently of the initial state. Results on synthetic data and real biomedical signals indicate that our approach offers advantages in terms of signal reconstruction compared to previously proposed Steepest Descent and Equiangular Tight Frame methods. This paper demonstrates the ability of Bayesian learning to generate parametric dictionaries that can reliably represent the exemplar data and provides the foundation towards inferring the entire variable set of the sparse approximation problem for signal denoising, adaptation and other applications. PMID:28649173

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

PubMed

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

2014-06-01

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

Ancestral sequence reconstruction in primate mitochondrial DNA: compositional bias and effect on functional inference.

PubMed

Krishnan, Neeraja M; Seligmann, Hervé; Stewart, Caro-Beth; De Koning, A P Jason; Pollock, David D

2004-10-01

Reconstruction of ancestral DNA and amino acid sequences is an important means of inferring information about past evolutionary events. Such reconstructions suggest changes in molecular function and evolutionary processes over the course of evolution and are used to infer adaptation and convergence. Maximum likelihood (ML) is generally thought to provide relatively accurate reconstructed sequences compared to parsimony, but both methods lead to the inference of multiple directional changes in nucleotide frequencies in primate mitochondrial DNA (mtDNA). To better understand this surprising result, as well as to better understand how parsimony and ML differ, we constructed a series of computationally simple "conditional pathway" methods that differed in the number of substitutions allowed per site along each branch, and we also evaluated the entire Bayesian posterior frequency distribution of reconstructed ancestral states. We analyzed primate mitochondrial cytochrome b (Cyt-b) and cytochrome oxidase subunit I (COI) genes and found that ML reconstructs ancestral frequencies that are often more different from tip sequences than are parsimony reconstructions. In contrast, frequency reconstructions based on the posterior ensemble more closely resemble extant nucleotide frequencies. Simulations indicate that these differences in ancestral sequence inference are probably due to deterministic bias caused by high uncertainty in the optimization-based ancestral reconstruction methods (parsimony, ML, Bayesian maximum a posteriori). In contrast, ancestral nucleotide frequencies based on an average of the Bayesian set of credible ancestral sequences are much less biased. The methods involving simpler conditional pathway calculations have slightly reduced likelihood values compared to full likelihood calculations, but they can provide fairly unbiased nucleotide reconstructions and may be useful in more complex phylogenetic analyses than considered here due to their speed and flexibility. To determine whether biased reconstructions using optimization methods might affect inferences of functional properties, ancestral primate mitochondrial tRNA sequences were inferred and helix-forming propensities for conserved pairs were evaluated in silico. For ambiguously reconstructed nucleotides at sites with high base composition variability, ancestral tRNA sequences from Bayesian analyses were more compatible with canonical base pairing than were those inferred by other methods. Thus, nucleotide bias in reconstructed sequences apparently can lead to serious bias and inaccuracies in functional predictions.

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 pedigree inference with small numbers of single nucleotide polymorphisms via a factor-graph representation.

PubMed

Anderson, Eric C; Ng, Thomas C

2016-02-01

We develop a computational framework for addressing pedigree inference problems using small numbers (80-400) of single nucleotide polymorphisms (SNPs). Our approach relaxes the assumptions, which are commonly made, that sampling is complete with respect to the pedigree and that there is no genotyping error. It relies on representing the inferred pedigree as a factor graph and invoking the Sum-Product algorithm to compute and store quantities that allow the joint probability of the data to be rapidly computed under a large class of rearrangements of the pedigree structure. This allows efficient MCMC sampling over the space of pedigrees, and, hence, Bayesian inference of pedigree structure. In this paper we restrict ourselves to inference of pedigrees without loops using SNPs assumed to be unlinked. We present the methodology in general for multigenerational inference, and we illustrate the method by applying it to the inference of full sibling groups in a large sample (n=1157) of Chinook salmon typed at 95 SNPs. The results show that our method provides a better point estimate and estimate of uncertainty than the currently best-available maximum-likelihood sibling reconstruction method. Extensions of this work to more complex scenarios are briefly discussed. Published by Elsevier Inc.

[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 data analysis in population ecology: motivations, methods, and benefits

USGS Publications Warehouse

Dorazio, Robert

2016-01-01

During the 20th century ecologists largely relied on the frequentist system of inference for the analysis of their data. However, in the past few decades ecologists have become increasingly interested in the use of Bayesian methods of data analysis. In this article I provide guidance to ecologists who would like to decide whether Bayesian methods can be used to improve their conclusions and predictions. I begin by providing a concise summary of Bayesian methods of analysis, including a comparison of differences between Bayesian and frequentist approaches to inference when using hierarchical models. Next I provide a list of problems where Bayesian methods of analysis may arguably be preferred over frequentist methods. These problems are usually encountered in analyses based on hierarchical models of data. I describe the essentials required for applying modern methods of Bayesian computation, and I use real-world examples to illustrate these methods. I conclude by summarizing what I perceive to be the main strengths and weaknesses of using Bayesian methods to solve ecological inference problems.

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

Bayesian Approaches to Imputation, Hypothesis Testing, and Parameter Estimation

ERIC Educational Resources Information Center

Ross, Steven J.; Mackey, Beth

2015-01-01

This chapter introduces three applications of Bayesian inference to common and novel issues in second language research. After a review of the critiques of conventional hypothesis testing, our focus centers on ways Bayesian inference can be used for dealing with missing data, for testing theory-driven substantive hypotheses without a default null…

Probabilistic modeling of bifurcations in single-cell gene expression data using a Bayesian mixture of factor analyzers.

PubMed

Campbell, Kieran R; Yau, Christopher

2017-03-15

Modeling bifurcations in single-cell transcriptomics data has become an increasingly popular field of research. Several methods have been proposed to infer bifurcation structure from such data, but all rely on heuristic non-probabilistic inference. Here we propose the first generative, fully probabilistic model for such inference based on a Bayesian hierarchical mixture of factor analyzers. Our model exhibits competitive performance on large datasets despite implementing full Markov-Chain Monte Carlo sampling, and its unique hierarchical prior structure enables automatic determination of genes driving the bifurcation process. We additionally propose an Empirical-Bayes like extension that deals with the high levels of zero-inflation in single-cell RNA-seq data and quantify when such models are useful. We apply or model to both real and simulated single-cell gene expression data and compare the results to existing pseudotime methods. Finally, we discuss both the merits and weaknesses of such a unified, probabilistic approach in the context practical bioinformatics analyses.

Bayesian Inference for Time Trends in Parameter Values using Weighted Evidence Sets

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

D. L. Kelly; A. Malkhasyan

2010-09-01

There is a nearly ubiquitous assumption in PSA that parameter values are at least piecewise-constant in time. As a result, Bayesian inference tends to incorporate many years of plant operation, over which there have been significant changes in plant operational and maintenance practices, plant management, etc. These changes can cause significant changes in parameter values over time; however, failure to perform Bayesian inference in the proper time-dependent framework can mask these changes. Failure to question the assumption of constant parameter values, and failure to perform Bayesian inference in the proper time-dependent framework were noted as important issues in NUREG/CR-6813, performedmore » for the U. S. Nuclear Regulatory Commission’s Advisory Committee on Reactor Safeguards in 2003. That report noted that “in-dustry lacks tools to perform time-trend analysis with Bayesian updating.” This paper describes an applica-tion of time-dependent Bayesian inference methods developed for the European Commission Ageing PSA Network. These methods utilize open-source software, implementing Markov chain Monte Carlo sampling. The paper also illustrates an approach to incorporating multiple sources of data via applicability weighting factors that address differences in key influences, such as vendor, component boundaries, conditions of the operating environment, etc.« less

Bayesian Inference for Time Trends in Parameter Values: Case Study for the Ageing PSA Network of the European Commission

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

Dana L. Kelly; Albert Malkhasyan

2010-06-01

There is a nearly ubiquitous assumption in PSA that parameter values are at least piecewise-constant in time. As a result, Bayesian inference tends to incorporate many years of plant operation, over which there have been significant changes in plant operational and maintenance practices, plant management, etc. These changes can cause significant changes in parameter values over time; however, failure to perform Bayesian inference in the proper time-dependent framework can mask these changes. Failure to question the assumption of constant parameter values, and failure to perform Bayesian inference in the proper time-dependent framework were noted as important issues in NUREG/CR-6813, performedmore » for the U. S. Nuclear Regulatory Commission’s Advisory Committee on Reactor Safeguards in 2003. That report noted that “industry lacks tools to perform time-trend analysis with Bayesian updating.” This paper describes an application of time-dependent Bayesian inference methods developed for the European Commission Ageing PSA Network. These methods utilize open-source software, implementing Markov chain Monte Carlo sampling. The paper also illustrates the development of a generic prior distribution, which incorporates multiple sources of generic data via weighting factors that address differences in key influences, such as vendor, component boundaries, conditions of the operating environment, etc.« less

A hybrid expectation maximisation and MCMC sampling algorithm to implement Bayesian mixture model based genomic prediction and QTL mapping.

PubMed

Wang, Tingting; Chen, Yi-Ping Phoebe; Bowman, Phil J; Goddard, Michael E; Hayes, Ben J

2016-09-21

Bayesian mixture models in which the effects of SNP are assumed to come from normal distributions with different variances are attractive for simultaneous genomic prediction and QTL mapping. These models are usually implemented with Monte Carlo Markov Chain (MCMC) sampling, which requires long compute times with large genomic data sets. Here, we present an efficient approach (termed HyB_BR), which is a hybrid of an Expectation-Maximisation algorithm, followed by a limited number of MCMC without the requirement for burn-in. To test prediction accuracy from HyB_BR, dairy cattle and human disease trait data were used. In the dairy cattle data, there were four quantitative traits (milk volume, protein kg, fat% in milk and fertility) measured in 16,214 cattle from two breeds genotyped for 632,002 SNPs. Validation of genomic predictions was in a subset of cattle either from the reference set or in animals from a third breeds that were not in the reference set. In all cases, HyB_BR gave almost identical accuracies to Bayesian mixture models implemented with full MCMC, however computational time was reduced by up to 1/17 of that required by full MCMC. The SNPs with high posterior probability of a non-zero effect were also very similar between full MCMC and HyB_BR, with several known genes affecting milk production in this category, as well as some novel genes. HyB_BR was also applied to seven human diseases with 4890 individuals genotyped for around 300 K SNPs in a case/control design, from the Welcome Trust Case Control Consortium (WTCCC). In this data set, the results demonstrated again that HyB_BR performed as well as Bayesian mixture models with full MCMC for genomic predictions and genetic architecture inference while reducing the computational time from 45 h with full MCMC to 3 h with HyB_BR. The results for quantitative traits in cattle and disease in humans demonstrate that HyB_BR can perform equally well as Bayesian mixture models implemented with full MCMC in terms of prediction accuracy, but with up to 17 times faster than the full MCMC implementations. The HyB_BR algorithm makes simultaneous genomic prediction, QTL mapping and inference of genetic architecture feasible in large genomic data sets.

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.

Bayesian inference based on stationary Fokker-Planck sampling.

PubMed

Berrones, Arturo

2010-06-01

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

Inference of reactive transport model parameters using a Bayesian multivariate approach

NASA Astrophysics Data System (ADS)

Carniato, Luca; Schoups, Gerrit; van de Giesen, Nick

2014-08-01

Parameter estimation of subsurface transport models from multispecies data requires the definition of an objective function that includes different types of measurements. Common approaches are weighted least squares (WLS), where weights are specified a priori for each measurement, and weighted least squares with weight estimation (WLS(we)) where weights are estimated from the data together with the parameters. In this study, we formulate the parameter estimation task as a multivariate Bayesian inference problem. The WLS and WLS(we) methods are special cases in this framework, corresponding to specific prior assumptions about the residual covariance matrix. The Bayesian perspective allows for generalizations to cases where residual correlation is important and for efficient inference by analytically integrating out the variances (weights) and selected covariances from the joint posterior. Specifically, the WLS and WLS(we) methods are compared to a multivariate (MV) approach that accounts for specific residual correlations without the need for explicit estimation of the error parameters. When applied to inference of reactive transport model parameters from column-scale data on dissolved species concentrations, the following results were obtained: (1) accounting for residual correlation between species provides more accurate parameter estimation for high residual correlation levels whereas its influence for predictive uncertainty is negligible, (2) integrating out the (co)variances leads to an efficient estimation of the full joint posterior with a reduced computational effort compared to the WLS(we) method, and (3) in the presence of model structural errors, none of the methods is able to identify the correct parameter values.

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.

Metis: A Pure Metropolis Markov Chain Monte Carlo Bayesian Inference Library

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

Bates, Cameron Russell; Mckigney, Edward Allen

The use of Bayesian inference in data analysis has become the standard for large scienti c experiments [1, 2]. The Monte Carlo Codes Group(XCP-3) at Los Alamos has developed a simple set of algorithms currently implemented in C++ and Python to easily perform at-prior Markov Chain Monte Carlo Bayesian inference with pure Metropolis sampling. These implementations are designed to be user friendly and extensible for customization based on speci c application requirements. This document describes the algorithmic choices made and presents two use cases.

Non-Bayesian Noun Generalization in 3-to 5-Year-Old Children: Probing the Role of Prior Knowledge in the Suspicious Coincidence Effect

ERIC Educational Resources Information Center

Jenkins, Gavin W.; Samuelson, Larissa K.; Smith, Jodi R.; Spencer, John P.

2015-01-01

It is unclear how children learn labels for multiple overlapping categories such as "Labrador," "dog," and "animal." Xu and Tenenbaum (2007a) suggested that learners infer correct meanings with the help of Bayesian inference. They instantiated these claims in a Bayesian model, which they tested with preschoolers and…

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

PubMed Central

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

2016-01-01

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

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

Sparse Bayesian Inference and the Temperature Structure of the Solar Corona

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

Warren, Harry P.; Byers, Jeff M.; Crump, Nicholas A.

Measuring the temperature structure of the solar atmosphere is critical to understanding how it is heated to high temperatures. Unfortunately, the temperature of the upper atmosphere cannot be observed directly, but must be inferred from spectrally resolved observations of individual emission lines that span a wide range of temperatures. Such observations are “inverted” to determine the distribution of plasma temperatures along the line of sight. This inversion is ill posed and, in the absence of regularization, tends to produce wildly oscillatory solutions. We introduce the application of sparse Bayesian inference to the problem of inferring the temperature structure of themore » solar corona. Within a Bayesian framework a preference for solutions that utilize a minimum number of basis functions can be encoded into the prior and many ad hoc assumptions can be avoided. We demonstrate the efficacy of the Bayesian approach by considering a test library of 40 assumed temperature distributions.« less

Quantifying uncertainty in soot volume fraction estimates using Bayesian inference of auto-correlated laser-induced incandescence measurements

NASA Astrophysics Data System (ADS)

Hadwin, Paul J.; Sipkens, T. A.; Thomson, K. A.; Liu, F.; Daun, K. J.

2016-01-01

Auto-correlated laser-induced incandescence (AC-LII) infers the soot volume fraction (SVF) of soot particles by comparing the spectral incandescence from laser-energized particles to the pyrometrically inferred peak soot temperature. This calculation requires detailed knowledge of model parameters such as the absorption function of soot, which may vary with combustion chemistry, soot age, and the internal structure of the soot. This work presents a Bayesian methodology to quantify such uncertainties. This technique treats the additional "nuisance" model parameters, including the soot absorption function, as stochastic variables and incorporates the current state of knowledge of these parameters into the inference process through maximum entropy priors. While standard AC-LII analysis provides a point estimate of the SVF, Bayesian techniques infer the posterior probability density, which will allow scientists and engineers to better assess the reliability of AC-LII inferred SVFs in the context of environmental regulations and competing diagnostics.

Multinomial Bayesian learning for modeling classical and nonclassical receptive field properties.

PubMed

Hosoya, Haruo

2012-08-01

We study the interplay of Bayesian inference and natural image learning in a hierarchical vision system, in relation to the response properties of early visual cortex. We particularly focus on a Bayesian network with multinomial variables that can represent discrete feature spaces similar to hypercolumns combining minicolumns, enforce sparsity of activation to learn efficient representations, and explain divisive normalization. We demonstrate that maximal-likelihood learning using sampling-based Bayesian inference gives rise to classical receptive field properties similar to V1 simple cells and V2 cells, while inference performed on the trained network yields nonclassical context-dependent response properties such as cross-orientation suppression and filling in. Comparison with known physiological properties reveals some qualitative and quantitative similarities.

Bayesian functional integral method for inferring continuous data from discrete measurements.

PubMed

Heuett, William J; Miller, Bernard V; Racette, Susan B; Holloszy, John O; Chow, Carson C; Periwal, Vipul

2012-02-08

Inference of the insulin secretion rate (ISR) from C-peptide measurements as a quantification of pancreatic β-cell function is clinically important in diseases related to reduced insulin sensitivity and insulin action. ISR derived from C-peptide concentration is an example of nonparametric Bayesian model selection where a proposed ISR time-course is considered to be a "model". An inferred value of inaccessible continuous variables from discrete observable data is often problematic in biology and medicine, because it is a priori unclear how robust the inference is to the deletion of data points, and a closely related question, how much smoothness or continuity the data actually support. Predictions weighted by the posterior distribution can be cast as functional integrals as used in statistical field theory. Functional integrals are generally difficult to evaluate, especially for nonanalytic constraints such as positivity of the estimated parameters. We propose a computationally tractable method that uses the exact solution of an associated likelihood function as a prior probability distribution for a Markov-chain Monte Carlo evaluation of the posterior for the full model. As a concrete application of our method, we calculate the ISR from actual clinical C-peptide measurements in human subjects with varying degrees of insulin sensitivity. Our method demonstrates the feasibility of functional integral Bayesian model selection as a practical method for such data-driven inference, allowing the data to determine the smoothing timescale and the width of the prior probability distribution on the space of models. In particular, our model comparison method determines the discrete time-step for interpolation of the unobservable continuous variable that is supported by the data. Attempts to go to finer discrete time-steps lead to less likely models. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

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.

An Intuitive Dashboard for Bayesian Network Inference

NASA Astrophysics Data System (ADS)

Reddy, Vikas; Charisse Farr, Anna; Wu, Paul; Mengersen, Kerrie; Yarlagadda, Prasad K. D. V.

2014-03-01

Current Bayesian network software packages provide good graphical interface for users who design and develop Bayesian networks for various applications. However, the intended end-users of these networks may not necessarily find such an interface appealing and at times it could be overwhelming, particularly when the number of nodes in the network is large. To circumvent this problem, this paper presents an intuitive dashboard, which provides an additional layer of abstraction, enabling the end-users to easily perform inferences over the Bayesian networks. Unlike most software packages, which display the nodes and arcs of the network, the developed tool organises the nodes based on the cause-and-effect relationship, making the user-interaction more intuitive and friendly. In addition to performing various types of inferences, the users can conveniently use the tool to verify the behaviour of the developed Bayesian network. The tool has been developed using QT and SMILE libraries in C++.

Bayesian estimation of the discrete coefficient of determination.

PubMed

Chen, Ting; Braga-Neto, Ulisses M

2016-12-01

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

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.

Weakly Informative Prior for Point Estimation of Covariance Matrices in Hierarchical Models

ERIC Educational Resources Information Center

Chung, Yeojin; Gelman, Andrew; Rabe-Hesketh, Sophia; Liu, Jingchen; Dorie, Vincent

2015-01-01

When fitting hierarchical regression models, maximum likelihood (ML) estimation has computational (and, for some users, philosophical) advantages compared to full Bayesian inference, but when the number of groups is small, estimates of the covariance matrix (S) of group-level varying coefficients are often degenerate. One can do better, even from…

Bayesian Nonparametric Inference – Why and How

PubMed Central

Müller, Peter; Mitra, Riten

2013-01-01

We review inference under models with nonparametric Bayesian (BNP) priors. The discussion follows a set of examples for some common inference problems. The examples are chosen to highlight problems that are challenging for standard parametric inference. We discuss inference for density estimation, clustering, regression and for mixed effects models with random effects distributions. While we focus on arguing for the need for the flexibility of BNP models, we also review some of the more commonly used BNP models, thus hopefully answering a bit of both questions, why and how to use BNP. PMID:24368932

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

PubMed

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

2017-02-01

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

Final Report, DOE Early Career Award: Predictive modeling of complex physical systems: new tools for statistical inference, uncertainty quantification, and experimental design

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

Marzouk, Youssef

Predictive simulation of complex physical systems increasingly rests on the interplay of experimental observations with computational models. Key inputs, parameters, or structural aspects of models may be incomplete or unknown, and must be developed from indirect and limited observations. At the same time, quantified uncertainties are needed to qualify computational predictions in the support of design and decision-making. In this context, Bayesian statistics provides a foundation for inference from noisy and limited data, but at prohibitive computional expense. This project intends to make rigorous predictive modeling *feasible* in complex physical systems, via accelerated and scalable tools for uncertainty quantification, Bayesianmore » inference, and experimental design. Specific objectives are as follows: 1. Develop adaptive posterior approximations and dimensionality reduction approaches for Bayesian inference in high-dimensional nonlinear systems. 2. Extend accelerated Bayesian methodologies to large-scale {\\em sequential} data assimilation, fully treating nonlinear models and non-Gaussian state and parameter distributions. 3. Devise efficient surrogate-based methods for Bayesian model selection and the learning of model structure. 4. Develop scalable simulation/optimization approaches to nonlinear Bayesian experimental design, for both parameter inference and model selection. 5. Demonstrate these inferential tools on chemical kinetic models in reacting flow, constructing and refining thermochemical and electrochemical models from limited data. Demonstrate Bayesian filtering on canonical stochastic PDEs and in the dynamic estimation of inhomogeneous subsurface properties and flow fields.« less

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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.

Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes.

PubMed

Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon

2017-12-01

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. © 2017, The International Biometric Society.

A sub-space greedy search method for efficient Bayesian Network inference.

PubMed

Zhang, Qing; Cao, Yong; Li, Yong; Zhu, Yanming; Sun, Samuel S M; Guo, Dianjing

2011-09-01

Bayesian network (BN) has been successfully used to infer the regulatory relationships of genes from microarray dataset. However, one major limitation of BN approach is the computational cost because the calculation time grows more than exponentially with the dimension of the dataset. In this paper, we propose a sub-space greedy search method for efficient Bayesian Network inference. Particularly, this method limits the greedy search space by only selecting gene pairs with higher partial correlation coefficients. Using both synthetic and real data, we demonstrate that the proposed method achieved comparable results with standard greedy search method yet saved ∼50% of the computational time. We believe that sub-space search method can be widely used for efficient BN inference in systems biology. Copyright © 2011 Elsevier Ltd. All rights reserved.

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.

Bayes factors and multimodel inference

USGS Publications Warehouse

Link, W.A.; Barker, R.J.; Thomson, David L.; Cooch, Evan G.; Conroy, Michael J.

2009-01-01

Multimodel inference has two main themes: model selection, and model averaging. Model averaging is a means of making inference conditional on a model set, rather than on a selected model, allowing formal recognition of the uncertainty associated with model choice. The Bayesian paradigm provides a natural framework for model averaging, and provides a context for evaluation of the commonly used AIC weights. We review Bayesian multimodel inference, noting the importance of Bayes factors. Noting the sensitivity of Bayes factors to the choice of priors on parameters, we define and propose nonpreferential priors as offering a reasonable standard for objective multimodel inference.

Bayesian Inference of High-Dimensional Dynamical Ocean Models

NASA Astrophysics Data System (ADS)

Lin, J.; Lermusiaux, P. F. J.; Lolla, S. V. T.; Gupta, A.; Haley, P. J., Jr.

2015-12-01

This presentation addresses a holistic set of challenges in high-dimension ocean Bayesian nonlinear estimation: i) predict the probability distribution functions (pdfs) of large nonlinear dynamical systems using stochastic partial differential equations (PDEs); ii) assimilate data using Bayes' law with these pdfs; iii) predict the future data that optimally reduce uncertainties; and (iv) rank the known and learn the new model formulations themselves. Overall, we allow the joint inference of the state, equations, geometry, boundary conditions and initial conditions of dynamical models. Examples are provided for time-dependent fluid and ocean flows, including cavity, double-gyre and Strait flows with jets and eddies. The Bayesian model inference, based on limited observations, is illustrated first by the estimation of obstacle shapes and positions in fluid flows. Next, the Bayesian inference of biogeochemical reaction equations and of their states and parameters is presented, illustrating how PDE-based machine learning can rigorously guide the selection and discovery of complex ecosystem models. Finally, the inference of multiscale bottom gravity current dynamics is illustrated, motivated in part by classic overflows and dense water formation sites and their relevance to climate monitoring and dynamics. This is joint work with our MSEAS group at MIT.

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.

Evaluating Great Lakes bald eagle nesting habitat with Bayesian inference

Treesearch

Teryl G. Grubb; William W. Bowerman; Allen J. Bath; John P. Giesy; D. V. Chip Weseloh

2003-01-01

Bayesian inference facilitated structured interpretation of a nonreplicated, experience-based survey of potential nesting habitat for bald eagles (Haliaeetus leucocephalus) along the five Great Lakes shorelines. We developed a pattern recognition (PATREC) model of our aerial search image with six habitat attributes: (a) tree cover, (b) proximity and...

Word Learning as Bayesian Inference

ERIC Educational Resources Information Center

Xu, Fei; Tenenbaum, Joshua B.

2007-01-01

The authors present a Bayesian framework for understanding how adults and children learn the meanings of words. The theory explains how learners can generalize meaningfully from just one or a few positive examples of a novel word's referents, by making rational inductive inferences that integrate prior knowledge about plausible word meanings with…

Pig Data and Bayesian Inference on Multinomial Probabilities

ERIC Educational Resources Information Center

Kern, John C.

2006-01-01

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

Entropic Inference

NASA Astrophysics Data System (ADS)

Caticha, Ariel

2011-03-01

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

Hilbertian sine as an absolute measure of Bayesian inference in ISR, homeland security, medicine, and defense

NASA Astrophysics Data System (ADS)

Jannson, Tomasz; Wang, Wenjian; Hodelin, Juan; Forrester, Thomas; Romanov, Volodymyr; Kostrzewski, Andrew

2016-05-01

In this paper, Bayesian Binary Sensing (BBS) is discussed as an effective tool for Bayesian Inference (BI) evaluation in interdisciplinary areas such as ISR (and, C3I), Homeland Security, QC, medicine, defense, and many others. In particular, Hilbertian Sine (HS) as an absolute measure of BI, is introduced, while avoiding relativity of decision threshold identification, as in the case of traditional measures of BI, related to false positives and false negatives.

Emerging Concepts of Data Integration in Pathogen Phylodynamics.

PubMed

Baele, Guy; Suchard, Marc A; Rambaut, Andrew; Lemey, Philippe

2017-01-01

Phylodynamics has become an increasingly popular statistical framework to extract evolutionary and epidemiological information from pathogen genomes. By harnessing such information, epidemiologists aim to shed light on the spatio-temporal patterns of spread and to test hypotheses about the underlying interaction of evolutionary and ecological dynamics in pathogen populations. Although the field has witnessed a rich development of statistical inference tools with increasing levels of sophistication, these tools initially focused on sequences as their sole primary data source. Integrating various sources of information, however, promises to deliver more precise insights in infectious diseases and to increase opportunities for statistical hypothesis testing. Here, we review how the emerging concept of data integration is stimulating new advances in Bayesian evolutionary inference methodology which formalize a marriage of statistical thinking and evolutionary biology. These approaches include connecting sequence to trait evolution, such as for host, phenotypic and geographic sampling information, but also the incorporation of covariates of evolutionary and epidemic processes in the reconstruction procedures. We highlight how a full Bayesian approach to covariate modeling and testing can generate further insights into sequence evolution, trait evolution, and population dynamics in pathogen populations. Specific examples demonstrate how such approaches can be used to test the impact of host on rabies and HIV evolutionary rates, to identify the drivers of influenza dispersal as well as the determinants of rabies cross-species transmissions, and to quantify the evolutionary dynamics of influenza antigenicity. Finally, we briefly discuss how data integration is now also permeating through the inference of transmission dynamics, leading to novel insights into tree-generative processes and detailed reconstructions of transmission trees. [Bayesian inference; birth–death models; coalescent models; continuous trait evolution; covariates; data integration; discrete trait evolution; pathogen phylodynamics.

Emerging Concepts of Data Integration in Pathogen Phylodynamics

PubMed Central

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

2017-01-01

Phylodynamics has become an increasingly popular statistical framework to extract evolutionary and epidemiological information from pathogen genomes. By harnessing such information, epidemiologists aim to shed light on the spatio-temporal patterns of spread and to test hypotheses about the underlying interaction of evolutionary and ecological dynamics in pathogen populations. Although the field has witnessed a rich development of statistical inference tools with increasing levels of sophistication, these tools initially focused on sequences as their sole primary data source. Integrating various sources of information, however, promises to deliver more precise insights in infectious diseases and to increase opportunities for statistical hypothesis testing. Here, we review how the emerging concept of data integration is stimulating new advances in Bayesian evolutionary inference methodology which formalize a marriage of statistical thinking and evolutionary biology. These approaches include connecting sequence to trait evolution, such as for host, phenotypic and geographic sampling information, but also the incorporation of covariates of evolutionary and epidemic processes in the reconstruction procedures. We highlight how a full Bayesian approach to covariate modeling and testing can generate further insights into sequence evolution, trait evolution, and population dynamics in pathogen populations. Specific examples demonstrate how such approaches can be used to test the impact of host on rabies and HIV evolutionary rates, to identify the drivers of influenza dispersal as well as the determinants of rabies cross-species transmissions, and to quantify the evolutionary dynamics of influenza antigenicity. Finally, we briefly discuss how data integration is now also permeating through the inference of transmission dynamics, leading to novel insights into tree-generative processes and detailed reconstructions of transmission trees. [Bayesian inference; birth–death models; coalescent models; continuous trait evolution; covariates; data integration; discrete trait evolution; pathogen phylodynamics. PMID:28173504

Quantifying Uncertainty in Near Surface Electromagnetic Imaging Using Bayesian Methods

NASA Astrophysics Data System (ADS)

Blatter, D. B.; Ray, A.; Key, K.

2017-12-01

Geoscientists commonly use electromagnetic methods to image the Earth's near surface. Field measurements of EM fields are made (often with the aid an artificial EM source) and then used to infer near surface electrical conductivity via a process known as inversion. In geophysics, the standard inversion tool kit is robust and can provide an estimate of the Earth's near surface conductivity that is both geologically reasonable and compatible with the measured field data. However, standard inverse methods struggle to provide a sense of the uncertainty in the estimate they provide. This is because the task of finding an Earth model that explains the data to within measurement error is non-unique - that is, there are many, many such models; but the standard methods provide only one "answer." An alternative method, known as Bayesian inversion, seeks to explore the full range of Earth model parameters that can adequately explain the measured data, rather than attempting to find a single, "ideal" model. Bayesian inverse methods can therefore provide a quantitative assessment of the uncertainty inherent in trying to infer near surface conductivity from noisy, measured field data. This study applies a Bayesian inverse method (called trans-dimensional Markov chain Monte Carlo) to transient airborne EM data previously collected over Taylor Valley - one of the McMurdo Dry Valleys in Antarctica. Our results confirm the reasonableness of previous estimates (made using standard methods) of near surface conductivity beneath Taylor Valley. In addition, we demonstrate quantitatively the uncertainty associated with those estimates. We demonstrate that Bayesian inverse methods can provide quantitative uncertainty to estimates of near surface conductivity.

Explaining Inference on a Population of Independent Agents Using Bayesian Networks

ERIC Educational Resources Information Center

Sutovsky, Peter

2013-01-01

The main goal of this research is to design, implement, and evaluate a novel explanation method, the hierarchical explanation method (HEM), for explaining Bayesian network (BN) inference when the network is modeling a population of conditionally independent agents, each of which is modeled as a subnetwork. For example, consider disease-outbreak…

Adaptability and phenotypic stability of common bean genotypes through Bayesian inference.

PubMed

Corrêa, A M; Teodoro, P E; Gonçalves, M C; Barroso, L M A; Nascimento, M; Santos, A; Torres, F E

2016-04-27

This study used Bayesian inference to investigate the genotype x environment interaction in common bean grown in Mato Grosso do Sul State, and it also evaluated the efficiency of using informative and minimally informative a priori distributions. Six trials were conducted in randomized blocks, and the grain yield of 13 common bean genotypes was assessed. To represent the minimally informative a priori distributions, a probability distribution with high variance was used, and a meta-analysis concept was adopted to represent the informative a priori distributions. Bayes factors were used to conduct comparisons between the a priori distributions. The Bayesian inference was effective for the selection of upright common bean genotypes with high adaptability and phenotypic stability using the Eberhart and Russell method. Bayes factors indicated that the use of informative a priori distributions provided more accurate results than minimally informative a priori distributions. According to Bayesian inference, the EMGOPA-201, BAMBUÍ, CNF 4999, CNF 4129 A 54, and CNFv 8025 genotypes had specific adaptability to favorable environments, while the IAPAR 14 and IAC CARIOCA ETE genotypes had specific adaptability to unfavorable environments.

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.

Optimal inference with suboptimal models: Addiction and active Bayesian inference

PubMed Central

Schwartenbeck, Philipp; FitzGerald, Thomas H.B.; Mathys, Christoph; Dolan, Ray; Wurst, Friedrich; Kronbichler, Martin; Friston, Karl

2015-01-01

When casting behaviour as active (Bayesian) inference, optimal inference is defined with respect to an agent’s beliefs – based on its generative model of the world. This contrasts with normative accounts of choice behaviour, in which optimal actions are considered in relation to the true structure of the environment – as opposed to the agent’s beliefs about worldly states (or the task). This distinction shifts an understanding of suboptimal or pathological behaviour away from aberrant inference as such, to understanding the prior beliefs of a subject that cause them to behave less ‘optimally’ than our prior beliefs suggest they should behave. Put simply, suboptimal or pathological behaviour does not speak against understanding behaviour in terms of (Bayes optimal) inference, but rather calls for a more refined understanding of the subject’s generative model upon which their (optimal) Bayesian inference is based. Here, we discuss this fundamental distinction and its implications for understanding optimality, bounded rationality and pathological (choice) behaviour. We illustrate our argument using addictive choice behaviour in a recently described ‘limited offer’ task. Our simulations of pathological choices and addictive behaviour also generate some clear hypotheses, which we hope to pursue in ongoing empirical work. PMID:25561321

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

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.

Model averaging, optimal inference, and habit formation

PubMed Central

FitzGerald, Thomas H. B.; Dolan, Raymond J.; Friston, Karl J.

2014-01-01

Postulating that the brain performs approximate Bayesian inference generates principled and empirically testable models of neuronal function—the subject of much current interest in neuroscience and related disciplines. Current formulations address inference and learning under some assumed and particular model. In reality, organisms are often faced with an additional challenge—that of determining which model or models of their environment are the best for guiding behavior. Bayesian model averaging—which says that an agent should weight the predictions of different models according to their evidence—provides a principled way to solve this problem. Importantly, because model evidence is determined by both the accuracy and complexity of the model, optimal inference requires that these be traded off against one another. This means an agent's behavior should show an equivalent balance. We hypothesize that Bayesian model averaging plays an important role in cognition, given that it is both optimal and realizable within a plausible neuronal architecture. We outline model averaging and how it might be implemented, and then explore a number of implications for brain and behavior. In particular, we propose that model averaging can explain a number of apparently suboptimal phenomena within the framework of approximate (bounded) Bayesian inference, focusing particularly upon the relationship between goal-directed and habitual behavior. PMID:25018724

Bayesian estimation of optical properties of the human head via 3D structural MRI

NASA Astrophysics Data System (ADS)

Barnett, Alexander H.; Culver, Joseph P.; Sorensen, A. Gregory; Dale, Anders M.; Boas, David A.

2003-10-01

Knowledge of the baseline optical properties of the tissues of the human head is essential for absolute cerebral oximetry, and for quantitative studies of brain activation. In this work we numerically model the utility of signals from a small 6-optode time-resolved diffuse optical tomographic apparatus for inferring baseline scattering and absorption coefficients of the scalp, skull and brain, when complete geometric information is available from magnetic resonance imaging (MRI). We use an optical model where MRI-segmented tissues are assumed homogeneous. We introduce a noise model capturing both photon shot noise and forward model numerical accuracy, and use Bayesian inference to predict errorbars and correlations on the measurments. We also sample from the full posterior distribution using Markov chain Monte Carlo. We conclude that ~ 106 detected photons are sufficient to measure the brain"s scattering and absorption to a few percent. We present preliminary results using a fast multi-layer slab model, comparing the case when layer thicknesses are known versus unknown.

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'…

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

PubMed

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

2015-09-01

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

Spectral likelihood expansions for Bayesian inference

NASA Astrophysics Data System (ADS)

Nagel, Joseph B.; Sudret, Bruno

2016-03-01

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

Nonadditive entropy maximization is inconsistent with Bayesian updating

NASA Astrophysics Data System (ADS)

Pressé, Steve

2014-11-01

The maximum entropy method—used to infer probabilistic models from data—is a special case of Bayes's model inference prescription which, in turn, is grounded in basic propositional logic. By contrast to the maximum entropy method, the compatibility of nonadditive entropy maximization with Bayes's model inference prescription has never been established. Here we demonstrate that nonadditive entropy maximization is incompatible with Bayesian updating and discuss the immediate implications of this finding. We focus our attention on special cases as illustrations.

Nonadditive entropy maximization is inconsistent with Bayesian updating.

PubMed

Pressé, Steve

2014-11-01

The maximum entropy method-used to infer probabilistic models from data-is a special case of Bayes's model inference prescription which, in turn, is grounded in basic propositional logic. By contrast to the maximum entropy method, the compatibility of nonadditive entropy maximization with Bayes's model inference prescription has never been established. Here we demonstrate that nonadditive entropy maximization is incompatible with Bayesian updating and discuss the immediate implications of this finding. We focus our attention on special cases as illustrations.

Bayesian model reduction and empirical Bayes for group (DCM) studies

PubMed Central

Friston, Karl J.; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E.; van Wijk, Bernadette C.M.; Ziegler, Gabriel; Zeidman, Peter

2016-01-01

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level – e.g., dynamic causal models – and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. PMID:26569570

Philosophy and the practice of Bayesian statistics

PubMed Central

Gelman, Andrew; Shalizi, Cosma Rohilla

2015-01-01

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework. PMID:22364575

Philosophy and the practice of Bayesian statistics.

PubMed

Gelman, Andrew; Shalizi, Cosma Rohilla

2013-02-01

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework. © 2012 The British Psychological Society.

Bayesian Inference in the Modern Design of Experiments

NASA Technical Reports Server (NTRS)

DeLoach, Richard

2008-01-01

This paper provides an elementary tutorial overview of Bayesian inference and its potential for application in aerospace experimentation in general and wind tunnel testing in particular. Bayes Theorem is reviewed and examples are provided to illustrate how it can be applied to objectively revise prior knowledge by incorporating insights subsequently obtained from additional observations, resulting in new (posterior) knowledge that combines information from both sources. A logical merger of Bayesian methods and certain aspects of Response Surface Modeling is explored. Specific applications to wind tunnel testing, computational code validation, and instrumentation calibration are discussed.

Bayesian Networks Improve Causal Environmental Assessments for Evidence-Based Policy.

PubMed

Carriger, John F; Barron, Mace G; Newman, Michael C

2016-12-20

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 valued ecological resources. These aspects are demonstrated through hypothetical problem scenarios that explore some major benefits of using Bayesian networks for reasoning and making inferences in evidence-based policy.

A Comparison of Full and Empirical Bayes Techniques for Inferring Sea Level Changes from Tide Gauge Records

NASA Astrophysics Data System (ADS)

Piecuch, C. G.; Huybers, P. J.; Tingley, M.

2016-12-01

Sea level observations from coastal tide gauges are some of the longest instrumental records of the ocean. However, these data can be noisy, biased, and gappy, featuring missing values, and reflecting land motion and local effects. Coping with these issues in a formal manner is a challenging task. Some studies use Bayesian approaches to estimate sea level from tide gauge records, making inference probabilistically. Such methods are typically empirically Bayesian in nature: model parameters are treated as known and assigned point values. But, in reality, parameters are not perfectly known. Empirical Bayes methods thus neglect a potentially important source of uncertainty, and so may overestimate the precision (i.e., underestimate the uncertainty) of sea level estimates. We consider whether empirical Bayes methods underestimate uncertainty in sea level from tide gauge data, comparing to a full Bayes method that treats parameters as unknowns to be solved for along with the sea level field. We develop a hierarchical algorithm that we apply to tide gauge data on the North American northeast coast over 1893-2015. The algorithm is run in full Bayes mode, solving for the sea level process and parameters, and in empirical mode, solving only for the process using fixed parameter values. Error bars on sea level from the empirical method are smaller than from the full Bayes method, and the relative discrepancies increase with time; the 95% credible interval on sea level values from the empirical Bayes method in 1910 and 2010 is 23% and 56% narrower, respectively, than from the full Bayes approach. To evaluate the representativeness of the credible intervals, empirical Bayes and full Bayes methods are applied to corrupted data of a known surrogate field. Using rank histograms to evaluate the solutions, we find that the full Bayes method produces generally reliable error bars, whereas the empirical Bayes method gives too-narrow error bars, such that the 90% credible interval only encompasses 70% of true process values. Results demonstrate that parameter uncertainty is an important source of process uncertainty, and advocate for the fully Bayesian treatment of tide gauge records in ocean circulation and climate studies.

A full-Bayesian approach to parameter inference from tracer travel time moments and investigation of scale effects at the Cape Cod experimental site

USGS Publications Warehouse

Woodbury, Allan D.; Rubin, Yoram

2000-01-01

A method for inverting the travel time moments of solutes in heterogeneous aquifers is presented and is based on peak concentration arrival times as measured at various samplers in an aquifer. The approach combines a Lagrangian [Rubin and Dagan, 1992] solute transport framework with full‐Bayesian hydrogeological parameter inference. In the full‐Bayesian approach the noise values in the observed data are treated as hyperparameters, and their effects are removed by marginalization. The prior probability density functions (pdfs) for the model parameters (horizontal integral scale, velocity, and log K variance) and noise values are represented by prior pdfs developed from minimum relative entropy considerations. Analysis of the Cape Cod (Massachusetts) field experiment is presented. Inverse results for the hydraulic parameters indicate an expected value for the velocity, variance of log hydraulic conductivity, and horizontal integral scale of 0.42 m/d, 0.26, and 3.0 m, respectively. While these results are consistent with various direct‐field determinations, the importance of the findings is in the reduction of confidence range about the various expected values. On selected control planes we compare observed travel time frequency histograms with the theoretical pdf, conditioned on the observed travel time moments. We observe a positive skew in the travel time pdf which tends to decrease as the travel time distance grows. We also test the hypothesis that there is no scale dependence of the integral scale λ with the scale of the experiment at Cape Cod. We adopt two strategies. The first strategy is to use subsets of the full data set and then to see if the resulting parameter fits are different as we use different data from control planes at expanding distances from the source. The second approach is from the viewpoint of entropy concentration. No increase in integral scale with distance is inferred from either approach over the range of the Cape Cod tracer experiment.

A comment on priors for Bayesian occupancy models.

PubMed

Northrup, Joseph M; Gerber, Brian D

2018-01-01

Understanding patterns of species occurrence and the processes underlying these patterns is fundamental to the study of ecology. One of the more commonly used approaches to investigate species occurrence patterns is occupancy modeling, which can account for imperfect detection of a species during surveys. In recent years, there has been a proliferation of Bayesian modeling in ecology, which includes fitting Bayesian occupancy models. The Bayesian framework is appealing to ecologists for many reasons, including the ability to incorporate prior information through the specification of prior distributions on parameters. While ecologists almost exclusively intend to choose priors so that they are "uninformative" or "vague", such priors can easily be unintentionally highly informative. Here we report on how the specification of a "vague" normally distributed (i.e., Gaussian) prior on coefficients in Bayesian occupancy models can unintentionally influence parameter estimation. Using both simulated data and empirical examples, we illustrate how this issue likely compromises inference about species-habitat relationships. While the extent to which these informative priors influence inference depends on the data set, researchers fitting Bayesian occupancy models should conduct sensitivity analyses to ensure intended inference, or employ less commonly used priors that are less informative (e.g., logistic or t prior distributions). We provide suggestions for addressing this issue in occupancy studies, and an online tool for exploring this issue under different contexts.

Perception as Evidence Accumulation and Bayesian Inference: Insights from Masked Priming

ERIC Educational Resources Information Center

Norris, Dennis; Kinoshita, Sachiko

2008-01-01

The authors argue that perception is Bayesian inference based on accumulation of noisy evidence and that, in masked priming, the perceptual system is tricked into treating the prime and the target as a single object. Of the 2 algorithms considered for formalizing how the evidence sampled from a prime and target is combined, only 1 was shown to be…

Inferring metabolic networks using the Bayesian adaptive graphical lasso with informative priors.

PubMed

Peterson, Christine; Vannucci, Marina; Karakas, Cemal; Choi, William; Ma, Lihua; Maletić-Savatić, Mirjana

2013-10-01

Metabolic processes are essential for cellular function and survival. We are interested in inferring a metabolic network in activated microglia, a major neuroimmune cell in the brain responsible for the neuroinflammation associated with neurological diseases, based on a set of quantified metabolites. To achieve this, we apply the Bayesian adaptive graphical lasso with informative priors that incorporate known relationships between covariates. To encourage sparsity, the Bayesian graphical lasso places double exponential priors on the off-diagonal entries of the precision matrix. The Bayesian adaptive graphical lasso allows each double exponential prior to have a unique shrinkage parameter. These shrinkage parameters share a common gamma hyperprior. We extend this model to create an informative prior structure by formulating tailored hyperpriors on the shrinkage parameters. By choosing parameter values for each hyperprior that shift probability mass toward zero for nodes that are close together in a reference network, we encourage edges between covariates with known relationships. This approach can improve the reliability of network inference when the sample size is small relative to the number of parameters to be estimated. When applied to the data on activated microglia, the inferred network includes both known relationships and associations of potential interest for further investigation.

Inferring metabolic networks using the Bayesian adaptive graphical lasso with informative priors

PubMed Central

PETERSON, CHRISTINE; VANNUCCI, MARINA; KARAKAS, CEMAL; CHOI, WILLIAM; MA, LIHUA; MALETIĆ-SAVATIĆ, MIRJANA

2014-01-01

Metabolic processes are essential for cellular function and survival. We are interested in inferring a metabolic network in activated microglia, a major neuroimmune cell in the brain responsible for the neuroinflammation associated with neurological diseases, based on a set of quantified metabolites. To achieve this, we apply the Bayesian adaptive graphical lasso with informative priors that incorporate known relationships between covariates. To encourage sparsity, the Bayesian graphical lasso places double exponential priors on the off-diagonal entries of the precision matrix. The Bayesian adaptive graphical lasso allows each double exponential prior to have a unique shrinkage parameter. These shrinkage parameters share a common gamma hyperprior. We extend this model to create an informative prior structure by formulating tailored hyperpriors on the shrinkage parameters. By choosing parameter values for each hyperprior that shift probability mass toward zero for nodes that are close together in a reference network, we encourage edges between covariates with known relationships. This approach can improve the reliability of network inference when the sample size is small relative to the number of parameters to be estimated. When applied to the data on activated microglia, the inferred network includes both known relationships and associations of potential interest for further investigation. PMID:24533172

Detection of multiple damages employing best achievable eigenvectors under Bayesian inference

NASA Astrophysics Data System (ADS)

Prajapat, Kanta; Ray-Chaudhuri, Samit

2018-05-01

A novel approach is presented in this work to localize simultaneously multiple damaged elements in a structure along with the estimation of damage severity for each of the damaged elements. For detection of damaged elements, a best achievable eigenvector based formulation has been derived. To deal with noisy data, Bayesian inference is employed in the formulation wherein the likelihood of the Bayesian algorithm is formed on the basis of errors between the best achievable eigenvectors and the measured modes. In this approach, the most probable damage locations are evaluated under Bayesian inference by generating combinations of various possible damaged elements. Once damage locations are identified, damage severities are estimated using a Bayesian inference Markov chain Monte Carlo simulation. The efficiency of the proposed approach has been demonstrated by carrying out a numerical study involving a 12-story shear building. It has been found from this study that damage scenarios involving as low as 10% loss of stiffness in multiple elements are accurately determined (localized and severities quantified) even when 2% noise contaminated modal data are utilized. Further, this study introduces a term parameter impact (evaluated based on sensitivity of modal parameters towards structural parameters) to decide the suitability of selecting a particular mode, if some idea about the damaged elements are available. It has been demonstrated here that the accuracy and efficiency of the Bayesian quantification algorithm increases if damage localization is carried out a-priori. An experimental study involving a laboratory scale shear building and different stiffness modification scenarios shows that the proposed approach is efficient enough to localize the stories with stiffness modification.

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.

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

PubMed

Yee, Eugene; Flesch, Thomas K

2010-03-01

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

Inferring Phylogenetic Networks Using PhyloNet.

PubMed

Wen, Dingqiao; Yu, Yun; Zhu, Jiafan; Nakhleh, Luay

2018-07-01

PhyloNet was released in 2008 as a software package for representing and analyzing phylogenetic networks. At the time of its release, the main functionalities in PhyloNet consisted of measures for comparing network topologies and a single heuristic for reconciling gene trees with a species tree. Since then, PhyloNet has grown significantly. The software package now includes a wide array of methods for inferring phylogenetic networks from data sets of unlinked loci while accounting for both reticulation (e.g., hybridization) and incomplete lineage sorting. In particular, PhyloNet now allows for maximum parsimony, maximum likelihood, and Bayesian inference of phylogenetic networks from gene tree estimates. Furthermore, Bayesian inference directly from sequence data (sequence alignments or biallelic markers) is implemented. Maximum parsimony is based on an extension of the "minimizing deep coalescences" criterion to phylogenetic networks, whereas maximum likelihood and Bayesian inference are based on the multispecies network coalescent. All methods allow for multiple individuals per species. As computing the likelihood of a phylogenetic network is computationally hard, PhyloNet allows for evaluation and inference of networks using a pseudolikelihood measure. PhyloNet summarizes the results of the various analyzes and generates phylogenetic networks in the extended Newick format that is readily viewable by existing visualization software.

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.

From individual to population level effects of toxicants in the tubicifid Branchiura sowerbyi using threshold effect models in a Bayesian framework.

PubMed

Ducrot, Virginie; Billoir, Elise; Péry, Alexandre R R; Garric, Jeanne; Charles, Sandrine

2010-05-01

Effects of zinc were studied in the freshwater worm Branchiura sowerbyi using partial and full life-cycle tests. Only newborn and juveniles were sensitive to zinc, displaying effects on survival, growth, and age at first brood at environmentally relevant concentrations. Threshold effect models were proposed to assess toxic effects on individuals. They were fitted to life-cycle test data using Bayesian inference and adequately described life-history trait data in exposed organisms. The daily asymptotic growth rate of theoretical populations was then simulated with a matrix population model, based upon individual-level outputs. Population-level outputs were in accordance with existing literature for controls. Working in a Bayesian framework allowed incorporating parameter uncertainty in the simulation of the population-level response to zinc exposure, thus increasing the relevance of test results in the context of ecological risk assessment.

Bayesian power spectrum inference with foreground and target contamination treatment

NASA Astrophysics Data System (ADS)

Jasche, J.; Lavaux, G.

2017-10-01

This work presents a joint and self-consistent Bayesian treatment of various foreground and target contaminations when inferring cosmological power spectra and three-dimensional density fields from galaxy redshift surveys. This is achieved by introducing additional block-sampling procedures for unknown coefficients of foreground and target contamination templates to the previously presented ARES framework for Bayesian large-scale structure analyses. As a result, the method infers jointly and fully self-consistently three-dimensional density fields, cosmological power spectra, luminosity-dependent galaxy biases, noise levels of the respective galaxy distributions, and coefficients for a set of a priori specified foreground templates. In addition, this fully Bayesian approach permits detailed quantification of correlated uncertainties amongst all inferred quantities and correctly marginalizes over observational systematic effects. We demonstrate the validity and efficiency of our approach in obtaining unbiased estimates of power spectra via applications to realistic mock galaxy observations that are subject to stellar contamination and dust extinction. While simultaneously accounting for galaxy biases and unknown noise levels, our method reliably and robustly infers three-dimensional density fields and corresponding cosmological power spectra from deep galaxy surveys. Furthermore, our approach correctly accounts for joint and correlated uncertainties between unknown coefficients of foreground templates and the amplitudes of the power spectrum. This effect amounts to correlations and anti-correlations of up to 10 per cent across wide ranges in Fourier space.

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…

Testing adaptive toolbox models: a Bayesian hierarchical approach.

PubMed

Scheibehenne, Benjamin; Rieskamp, Jörg; Wagenmakers, Eric-Jan

2013-01-01

Many theories of human cognition postulate that people are equipped with a repertoire of strategies to solve the tasks they face. This theoretical framework of a cognitive toolbox provides a plausible account of intra- and interindividual differences in human behavior. Unfortunately, it is often unclear how to rigorously test the toolbox framework. How can a toolbox model be quantitatively specified? How can the number of toolbox strategies be limited to prevent uncontrolled strategy sprawl? How can a toolbox model be formally tested against alternative theories? The authors show how these challenges can be met by using Bayesian inference techniques. By means of parameter recovery simulations and the analysis of empirical data across a variety of domains (i.e., judgment and decision making, children's cognitive development, function learning, and perceptual categorization), the authors illustrate how Bayesian inference techniques allow toolbox models to be quantitatively specified, strategy sprawl to be contained, and toolbox models to be rigorously tested against competing theories. The authors demonstrate that their approach applies at the individual level but can also be generalized to the group level with hierarchical Bayesian procedures. The suggested Bayesian inference techniques represent a theoretical and methodological advancement for toolbox theories of cognition and behavior.

Inferring mass in complex scenes by mental simulation.

PubMed

Hamrick, Jessica B; Battaglia, Peter W; Griffiths, Thomas L; Tenenbaum, Joshua B

2016-12-01

After observing a collision between two boxes, you can immediately tell which is empty and which is full of books based on how the boxes moved. People form rich perceptions about the physical properties of objects from their interactions, an ability that plays a crucial role in learning about the physical world through our experiences. Here, we present three experiments that demonstrate people's capacity to reason about the relative masses of objects in naturalistic 3D scenes. We find that people make accurate inferences, and that they continue to fine-tune their beliefs over time. To explain our results, we propose a cognitive model that combines Bayesian inference with approximate knowledge of Newtonian physics by estimating probabilities from noisy physical simulations. We find that this model accurately predicts judgments from our experiments, suggesting that the same simulation mechanism underlies both peoples' predictions and inferences about the physical world around them. Copyright © 2016 Elsevier B.V. All rights reserved.

Inference of epidemiological parameters from household stratified data

PubMed Central

Walker, James N.; Ross, Joshua V.

2017-01-01

We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters—governing within-household transmission, recovery, and between-household transmission—from data of the day upon which each individual became infectious and the household in which each infection occurred, as might be available from First Few Hundred studies. Each method is a form of Bayesian Markov Chain Monte Carlo that allows us to calculate a joint posterior distribution for all parameters and hence the household reproduction number and the early growth rate of the epidemic. The first method performs exact Bayesian inference using a standard data-augmentation approach; the second performs approximate Bayesian inference based on a likelihood approximation derived from branching processes. These methods are compared for computational efficiency and posteriors from each are compared. The branching process is shown to be a good approximation and remains computationally efficient as the amount of data is increased. PMID:29045456

Model selection and Bayesian inference for high-resolution seabed reflection inversion.

PubMed

Dettmer, Jan; Dosso, Stan E; Holland, Charles W

2009-02-01

This paper applies Bayesian inference, including model selection and posterior parameter inference, to inversion of seabed reflection data to resolve sediment structure at a spatial scale below the pulse length of the acoustic source. A practical approach to model selection is used, employing the Bayesian information criterion to decide on the number of sediment layers needed to sufficiently fit the data while satisfying parsimony to avoid overparametrization. Posterior parameter inference is carried out using an efficient Metropolis-Hastings algorithm for high-dimensional models, and results are presented as marginal-probability depth distributions for sound velocity, density, and attenuation. The approach is applied to plane-wave reflection-coefficient inversion of single-bounce data collected on the Malta Plateau, Mediterranean Sea, which indicate complex fine structure close to the water-sediment interface. This fine structure is resolved in the geoacoustic inversion results in terms of four layers within the upper meter of sediments. The inversion results are in good agreement with parameter estimates from a gravity core taken at the experiment site.

Bayesian inference of interaction properties of noisy dynamical systems with time-varying coupling: capabilities and limitations

NASA Astrophysics Data System (ADS)

Wilting, Jens; Lehnertz, Klaus

2015-08-01

We investigate a recently published analysis framework based on Bayesian inference for the time-resolved characterization of interaction properties of noisy, coupled dynamical systems. It promises wide applicability and a better time resolution than well-established methods. At the example of representative model systems, we show that the analysis framework has the same weaknesses as previous methods, particularly when investigating interacting, structurally different non-linear oscillators. We also inspect the tracking of time-varying interaction properties and propose a further modification of the algorithm, which improves the reliability of obtained results. We exemplarily investigate the suitability of this algorithm to infer strength and direction of interactions between various regions of the human brain during an epileptic seizure. Within the limitations of the applicability of this analysis tool, we show that the modified algorithm indeed allows a better time resolution through Bayesian inference when compared to previous methods based on least square fits.

Comparing Families of Dynamic Causal Models

PubMed Central

Penny, Will D.; Stephan, Klaas E.; Daunizeau, Jean; Rosa, Maria J.; Friston, Karl J.; Schofield, Thomas M.; Leff, Alex P.

2010-01-01

Mathematical models of scientific data can be formally compared using Bayesian model evidence. Previous applications in the biological sciences have mainly focussed on model selection in which one first selects the model with the highest evidence and then makes inferences based on the parameters of that model. This “best model” approach is very useful but can become brittle if there are a large number of models to compare, and if different subjects use different models. To overcome this shortcoming we propose the combination of two further approaches: (i) family level inference and (ii) Bayesian model averaging within families. Family level inference removes uncertainty about aspects of model structure other than the characteristic of interest. For example: What are the inputs to the system? Is processing serial or parallel? Is it linear or nonlinear? Is it mediated by a single, crucial connection? We apply Bayesian model averaging within families to provide inferences about parameters that are independent of further assumptions about model structure. We illustrate the methods using Dynamic Causal Models of brain imaging data. PMID:20300649

Bayesian model reduction and empirical Bayes for group (DCM) studies.

PubMed

Friston, Karl J; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E; van Wijk, Bernadette C M; Ziegler, Gabriel; Zeidman, Peter

2016-03-01

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level - e.g., dynamic causal models - and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

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.

Inference of domain-disease associations from domain-protein, protein-disease and disease-disease relationships.

PubMed

Zhang, Wangshu; Coba, Marcelo P; Sun, Fengzhu

2016-01-11

Protein domains can be viewed as portable units of biological function that defines the functional properties of proteins. Therefore, if a protein is associated with a disease, protein domains might also be associated and define disease endophenotypes. However, knowledge about such domain-disease relationships is rarely available. Thus, identification of domains associated with human diseases would greatly improve our understanding of the mechanism of human complex diseases and further improve the prevention, diagnosis and treatment of these diseases. Based on phenotypic similarities among diseases, we first group diseases into overlapping modules. We then develop a framework to infer associations between domains and diseases through known relationships between diseases and modules, domains and proteins, as well as proteins and disease modules. Different methods including Association, Maximum likelihood estimation (MLE), Domain-disease pair exclusion analysis (DPEA), Bayesian, and Parsimonious explanation (PE) approaches are developed to predict domain-disease associations. We demonstrate the effectiveness of all the five approaches via a series of validation experiments, and show the robustness of the MLE, Bayesian and PE approaches to the involved parameters. We also study the effects of disease modularization in inferring novel domain-disease associations. Through validation, the AUC (Area Under the operating characteristic Curve) scores for Bayesian, MLE, DPEA, PE, and Association approaches are 0.86, 0.84, 0.83, 0.83 and 0.79, respectively, indicating the usefulness of these approaches for predicting domain-disease relationships. Finally, we choose the Bayesian approach to infer domains associated with two common diseases, Crohn's disease and type 2 diabetes. The Bayesian approach has the best performance for the inference of domain-disease relationships. The predicted landscape between domains and diseases provides a more detailed view about the disease mechanisms.

Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies.

PubMed

Chen, Bo; Chen, Minhua; Paisley, John; Zaas, Aimee; Woods, Christopher; Ginsburg, Geoffrey S; Hero, Alfred; Lucas, Joseph; Dunson, David; Carin, Lawrence

2010-11-09

Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data.

Computational Neuropsychology and Bayesian Inference.

PubMed

Parr, Thomas; Rees, Geraint; Friston, Karl J

2018-01-01

Computational theories of brain function have become very influential in neuroscience. They have facilitated the growth of formal approaches to disease, particularly in psychiatric research. In this paper, we provide a narrative review of the body of computational research addressing neuropsychological syndromes, and focus on those that employ Bayesian frameworks. Bayesian approaches to understanding brain function formulate perception and action as inferential processes. These inferences combine 'prior' beliefs with a generative (predictive) model to explain the causes of sensations. Under this view, neuropsychological deficits can be thought of as false inferences that arise due to aberrant prior beliefs (that are poor fits to the real world). This draws upon the notion of a Bayes optimal pathology - optimal inference with suboptimal priors - and provides a means for computational phenotyping. In principle, any given neuropsychological disorder could be characterized by the set of prior beliefs that would make a patient's behavior appear Bayes optimal. We start with an overview of some key theoretical constructs and use these to motivate a form of computational neuropsychology that relates anatomical structures in the brain to the computations they perform. Throughout, we draw upon computational accounts of neuropsychological syndromes. These are selected to emphasize the key features of a Bayesian approach, and the possible types of pathological prior that may be present. They range from visual neglect through hallucinations to autism. Through these illustrative examples, we review the use of Bayesian approaches to understand the link between biology and computation that is at the heart of neuropsychology.

Computational Neuropsychology and Bayesian Inference

PubMed Central

Parr, Thomas; Rees, Geraint; Friston, Karl J.

2018-01-01

Computational theories of brain function have become very influential in neuroscience. They have facilitated the growth of formal approaches to disease, particularly in psychiatric research. In this paper, we provide a narrative review of the body of computational research addressing neuropsychological syndromes, and focus on those that employ Bayesian frameworks. Bayesian approaches to understanding brain function formulate perception and action as inferential processes. These inferences combine ‘prior’ beliefs with a generative (predictive) model to explain the causes of sensations. Under this view, neuropsychological deficits can be thought of as false inferences that arise due to aberrant prior beliefs (that are poor fits to the real world). This draws upon the notion of a Bayes optimal pathology – optimal inference with suboptimal priors – and provides a means for computational phenotyping. In principle, any given neuropsychological disorder could be characterized by the set of prior beliefs that would make a patient’s behavior appear Bayes optimal. We start with an overview of some key theoretical constructs and use these to motivate a form of computational neuropsychology that relates anatomical structures in the brain to the computations they perform. Throughout, we draw upon computational accounts of neuropsychological syndromes. These are selected to emphasize the key features of a Bayesian approach, and the possible types of pathological prior that may be present. They range from visual neglect through hallucinations to autism. Through these illustrative examples, we review the use of Bayesian approaches to understand the link between biology and computation that is at the heart of neuropsychology. PMID:29527157

Discriminative Relational Topic Models.

PubMed

Chen, Ning; Zhu, Jun; Xia, Fei; Zhang, Bo

2015-05-01

Relational topic models (RTMs) provide a probabilistic generative process to describe both the link structure and document contents for document networks, and they have shown promise on predicting network structures and discovering latent topic representations. However, existing RTMs have limitations in both the restricted model expressiveness and incapability of dealing with imbalanced network data. To expand the scope and improve the inference accuracy of RTMs, this paper presents three extensions: 1) unlike the common link likelihood with a diagonal weight matrix that allows the-same-topic interactions only, we generalize it to use a full weight matrix that captures all pairwise topic interactions and is applicable to asymmetric networks; 2) instead of doing standard Bayesian inference, we perform regularized Bayesian inference (RegBayes) with a regularization parameter to deal with the imbalanced link structure issue in real networks and improve the discriminative ability of learned latent representations; and 3) instead of doing variational approximation with strict mean-field assumptions, we present collapsed Gibbs sampling algorithms for the generalized relational topic models by exploring data augmentation without making restricting assumptions. Under the generic RegBayes framework, we carefully investigate two popular discriminative loss functions, namely, the logistic log-loss and the max-margin hinge loss. Experimental results on several real network datasets demonstrate the significance of these extensions on improving prediction performance.

Dynamical Bayesian inference of time-evolving interactions: from a pair of coupled oscillators to networks of oscillators.

PubMed

Duggento, Andrea; Stankovski, Tomislav; McClintock, Peter V E; Stefanovska, Aneta

2012-12-01

Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski et al. [Phys. Rev. Lett. 109, 024101 (2012)] introduced a method based on dynamical Bayesian inference that facilitates the simultaneous detection of time-varying synchronization, directionality of influence, and coupling functions. It can distinguish unsynchronized dynamics from noise-induced phase slips. The method is based on phase dynamics, with Bayesian inference of the time-evolving parameters being achieved by shaping the prior densities to incorporate knowledge of previous samples. We now present the method in detail using numerically generated data, data from an analog electronic circuit, and cardiorespiratory data. We also generalize the method to encompass networks of interacting oscillators and thus demonstrate its applicability to small-scale networks.

Evolution in Mind: Evolutionary Dynamics, Cognitive Processes, and Bayesian Inference.

PubMed

Suchow, Jordan W; Bourgin, David D; Griffiths, Thomas L

2017-07-01

Evolutionary theory describes the dynamics of population change in settings affected by reproduction, selection, mutation, and drift. In the context of human cognition, evolutionary theory is most often invoked to explain the origins of capacities such as language, metacognition, and spatial reasoning, framing them as functional adaptations to an ancestral environment. However, evolutionary theory is useful for understanding the mind in a second way: as a mathematical framework for describing evolving populations of thoughts, ideas, and memories within a single mind. In fact, deep correspondences exist between the mathematics of evolution and of learning, with perhaps the deepest being an equivalence between certain evolutionary dynamics and Bayesian inference. This equivalence permits reinterpretation of evolutionary processes as algorithms for Bayesian inference and has relevance for understanding diverse cognitive capacities, including memory and creativity. Copyright © 2017 Elsevier Ltd. All rights reserved.

A comment on priors for Bayesian occupancy models

PubMed Central

Gerber, Brian D.

2018-01-01

Understanding patterns of species occurrence and the processes underlying these patterns is fundamental to the study of ecology. One of the more commonly used approaches to investigate species occurrence patterns is occupancy modeling, which can account for imperfect detection of a species during surveys. In recent years, there has been a proliferation of Bayesian modeling in ecology, which includes fitting Bayesian occupancy models. The Bayesian framework is appealing to ecologists for many reasons, including the ability to incorporate prior information through the specification of prior distributions on parameters. While ecologists almost exclusively intend to choose priors so that they are “uninformative” or “vague”, such priors can easily be unintentionally highly informative. Here we report on how the specification of a “vague” normally distributed (i.e., Gaussian) prior on coefficients in Bayesian occupancy models can unintentionally influence parameter estimation. Using both simulated data and empirical examples, we illustrate how this issue likely compromises inference about species-habitat relationships. While the extent to which these informative priors influence inference depends on the data set, researchers fitting Bayesian occupancy models should conduct sensitivity analyses to ensure intended inference, or employ less commonly used priors that are less informative (e.g., logistic or t prior distributions). We provide suggestions for addressing this issue in occupancy studies, and an online tool for exploring this issue under different contexts. PMID:29481554

Bayesian outcome-based strategy classification.

PubMed

Lee, Michael D

2016-03-01

Hilbig and Moshagen (Psychonomic Bulletin & Review, 21, 1431-1443, 2014) recently developed a method for making inferences about the decision processes people use in multi-attribute forced choice tasks. Their paper makes a number of worthwhile theoretical and methodological contributions. Theoretically, they provide an insightful psychological motivation for a probabilistic extension of the widely-used "weighted additive" (WADD) model, and show how this model, as well as other important models like "take-the-best" (TTB), can and should be expressed in terms of meaningful priors. Methodologically, they develop an inference approach based on the Minimum Description Length (MDL) principles that balances both the goodness-of-fit and complexity of the decision models they consider. This paper aims to preserve these useful contributions, but provide a complementary Bayesian approach with some theoretical and methodological advantages. We develop a simple graphical model, implemented in JAGS, that allows for fully Bayesian inferences about which models people use to make decisions. To demonstrate the Bayesian approach, we apply it to the models and data considered by Hilbig and Moshagen (Psychonomic Bulletin & Review, 21, 1431-1443, 2014), showing how a prior predictive analysis of the models, and posterior inferences about which models people use and the parameter settings at which they use them, can contribute to our understanding of human decision making.

HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python.

PubMed

Wiecki, Thomas V; Sofer, Imri; Frank, Michael J

2013-01-01

The diffusion model is a commonly used tool to infer latent psychological processes underlying decision-making, and to link them to neural mechanisms based on response times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of response time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model), which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject/condition than non-hierarchical methods, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g., fMRI) influence decision-making parameters. This paper will first describe the theoretical background of the drift diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the χ(2)-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs/

The Dopaminergic Midbrain Encodes the Expected Certainty about Desired Outcomes.

PubMed

Schwartenbeck, Philipp; FitzGerald, Thomas H B; Mathys, Christoph; Dolan, Ray; Friston, Karl

2015-10-01

Dopamine plays a key role in learning; however, its exact function in decision making and choice remains unclear. Recently, we proposed a generic model based on active (Bayesian) inference wherein dopamine encodes the precision of beliefs about optimal policies. Put simply, dopamine discharges reflect the confidence that a chosen policy will lead to desired outcomes. We designed a novel task to test this hypothesis, where subjects played a "limited offer" game in a functional magnetic resonance imaging experiment. Subjects had to decide how long to wait for a high offer before accepting a low offer, with the risk of losing everything if they waited too long. Bayesian model comparison showed that behavior strongly supported active inference, based on surprise minimization, over classical utility maximization schemes. Furthermore, midbrain activity, encompassing dopamine projection neurons, was accurately predicted by trial-by-trial variations in model-based estimates of precision. Our findings demonstrate that human subjects infer both optimal policies and the precision of those inferences, and thus support the notion that humans perform hierarchical probabilistic Bayesian inference. In other words, subjects have to infer both what they should do as well as how confident they are in their choices, where confidence may be encoded by dopaminergic firing. © The Author 2014. Published by Oxford University Press.

The Dopaminergic Midbrain Encodes the Expected Certainty about Desired Outcomes

PubMed Central

Schwartenbeck, Philipp; FitzGerald, Thomas H. B.; Mathys, Christoph; Dolan, Ray; Friston, Karl

2015-01-01

Dopamine plays a key role in learning; however, its exact function in decision making and choice remains unclear. Recently, we proposed a generic model based on active (Bayesian) inference wherein dopamine encodes the precision of beliefs about optimal policies. Put simply, dopamine discharges reflect the confidence that a chosen policy will lead to desired outcomes. We designed a novel task to test this hypothesis, where subjects played a “limited offer” game in a functional magnetic resonance imaging experiment. Subjects had to decide how long to wait for a high offer before accepting a low offer, with the risk of losing everything if they waited too long. Bayesian model comparison showed that behavior strongly supported active inference, based on surprise minimization, over classical utility maximization schemes. Furthermore, midbrain activity, encompassing dopamine projection neurons, was accurately predicted by trial-by-trial variations in model-based estimates of precision. Our findings demonstrate that human subjects infer both optimal policies and the precision of those inferences, and thus support the notion that humans perform hierarchical probabilistic Bayesian inference. In other words, subjects have to infer both what they should do as well as how confident they are in their choices, where confidence may be encoded by dopaminergic firing. PMID:25056572

On Bayesian Testing of Additive Conjoint Measurement Axioms Using Synthetic Likelihood

ERIC Educational Resources Information Center

Karabatsos, George

2017-01-01

This article introduces a Bayesian method for testing the axioms of additive conjoint measurement. The method is based on an importance sampling algorithm that performs likelihood-free, approximate Bayesian inference using a synthetic likelihood to overcome the analytical intractability of this testing problem. This new method improves upon…

Modeling Diagnostic Assessments with Bayesian Networks

ERIC Educational Resources Information Center

Almond, Russell G.; DiBello, Louis V.; Moulder, Brad; Zapata-Rivera, Juan-Diego

2007-01-01

This paper defines Bayesian network models and examines their applications to IRT-based cognitive diagnostic modeling. These models are especially suited to building inference engines designed to be synchronous with the finer grained student models that arise in skills diagnostic assessment. Aspects of the theory and use of Bayesian network models…

Discriminative Bayesian Dictionary Learning for Classification.

PubMed

Akhtar, Naveed; Shafait, Faisal; Mian, Ajmal

2016-12-01

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

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.

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.

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.

Bayesian propensity scores for high-dimensional causal inference: A comparison of drug-eluting to bare-metal coronary stents.

PubMed

Spertus, Jacob V; Normand, Sharon-Lise T

2018-04-23

High-dimensional data provide many potential confounders that may bolster the plausibility of the ignorability assumption in causal inference problems. Propensity score methods are powerful causal inference tools, which are popular in health care research and are particularly useful for high-dimensional data. Recent interest has surrounded a Bayesian treatment of propensity scores in order to flexibly model the treatment assignment mechanism and summarize posterior quantities while incorporating variance from the treatment model. We discuss methods for Bayesian propensity score analysis of binary treatments, focusing on modern methods for high-dimensional Bayesian regression and the propagation of uncertainty. We introduce a novel and simple estimator for the average treatment effect that capitalizes on conjugacy of the beta and binomial distributions. Through simulations, we show the utility of horseshoe priors and Bayesian additive regression trees paired with our new estimator, while demonstrating the importance of including variance from the treatment regression model. An application to cardiac stent data with almost 500 confounders and 9000 patients illustrates approaches and facilitates comparison with existing alternatives. As measured by a falsifiability endpoint, we improved confounder adjustment compared with past observational research of the same problem. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Clinical Outcome Prediction in Aneurysmal Subarachnoid Hemorrhage Using Bayesian Neural Networks with Fuzzy Logic Inferences

PubMed Central

Lo, Benjamin W. Y.; Macdonald, R. Loch; Baker, Andrew; Levine, Mitchell A. H.

2013-01-01

Objective. The novel clinical prediction approach of Bayesian neural networks with fuzzy logic inferences is created and applied to derive prognostic decision rules in cerebral aneurysmal subarachnoid hemorrhage (aSAH). Methods. The approach of Bayesian neural networks with fuzzy logic inferences was applied to data from five trials of Tirilazad for aneurysmal subarachnoid hemorrhage (3551 patients). Results. Bayesian meta-analyses of observational studies on aSAH prognostic factors gave generalizable posterior distributions of population mean log odd ratios (ORs). Similar trends were noted in Bayesian and linear regression ORs. Significant outcome predictors include normal motor response, cerebral infarction, history of myocardial infarction, cerebral edema, history of diabetes mellitus, fever on day 8, prior subarachnoid hemorrhage, admission angiographic vasospasm, neurological grade, intraventricular hemorrhage, ruptured aneurysm size, history of hypertension, vasospasm day, age and mean arterial pressure. Heteroscedasticity was present in the nontransformed dataset. Artificial neural networks found nonlinear relationships with 11 hidden variables in 1 layer, using the multilayer perceptron model. Fuzzy logic decision rules (centroid defuzzification technique) denoted cut-off points for poor prognosis at greater than 2.5 clusters. Discussion. This aSAH prognostic system makes use of existing knowledge, recognizes unknown areas, incorporates one's clinical reasoning, and compensates for uncertainty in prognostication. PMID:23690884

Natural frequencies facilitate diagnostic inferences of managers

PubMed Central

Hoffrage, Ulrich; Hafenbrädl, Sebastian; Bouquet, Cyril

2015-01-01

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

Bayesian inference and decision theory - A framework for decision making in natural resource management

USGS Publications Warehouse

Dorazio, R.M.; Johnson, F.A.

2003-01-01

Bayesian inference and decision theory may be used in the solution of relatively complex problems of natural resource management, owing to recent advances in statistical theory and computing. In particular, Markov chain Monte Carlo algorithms provide a computational framework for fitting models of adequate complexity and for evaluating the expected consequences of alternative management actions. We illustrate these features using an example based on management of waterfowl habitat.

Inference of Gene Regulatory Networks Using Bayesian Nonparametric Regression and Topology Information.

PubMed

Fan, Yue; Wang, Xiao; Peng, Qinke

2017-01-01

Gene regulatory networks (GRNs) play an important role in cellular systems and are important for understanding biological processes. Many algorithms have been developed to infer the GRNs. However, most algorithms only pay attention to the gene expression data but do not consider the topology information in their inference process, while incorporating this information can partially compensate for the lack of reliable expression data. Here we develop a Bayesian group lasso with spike and slab priors to perform gene selection and estimation for nonparametric models. B-spline basis functions are used to capture the nonlinear relationships flexibly and penalties are used to avoid overfitting. Further, we incorporate the topology information into the Bayesian method as a prior. We present the application of our method on DREAM3 and DREAM4 datasets and two real biological datasets. The results show that our method performs better than existing methods and the topology information prior can improve the result.

Bayesian 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

The NIFTy way of Bayesian signal inference

NASA Astrophysics Data System (ADS)

Selig, Marco

2014-12-01

We introduce NIFTy, "Numerical Information Field Theory", a software package for the development of Bayesian signal inference algorithms that operate independently from any underlying spatial grid and its resolution. A large number of Bayesian and Maximum Entropy methods for 1D signal reconstruction, 2D imaging, as well as 3D tomography, appear formally similar, but one often finds individualized implementations that are neither flexible nor easily transferable. Signal inference in the framework of NIFTy can be done in an abstract way, such that algorithms, prototyped in 1D, can be applied to real world problems in higher-dimensional settings. NIFTy as a versatile library is applicable and already has been applied in 1D, 2D, 3D and spherical settings. A recent application is the D3PO algorithm targeting the non-trivial task of denoising, deconvolving, and decomposing photon observations in high energy astronomy.

Dynamical Bayesian inference of time-evolving interactions: From a pair of coupled oscillators to networks of oscillators

NASA Astrophysics Data System (ADS)

Duggento, Andrea; Stankovski, Tomislav; McClintock, Peter V. E.; Stefanovska, Aneta

2012-12-01

Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.109.024101 109, 024101 (2012)] introduced a method based on dynamical Bayesian inference that facilitates the simultaneous detection of time-varying synchronization, directionality of influence, and coupling functions. It can distinguish unsynchronized dynamics from noise-induced phase slips. The method is based on phase dynamics, with Bayesian inference of the time-evolving parameters being achieved by shaping the prior densities to incorporate knowledge of previous samples. We now present the method in detail using numerically generated data, data from an analog electronic circuit, and cardiorespiratory data. We also generalize the method to encompass networks of interacting oscillators and thus demonstrate its applicability to small-scale networks.

Bayesian Cue Integration as a Developmental Outcome of Reward Mediated Learning

PubMed Central

Weisswange, Thomas H.; Rothkopf, Constantin A.; Rodemann, Tobias; Triesch, Jochen

2011-01-01

Average human behavior in cue combination tasks is well predicted by Bayesian inference models. As this capability is acquired over developmental timescales, the question arises, how it is learned. Here we investigated whether reward dependent learning, that is well established at the computational, behavioral, and neuronal levels, could contribute to this development. It is shown that a model free reinforcement learning algorithm can indeed learn to do cue integration, i.e. weight uncertain cues according to their respective reliabilities and even do so if reliabilities are changing. We also consider the case of causal inference where multimodal signals can originate from one or multiple separate objects and should not always be integrated. In this case, the learner is shown to develop a behavior that is closest to Bayesian model averaging. We conclude that reward mediated learning could be a driving force for the development of cue integration and causal inference. PMID:21750717

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.

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

Brewer, Brendon J.; Foreman-Mackey, Daniel; Hogg, David W., E-mail: bj.brewer@auckland.ac.nz

We present and implement a probabilistic (Bayesian) method for producing catalogs from images of stellar fields. The method is capable of inferring the number of sources N in the image and can also handle the challenges introduced by noise, overlapping sources, and an unknown point-spread function. The luminosity function of the stars can also be inferred, even when the precise luminosity of each star is uncertain, via the use of a hierarchical Bayesian model. The computational feasibility of the method is demonstrated on two simulated images with different numbers of stars. We find that our method successfully recovers the inputmore » parameter values along with principled uncertainties even when the field is crowded. We also compare our results with those obtained from the SExtractor software. While the two approaches largely agree about the fluxes of the bright stars, the Bayesian approach provides more accurate inferences about the faint stars and the number of stars, particularly in the crowded case.« less

Unraveling multiple changes in complex climate time series using Bayesian inference

NASA Astrophysics Data System (ADS)

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

2016-04-01

Change points in time series are perceived as heterogeneities in the statistical or dynamical characteristics of observations. Unraveling such transitions yields essential information for the understanding of the observed system. The precise detection and basic characterization of underlying changes is therefore of particular importance in environmental sciences. We present a kernel-based Bayesian inference approach to investigate direct as well as indirect climate observations for multiple generic transition events. In order to develop a diagnostic approach designed to capture a variety of natural processes, the basic statistical features of central tendency and dispersion are used to locally approximate a complex time series by a generic transition model. A Bayesian inversion approach is developed to robustly infer on the location and the generic patterns of such a transition. To systematically investigate time series for multiple changes occurring at different temporal scales, the Bayesian inversion is extended to a kernel-based inference approach. By introducing basic kernel measures, the kernel inference results are composed into a proxy probability to a posterior distribution of multiple transitions. Thus, based on a generic transition model a probability expression is derived that is capable to indicate multiple changes within a complex time series. We discuss the method's performance by investigating direct and indirect climate observations. The approach is applied to environmental time series (about 100 a), from the weather station in Tuscaloosa, Alabama, and confirms documented instrumentation changes. Moreover, the approach is used to investigate a set of complex terrigenous dust records from the ODP sites 659, 721/722 and 967 interpreted as climate indicators of the African region of the Plio-Pleistocene period (about 5 Ma). The detailed inference unravels multiple transitions underlying the indirect climate observations coinciding with established global climate events.

Bayesian Estimation of Small Effects in Exercise and Sports Science.

PubMed

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

2016-01-01

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

Rational hypocrisy: a Bayesian analysis based on informal argumentation and slippery slopes.

PubMed

Rai, Tage S; Holyoak, Keith J

2014-01-01

Moral hypocrisy is typically viewed as an ethical accusation: Someone is applying different moral standards to essentially identical cases, dishonestly claiming that one action is acceptable while otherwise equivalent actions are not. We suggest that in some instances the apparent logical inconsistency stems from different evaluations of a weak argument, rather than dishonesty per se. Extending Corner, Hahn, and Oaksford's (2006) analysis of slippery slope arguments, we develop a Bayesian framework in which accusations of hypocrisy depend on inferences of shared category membership between proposed actions and previous standards, based on prior probabilities that inform the strength of competing hypotheses. Across three experiments, we demonstrate that inferences of hypocrisy increase as perceptions of the likelihood of shared category membership between precedent cases and current cases increase, that these inferences follow established principles of category induction, and that the presence of self-serving motives increases inferences of hypocrisy independent of changes in the actions themselves. Taken together, these results demonstrate that Bayesian analyses of weak arguments may have implications for assessing moral reasoning. © 2014 Cognitive Science Society, Inc.

Application of Bayesian inference to the study of hierarchical organization in self-organized complex adaptive systems

NASA Astrophysics Data System (ADS)

Knuth, K. H.

2001-05-01

We consider the application of Bayesian inference to the study of self-organized structures in complex adaptive systems. In particular, we examine the distribution of elements, agents, or processes in systems dominated by hierarchical structure. We demonstrate that results obtained by Caianiello [1] on Hierarchical Modular Systems (HMS) can be found by applying Jaynes' Principle of Group Invariance [2] to a few key assumptions about our knowledge of hierarchical organization. Subsequent application of the Principle of Maximum Entropy allows inferences to be made about specific systems. The utility of the Bayesian method is considered by examining both successes and failures of the hierarchical model. We discuss how Caianiello's original statements suffer from the Mind Projection Fallacy [3] and we restate his assumptions thus widening the applicability of the HMS model. The relationship between inference and statistical physics, described by Jaynes [4], is reiterated with the expectation that this realization will aid the field of complex systems research by moving away from often inappropriate direct application of statistical mechanics to a more encompassing inferential methodology.

Improved inference in Bayesian segmentation using Monte Carlo sampling: application to hippocampal subfield volumetry.

PubMed

Iglesias, Juan Eugenio; Sabuncu, Mert Rory; Van Leemput, Koen

2013-10-01

Many segmentation algorithms in medical image analysis use Bayesian modeling to augment local image appearance with prior anatomical knowledge. Such methods often contain a large number of free parameters that are first estimated and then kept fixed during the actual segmentation process. However, a faithful Bayesian analysis would marginalize over such parameters, accounting for their uncertainty by considering all possible values they may take. Here we propose to incorporate this uncertainty into Bayesian segmentation methods in order to improve the inference process. In particular, we approximate the required marginalization over model parameters using computationally efficient Markov chain Monte Carlo techniques. We illustrate the proposed approach using a recently developed Bayesian method for the segmentation of hippocampal subfields in brain MRI scans, showing a significant improvement in an Alzheimer's disease classification task. As an additional benefit, the technique also allows one to compute informative "error bars" on the volume estimates of individual structures. Copyright © 2013 Elsevier B.V. All rights reserved.

Improved Inference in Bayesian Segmentation Using Monte Carlo Sampling: Application to Hippocampal Subfield Volumetry

PubMed Central

Iglesias, Juan Eugenio; Sabuncu, Mert Rory; Leemput, Koen Van

2013-01-01

Many segmentation algorithms in medical image analysis use Bayesian modeling to augment local image appearance with prior anatomical knowledge. Such methods often contain a large number of free parameters that are first estimated and then kept fixed during the actual segmentation process. However, a faithful Bayesian analysis would marginalize over such parameters, accounting for their uncertainty by considering all possible values they may take. Here we propose to incorporate this uncertainty into Bayesian segmentation methods in order to improve the inference process. In particular, we approximate the required marginalization over model parameters using computationally efficient Markov chain Monte Carlo techniques. We illustrate the proposed approach using a recently developed Bayesian method for the segmentation of hippocampal subfields in brain MRI scans, showing a significant improvement in an Alzheimer’s disease classification task. As an additional benefit, the technique also allows one to compute informative “error bars” on the volume estimates of individual structures. PMID:23773521

IMAGINE: Interstellar MAGnetic field INference Engine

NASA Astrophysics Data System (ADS)

Steininger, Theo

2018-03-01

IMAGINE (Interstellar MAGnetic field INference Engine) performs inference on generic parametric models of the Galaxy. The modular open source framework uses highly optimized tools and technology such as the MultiNest sampler (ascl:1109.006) and the information field theory framework NIFTy (ascl:1302.013) to create an instance of the Milky Way based on a set of parameters for physical observables, using Bayesian statistics to judge the mismatch between measured data and model prediction. The flexibility of the IMAGINE framework allows for simple refitting for newly available data sets and makes state-of-the-art Bayesian methods easily accessible particularly for random components of the Galactic magnetic field.

Estimating mountain basin-mean precipitation from streamflow using Bayesian inference

NASA Astrophysics Data System (ADS)

Henn, Brian; Clark, Martyn P.; Kavetski, Dmitri; Lundquist, Jessica D.

2015-10-01

Estimating basin-mean precipitation in complex terrain is difficult due to uncertainty in the topographical representativeness of precipitation gauges relative to the basin. To address this issue, we use Bayesian methodology coupled with a multimodel framework to infer basin-mean precipitation from streamflow observations, and we apply this approach to snow-dominated basins in the Sierra Nevada of California. Using streamflow observations, forcing data from lower-elevation stations, the Bayesian Total Error Analysis (BATEA) methodology and the Framework for Understanding Structural Errors (FUSE), we infer basin-mean precipitation, and compare it to basin-mean precipitation estimated using topographically informed interpolation from gauges (PRISM, the Parameter-elevation Regression on Independent Slopes Model). The BATEA-inferred spatial patterns of precipitation show agreement with PRISM in terms of the rank of basins from wet to dry but differ in absolute values. In some of the basins, these differences may reflect biases in PRISM, because some implied PRISM runoff ratios may be inconsistent with the regional climate. We also infer annual time series of basin precipitation using a two-step calibration approach. Assessment of the precision and robustness of the BATEA approach suggests that uncertainty in the BATEA-inferred precipitation is primarily related to uncertainties in hydrologic model structure. Despite these limitations, time series of inferred annual precipitation under different model and parameter assumptions are strongly correlated with one another, suggesting that this approach is capable of resolving year-to-year variability in basin-mean precipitation.

A formal model of interpersonal inference

PubMed Central

Moutoussis, Michael; Trujillo-Barreto, Nelson J.; El-Deredy, Wael; Dolan, Raymond J.; Friston, Karl J.

2014-01-01

Introduction: We propose that active Bayesian inference—a general framework for decision-making—can equally be applied to interpersonal exchanges. Social cognition, however, entails special challenges. We address these challenges through a novel formulation of a formal model and demonstrate its psychological significance. Method: We review relevant literature, especially with regards to interpersonal representations, formulate a mathematical model and present a simulation study. The model accommodates normative models from utility theory and places them within the broader setting of Bayesian inference. Crucially, we endow people's prior beliefs, into which utilities are absorbed, with preferences of self and others. The simulation illustrates the model's dynamics and furnishes elementary predictions of the theory. Results: (1) Because beliefs about self and others inform both the desirability and plausibility of outcomes, in this framework interpersonal representations become beliefs that have to be actively inferred. This inference, akin to “mentalizing” in the psychological literature, is based upon the outcomes of interpersonal exchanges. (2) We show how some well-known social-psychological phenomena (e.g., self-serving biases) can be explained in terms of active interpersonal inference. (3) Mentalizing naturally entails Bayesian updating of how people value social outcomes. Crucially this includes inference about one's own qualities and preferences. Conclusion: We inaugurate a Bayes optimal framework for modeling intersubject variability in mentalizing during interpersonal exchanges. Here, interpersonal representations are endowed with explicit functional and affective properties. We suggest the active inference framework lends itself to the study of psychiatric conditions where mentalizing is distorted. PMID:24723872

Comparative evaluation of reverse engineering gene regulatory networks with relevance networks, graphical gaussian models and bayesian networks.

PubMed

Werhli, Adriano V; Grzegorczyk, Marco; Husmeier, Dirk

2006-10-15

An important problem in systems biology is the inference of biochemical pathways and regulatory networks from postgenomic data. Various reverse engineering methods have been proposed in the literature, and it is important to understand their relative merits and shortcomings. In the present paper, we compare the accuracy of reconstructing gene regulatory networks with three different modelling and inference paradigms: (1) Relevance networks (RNs): pairwise association scores independent of the remaining network; (2) graphical Gaussian models (GGMs): undirected graphical models with constraint-based inference, and (3) Bayesian networks (BNs): directed graphical models with score-based inference. The evaluation is carried out on the Raf pathway, a cellular signalling network describing the interaction of 11 phosphorylated proteins and phospholipids in human immune system cells. We use both laboratory data from cytometry experiments as well as data simulated from the gold-standard network. We also compare passive observations with active interventions. On Gaussian observational data, BNs and GGMs were found to outperform RNs. The difference in performance was not significant for the non-linear simulated data and the cytoflow data, though. Also, we did not observe a significant difference between BNs and GGMs on observational data in general. However, for interventional data, BNs outperform GGMs and RNs, especially when taking the edge directions rather than just the skeletons of the graphs into account. This suggests that the higher computational costs of inference with BNs over GGMs and RNs are not justified when using only passive observations, but that active interventions in the form of gene knockouts and over-expressions are required to exploit the full potential of BNs. Data, software and supplementary material are available from http://www.bioss.sari.ac.uk/staff/adriano/research.html

Approximate Bayesian computation in large-scale structure: constraining the galaxy-halo connection

NASA Astrophysics Data System (ADS)

Hahn, ChangHoon; Vakili, Mohammadjavad; Walsh, Kilian; Hearin, Andrew P.; Hogg, David W.; Campbell, Duncan

2017-08-01

Standard approaches to Bayesian parameter inference in large-scale structure assume a Gaussian functional form (chi-squared form) for the likelihood. This assumption, in detail, cannot be correct. Likelihood free inferences such as approximate Bayesian computation (ABC) relax these restrictions and make inference possible without making any assumptions on the likelihood. Instead ABC relies on a forward generative model of the data and a metric for measuring the distance between the model and data. In this work, we demonstrate that ABC is feasible for LSS parameter inference by using it to constrain parameters of the halo occupation distribution (HOD) model for populating dark matter haloes with galaxies. Using specific implementation of ABC supplemented with population Monte Carlo importance sampling, a generative forward model using HOD and a distance metric based on galaxy number density, two-point correlation function and galaxy group multiplicity function, we constrain the HOD parameters of mock observation generated from selected 'true' HOD parameters. The parameter constraints we obtain from ABC are consistent with the 'true' HOD parameters, demonstrating that ABC can be reliably used for parameter inference in LSS. Furthermore, we compare our ABC constraints to constraints we obtain using a pseudo-likelihood function of Gaussian form with MCMC and find consistent HOD parameter constraints. Ultimately, our results suggest that ABC can and should be applied in parameter inference for LSS analyses.

Scale Mixture Models with Applications to Bayesian Inference

NASA Astrophysics Data System (ADS)

Qin, Zhaohui S.; Damien, Paul; Walker, Stephen

2003-11-01

Scale mixtures of uniform distributions are used to model non-normal data in time series and econometrics in a Bayesian framework. Heteroscedastic and skewed data models are also tackled using scale mixture of uniform distributions.

A quantum probability framework for human probabilistic inference.

PubMed

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

2017-09-01

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

Analogical and category-based inference: a theoretical integration with Bayesian causal models.

PubMed

Holyoak, Keith J; Lee, Hee Seung; Lu, Hongjing

2010-11-01

A fundamental issue for theories of human induction is to specify constraints on potential inferences. For inferences based on shared category membership, an analogy, and/or a relational schema, it appears that the basic goal of induction is to make accurate and goal-relevant inferences that are sensitive to uncertainty. People can use source information at various levels of abstraction (including both specific instances and more general categories), coupled with prior causal knowledge, to build a causal model for a target situation, which in turn constrains inferences about the target. We propose a computational theory in the framework of Bayesian inference and test its predictions (parameter-free for the cases we consider) in a series of experiments in which people were asked to assess the probabilities of various causal predictions and attributions about a target on the basis of source knowledge about generative and preventive causes. The theory proved successful in accounting for systematic patterns of judgments about interrelated types of causal inferences, including evidence that analogical inferences are partially dissociable from overall mapping quality.

Efficient Implementation of MrBayes on Multi-GPU

PubMed Central

Zhou, Jianfu; Liu, Xiaoguang; Wang, Gang

2013-01-01

MrBayes, using Metropolis-coupled Markov chain Monte Carlo (MCMCMC or (MC)3), is a popular program for Bayesian inference. As a leading method of using DNA data to infer phylogeny, the (MC)3 Bayesian algorithm and its improved and parallel versions are now not fast enough for biologists to analyze massive real-world DNA data. Recently, graphics processor unit (GPU) has shown its power as a coprocessor (or rather, an accelerator) in many fields. This article describes an efficient implementation a(MC)3 (aMCMCMC) for MrBayes (MC)3 on compute unified device architecture. By dynamically adjusting the task granularity to adapt to input data size and hardware configuration, it makes full use of GPU cores with different data sets. An adaptive method is also developed to split and combine DNA sequences to make full use of a large number of GPU cards. Furthermore, a new “node-by-node” task scheduling strategy is developed to improve concurrency, and several optimizing methods are used to reduce extra overhead. Experimental results show that a(MC)3 achieves up to 63× speedup over serial MrBayes on a single machine with one GPU card, and up to 170× speedup with four GPU cards, and up to 478× speedup with a 32-node GPU cluster. a(MC)3 is dramatically faster than all the previous (MC)3 algorithms and scales well to large GPU clusters. PMID:23493260

Efficient implementation of MrBayes on multi-GPU.

PubMed

Bao, Jie; Xia, Hongju; Zhou, Jianfu; Liu, Xiaoguang; Wang, Gang

2013-06-01

MrBayes, using Metropolis-coupled Markov chain Monte Carlo (MCMCMC or (MC)(3)), is a popular program for Bayesian inference. As a leading method of using DNA data to infer phylogeny, the (MC)(3) Bayesian algorithm and its improved and parallel versions are now not fast enough for biologists to analyze massive real-world DNA data. Recently, graphics processor unit (GPU) has shown its power as a coprocessor (or rather, an accelerator) in many fields. This article describes an efficient implementation a(MC)(3) (aMCMCMC) for MrBayes (MC)(3) on compute unified device architecture. By dynamically adjusting the task granularity to adapt to input data size and hardware configuration, it makes full use of GPU cores with different data sets. An adaptive method is also developed to split and combine DNA sequences to make full use of a large number of GPU cards. Furthermore, a new "node-by-node" task scheduling strategy is developed to improve concurrency, and several optimizing methods are used to reduce extra overhead. Experimental results show that a(MC)(3) achieves up to 63× speedup over serial MrBayes on a single machine with one GPU card, and up to 170× speedup with four GPU cards, and up to 478× speedup with a 32-node GPU cluster. a(MC)(3) is dramatically faster than all the previous (MC)(3) algorithms and scales well to large GPU clusters.

Python Environment for Bayesian Learning: Inferring the Structure of Bayesian Networks from Knowledge and Data

PubMed Central

Shah, Abhik; Woolf, Peter

2009-01-01

Summary In this paper, we introduce pebl, a Python library and application for learning Bayesian network structure from data and prior knowledge that provides features unmatched by alternative software packages: the ability to use interventional data, flexible specification of structural priors, modeling with hidden variables and exploitation of parallel processing. PMID:20161541

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

PubMed Central

Hafenbrädl, Sebastian; Hoffrage, Ulrich

2015-01-01

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

Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies

PubMed Central

2010-01-01

Background Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. Results Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. Conclusions Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data. PMID:21062443

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

PubMed Central

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

2017-01-01

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

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

PubMed

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

2017-06-07

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

A general framework for updating belief distributions.

PubMed

Bissiri, P G; Holmes, C C; Walker, S G

2016-11-01

We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the traditional likelihood function, which is recovered as a special case. Modern application areas make it increasingly challenging for Bayesians to attempt to model the true data-generating mechanism. For instance, when the object of interest is low dimensional, such as a mean or median, it is cumbersome to have to achieve this via a complete model for the whole data distribution. More importantly, there are settings where the parameter of interest does not directly index a family of density functions and thus the Bayesian approach to learning about such parameters is currently regarded as problematic. Our framework uses loss functions to connect information in the data to functionals of interest. The updating of beliefs then follows from a decision theoretic approach involving cumulative loss functions. Importantly, the procedure coincides with Bayesian updating when a true likelihood is known yet provides coherent subjective inference in much more general settings. Connections to other inference frameworks are highlighted.

Quantum Inference on Bayesian Networks

NASA Astrophysics Data System (ADS)

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

2014-03-01

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

A 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.

Probabilistic inference using linear Gaussian importance sampling for hybrid Bayesian networks

NASA Astrophysics Data System (ADS)

Sun, Wei; Chang, K. C.

2005-05-01

Probabilistic inference for Bayesian networks is in general NP-hard using either exact algorithms or approximate methods. However, for very complex networks, only the approximate methods such as stochastic sampling could be used to provide a solution given any time constraint. There are several simulation methods currently available. They include logic sampling (the first proposed stochastic method for Bayesian networks, the likelihood weighting algorithm) the most commonly used simulation method because of its simplicity and efficiency, the Markov blanket scoring method, and the importance sampling algorithm. In this paper, we first briefly review and compare these available simulation methods, then we propose an improved importance sampling algorithm called linear Gaussian importance sampling algorithm for general hybrid model (LGIS). LGIS is aimed for hybrid Bayesian networks consisting of both discrete and continuous random variables with arbitrary distributions. It uses linear function and Gaussian additive noise to approximate the true conditional probability distribution for continuous variable given both its parents and evidence in a Bayesian network. One of the most important features of the newly developed method is that it can adaptively learn the optimal important function from the previous samples. We test the inference performance of LGIS using a 16-node linear Gaussian model and a 6-node general hybrid model. The performance comparison with other well-known methods such as Junction tree (JT) and likelihood weighting (LW) shows that LGIS-GHM is very promising.

Bayesian Inference in Satellite Gravity Inversion

NASA Technical Reports Server (NTRS)

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

2005-01-01

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

Modeling the Perception of Audiovisual Distance: Bayesian Causal Inference and Other Models

PubMed Central

2016-01-01

Studies of audiovisual perception of distance are rare. Here, visual and auditory cue interactions in distance are tested against several multisensory models, including a modified causal inference model. In this causal inference model predictions of estimate distributions are included. In our study, the audiovisual perception of distance was overall better explained by Bayesian causal inference than by other traditional models, such as sensory dominance and mandatory integration, and no interaction. Causal inference resolved with probability matching yielded the best fit to the data. Finally, we propose that sensory weights can also be estimated from causal inference. The analysis of the sensory weights allows us to obtain windows within which there is an interaction between the audiovisual stimuli. We find that the visual stimulus always contributes by more than 80% to the perception of visual distance. The visual stimulus also contributes by more than 50% to the perception of auditory distance, but only within a mobile window of interaction, which ranges from 1 to 4 m. PMID:27959919

Bayesian Estimation and Inference Using Stochastic Electronics

PubMed Central

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

2016-01-01

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

Bayesian Estimation and Inference Using Stochastic Electronics.

PubMed

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

2016-01-01

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

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.

Analogical and Category-Based Inference: A Theoretical Integration with Bayesian Causal Models

ERIC Educational Resources Information Center

Holyoak, Keith J.; Lee, Hee Seung; Lu, Hongjing

2010-01-01

A fundamental issue for theories of human induction is to specify constraints on potential inferences. For inferences based on shared category membership, an analogy, and/or a relational schema, it appears that the basic goal of induction is to make accurate and goal-relevant inferences that are sensitive to uncertainty. People can use source…

Bayesian Approach to the Joint Inversion of Gravity and Magnetic Data, with Application to the Ismenius Area of Mars

NASA Technical Reports Server (NTRS)

Jewell, Jeffrey B.; Raymond, C.; Smrekar, S.; Millbury, C.

2004-01-01

This viewgraph presentation reviews a Bayesian approach to the inversion of gravity and magnetic data with specific application to the Ismenius Area of Mars. Many inverse problems encountered in geophysics and planetary science are well known to be non-unique (i.e. inversion of gravity the density structure of a body). In hopes of reducing the non-uniqueness of solutions, there has been interest in the joint analysis of data. An example is the joint inversion of gravity and magnetic data, with the assumption that the same physical anomalies generate both the observed magnetic and gravitational anomalies. In this talk, we formulate the joint analysis of different types of data in a Bayesian framework and apply the formalism to the inference of the density and remanent magnetization structure for a local region in the Ismenius area of Mars. The Bayesian approach allows prior information or constraints in the solutions to be incorporated in the inversion, with the "best" solutions those whose forward predictions most closely match the data while remaining consistent with assumed constraints. The application of this framework to the inversion of gravity and magnetic data on Mars reveals two typical challenges - the forward predictions of the data have a linear dependence on some of the quantities of interest, and non-linear dependence on others (termed the "linear" and "non-linear" variables, respectively). For observations with Gaussian noise, a Bayesian approach to inversion for "linear" variables reduces to a linear filtering problem, with an explicitly computable "error" matrix. However, for models whose forward predictions have non-linear dependencies, inference is no longer given by such a simple linear problem, and moreover, the uncertainty in the solution is no longer completely specified by a computable "error matrix". It is therefore important to develop methods for sampling from the full Bayesian posterior to provide a complete and statistically consistent picture of model uncertainty, and what has been learned from observations. We will discuss advanced numerical techniques, including Monte Carlo Markov

A Tutorial Introduction to Bayesian Models of Cognitive Development

ERIC Educational Resources Information Center

Perfors, Amy; Tenenbaum, Joshua B.; Griffiths, Thomas L.; Xu, Fei

2011-01-01

We present an introduction to Bayesian inference as it is used in probabilistic models of cognitive development. Our goal is to provide an intuitive and accessible guide to the "what", the "how", and the "why" of the Bayesian approach: what sorts of problems and data the framework is most relevant for, and how and why it may be useful for…

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

Bayesian analysis of non-homogeneous Markov chains: application to mental health data.

PubMed

Sung, Minje; Soyer, Refik; Nhan, Nguyen

2007-07-10

In this paper we present a formal treatment of non-homogeneous Markov chains by introducing a hierarchical Bayesian framework. Our work is motivated by the analysis of correlated categorical data which arise in assessment of psychiatric treatment programs. In our development, we introduce a Markovian structure to describe the non-homogeneity of transition patterns. In doing so, we introduce a logistic regression set-up for Markov chains and incorporate covariates in our model. We present a Bayesian model using Markov chain Monte Carlo methods and develop inference procedures to address issues encountered in the analyses of data from psychiatric treatment programs. Our model and inference procedures are implemented to some real data from a psychiatric treatment study. Copyright 2006 John Wiley & Sons, Ltd.

Moving in time: Bayesian causal inference explains movement coordination to auditory beats

PubMed Central

Elliott, Mark T.; Wing, Alan M.; Welchman, Andrew E.

2014-01-01

Many everyday skilled actions depend on moving in time with signals that are embedded in complex auditory streams (e.g. musical performance, dancing or simply holding a conversation). Such behaviour is apparently effortless; however, it is not known how humans combine auditory signals to support movement production and coordination. Here, we test how participants synchronize their movements when there are potentially conflicting auditory targets to guide their actions. Participants tapped their fingers in time with two simultaneously presented metronomes of equal tempo, but differing in phase and temporal regularity. Synchronization therefore depended on integrating the two timing cues into a single-event estimate or treating the cues as independent and thereby selecting one signal over the other. We show that a Bayesian inference process explains the situations in which participants choose to integrate or separate signals, and predicts motor timing errors. Simulations of this causal inference process demonstrate that this model provides a better description of the data than other plausible models. Our findings suggest that humans exploit a Bayesian inference process to control movement timing in situations where the origin of auditory signals needs to be resolved. PMID:24850915

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.

Convergence analysis of surrogate-based methods for Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Yan, Liang; Zhang, Yuan-Xiang

2017-12-01

The major challenges in the Bayesian inverse problems arise from the need for repeated evaluations of the forward model, as required by Markov chain Monte Carlo (MCMC) methods for posterior sampling. Many attempts at accelerating Bayesian inference have relied on surrogates for the forward model, typically constructed through repeated forward simulations that are performed in an offline phase. Although such approaches can be quite effective at reducing computation cost, there has been little analysis of the approximation on posterior inference. In this work, we prove error bounds on the Kullback-Leibler (KL) distance between the true posterior distribution and the approximation based on surrogate models. Our rigorous error analysis show that if the forward model approximation converges at certain rate in the prior-weighted L 2 norm, then the posterior distribution generated by the approximation converges to the true posterior at least two times faster in the KL sense. The error bound on the Hellinger distance is also provided. To provide concrete examples focusing on the use of the surrogate model based methods, we present an efficient technique for constructing stochastic surrogate models to accelerate the Bayesian inference approach. The Christoffel least squares algorithms, based on generalized polynomial chaos, are used to construct a polynomial approximation of the forward solution over the support of the prior distribution. The numerical strategy and the predicted convergence rates are then demonstrated on the nonlinear inverse problems, involving the inference of parameters appearing in partial differential equations.

Coestimation of recombination, substitution and molecular adaptation rates by approximate Bayesian computation.

PubMed

Lopes, J S; Arenas, M; Posada, D; Beaumont, M A

2014-03-01

The estimation of parameters in molecular evolution may be biased when some processes are not considered. For example, the estimation of selection at the molecular level using codon-substitution models can have an upward bias when recombination is ignored. Here we address the joint estimation of recombination, molecular adaptation and substitution rates from coding sequences using approximate Bayesian computation (ABC). We describe the implementation of a regression-based strategy for choosing subsets of summary statistics for coding data, and show that this approach can accurately infer recombination allowing for intracodon recombination breakpoints, molecular adaptation and codon substitution rates. We demonstrate that our ABC approach can outperform other analytical methods under a variety of evolutionary scenarios. We also show that although the choice of the codon-substitution model is important, our inferences are robust to a moderate degree of model misspecification. In addition, we demonstrate that our approach can accurately choose the evolutionary model that best fits the data, providing an alternative for when the use of full-likelihood methods is impracticable. Finally, we applied our ABC method to co-estimate recombination, substitution and molecular adaptation rates from 24 published human immunodeficiency virus 1 coding data sets.

Context-dependent decision-making: a simple Bayesian model

PubMed Central

Lloyd, Kevin; Leslie, David S.

2013-01-01

Many phenomena in animal learning can be explained by a context-learning process whereby an animal learns about different patterns of relationship between environmental variables. Differentiating between such environmental regimes or ‘contexts’ allows an animal to rapidly adapt its behaviour when context changes occur. The current work views animals as making sequential inferences about current context identity in a world assumed to be relatively stable but also capable of rapid switches to previously observed or entirely new contexts. We describe a novel decision-making model in which contexts are assumed to follow a Chinese restaurant process with inertia and full Bayesian inference is approximated by a sequential-sampling scheme in which only a single hypothesis about current context is maintained. Actions are selected via Thompson sampling, allowing uncertainty in parameters to drive exploration in a straightforward manner. The model is tested on simple two-alternative choice problems with switching reinforcement schedules and the results compared with rat behavioural data from a number of T-maze studies. The model successfully replicates a number of important behavioural effects: spontaneous recovery, the effect of partial reinforcement on extinction and reversal, the overtraining reversal effect, and serial reversal-learning effects. PMID:23427101

Context-dependent decision-making: a simple Bayesian model.

PubMed

Lloyd, Kevin; Leslie, David S

2013-05-06

Many phenomena in animal learning can be explained by a context-learning process whereby an animal learns about different patterns of relationship between environmental variables. Differentiating between such environmental regimes or 'contexts' allows an animal to rapidly adapt its behaviour when context changes occur. The current work views animals as making sequential inferences about current context identity in a world assumed to be relatively stable but also capable of rapid switches to previously observed or entirely new contexts. We describe a novel decision-making model in which contexts are assumed to follow a Chinese restaurant process with inertia and full Bayesian inference is approximated by a sequential-sampling scheme in which only a single hypothesis about current context is maintained. Actions are selected via Thompson sampling, allowing uncertainty in parameters to drive exploration in a straightforward manner. The model is tested on simple two-alternative choice problems with switching reinforcement schedules and the results compared with rat behavioural data from a number of T-maze studies. The model successfully replicates a number of important behavioural effects: spontaneous recovery, the effect of partial reinforcement on extinction and reversal, the overtraining reversal effect, and serial reversal-learning effects.

Semantic Likelihood Models for Bayesian Inference in Human-Robot Interaction

NASA Astrophysics Data System (ADS)

Sweet, Nicholas

Autonomous systems, particularly unmanned aerial systems (UAS), remain limited in au- tonomous capabilities largely due to a poor understanding of their environment. Current sensors simply do not match human perceptive capabilities, impeding progress towards full autonomy. Recent work has shown the value of humans as sources of information within a human-robot team; in target applications, communicating human-generated 'soft data' to autonomous systems enables higher levels of autonomy through large, efficient information gains. This requires development of a 'human sensor model' that allows soft data fusion through Bayesian inference to update the probabilistic belief representations maintained by autonomous systems. Current human sensor models that capture linguistic inputs as semantic information are limited in their ability to generalize likelihood functions for semantic statements: they may be learned from dense data; they do not exploit the contextual information embedded within groundings; and they often limit human input to restrictive and simplistic interfaces. This work provides mechanisms to synthesize human sensor models from constraints based on easily attainable a priori knowledge, develops compression techniques to capture information-dense semantics, and investigates the problem of capturing and fusing semantic information contained within unstructured natural language. A robotic experimental testbed is also developed to validate the above contributions.

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

ERIC Educational Resources Information Center

Mislevy, Robert J.; Gitomer, Drew H.

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

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.

Dynamic Bayesian wavelet transform: New methodology for extraction of repetitive transients

NASA Astrophysics Data System (ADS)

Wang, Dong; Tsui, Kwok-Leung

2017-05-01

Thanks to some recent research works, dynamic Bayesian wavelet transform as new methodology for extraction of repetitive transients is proposed in this short communication to reveal fault signatures hidden in rotating machine. The main idea of the dynamic Bayesian wavelet transform is to iteratively estimate posterior parameters of wavelet transform via artificial observations and dynamic Bayesian inference. First, a prior wavelet parameter distribution can be established by one of many fast detection algorithms, such as the fast kurtogram, the improved kurtogram, the enhanced kurtogram, the sparsogram, the infogram, continuous wavelet transform, discrete wavelet transform, wavelet packets, multiwavelets, empirical wavelet transform, empirical mode decomposition, local mean decomposition, etc.. Second, artificial observations can be constructed based on one of many metrics, such as kurtosis, the sparsity measurement, entropy, approximate entropy, the smoothness index, a synthesized criterion, etc., which are able to quantify repetitive transients. Finally, given artificial observations, the prior wavelet parameter distribution can be posteriorly updated over iterations by using dynamic Bayesian inference. More importantly, the proposed new methodology can be extended to establish the optimal parameters required by many other signal processing methods for extraction of repetitive transients.

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 truthing as experimental verification of C4ISR sensors

NASA Astrophysics Data System (ADS)

Jannson, Tomasz; Forrester, Thomas; Romanov, Volodymyr; Wang, Wenjian; Nielsen, Thomas; Kostrzewski, Andrew

2015-05-01

In this paper, the general methodology for experimental verification/validation of C4ISR and other sensors' performance, is presented, based on Bayesian inference, in general, and binary sensors, in particular. This methodology, called Bayesian Truthing, defines Performance Metrics for binary sensors in: physics, optics, electronics, medicine, law enforcement, C3ISR, QC, ATR (Automatic Target Recognition), terrorism related events, and many others. For Bayesian Truthing, the sensing medium itself is not what is truly important; it is how the decision process is affected.

Predicting the Future as Bayesian Inference: People Combine Prior Knowledge with Observations when Estimating Duration and Extent

ERIC Educational Resources Information Center

Griffiths, Thomas L.; Tenenbaum, Joshua B.

2011-01-01

Predicting the future is a basic problem that people have to solve every day and a component of planning, decision making, memory, and causal reasoning. In this article, we present 5 experiments testing a Bayesian model of predicting the duration or extent of phenomena from their current state. This Bayesian model indicates how people should…

Investigating different approaches to develop informative priors in hierarchical Bayesian safety performance functions.

PubMed

Yu, Rongjie; Abdel-Aty, Mohamed

2013-07-01

The Bayesian inference method has been frequently adopted to develop safety performance functions. One advantage of the Bayesian inference is that prior information for the independent variables can be included in the inference procedures. However, there are few studies that discussed how to formulate informative priors for the independent variables and evaluated the effects of incorporating informative priors in developing safety performance functions. This paper addresses this deficiency by introducing four approaches of developing informative priors for the independent variables based on historical data and expert experience. Merits of these informative priors have been tested along with two types of Bayesian hierarchical models (Poisson-gamma and Poisson-lognormal models). Deviance information criterion (DIC), R-square values, and coefficients of variance for the estimations were utilized as evaluation measures to select the best model(s). Comparison across the models indicated that the Poisson-gamma model is superior with a better model fit and it is much more robust with the informative priors. Moreover, the two-stage Bayesian updating informative priors provided the best goodness-of-fit and coefficient estimation accuracies. Furthermore, informative priors for the inverse dispersion parameter have also been introduced and tested. Different types of informative priors' effects on the model estimations and goodness-of-fit have been compared and concluded. Finally, based on the results, recommendations for future research topics and study applications have been made. Copyright © 2013 Elsevier Ltd. All rights reserved.

Bayesian networks improve causal environmental assessments for evidence-based policy

EPA Science Inventory

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 p...

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.

An inquiry into computer understanding

NASA Technical Reports Server (NTRS)

Cheeseman, Peter

1988-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2004-07-01

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

Data free inference with processed data products

DOE PAGES

Chowdhary, K.; Najm, H. N.

2014-07-12

Here, we consider the context of probabilistic inference of model parameters given error bars or confidence intervals on model output values, when the data is unavailable. We introduce a class of algorithms in a Bayesian framework, relying on maximum entropy arguments and approximate Bayesian computation methods, to generate consistent data with the given summary statistics. Once we obtain consistent data sets, we pool the respective posteriors, to arrive at a single, averaged density on the parameters. This approach allows us to perform accurate forward uncertainty propagation consistent with the reported statistics.

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

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.

Receptive Field Inference with Localized Priors

PubMed Central

Park, Mijung; Pillow, Jonathan W.

2011-01-01

The linear receptive field describes a mapping from sensory stimuli to a one-dimensional variable governing a neuron's spike response. However, traditional receptive field estimators such as the spike-triggered average converge slowly and often require large amounts of data. Bayesian methods seek to overcome this problem by biasing estimates towards solutions that are more likely a priori, typically those with small, smooth, or sparse coefficients. Here we introduce a novel Bayesian receptive field estimator designed to incorporate locality, a powerful form of prior information about receptive field structure. The key to our approach is a hierarchical receptive field model that flexibly adapts to localized structure in both spacetime and spatiotemporal frequency, using an inference method known as empirical Bayes. We refer to our method as automatic locality determination (ALD), and show that it can accurately recover various types of smooth, sparse, and localized receptive fields. We apply ALD to neural data from retinal ganglion cells and V1 simple cells, and find it achieves error rates several times lower than standard estimators. Thus, estimates of comparable accuracy can be achieved with substantially less data. Finally, we introduce a computationally efficient Markov Chain Monte Carlo (MCMC) algorithm for fully Bayesian inference under the ALD prior, yielding accurate Bayesian confidence intervals for small or noisy datasets. PMID:22046110

FBST for Cointegration Problems

NASA Astrophysics Data System (ADS)

Diniz, M.; Pereira, C. A. B.; Stern, J. M.

2008-11-01

In order to estimate causal relations, the time series econometrics has to be aware of spurious correlation, a problem first mentioned by Yule [21]. To solve the problem, one can work with differenced series or use multivariate models like VAR or VEC models. In this case, the analysed series are going to present a long run relation i.e. a cointegration relation. Even though the Bayesian literature about inference on VAR/VEC models is quite advanced, Bauwens et al. [2] highlight that "the topic of selecting the cointegrating rank has not yet given very useful and convincing results." This paper presents the Full Bayesian Significance Test applied to cointegration rank selection tests in multivariate (VAR/VEC) time series models and shows how to implement it using available in the literature and simulated data sets. A standard non-informative prior is assumed.

Bayesian coronal seismology

NASA Astrophysics Data System (ADS)

Arregui, Iñigo

2018-01-01

In contrast to the situation in a laboratory, the study of the solar atmosphere has to be pursued without direct access to the physical conditions of interest. Information is therefore incomplete and uncertain and inference methods need to be employed to diagnose the physical conditions and processes. One of such methods, solar atmospheric seismology, makes use of observed and theoretically predicted properties of waves to infer plasma and magnetic field properties. A recent development in solar atmospheric seismology consists in the use of inversion and model comparison methods based on Bayesian analysis. In this paper, the philosophy and methodology of Bayesian analysis are first explained. Then, we provide an account of what has been achieved so far from the application of these techniques to solar atmospheric seismology and a prospect of possible future extensions.

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

PubMed

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

2010-12-01

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

Fast model updating coupling Bayesian inference and PGD model reduction

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

GPU Computing in Bayesian Inference of Realized Stochastic Volatility Model

NASA Astrophysics Data System (ADS)

Takaishi, Tetsuya

2015-01-01

The realized stochastic volatility (RSV) model that utilizes the realized volatility as additional information has been proposed to infer volatility of financial time series. We consider the Bayesian inference of the RSV model by the Hybrid Monte Carlo (HMC) algorithm. The HMC algorithm can be parallelized and thus performed on the GPU for speedup. The GPU code is developed with CUDA Fortran. We compare the computational time in performing the HMC algorithm on GPU (GTX 760) and CPU (Intel i7-4770 3.4GHz) and find that the GPU can be up to 17 times faster than the CPU. We also code the program with OpenACC and find that appropriate coding can achieve the similar speedup with CUDA Fortran.

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

Semi-blind Bayesian inference of CMB map and power spectrum

NASA Astrophysics Data System (ADS)

Vansyngel, Flavien; Wandelt, Benjamin D.; Cardoso, Jean-François; Benabed, Karim

2016-04-01

We present a new blind formulation of the cosmic microwave background (CMB) inference problem. The approach relies on a phenomenological model of the multifrequency microwave sky without the need for physical models of the individual components. For all-sky and high resolution data, it unifies parts of the analysis that had previously been treated separately such as component separation and power spectrum inference. We describe an efficient sampling scheme that fully explores the component separation uncertainties on the inferred CMB products such as maps and/or power spectra. External information about individual components can be incorporated as a prior giving a flexible way to progressively and continuously introduce physical component separation from a maximally blind approach. We connect our Bayesian formalism to existing approaches such as Commander, spectral mismatch independent component analysis (SMICA), and internal linear combination (ILC), and discuss possible future extensions.

Bayesian Action–Perception Computational Model: Interaction of Production and Recognition of Cursive Letters

PubMed Central

Gilet, Estelle; Diard, Julien; Bessière, Pierre

2011-01-01

In this paper, we study the collaboration of perception and action representations involved in cursive letter recognition and production. We propose a mathematical formulation for the whole perception–action loop, based on probabilistic modeling and Bayesian inference, which we call the Bayesian Action–Perception (BAP) model. Being a model of both perception and action processes, the purpose of this model is to study the interaction of these processes. More precisely, the model includes a feedback loop from motor production, which implements an internal simulation of movement. Motor knowledge can therefore be involved during perception tasks. In this paper, we formally define the BAP model and show how it solves the following six varied cognitive tasks using Bayesian inference: i) letter recognition (purely sensory), ii) writer recognition, iii) letter production (with different effectors), iv) copying of trajectories, v) copying of letters, and vi) letter recognition (with internal simulation of movements). We present computer simulations of each of these cognitive tasks, and discuss experimental predictions and theoretical developments. PMID:21674043

Bayesian Population Genomic Inference of Crossing Over and Gene Conversion

PubMed Central

Padhukasahasram, Badri; Rannala, Bruce

2011-01-01

Meiotic recombination is a fundamental cellular mechanism in sexually reproducing organisms and its different forms, crossing over and gene conversion both play an important role in shaping genetic variation in populations. Here, we describe a coalescent-based full-likelihood Markov chain Monte Carlo (MCMC) method for jointly estimating the crossing-over, gene-conversion, and mean tract length parameters from population genomic data under a Bayesian framework. Although computationally more expensive than methods that use approximate likelihoods, the relative efficiency of our method is expected to be optimal in theory. Furthermore, it is also possible to obtain a posterior sample of genealogies for the data using this method. We first check the performance of the new method on simulated data and verify its correctness. We also extend the method for inference under models with variable gene-conversion and crossing-over rates and demonstrate its ability to identify recombination hotspots. Then, we apply the method to two empirical data sets that were sequenced in the telomeric regions of the X chromosome of Drosophila melanogaster. Our results indicate that gene conversion occurs more frequently than crossing over in the su-w and su-s gene sequences while the local rates of crossing over as inferred by our program are not low. The mean tract lengths for gene-conversion events are estimated to be ∼70 bp and 430 bp, respectively, for these data sets. Finally, we discuss ideas and optimizations for reducing the execution time of our algorithm. PMID:21840857

Non-Bayesian Optical Inference Machines

NASA Astrophysics Data System (ADS)

Kadar, Ivan; Eichmann, George

1987-01-01

In a recent paper, Eichmann and Caulfield) presented a preliminary exposition of optical learning machines suited for use in expert systems. In this paper, we extend the previous ideas by introducing learning as a means of reinforcement by information gathering and reasoning with uncertainty in a non-Bayesian framework2. More specifically, the non-Bayesian approach allows the representation of total ignorance (not knowing) as opposed to assuming equally likely prior distributions.

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 that have plagued previous theoretical movements.

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

La Russa, D

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

The anatomy of choice: dopamine and decision-making

PubMed Central

Friston, Karl; Schwartenbeck, Philipp; FitzGerald, Thomas; Moutoussis, Michael; Behrens, Timothy; Dolan, Raymond J.

2014-01-01

This paper considers goal-directed decision-making in terms of embodied or active inference. We associate bounded rationality with approximate Bayesian inference that optimizes a free energy bound on model evidence. Several constructs such as expected utility, exploration or novelty bonuses, softmax choice rules and optimism bias emerge as natural consequences of free energy minimization. Previous accounts of active inference have focused on predictive coding. In this paper, we consider variational Bayes as a scheme that the brain might use for approximate Bayesian inference. This scheme provides formal constraints on the computational anatomy of inference and action, which appear to be remarkably consistent with neuroanatomy. Active inference contextualizes optimal decision theory within embodied inference, where goals become prior beliefs. For example, expected utility theory emerges as a special case of free energy minimization, where the sensitivity or inverse temperature (associated with softmax functions and quantal response equilibria) has a unique and Bayes-optimal solution. Crucially, this sensitivity corresponds to the precision of beliefs about behaviour. The changes in precision during variational updates are remarkably reminiscent of empirical dopaminergic responses—and they may provide a new perspective on the role of dopamine in assimilating reward prediction errors to optimize decision-making. PMID:25267823

The anatomy of choice: dopamine and decision-making.

PubMed

Friston, Karl; Schwartenbeck, Philipp; FitzGerald, Thomas; Moutoussis, Michael; Behrens, Timothy; Dolan, Raymond J

2014-11-05

This paper considers goal-directed decision-making in terms of embodied or active inference. We associate bounded rationality with approximate Bayesian inference that optimizes a free energy bound on model evidence. Several constructs such as expected utility, exploration or novelty bonuses, softmax choice rules and optimism bias emerge as natural consequences of free energy minimization. Previous accounts of active inference have focused on predictive coding. In this paper, we consider variational Bayes as a scheme that the brain might use for approximate Bayesian inference. This scheme provides formal constraints on the computational anatomy of inference and action, which appear to be remarkably consistent with neuroanatomy. Active inference contextualizes optimal decision theory within embodied inference, where goals become prior beliefs. For example, expected utility theory emerges as a special case of free energy minimization, where the sensitivity or inverse temperature (associated with softmax functions and quantal response equilibria) has a unique and Bayes-optimal solution. Crucially, this sensitivity corresponds to the precision of beliefs about behaviour. The changes in precision during variational updates are remarkably reminiscent of empirical dopaminergic responses-and they may provide a new perspective on the role of dopamine in assimilating reward prediction errors to optimize decision-making.

Nonparametric Bayesian inference of the microcanonical stochastic block model

NASA Astrophysics Data System (ADS)

Peixoto, Tiago P.

2017-01-01

A principled approach to characterize the hidden modular structure of networks is to formulate generative models and then infer their parameters from data. When the desired structure is composed of modules or "communities," a suitable choice for this task is the stochastic block model (SBM), where nodes are divided into groups, and the placement of edges is conditioned on the group memberships. Here, we present a nonparametric Bayesian method to infer the modular structure of empirical networks, including the number of modules and their hierarchical organization. We focus on a microcanonical variant of the SBM, where the structure is imposed via hard constraints, i.e., the generated networks are not allowed to violate the patterns imposed by the model. We show how this simple model variation allows simultaneously for two important improvements over more traditional inference approaches: (1) deeper Bayesian hierarchies, with noninformative priors replaced by sequences of priors and hyperpriors, which not only remove limitations that seriously degrade the inference on large networks but also reveal structures at multiple scales; (2) a very efficient inference algorithm that scales well not only for networks with a large number of nodes and edges but also with an unlimited number of modules. We show also how this approach can be used to sample modular hierarchies from the posterior distribution, as well as to perform model selection. We discuss and analyze the differences between sampling from the posterior and simply finding the single parameter estimate that maximizes it. Furthermore, we expose a direct equivalence between our microcanonical approach and alternative derivations based on the canonical SBM.

Detailed phylogenetic analysis of primate T-lymphotropic virus type 1 (PTLV-1) sequences from orangutans (Pongo pygmaeus) reveals new insights into the evolutionary history of PTLV-1 in Asia.

PubMed

Reid, Michael J C; Switzer, William M; Schillaci, Michael A; Ragonnet-Cronin, Manon; Joanisse, Isabelle; Caminiti, Kyna; Lowenberger, Carl A; Galdikas, Birute Mary F; Sandstrom, Paul A; Brooks, James I

2016-09-01

While human T-lymphotropic virus type 1 (HTLV-1) originates from ancient cross-species transmission of simian T-lymphotropic virus type 1 (STLV-1) from infected nonhuman primates, much debate exists on whether the first HTLV-1 occurred in Africa, or in Asia during early human evolution and migration. This topic is complicated by a lack of representative Asian STLV-1 to infer PTLV-1 evolutionary histories. In this study we obtained new STLV-1 LTR and tax sequences from a wild-born Bornean orangutan (Pongo pygmaeus) and performed detailed phylogenetic analyses using both maximum likelihood and Bayesian inference of available Asian PTLV-1 and African STLV-1 sequences. Phylogenies, divergence dates and nucleotide substitution rates were co-inferred and compared using six different molecular clock calibrations in a Bayesian framework, including both archaeological and/or nucleotide substitution rate calibrations. We then combined our molecular results with paleobiogeographical and ecological data to infer the most likely evolutionary history of PTLV-1. Based on the preferred models our analyses robustly inferred an Asian source for PTLV-1 with cross-species transmission of STLV-1 likely from a macaque (Macaca sp.) to an orangutan about 37.9-48.9kya, and to humans between 20.3-25.5kya. An orangutan diversification of STLV-1 commenced approximately 6.4-7.3kya. Our analyses also inferred that HTLV-1 was first introduced into Australia ~3.1-3.7kya, corresponding to both genetic and archaeological changes occurring in Australia at that time. Finally, HTLV-1 appears in Melanesia at ~2.3-2.7kya corresponding to the migration of the Lapita peoples into the region. Our results also provide an important future reference for calibrating information essential for PTLV evolutionary timescale inference. Longer sequence data, or full genomes from a greater representation of Asian primates, including gibbons, leaf monkeys, and Sumatran orangutans are needed to fully elucidate these evolutionary dates and relationships using the model criteria suggested herein. Copyright © 2016 Elsevier B.V. All rights reserved.

A Bayesian method for detecting pairwise associations in compositional data

PubMed Central

Ventz, Steffen; Huttenhower, Curtis

2017-01-01

Compositional data consist of vectors of proportions normalized to a constant sum from a basis of unobserved counts. The sum constraint makes inference on correlations between unconstrained features challenging due to the information loss from normalization. However, such correlations are of long-standing interest in fields including ecology. We propose a novel Bayesian framework (BAnOCC: Bayesian Analysis of Compositional Covariance) to estimate a sparse precision matrix through a LASSO prior. The resulting posterior, generated by MCMC sampling, allows uncertainty quantification of any function of the precision matrix, including the correlation matrix. We also use a first-order Taylor expansion to approximate the transformation from the unobserved counts to the composition in order to investigate what characteristics of the unobserved counts can make the correlations more or less difficult to infer. On simulated datasets, we show that BAnOCC infers the true network as well as previous methods while offering the advantage of posterior inference. Larger and more realistic simulated datasets further showed that BAnOCC performs well as measured by type I and type II error rates. Finally, we apply BAnOCC to a microbial ecology dataset from the Human Microbiome Project, which in addition to reproducing established ecological results revealed unique, competition-based roles for Proteobacteria in multiple distinct habitats. PMID:29140991

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

Bayesian Semiparametric Structural Equation Models with Latent Variables

ERIC Educational Resources Information Center

Yang, Mingan; Dunson, David B.

2010-01-01

Structural equation models (SEMs) with latent variables are widely useful for sparse covariance structure modeling and for inferring relationships among latent variables. Bayesian SEMs are appealing in allowing for the incorporation of prior information and in providing exact posterior distributions of unknowns, including the latent variables. In…

A Bayesian network approach for causal inferences in pesticide risk assessment and management

EPA Science Inventory

Pesticide risk assessment and management must balance societal benefits and ecosystem protection, based on quantified risks and the strength of the causal linkages between uses of the pesticide and socioeconomic and ecological endpoints of concern. A Bayesian network (BN) is a gr...

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.

Confidence set inference with a prior quadratic bound

NASA Technical Reports Server (NTRS)

Backus, George E.

1989-01-01

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.

State Space Model with hidden variables for reconstruction of gene regulatory networks.

PubMed

Wu, Xi; Li, Peng; Wang, Nan; Gong, Ping; Perkins, Edward J; Deng, Youping; Zhang, Chaoyang

2011-01-01

State Space Model (SSM) is a relatively new approach to inferring gene regulatory networks. It requires less computational time than Dynamic Bayesian Networks (DBN). There are two types of variables in the linear SSM, observed variables and hidden variables. SSM uses an iterative method, namely Expectation-Maximization, to infer regulatory relationships from microarray datasets. The hidden variables cannot be directly observed from experiments. How to determine the number of hidden variables has a significant impact on the accuracy of network inference. In this study, we used SSM to infer Gene regulatory networks (GRNs) from synthetic time series datasets, investigated Bayesian Information Criterion (BIC) and Principle Component Analysis (PCA) approaches to determining the number of hidden variables in SSM, and evaluated the performance of SSM in comparison with DBN. True GRNs and synthetic gene expression datasets were generated using GeneNetWeaver. Both DBN and linear SSM were used to infer GRNs from the synthetic datasets. The inferred networks were compared with the true networks. Our results show that inference precision varied with the number of hidden variables. For some regulatory networks, the inference precision of DBN was higher but SSM performed better in other cases. Although the overall performance of the two approaches is compatible, SSM is much faster and capable of inferring much larger networks than DBN. This study provides useful information in handling the hidden variables and improving the inference precision.

Bayesian estimation of differential transcript usage from RNA-seq data.

PubMed

Papastamoulis, Panagiotis; Rattray, Magnus

2017-11-27

Next generation sequencing allows the identification of genes consisting of differentially expressed transcripts, a term which usually refers to changes in the overall expression level. A specific type of differential expression is differential transcript usage (DTU) and targets changes in the relative within gene expression of a transcript. The contribution of this paper is to: (a) extend the use of cjBitSeq to the DTU context, a previously introduced Bayesian model which is originally designed for identifying changes in overall expression levels and (b) propose a Bayesian version of DRIMSeq, a frequentist model for inferring DTU. cjBitSeq is a read based model and performs fully Bayesian inference by MCMC sampling on the space of latent state of each transcript per gene. BayesDRIMSeq is a count based model and estimates the Bayes Factor of a DTU model against a null model using Laplace's approximation. The proposed models are benchmarked against the existing ones using a recent independent simulation study as well as a real RNA-seq dataset. Our results suggest that the Bayesian methods exhibit similar performance with DRIMSeq in terms of precision/recall but offer better calibration of False Discovery Rate.

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

PubMed

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

2009-01-01

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

A Fast Surrogate-facilitated Data-driven Bayesian Approach to Uncertainty Quantification of a Regional Groundwater Flow Model with Structural Error

NASA Astrophysics Data System (ADS)

Xu, T.; Valocchi, A. J.; Ye, M.; Liang, F.

2016-12-01

Due to simplification and/or misrepresentation of the real aquifer system, numerical groundwater flow and solute transport models are usually subject to model structural error. During model calibration, the hydrogeological parameters may be overly adjusted to compensate for unknown structural error. This may result in biased predictions when models are used to forecast aquifer response to new forcing. In this study, we extend a fully Bayesian method [Xu and Valocchi, 2015] to calibrate a real-world, regional groundwater flow model. The method uses a data-driven error model to describe model structural error and jointly infers model parameters and structural error. In this study, Bayesian inference is facilitated using high performance computing and fast surrogate models. The surrogate models are constructed using machine learning techniques to emulate the response simulated by the computationally expensive groundwater model. We demonstrate in the real-world case study that explicitly accounting for model structural error yields parameter posterior distributions that are substantially different from those derived by the classical Bayesian calibration that does not account for model structural error. In addition, the Bayesian with error model method gives significantly more accurate prediction along with reasonable credible intervals.

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.

A measure of uncertainty regarding the interval constraint of normal mean elicited by two stages of a prior hierarchy.

PubMed

Kim, Hea-Jung

2014-01-01

This paper considers a hierarchical screened Gaussian model (HSGM) for Bayesian inference of normal models when an interval constraint in the mean parameter space needs to be incorporated in the modeling but when such a restriction is uncertain. An objective measure of the uncertainty, regarding the interval constraint, accounted for by using the HSGM is proposed for the Bayesian inference. For this purpose, we drive a maximum entropy prior of the normal mean, eliciting the uncertainty regarding the interval constraint, and then obtain the uncertainty measure by considering the relationship between the maximum entropy prior and the marginal prior of the normal mean in HSGM. Bayesian estimation procedure of HSGM is developed and two numerical illustrations pertaining to the properties of the uncertainty measure are provided.

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.

Diagnostics for insufficiencies of posterior calculations in Bayesian signal inference.

PubMed

Dorn, Sebastian; Oppermann, Niels; Ensslin, Torsten A

2013-11-01

We present an error-diagnostic validation method for posterior distributions in Bayesian signal inference, an advancement of a previous work. It transfers deviations from the correct posterior into characteristic deviations from a uniform distribution of a quantity constructed for this purpose. We show that this method is able to reveal and discriminate several kinds of numerical and approximation errors, as well as their impact on the posterior distribution. For this we present four typical analytical examples of posteriors with incorrect variance, skewness, position of the maximum, or normalization. We show further how this test can be applied to multidimensional signals.

Language Evolution by Iterated Learning with Bayesian Agents

ERIC Educational Resources Information Center

Griffiths, Thomas L.; Kalish, Michael L.

2007-01-01

Languages are transmitted from person to person and generation to generation via a process of iterated learning: people learn a language from other people who once learned that language themselves. We analyze the consequences of iterated learning for learning algorithms based on the principles of Bayesian inference, assuming that learners compute…

Bayesian Unimodal Density Regression for Causal Inference

ERIC Educational Resources Information Center

Karabatsos, George; Walker, Stephen G.

2011-01-01

Karabatsos and Walker (2011) introduced a new Bayesian nonparametric (BNP) regression model. Through analyses of real and simulated data, they showed that the BNP regression model outperforms other parametric and nonparametric regression models of common use, in terms of predictive accuracy of the outcome (dependent) variable. The other,…

Advances in computer simulation of genome evolution: toward more realistic evolutionary genomics analysis by approximate bayesian computation.

PubMed

Arenas, Miguel

2015-04-01

NGS technologies present a fast and cheap generation of genomic data. Nevertheless, ancestral genome inference is not so straightforward due to complex evolutionary processes acting on this material such as inversions, translocations, and other genome rearrangements that, in addition to their implicit complexity, can co-occur and confound ancestral inferences. Recently, models of genome evolution that accommodate such complex genomic events are emerging. This letter explores these novel evolutionary models and proposes their incorporation into robust statistical approaches based on computer simulations, such as approximate Bayesian computation, that may produce a more realistic evolutionary analysis of genomic data. Advantages and pitfalls in using these analytical methods are discussed. Potential applications of these ancestral genomic inferences are also pointed out.

The visual system’s internal model of the world

PubMed Central

Lee, Tai Sing

2015-01-01

The Bayesian paradigm has provided a useful conceptual theory for understanding perceptual computation in the brain. While the detailed neural mechanisms of Bayesian inference are not fully understood, recent computational and neurophysiological works have illuminated the underlying computational principles and representational architecture. The fundamental insights are that the visual system is organized as a modular hierarchy to encode an internal model of the world, and that perception is realized by statistical inference based on such internal model. In this paper, I will discuss and analyze the varieties of representational schemes of these internal models and how they might be used to perform learning and inference. I will argue for a unified theoretical framework for relating the internal models to the observed neural phenomena and mechanisms in the visual cortex. PMID:26566294

Neuronal integration of dynamic sources: Bayesian learning and Bayesian inference.

PubMed

Siegelmann, Hava T; Holzman, Lars E

2010-09-01

One of the brain's most basic functions is integrating sensory data from diverse sources. This ability causes us to question whether the neural system is computationally capable of intelligently integrating data, not only when sources have known, fixed relative dependencies but also when it must determine such relative weightings based on dynamic conditions, and then use these learned weightings to accurately infer information about the world. We suggest that the brain is, in fact, fully capable of computing this parallel task in a single network and describe a neural inspired circuit with this property. Our implementation suggests the possibility that evidence learning requires a more complex organization of the network than was previously assumed, where neurons have different specialties, whose emergence brings the desired adaptivity seen in human online inference.

A Computationally-Efficient Inverse Approach to Probabilistic Strain-Based Damage Diagnosis

NASA Technical Reports Server (NTRS)

Warner, James E.; Hochhalter, Jacob D.; Leser, William P.; Leser, Patrick E.; Newman, John A

2016-01-01

This work presents a computationally-efficient inverse approach to probabilistic damage diagnosis. Given strain data at a limited number of measurement locations, Bayesian inference and Markov Chain Monte Carlo (MCMC) sampling are used to estimate probability distributions of the unknown location, size, and orientation of damage. Substantial computational speedup is obtained by replacing a three-dimensional finite element (FE) model with an efficient surrogate model. The approach is experimentally validated on cracked test specimens where full field strains are determined using digital image correlation (DIC). Access to full field DIC data allows for testing of different hypothetical sensor arrangements, facilitating the study of strain-based diagnosis effectiveness as the distance between damage and measurement locations increases. The ability of the framework to effectively perform both probabilistic damage localization and characterization in cracked plates is demonstrated and the impact of measurement location on uncertainty in the predictions is shown. Furthermore, the analysis time to produce these predictions is orders of magnitude less than a baseline Bayesian approach with the FE method by utilizing surrogate modeling and effective numerical sampling approaches.

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

A dust spectral energy distribution model with hierarchical Bayesian inference - I. Formalism and benchmarking

NASA Astrophysics Data System (ADS)

Galliano, Frédéric

2018-05-01

This article presents a new dust spectral energy distribution (SED) model, named HerBIE, aimed at eliminating the noise-induced correlations and large scatter obtained when performing least-squares fits. The originality of this code is to apply the hierarchical Bayesian approach to full dust models, including realistic optical properties, stochastic heating, and the mixing of physical conditions in the observed regions. We test the performances of our model by applying it to synthetic observations. We explore the impact on the recovered parameters of several effects: signal-to-noise ratio, SED shape, sample size, the presence of intrinsic correlations, the wavelength coverage, and the use of different SED model components. We show that this method is very efficient: the recovered parameters are consistently distributed around their true values. We do not find any clear bias, even for the most degenerate parameters, or with extreme signal-to-noise ratios.

BiomeNet: A Bayesian Model for Inference of Metabolic Divergence among Microbial Communities

PubMed Central

Chipman, Hugh; Gu, Hong; Bielawski, Joseph P.

2014-01-01

Metagenomics yields enormous numbers of microbial sequences that can be assigned a metabolic function. Using such data to infer community-level metabolic divergence is hindered by the lack of a suitable statistical framework. Here, we describe a novel hierarchical Bayesian model, called BiomeNet (Bayesian inference of metabolic networks), for inferring differential prevalence of metabolic subnetworks among microbial communities. To infer the structure of community-level metabolic interactions, BiomeNet applies a mixed-membership modelling framework to enzyme abundance information. The basic idea is that the mixture components of the model (metabolic reactions, subnetworks, and networks) are shared across all groups (microbiome samples), but the mixture proportions vary from group to group. Through this framework, the model can capture nested structures within the data. BiomeNet is unique in modeling each metagenome sample as a mixture of complex metabolic systems (metabosystems). The metabosystems are composed of mixtures of tightly connected metabolic subnetworks. BiomeNet differs from other unsupervised methods by allowing researchers to discriminate groups of samples through the metabolic patterns it discovers in the data, and by providing a framework for interpreting them. We describe a collapsed Gibbs sampler for inference of the mixture weights under BiomeNet, and we use simulation to validate the inference algorithm. Application of BiomeNet to human gut metagenomes revealed a metabosystem with greater prevalence among inflammatory bowel disease (IBD) patients. Based on the discriminatory subnetworks for this metabosystem, we inferred that the community is likely to be closely associated with the human gut epithelium, resistant to dietary interventions, and interfere with human uptake of an antioxidant connected to IBD. Because this metabosystem has a greater capacity to exploit host-associated glycans, we speculate that IBD-associated communities might arise from opportunist growth of bacteria that can circumvent the host's nutrient-based mechanism for bacterial partner selection. PMID:25412107

Bayes in biological anthropology.

PubMed

Konigsberg, Lyle W; Frankenberg, Susan R

2013-12-01

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

Impact of Bayesian Priors on the Characterization of Binary Black Hole Coalescences

NASA Astrophysics Data System (ADS)

Vitale, Salvatore; Gerosa, Davide; Haster, Carl-Johan; Chatziioannou, Katerina; Zimmerman, Aaron

2017-12-01

In a regime where data are only mildly informative, prior choices can play a significant role in Bayesian statistical inference, potentially affecting the inferred physics. We show this is indeed the case for some of the parameters inferred from current gravitational-wave measurements of binary black hole coalescences. We reanalyze the first detections performed by the twin LIGO interferometers using alternative (and astrophysically motivated) prior assumptions. We find different prior distributions can introduce deviations in the resulting posteriors that impact the physical interpretation of these systems. For instance, (i) limits on the 90% credible interval on the effective black hole spin χeff are subject to variations of ˜10 % if a prior with black hole spins mostly aligned to the binary's angular momentum is considered instead of the standard choice of isotropic spin directions, and (ii) under priors motivated by the initial stellar mass function, we infer tighter constraints on the black hole masses, and in particular, we find no support for any of the inferred masses within the putative mass gap M ≲5 M⊙.

Impact of Bayesian Priors on the Characterization of Binary Black Hole Coalescences.

PubMed

Vitale, Salvatore; Gerosa, Davide; Haster, Carl-Johan; Chatziioannou, Katerina; Zimmerman, Aaron

2017-12-22

In a regime where data are only mildly informative, prior choices can play a significant role in Bayesian statistical inference, potentially affecting the inferred physics. We show this is indeed the case for some of the parameters inferred from current gravitational-wave measurements of binary black hole coalescences. We reanalyze the first detections performed by the twin LIGO interferometers using alternative (and astrophysically motivated) prior assumptions. We find different prior distributions can introduce deviations in the resulting posteriors that impact the physical interpretation of these systems. For instance, (i) limits on the 90% credible interval on the effective black hole spin χ_{eff} are subject to variations of ∼10% if a prior with black hole spins mostly aligned to the binary's angular momentum is considered instead of the standard choice of isotropic spin directions, and (ii) under priors motivated by the initial stellar mass function, we infer tighter constraints on the black hole masses, and in particular, we find no support for any of the inferred masses within the putative mass gap M≲5  M_{⊙}.

"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.

A Bayesian goodness of fit test and semiparametric generalization of logistic regression with measurement data.

PubMed

Schörgendorfer, Angela; Branscum, Adam J; Hanson, Timothy E

2013-06-01

Logistic regression is a popular tool for risk analysis in medical and population health science. With continuous response data, it is common to create a dichotomous outcome for logistic regression analysis by specifying a threshold for positivity. Fitting a linear regression to the nondichotomized response variable assuming a logistic sampling model for the data has been empirically shown to yield more efficient estimates of odds ratios than ordinary logistic regression of the dichotomized endpoint. We illustrate that risk inference is not robust to departures from the parametric logistic distribution. Moreover, the model assumption of proportional odds is generally not satisfied when the condition of a logistic distribution for the data is violated, leading to biased inference from a parametric logistic analysis. We develop novel Bayesian semiparametric methodology for testing goodness of fit of parametric logistic regression with continuous measurement data. The testing procedures hold for any cutoff threshold and our approach simultaneously provides the ability to perform semiparametric risk estimation. Bayes factors are calculated using the Savage-Dickey ratio for testing the null hypothesis of logistic regression versus a semiparametric generalization. We propose a fully Bayesian and a computationally efficient empirical Bayesian approach to testing, and we present methods for semiparametric estimation of risks, relative risks, and odds ratios when parametric logistic regression fails. Theoretical results establish the consistency of the empirical Bayes test. Results from simulated data show that the proposed approach provides accurate inference irrespective of whether parametric assumptions hold or not. Evaluation of risk factors for obesity shows that different inferences are derived from an analysis of a real data set when deviations from a logistic distribution are permissible in a flexible semiparametric framework. © 2013, The International Biometric Society.

Bayesian Inference for Source Term Estimation: Application to the International Monitoring System Radionuclide Network

DTIC Science & Technology

2014-10-01

de l’exactitude et de la précision), comparativement au modèle de mesure plus simple qui n’utilise pas de multiplicateurs. Importance pour la défense...3) Bayesian experimental design for receptor placement in order to maximize the expected information in the measured concen- tration data for...applications of the Bayesian inferential methodology for source recon- struction have used high-quality concentration data from well- designed atmospheric

[Bayesian statistics in medicine -- part II: main applications and inference].

PubMed

Montomoli, C; Nichelatti, M

2008-01-01

Bayesian statistics is not only used when one is dealing with 2-way tables, but it can be used for inferential purposes. Using the basic concepts presented in the first part, this paper aims to give a simple overview of Bayesian methods by introducing its foundation (Bayes' theorem) and then applying this rule to a very simple practical example; whenever possible, the elementary processes at the basis of analysis are compared to those of frequentist (classical) statistical analysis. The Bayesian reasoning is naturally connected to medical activity, since it appears to be quite similar to a diagnostic process.

Measuring Learning Progressions Using Bayesian Modeling in Complex Assessments

ERIC Educational Resources Information Center

Rutstein, Daisy Wise

2012-01-01

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

Predicting site locations for biomass using facilities with Bayesian methods

Treesearch

Timothy M. Young; James H. Perdue; Xia Huang

2017-01-01

Logistic regression models combined with Bayesian inference were developed to predict locations and quantify factors that influence the siting of biomass-using facilities that use woody biomass in the Southeastern United States. Predictions were developed for two groups of mills, one representing larger capacity mills similar to pulp and paper mills (Group II...

Pretense, Counterfactuals, and Bayesian Causal Models: Why What Is Not Real Really Matters

ERIC Educational Resources Information Center

Weisberg, Deena S.; Gopnik, Alison

2013-01-01

Young children spend a large portion of their time pretending about non-real situations. Why? We answer this question by using the framework of Bayesian causal models to argue that pretending and counterfactual reasoning engage the same component cognitive abilities: disengaging with current reality, making inferences about an alternative…

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…

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...

Bayesian Estimation of the Logistic Positive Exponent IRT Model

ERIC Educational Resources Information Center

Bolfarine, Heleno; Bazan, Jorge Luis

2010-01-01

A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric…

Enhanced optical alignment of a digital micro mirror device through Bayesian adaptive exploration

NASA Astrophysics Data System (ADS)

Wynne, Kevin B.; Knuth, Kevin H.; Petruccelli, Jonathan

2017-12-01

As the use of Digital Micro Mirror Devices (DMDs) becomes more prevalent in optics research, the ability to precisely locate the Fourier "footprint" of an image beam at the Fourier plane becomes a pressing need. In this approach, Bayesian adaptive exploration techniques were employed to characterize the size and position of the beam on a DMD located at the Fourier plane. It couples a Bayesian inference engine with an inquiry engine to implement the search. The inquiry engine explores the DMD by engaging mirrors and recording light intensity values based on the maximization of the expected information gain. Using the data collected from this exploration, the Bayesian inference engine updates the posterior probability describing the beam's characteristics. The process is iterated until the beam is located to within the desired precision. This methodology not only locates the center and radius of the beam with remarkable precision but accomplishes the task in far less time than a brute force search. The employed approach has applications to system alignment for both Fourier processing and coded aperture design.

Bayesian modelling of the emission spectrum of the Joint European Torus Lithium Beam Emission Spectroscopy system.

PubMed

Kwak, Sehyun; Svensson, J; Brix, M; Ghim, Y-C

2016-02-01

A Bayesian model of the emission spectrum of the JET lithium beam has been developed to infer the intensity of the Li I (2p-2s) line radiation and associated uncertainties. The detected spectrum for each channel of the lithium beam emission spectroscopy system is here modelled by a single Li line modified by an instrumental function, Bremsstrahlung background, instrumental offset, and interference filter curve. Both the instrumental function and the interference filter curve are modelled with non-parametric Gaussian processes. All free parameters of the model, the intensities of the Li line, Bremsstrahlung background, and instrumental offset, are inferred using Bayesian probability theory with a Gaussian likelihood for photon statistics and electronic background noise. The prior distributions of the free parameters are chosen as Gaussians. Given these assumptions, the intensity of the Li line and corresponding uncertainties are analytically available using a Bayesian linear inversion technique. The proposed approach makes it possible to extract the intensity of Li line without doing a separate background subtraction through modulation of the Li beam.

Encoding probabilistic brain atlases using Bayesian inference.

PubMed

Van Leemput, Koen

2009-06-01

This paper addresses the problem of creating probabilistic brain atlases from manually labeled training data. Probabilistic atlases are typically constructed by counting the relative frequency of occurrence of labels in corresponding locations across the training images. However, such an "averaging" approach generalizes poorly to unseen cases when the number of training images is limited, and provides no principled way of aligning the training datasets using deformable registration. In this paper, we generalize the generative image model implicitly underlying standard "average" atlases, using mesh-based representations endowed with an explicit deformation model. Bayesian inference is used to infer the optimal model parameters from the training data, leading to a simultaneous group-wise registration and atlas estimation scheme that encompasses standard averaging as a special case. We also use Bayesian inference to compare alternative atlas models in light of the training data, and show how this leads to a data compression problem that is intuitive to interpret and computationally feasible. Using this technique, we automatically determine the optimal amount of spatial blurring, the best deformation field flexibility, and the most compact mesh representation. We demonstrate, using 2-D training datasets, that the resulting models are better at capturing the structure in the training data than conventional probabilistic atlases. We also present experiments of the proposed atlas construction technique in 3-D, and show the resulting atlases' potential in fully-automated, pulse sequence-adaptive segmentation of 36 neuroanatomical structures in brain MRI scans.

Neglected chaos in international stock markets: Bayesian analysis of the joint return-volatility dynamical system

NASA Astrophysics Data System (ADS)

Tsionas, Mike G.; Michaelides, Panayotis G.

2017-09-01

We use a novel Bayesian inference procedure for the Lyapunov exponent in the dynamical system of returns and their unobserved volatility. In the dynamical system, computation of largest Lyapunov exponent by traditional methods is impossible as the stochastic nature has to be taken explicitly into account due to unobserved volatility. We apply the new techniques to daily stock return data for a group of six countries, namely USA, UK, Switzerland, Netherlands, Germany and France, from 2003 to 2014, by means of Sequential Monte Carlo for Bayesian inference. The evidence points to the direction that there is indeed noisy chaos both before and after the recent financial crisis. However, when a much simpler model is examined where the interaction between returns and volatility is not taken into consideration jointly, the hypothesis of chaotic dynamics does not receive much support by the data ("neglected chaos").

Nonparametric Bayesian Segmentation of a Multivariate Inhomogeneous Space-Time Poisson Process.

PubMed

Ding, Mingtao; He, Lihan; Dunson, David; Carin, Lawrence

2012-12-01

A nonparametric Bayesian model is proposed for segmenting time-evolving multivariate spatial point process data. An inhomogeneous Poisson process is assumed, with a logistic stick-breaking process (LSBP) used to encourage piecewise-constant spatial Poisson intensities. The LSBP explicitly favors spatially contiguous segments, and infers the number of segments based on the observed data. The temporal dynamics of the segmentation and of the Poisson intensities are modeled with exponential correlation in time, implemented in the form of a first-order autoregressive model for uniformly sampled discrete data, and via a Gaussian process with an exponential kernel for general temporal sampling. We consider and compare two different inference techniques: a Markov chain Monte Carlo sampler, which has relatively high computational complexity; and an approximate and efficient variational Bayesian analysis. The model is demonstrated with a simulated example and a real example of space-time crime events in Cincinnati, Ohio, USA.

F-MAP: A Bayesian approach to infer the gene regulatory network using external hints

PubMed Central

Shahdoust, Maryam; Mahjub, Hossein; Sadeghi, Mehdi

2017-01-01

The Common topological features of related species gene regulatory networks suggest reconstruction of the network of one species by using the further information from gene expressions profile of related species. We present an algorithm to reconstruct the gene regulatory network named; F-MAP, which applies the knowledge about gene interactions from related species. Our algorithm sets a Bayesian framework to estimate the precision matrix of one species microarray gene expressions dataset to infer the Gaussian Graphical model of the network. The conjugate Wishart prior is used and the information from related species is applied to estimate the hyperparameters of the prior distribution by using the factor analysis. Applying the proposed algorithm on six related species of drosophila shows that the precision of reconstructed networks is improved considerably compared to the precision of networks constructed by other Bayesian approaches. PMID:28938012

When Absence of Evidence Is Evidence of Absence: Rational Inferences From Absent Data.

PubMed

Hsu, Anne S; Horng, Andy; Griffiths, Thomas L; Chater, Nick

2017-05-01

Identifying patterns in the world requires noticing not only unusual occurrences, but also unusual absences. We examined how people learn from absences, manipulating the extent to which an absence is expected. People can make two types of inferences from the absence of an event: either the event is possible but has not yet occurred, or the event never occurs. A rational analysis using Bayesian inference predicts that inferences from absent data should depend on how much the absence is expected to occur, with less probable absences being more salient. We tested this prediction in two experiments in which we elicited people's judgments about patterns in the data as a function of absence salience. We found that people were able to decide that absences either were mere coincidences or were indicative of a significant pattern in the data in a manner that was consistent with predictions of a simple Bayesian model. Copyright © 2016 Cognitive Science Society, Inc.

MultiNest: Efficient and Robust Bayesian Inference

NASA Astrophysics Data System (ADS)

Feroz, F.; Hobson, M. P.; Bridges, M.

2011-09-01

We present further development and the first public release of our multimodal nested sampling algorithm, called MultiNest. This Bayesian inference tool calculates the evidence, with an associated error estimate, and produces posterior samples from distributions that may contain multiple modes and pronounced (curving) degeneracies in high dimensions. The developments presented here lead to further substantial improvements in sampling efficiency and robustness, as compared to the original algorithm presented in Feroz & Hobson (2008), which itself significantly outperformed existing MCMC techniques in a wide range of astrophysical inference problems. The accuracy and economy of the MultiNest algorithm is demonstrated by application to two toy problems and to a cosmological inference problem focusing on the extension of the vanilla LambdaCDM model to include spatial curvature and a varying equation of state for dark energy. The MultiNest software is fully parallelized using MPI and includes an interface to CosmoMC. It will also be released as part of the SuperBayeS package, for the analysis of supersymmetric theories of particle physics, at this http URL.

Sequential inference as a mode of cognition and its correlates in fronto-parietal and hippocampal brain regions

PubMed Central

Friston, Karl J.; Dolan, Raymond J.

2017-01-01

Normative models of human cognition often appeal to Bayesian filtering, which provides optimal online estimates of unknown or hidden states of the world, based on previous observations. However, in many cases it is necessary to optimise beliefs about sequences of states rather than just the current state. Importantly, Bayesian filtering and sequential inference strategies make different predictions about beliefs and subsequent choices, rendering them behaviourally dissociable. Taking data from a probabilistic reversal task we show that subjects’ choices provide strong evidence that they are representing short sequences of states. Between-subject measures of this implicit sequential inference strategy had a neurobiological underpinning and correlated with grey matter density in prefrontal and parietal cortex, as well as the hippocampus. Our findings provide, to our knowledge, the first evidence for sequential inference in human cognition, and by exploiting between-subject variation in this measure we provide pointers to its neuronal substrates. PMID:28486504

The Universe Is Reionizing at z ∼ 7: Bayesian Inference of the IGM Neutral Fraction Using Lyα Emission from Galaxies

NASA Astrophysics Data System (ADS)

Mason, Charlotte A.; Treu, Tommaso; Dijkstra, Mark; Mesinger, Andrei; Trenti, Michele; Pentericci, Laura; de Barros, Stephane; Vanzella, Eros

2018-03-01

We present a new flexible Bayesian framework for directly inferring the fraction of neutral hydrogen in the intergalactic medium (IGM) during the Epoch of Reionization (EoR, z ∼ 6–10) from detections and non-detections of Lyman Alpha (Lyα) emission from Lyman Break galaxies (LBGs). Our framework combines sophisticated reionization simulations with empirical models of the interstellar medium (ISM) radiative transfer effects on Lyα. We assert that the Lyα line profile emerging from the ISM has an important impact on the resulting transmission of photons through the IGM, and that these line profiles depend on galaxy properties. We model this effect by considering the peak velocity offset of Lyα lines from host galaxies’ systemic redshifts, which are empirically correlated with UV luminosity and redshift (or halo mass at fixed redshift). We use our framework on the sample of LBGs presented in Pentericci et al. and infer a global neutral fraction at z ∼ 7 of {\\overline{x}}{{H}{{I}}}={0.59}-0.15+0.11, consistent with other robust probes of the EoR and confirming that reionization is ongoing ∼700 Myr after the Big Bang. We show that using the full distribution of Lyα equivalent width detections and upper limits from LBGs places tighter constraints on the evolving IGM than the standard Lyα emitter fraction, and that larger samples are within reach of deep spectroscopic surveys of gravitationally lensed fields and James Webb Space Telescope NIRSpec.

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.

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

NASA Astrophysics Data System (ADS)

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

2013-03-01

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

Joint Bayesian inference for near-surface explosion yield

NASA Astrophysics Data System (ADS)

Bulaevskaya, V.; Ford, S. R.; Ramirez, A. L.; Rodgers, A. J.

2016-12-01

A near-surface explosion generates seismo-acoustic motion that is related to its yield. However, the recorded motion is affected by near-source effects such as depth-of-burial, and propagation-path effects such as variable geology. We incorporate these effects in a forward model relating yield to seismo-acoustic motion, and use Bayesian inference to estimate yield given recordings of the seismo-acoustic wavefield. The Bayesian approach to this inverse problem allows us to obtain the probability distribution of plausible yield values and thus quantify the uncertainty in the yield estimate. Moreover, the sensitivity of the acoustic signal falls as a function of the depth-of-burial, while the opposite relationship holds for the seismic signal. Therefore, using both the acoustic and seismic wavefield data allows us to avoid the trade-offs associated with using only one of these signals alone. In addition, our inference framework allows for correlated features of the same data type (seismic or acoustic) to be incorporated in the estimation of yield in order to make use of as much information from the same waveform as possible. We demonstrate our approach with a historical dataset and a contemporary field experiment.

Mobile sensing of point-source fugitive methane emissions using Bayesian inference: the determination of the likelihood function

NASA Astrophysics Data System (ADS)

Zhou, X.; Albertson, J. D.

2016-12-01

Natural gas is considered as a bridge fuel towards clean energy due to its potential lower greenhouse gas emission comparing with other fossil fuels. Despite numerous efforts, an efficient and cost-effective approach to monitor fugitive methane emissions along the natural gas production-supply chain has not been developed yet. Recently, mobile methane measurement has been introduced which applies a Bayesian approach to probabilistically infer methane emission rates and update estimates recursively when new measurements become available. However, the likelihood function, especially the error term which determines the shape of the estimate uncertainty, is not rigorously defined and evaluated with field data. To address this issue, we performed a series of near-source (< 30 m) controlled methane release experiments using a specialized vehicle mounted with fast response methane analyzers and a GPS unit. Methane concentrations were measured at two different heights along mobile traversals downwind of the sources, and concurrent wind and temperature data are recorded by nearby 3-D sonic anemometers. With known methane release rates, the measurements were used to determine the functional form and the parameterization of the likelihood function in the Bayesian inference scheme under different meteorological conditions.

SIG-VISA: Signal-based Vertically Integrated Seismic Monitoring

NASA Astrophysics Data System (ADS)

Moore, D.; Mayeda, K. M.; Myers, S. C.; Russell, S.

2013-12-01

Traditional seismic monitoring systems rely on discrete detections produced by station processing software; however, while such detections may constitute a useful summary of station activity, they discard large amounts of information present in the original recorded signal. We present SIG-VISA (Signal-based Vertically Integrated Seismic Analysis), a system for seismic monitoring through Bayesian inference on seismic signals. By directly modeling the recorded signal, our approach incorporates additional information unavailable to detection-based methods, enabling higher sensitivity and more accurate localization using techniques such as waveform matching. SIG-VISA's Bayesian forward model of seismic signal envelopes includes physically-derived models of travel times and source characteristics as well as Gaussian process (kriging) statistical models of signal properties that combine interpolation of historical data with extrapolation of learned physical trends. Applying Bayesian inference, we evaluate the model on earthquakes as well as the 2009 DPRK test event, demonstrating a waveform matching effect as part of the probabilistic inference, along with results on event localization and sensitivity. In particular, we demonstrate increased sensitivity from signal-based modeling, in which the SIGVISA signal model finds statistical evidence for arrivals even at stations for which the IMS station processing failed to register any detection.

Bayesian Inference for Generalized Linear Models for Spiking Neurons

PubMed Central

Gerwinn, Sebastian; Macke, Jakob H.; Bethge, Matthias

2010-01-01

Generalized Linear Models (GLMs) are commonly used statistical methods for modelling the relationship between neural population activity and presented stimuli. When the dimension of the parameter space is large, strong regularization has to be used in order to fit GLMs to datasets of realistic size without overfitting. By imposing properly chosen priors over parameters, Bayesian inference provides an effective and principled approach for achieving regularization. Here we show how the posterior distribution over model parameters of GLMs can be approximated by a Gaussian using the Expectation Propagation algorithm. In this way, we obtain an estimate of the posterior mean and posterior covariance, allowing us to calculate Bayesian confidence intervals that characterize the uncertainty about the optimal solution. From the posterior we also obtain a different point estimate, namely the posterior mean as opposed to the commonly used maximum a posteriori estimate. We systematically compare the different inference techniques on simulated as well as on multi-electrode recordings of retinal ganglion cells, and explore the effects of the chosen prior and the performance measure used. We find that good performance can be achieved by choosing an Laplace prior together with the posterior mean estimate. PMID:20577627

Bayesian reconstruction of transmission within outbreaks using genomic variants.

PubMed

De Maio, Nicola; Worby, Colin J; Wilson, Daniel J; Stoesser, Nicole

2018-04-01

Pathogen genome sequencing can reveal details of transmission histories and is a powerful tool in the fight against infectious disease. In particular, within-host pathogen genomic variants identified through heterozygous nucleotide base calls are a potential source of information to identify linked cases and infer direction and time of transmission. However, using such data effectively to model disease transmission presents a number of challenges, including differentiating genuine variants from those observed due to sequencing error, as well as the specification of a realistic model for within-host pathogen population dynamics. Here we propose a new Bayesian approach to transmission inference, BadTrIP (BAyesian epiDemiological TRansmission Inference from Polymorphisms), that explicitly models evolution of pathogen populations in an outbreak, transmission (including transmission bottlenecks), and sequencing error. BadTrIP enables the inference of host-to-host transmission from pathogen sequencing data and epidemiological data. By assuming that genomic variants are unlinked, our method does not require the computationally intensive and unreliable reconstruction of individual haplotypes. Using simulations we show that BadTrIP is robust in most scenarios and can accurately infer transmission events by efficiently combining information from genetic and epidemiological sources; thanks to its realistic model of pathogen evolution and the inclusion of epidemiological data, BadTrIP is also more accurate than existing approaches. BadTrIP is distributed as an open source package (https://bitbucket.org/nicofmay/badtrip) for the phylogenetic software BEAST2. We apply our method to reconstruct transmission history at the early stages of the 2014 Ebola outbreak, showcasing the power of within-host genomic variants to reconstruct transmission events.

Inferring gene and protein interactions using PubMed citations and consensus Bayesian networks.

PubMed

Deeter, Anthony; Dalman, Mark; Haddad, Joseph; Duan, Zhong-Hui

2017-01-01

The PubMed database offers an extensive set of publication data that can be useful, yet inherently complex to use without automated computational techniques. Data repositories such as the Genomic Data Commons (GDC) and the Gene Expression Omnibus (GEO) offer experimental data storage and retrieval as well as curated gene expression profiles. Genetic interaction databases, including Reactome and Ingenuity Pathway Analysis, offer pathway and experiment data analysis using data curated from these publications and data repositories. We have created a method to generate and analyze consensus networks, inferring potential gene interactions, using large numbers of Bayesian networks generated by data mining publications in the PubMed database. Through the concept of network resolution, these consensus networks can be tailored to represent possible genetic interactions. We designed a set of experiments to confirm that our method is stable across variation in both sample and topological input sizes. Using gene product interactions from the KEGG pathway database and data mining PubMed publication abstracts, we verify that regardless of the network resolution or the inferred consensus network, our method is capable of inferring meaningful gene interactions through consensus Bayesian network generation with multiple, randomized topological orderings. Our method can not only confirm the existence of currently accepted interactions, but has the potential to hypothesize new ones as well. We show our method confirms the existence of known gene interactions such as JAK-STAT-PI3K-AKT-mTOR, infers novel gene interactions such as RAS- Bcl-2 and RAS-AKT, and found significant pathway-pathway interactions between the JAK-STAT signaling and Cardiac Muscle Contraction KEGG pathways.

Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach

NASA Technical Reports Server (NTRS)

Warner, James E.; Hochhalter, Jacob D.

2016-01-01

This work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches.

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…

Evaluating Bayesian spatial methods for modelling species distributions with clumped and restricted occurrence data.

PubMed

Redding, David W; Lucas, Tim C D; Blackburn, Tim M; Jones, Kate E

2017-01-01

Statistical approaches for inferring the spatial distribution of taxa (Species Distribution Models, SDMs) commonly rely on available occurrence data, which is often clumped and geographically restricted. Although available SDM methods address some of these factors, they could be more directly and accurately modelled using a spatially-explicit approach. Software to fit models with spatial autocorrelation parameters in SDMs are now widely available, but whether such approaches for inferring SDMs aid predictions compared to other methodologies is unknown. Here, within a simulated environment using 1000 generated species' ranges, we compared the performance of two commonly used non-spatial SDM methods (Maximum Entropy Modelling, MAXENT and boosted regression trees, BRT), to a spatial Bayesian SDM method (fitted using R-INLA), when the underlying data exhibit varying combinations of clumping and geographic restriction. Finally, we tested how any recommended methodological settings designed to account for spatially non-random patterns in the data impact inference. Spatial Bayesian SDM method was the most consistently accurate method, being in the top 2 most accurate methods in 7 out of 8 data sampling scenarios. Within high-coverage sample datasets, all methods performed fairly similarly. When sampling points were randomly spread, BRT had a 1-3% greater accuracy over the other methods and when samples were clumped, the spatial Bayesian SDM method had a 4%-8% better AUC score. Alternatively, when sampling points were restricted to a small section of the true range all methods were on average 10-12% less accurate, with greater variation among the methods. Model inference under the recommended settings to account for autocorrelation was not impacted by clumping or restriction of data, except for the complexity of the spatial regression term in the spatial Bayesian model. Methods, such as those made available by R-INLA, can be successfully used to account for spatial autocorrelation in an SDM context and, by taking account of random effects, produce outputs that can better elucidate the role of covariates in predicting species occurrence. Given that it is often unclear what the drivers are behind data clumping in an empirical occurrence dataset, or indeed how geographically restricted these data are, spatially-explicit Bayesian SDMs may be the better choice when modelling the spatial distribution of target species.

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

ERIC Educational Resources Information Center

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

2017-01-01

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

Bayesian Inference for Growth Mixture Models with Latent Class Dependent Missing Data

ERIC Educational Resources Information Center

Lu, Zhenqiu Laura; Zhang, Zhiyong; Lubke, Gitta

2011-01-01

"Growth mixture models" (GMMs) with nonignorable missing data have drawn increasing attention in research communities but have not been fully studied. The goal of this article is to propose and to evaluate a Bayesian method to estimate the GMMs with latent class dependent missing data. An extended GMM is first presented in which class…

Brief Report: Suboptimal Auditory Localization in Autism Spectrum Disorder--Support for the Bayesian Account of Sensory Symptoms

ERIC Educational Resources Information Center

Skewes, Joshua C.; Gebauer, Line

2016-01-01

Convergent research suggests that people with ASD have difficulties localizing sounds in space. These difficulties have implications for communication, the development of social behavior, and quality of life. Recently, a theory has emerged which treats perceptual symptoms in ASD as the product of impairments in implicit Bayesian inference; as…

On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization

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

Konomi, Bledar A.; Karagiannis, Georgios; Lin, Guang

2015-02-01

The Bayesian treed Gaussian process (BTGP) has gained popularity in recent years because it provides a straightforward mechanism for modeling non-stationary data and can alleviate computational demands by fitting models to less data. The extension of BTGP to the multivariate setting requires us to model the cross-covariance and to propose efficient algorithms that can deal with trans-dimensional MCMC moves. In this paper we extend the cross-covariance of the Bayesian treed multivariate Gaussian process (BTMGP) to that of linear model of Coregionalization (LMC) cross-covariances. Different strategies have been developed to improve the MCMC mixing and invert smaller matrices in the Bayesianmore » inference. Moreover, we compare the proposed BTMGP with existing multiple BTGP and BTMGP in test cases and multiphase flow computer experiment in a full scale regenerator of a carbon capture unit. The use of the BTMGP with LMC cross-covariance helped to predict the computer experiments relatively better than existing competitors. The proposed model has a wide variety of applications, such as computer experiments and environmental data. In the case of computer experiments we also develop an adaptive sampling strategy for the BTMGP with LMC cross-covariance function.« less

Why environmental scientists are becoming Bayesians

Treesearch

James S. Clark

2005-01-01

Advances in computational statistics provide a general framework for the high dimensional models typically needed for ecological inference and prediction. Hierarchical Bayes (HB) represents a modelling structure with capacity to exploit diverse sources of information, to accommodate influences that are unknown (or unknowable), and to draw inference on large numbers of...

Data Analysis Techniques for Physical Scientists

NASA Astrophysics Data System (ADS)

Pruneau, Claude A.

2017-10-01

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

Quantification of uncertainty in photon source spot size inference during laser-driven radiography experiments at TRIDENT

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

Tobias, Benjamin John; Palaniyappan, Sasikumar; Gautier, Donald Cort

Images of the R2DTO resolution target were obtained during laser-driven-radiography experiments performed at the TRIDENT laser facility, and analysis of these images using the Bayesian Inference Engine (BIE) determines a most probable full-width half maximum (FWHM) spot size of 78 μm. However, significant uncertainty prevails due to variation in the measured detector blur. Propagating this uncertainty in detector blur through the forward model results in an interval of probabilistic ambiguity spanning approximately 35-195 μm when the laser energy impinges on a thick (1 mm) tantalum target. In other phases of the experiment, laser energy is deposited on a thin (~100more » nm) aluminum target placed 250 μm ahead of the tantalum converter. When the energetic electron beam is generated in this manner, upstream from the bremsstrahlung converter, the inferred spot size shifts to a range of much larger values, approximately 270-600 μm FWHM. This report discusses methods applied to obtain these intervals as well as concepts necessary for interpreting the result within a context of probabilistic quantitative inference.« less

Automated recognition and characterization of solar active regions based on the SOHO/MDI images

NASA Technical Reports Server (NTRS)

Pap, J. M.; Turmon, M.; Mukhtar, S.; Bogart, R.; Ulrich, R.; Froehlich, C.; Wehrli, C.

1997-01-01

The first results of a new method to identify and characterize the various surface structures on the sun, which may contribute to the changes in solar total and spectral irradiance, are shown. The full disk magnetograms (1024 x 1024 pixels) of the Michelson Doppler Imager (MDI) experiment onboard SOHO are analyzed. Use of a Bayesian inference scheme allows objective, uniform, automated processing of a long sequence of images. The main goal is to identify the solar magnetic features causing irradiance changes. The results presented are based on a pilot time interval of August 1996.

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

PubMed

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

2012-03-01

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

Inference of missing data and chemical model parameters using experimental statistics

NASA Astrophysics Data System (ADS)

Casey, Tiernan; Najm, Habib

2017-11-01

A method for determining the joint parameter density of Arrhenius rate expressions through the inference of missing experimental data is presented. This approach proposes noisy hypothetical data sets from target experiments and accepts those which agree with the reported statistics, in the form of nominal parameter values and their associated uncertainties. The data exploration procedure is formalized using Bayesian inference, employing maximum entropy and approximate Bayesian computation methods to arrive at a joint density on data and parameters. The method is demonstrated in the context of reactions in the H2-O2 system for predictive modeling of combustion systems of interest. Work supported by the US DOE BES CSGB. Sandia National Labs is a multimission lab managed and operated by Nat. Technology and Eng'g Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell Intl, for the US DOE NCSA under contract DE-NA-0003525.

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.

Efficient Bayesian inference for natural time series using ARFIMA processes

NASA Astrophysics Data System (ADS)

Graves, T.; Gramacy, R. B.; Franzke, C. L. E.; Watkins, N. W.

2015-11-01

Many geophysical quantities, such as atmospheric temperature, water levels in rivers, and wind speeds, have shown evidence of long memory (LM). LM implies that these quantities experience non-trivial temporal memory, which potentially not only enhances their predictability, but also hampers the detection of externally forced trends. Thus, it is important to reliably identify whether or not a system exhibits LM. In this paper we present a modern and systematic approach to the inference of LM. We use the flexible autoregressive fractional integrated moving average (ARFIMA) model, which is widely used in time series analysis, and of increasing interest in climate science. Unlike most previous work on the inference of LM, which is frequentist in nature, we provide a systematic treatment of Bayesian inference. In particular, we provide a new approximate likelihood for efficient parameter inference, and show how nuisance parameters (e.g., short-memory effects) can be integrated over in order to focus on long-memory parameters and hypothesis testing more directly. We illustrate our new methodology on the Nile water level data and the central England temperature (CET) time series, with favorable comparison to the standard estimators. For CET we also extend our method to seasonal long memory.

Higher-level phylogeny of paraneopteran insects inferred from mitochondrial genome sequences

PubMed Central

Li, Hu; Shao, Renfu; Song, Nan; Song, Fan; Jiang, Pei; Li, Zhihong; Cai, Wanzhi

2015-01-01

Mitochondrial (mt) genome data have been proven to be informative for animal phylogenetic studies but may also suffer from systematic errors, due to the effects of accelerated substitution rate and compositional heterogeneity. We analyzed the mt genomes of 25 insect species from the four paraneopteran orders, aiming to better understand how accelerated substitution rate and compositional heterogeneity affect the inferences of the higher-level phylogeny of this diverse group of hemimetabolous insects. We found substantial heterogeneity in base composition and contrasting rates in nucleotide substitution among these paraneopteran insects, which complicate the inference of higher-level phylogeny. The phylogenies inferred with concatenated sequences of mt genes using maximum likelihood and Bayesian methods and homogeneous models failed to recover Psocodea and Hemiptera as monophyletic groups but grouped, instead, the taxa that had accelerated substitution rates together, including Sternorrhyncha (a suborder of Hemiptera), Thysanoptera, Phthiraptera and Liposcelididae (a family of Psocoptera). Bayesian inference with nucleotide sequences and heterogeneous models (CAT and CAT + GTR), however, recovered Psocodea, Thysanoptera and Hemiptera each as a monophyletic group. Within Psocodea, Liposcelididae is more closely related to Phthiraptera than to other species of Psocoptera. Furthermore, Thysanoptera was recovered as the sister group to Hemiptera. PMID:25704094

Causal learning and inference as a rational process: the new synthesis.

PubMed

Holyoak, Keith J; Cheng, Patricia W

2011-01-01

Over the past decade, an active line of research within the field of human causal learning and inference has converged on a general representational framework: causal models integrated with bayesian probabilistic inference. We describe this new synthesis, which views causal learning and inference as a fundamentally rational process, and review a sample of the empirical findings that support the causal framework over associative alternatives. Causal events, like all events in the distal world as opposed to our proximal perceptual input, are inherently unobservable. A central assumption of the causal approach is that humans (and potentially nonhuman animals) have been designed in such a way as to infer the most invariant causal relations for achieving their goals based on observed events. In contrast, the associative approach assumes that learners only acquire associations among important observed events, omitting the representation of the distal relations. By incorporating bayesian inference over distributions of causal strength and causal structures, along with noisy-logical (i.e., causal) functions for integrating the influences of multiple causes on a single effect, human judgments about causal strength and structure can be predicted accurately for relatively simple causal structures. Dynamic models of learning based on the causal framework can explain patterns of acquisition observed with serial presentation of contingency data and are consistent with available neuroimaging data. The approach has been extended to a diverse range of inductive tasks, including category-based and analogical inferences.

Calibrated birth-death phylogenetic time-tree priors for bayesian inference.

PubMed

Heled, Joseph; Drummond, Alexei J

2015-05-01

Here we introduce a general class of multiple calibration birth-death tree priors for use in Bayesian phylogenetic inference. All tree priors in this class separate ancestral node heights into a set of "calibrated nodes" and "uncalibrated nodes" such that the marginal distribution of the calibrated nodes is user-specified whereas the density ratio of the birth-death prior is retained for trees with equal values for the calibrated nodes. We describe two formulations, one in which the calibration information informs the prior on ranked tree topologies, through the (conditional) prior, and the other which factorizes the prior on divergence times and ranked topologies, thus allowing uniform, or any arbitrary prior distribution on ranked topologies. Although the first of these formulations has some attractive properties, the algorithm we present for computing its prior density is computationally intensive. However, the second formulation is always faster and computationally efficient for up to six calibrations. We demonstrate the utility of the new class of multiple-calibration tree priors using both small simulations and a real-world analysis and compare the results to existing schemes. The two new calibrated tree priors described in this article offer greater flexibility and control of prior specification in calibrated time-tree inference and divergence time dating, and will remove the need for indirect approaches to the assessment of the combined effect of calibration densities and tree priors in Bayesian phylogenetic inference. © The Author(s) 2014. Published by Oxford University Press, on behalf of the Society of Systematic Biologists.

Uncertainty Reduction using Bayesian Inference and Sensitivity Analysis: A Sequential Approach to the NASA Langley Uncertainty Quantification Challenge

NASA Technical Reports Server (NTRS)

Sankararaman, Shankar

2016-01-01

This paper presents a computational framework for uncertainty characterization and propagation, and sensitivity analysis under the presence of aleatory and epistemic un- certainty, and develops a rigorous methodology for efficient refinement of epistemic un- certainty by identifying important epistemic variables that significantly affect the overall performance of an engineering system. The proposed methodology is illustrated using the NASA Langley Uncertainty Quantification Challenge (NASA-LUQC) problem that deals with uncertainty analysis of a generic transport model (GTM). First, Bayesian inference is used to infer subsystem-level epistemic quantities using the subsystem-level model and corresponding data. Second, tools of variance-based global sensitivity analysis are used to identify four important epistemic variables (this limitation specified in the NASA-LUQC is reflective of practical engineering situations where not all epistemic variables can be refined due to time/budget constraints) that significantly affect system-level performance. The most significant contribution of this paper is the development of the sequential refine- ment methodology, where epistemic variables for refinement are not identified all-at-once. Instead, only one variable is first identified, and then, Bayesian inference and global sensi- tivity calculations are repeated to identify the next important variable. This procedure is continued until all 4 variables are identified and the refinement in the system-level perfor- mance is computed. The advantages of the proposed sequential refinement methodology over the all-at-once uncertainty refinement approach are explained, and then applied to the NASA Langley Uncertainty Quantification Challenge problem.

Learning abstract visual concepts via probabilistic program induction in a Language of Thought.

PubMed

Overlan, Matthew C; Jacobs, Robert A; Piantadosi, Steven T

2017-11-01

The ability to learn abstract concepts is a powerful component of human cognition. It has been argued that variable binding is the key element enabling this ability, but the computational aspects of variable binding remain poorly understood. Here, we address this shortcoming by formalizing the Hierarchical Language of Thought (HLOT) model of rule learning. Given a set of data items, the model uses Bayesian inference to infer a probability distribution over stochastic programs that implement variable binding. Because the model makes use of symbolic variables as well as Bayesian inference and programs with stochastic primitives, it combines many of the advantages of both symbolic and statistical approaches to cognitive modeling. To evaluate the model, we conducted an experiment in which human subjects viewed training items and then judged which test items belong to the same concept as the training items. We found that the HLOT model provides a close match to human generalization patterns, significantly outperforming two variants of the Generalized Context Model, one variant based on string similarity and the other based on visual similarity using features from a deep convolutional neural network. Additional results suggest that variable binding happens automatically, implying that binding operations do not add complexity to peoples' hypothesized rules. Overall, this work demonstrates that a cognitive model combining symbolic variables with Bayesian inference and stochastic program primitives provides a new perspective for understanding people's patterns of generalization. Copyright © 2017 Elsevier B.V. All rights reserved.

cosmoabc: Likelihood-free inference for cosmology

NASA Astrophysics Data System (ADS)

Ishida, Emille E. O.; Vitenti, Sandro D. P.; Penna-Lima, Mariana; Trindade, Arlindo M.; Cisewski, Jessi; M.; de Souza, Rafael; Cameron, Ewan; Busti, Vinicius C.

2015-05-01

Approximate Bayesian Computation (ABC) enables parameter inference for complex physical systems in cases where the true likelihood function is unknown, unavailable, or computationally too expensive. It relies on the forward simulation of mock data and comparison between observed and synthetic catalogs. cosmoabc is a Python Approximate Bayesian Computation (ABC) sampler featuring a Population Monte Carlo variation of the original ABC algorithm, which uses an adaptive importance sampling scheme. The code can be coupled to an external simulator to allow incorporation of arbitrary distance and prior functions. When coupled with the numcosmo library, it has been used to estimate posterior probability distributions over cosmological parameters based on measurements of galaxy clusters number counts without computing the likelihood function.

Inferring the Growth of Massive Galaxies Using Bayesian Spectral Synthesis Modeling

NASA Astrophysics Data System (ADS)

Stillman, Coley Michael; Poremba, Megan R.; Moustakas, John

2018-01-01

The most massive galaxies in the universe are typically found at the centers of massive galaxy clusters. Studying these galaxies can provide valuable insight into the hierarchical growth of massive dark matter halos. One of the key challenges of measuring the stellar mass growth of massive galaxies is converting the measured light profiles into stellar mass. We use Prospector, a state-of-the-art Bayesian spectral synthesis modeling code, to infer the total stellar masses of a pilot sample of massive central galaxies selected from the Sloan Digital Sky Survey. We compare our stellar mass estimates to previous measurements, and present some of the quantitative diagnostics provided by Prospector.

A Dynamic Bayesian Network Based Structural Learning towards Automated Handwritten Digit Recognition

NASA Astrophysics Data System (ADS)

Pauplin, Olivier; Jiang, Jianmin

Pattern recognition using Dynamic Bayesian Networks (DBNs) is currently a growing area of study. In this paper, we present DBN models trained for classification of handwritten digit characters. The structure of these models is partly inferred from the training data of each class of digit before performing parameter learning. Classification results are presented for the four described models.

Virtual Representation of IID Observations in Bayesian Belief Networks

DTIC Science & Technology

1994-04-01

programs for structuring and using Bayesian inference include ERGO ( Noetic Systems, Inc., 1991) and HUGIN (Andersen, Jensen, Olesen, & Jensen, 1989...Nichols, S.. Chipman, & R. Brennan (Eds.), Cognitively diagnostic assessment. Hillsdale, NJ: Erlbaum. Noetic Systems, Inc. (1991). ERGO [computer...Dr Geore Eageiard Jr Chicago IL 60612 US Naval Academy Division of Educational Studies Annapolis MD 21402-5002 Emory University Dr Janice Gifford 210

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

NASA Astrophysics Data System (ADS)

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

2007-06-01

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

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

Bayesian Inference of Physics Parameters in the DIII-D Charge-Exchange Recombination Spectroscopy System

NASA Astrophysics Data System (ADS)

Bowman, C.; Gibson, K. J.; La Haye, R. J.; Groebner, R. J.; Taylor, N. Z.; Grierson, B. A.

2014-10-01

A Bayesian inference framework has been developed for the DIII-D charge-exchange recombination (CER) system, capable of computing probability distribution functions (PDFs) for desired parameters. CER is a key diagnostic system at DIII-D, measuring important physics parameters such as plasma rotation and impurity ion temperature. This work is motivated by a case in which the CER system was used to probe the plasma rotation radial profile around an m/n = 2/1 tearing mode island rotating at ~ 1 kHz. Due to limited resolution in the tearing mode phase and short integration time, it has proven challenging to observe the structure of the rotation profile across the island. We seek to solve this problem by using the Bayesian framework to improve the estimation accuracy of the plasma rotation, helping to reveal details of how it is perturbed in the magnetic island vicinity. Examples of the PDFs obtained through the Bayesian framework will be presented, and compared with results from a conventional least-squares analysis of the CER data. Work supported by the US DOE under DE-FC02-04ER54698 and DE-AC02-09CH11466.

A Bayesian Framework for Analysis of Pseudo-Spatial Models of Comparable Engineered Systems with Application to Spacecraft Anomaly Prediction Based on Precedent Data

NASA Astrophysics Data System (ADS)

Ndu, Obibobi Kamtochukwu

To ensure that estimates of risk and reliability inform design and resource allocation decisions in the development of complex engineering systems, early engagement in the design life cycle is necessary. An unfortunate constraint on the accuracy of such estimates at this stage of concept development is the limited amount of high fidelity design and failure information available on the actual system under development. Applying the human ability to learn from experience and augment our state of knowledge to evolve better solutions mitigates this limitation. However, the challenge lies in formalizing a methodology that takes this highly abstract, but fundamentally human cognitive, ability and extending it to the field of risk analysis while maintaining the tenets of generalization, Bayesian inference, and probabilistic risk analysis. We introduce an integrated framework for inferring the reliability, or other probabilistic measures of interest, of a new system or a conceptual variant of an existing system. Abstractly, our framework is based on learning from the performance of precedent designs and then applying the acquired knowledge, appropriately adjusted based on degree of relevance, to the inference process. This dissertation presents a method for inferring properties of the conceptual variant using a pseudo-spatial model that describes the spatial configuration of the family of systems to which the concept belongs. Through non-metric multidimensional scaling, we formulate the pseudo-spatial model based on rank-ordered subjective expert perception of design similarity between systems that elucidate the psychological space of the family. By a novel extension of Kriging methods for analysis of geospatial data to our "pseudo-space of comparable engineered systems", we develop a Bayesian inference model that allows prediction of the probabilistic measure of interest.

Inferring gene and protein interactions using PubMed citations and consensus Bayesian networks

PubMed Central

Dalman, Mark; Haddad, Joseph; Duan, Zhong-Hui

2017-01-01

The PubMed database offers an extensive set of publication data that can be useful, yet inherently complex to use without automated computational techniques. Data repositories such as the Genomic Data Commons (GDC) and the Gene Expression Omnibus (GEO) offer experimental data storage and retrieval as well as curated gene expression profiles. Genetic interaction databases, including Reactome and Ingenuity Pathway Analysis, offer pathway and experiment data analysis using data curated from these publications and data repositories. We have created a method to generate and analyze consensus networks, inferring potential gene interactions, using large numbers of Bayesian networks generated by data mining publications in the PubMed database. Through the concept of network resolution, these consensus networks can be tailored to represent possible genetic interactions. We designed a set of experiments to confirm that our method is stable across variation in both sample and topological input sizes. Using gene product interactions from the KEGG pathway database and data mining PubMed publication abstracts, we verify that regardless of the network resolution or the inferred consensus network, our method is capable of inferring meaningful gene interactions through consensus Bayesian network generation with multiple, randomized topological orderings. Our method can not only confirm the existence of currently accepted interactions, but has the potential to hypothesize new ones as well. We show our method confirms the existence of known gene interactions such as JAK-STAT-PI3K-AKT-mTOR, infers novel gene interactions such as RAS- Bcl-2 and RAS-AKT, and found significant pathway-pathway interactions between the JAK-STAT signaling and Cardiac Muscle Contraction KEGG pathways. PMID:29049295

Specimen-level phylogenetics in paleontology using the Fossilized Birth-Death model with sampled ancestors.

PubMed

Cau, Andrea

2017-01-01

Bayesian phylogenetic methods integrating simultaneously morphological and stratigraphic information have been applied increasingly among paleontologists. Most of these studies have used Bayesian methods as an alternative to the widely-used parsimony analysis, to infer macroevolutionary patterns and relationships among species-level or higher taxa. Among recently introduced Bayesian methodologies, the Fossilized Birth-Death (FBD) model allows incorporation of hypotheses on ancestor-descendant relationships in phylogenetic analyses including fossil taxa. Here, the FBD model is used to infer the relationships among an ingroup formed exclusively by fossil individuals, i.e., dipnoan tooth plates from four localities in the Ain el Guettar Formation of Tunisia. Previous analyses of this sample compared the results of phylogenetic analysis using parsimony with stratigraphic methods, inferred a high diversity (five or more genera) in the Ain el Guettar Formation, and interpreted it as an artifact inflated by depositional factors. In the analysis performed here, the uncertainty on the chronostratigraphic relationships among the specimens was included among the prior settings. The results of the analysis confirm the referral of most of the specimens to the taxa Asiatoceratodus , Equinoxiodus, Lavocatodus and Neoceratodus , but reject those to Ceratodus and Ferganoceratodus . The resulting phylogeny constrained the evolution of the Tunisian sample exclusively in the Early Cretaceous, contrasting with the previous scenario inferred by the stratigraphically-calibrated topology resulting from parsimony analysis. The phylogenetic framework also suggests that (1) the sampled localities are laterally equivalent, (2) but three localities are restricted to the youngest part of the section; both results are in agreement with previous stratigraphic analyses of these localities. The FBD model of specimen-level units provides a novel tool for phylogenetic inference among fossils but also for independent tests of stratigraphic scenarios.

Inferring on the Intentions of Others by Hierarchical Bayesian Learning

PubMed Central

Diaconescu, Andreea O.; Mathys, Christoph; Weber, Lilian A. E.; Daunizeau, Jean; Kasper, Lars; Lomakina, Ekaterina I.; Fehr, Ernst; Stephan, Klaas E.

2014-01-01

Inferring on others' (potentially time-varying) intentions is a fundamental problem during many social transactions. To investigate the underlying mechanisms, we applied computational modeling to behavioral data from an economic game in which 16 pairs of volunteers (randomly assigned to “player” or “adviser” roles) interacted. The player performed a probabilistic reinforcement learning task, receiving information about a binary lottery from a visual pie chart. The adviser, who received more predictive information, issued an additional recommendation. Critically, the game was structured such that the adviser's incentives to provide helpful or misleading information varied in time. Using a meta-Bayesian modeling framework, we found that the players' behavior was best explained by the deployment of hierarchical learning: they inferred upon the volatility of the advisers' intentions in order to optimize their predictions about the validity of their advice. Beyond learning, volatility estimates also affected the trial-by-trial variability of decisions: participants were more likely to rely on their estimates of advice accuracy for making choices when they believed that the adviser's intentions were presently stable. Finally, our model of the players' inference predicted the players' interpersonal reactivity index (IRI) scores, explicit ratings of the advisers' helpfulness and the advisers' self-reports on their chosen strategy. Overall, our results suggest that humans (i) employ hierarchical generative models to infer on the changing intentions of others, (ii) use volatility estimates to inform decision-making in social interactions, and (iii) integrate estimates of advice accuracy with non-social sources of information. The Bayesian framework presented here can quantify individual differences in these mechanisms from simple behavioral readouts and may prove useful in future clinical studies of maladaptive social cognition. PMID:25187943

Statistical Inference in the Learning of Novel Phonetic Categories

ERIC Educational Resources Information Center

Zhao, Yuan

2010-01-01

Learning a phonetic category (or any linguistic category) requires integrating different sources of information. A crucial unsolved problem for phonetic learning is how this integration occurs: how can we update our previous knowledge about a phonetic category as we hear new exemplars of the category? One model of learning is Bayesian Inference,…

Finite‐fault Bayesian inversion of teleseismic body waves

USGS Publications Warehouse

Clayton, Brandon; Hartzell, Stephen; Moschetti, Morgan P.; Minson, Sarah E.

2017-01-01

Inverting geophysical data has provided fundamental information about the behavior of earthquake rupture. However, inferring kinematic source model parameters for finite‐fault ruptures is an intrinsically underdetermined problem (the problem of nonuniqueness), because we are restricted to finite noisy observations. Although many studies use least‐squares techniques to make the finite‐fault problem tractable, these methods generally lack the ability to apply non‐Gaussian error analysis and the imposition of nonlinear constraints. However, the Bayesian approach can be employed to find a Gaussian or non‐Gaussian distribution of all probable model parameters, while utilizing nonlinear constraints. We present case studies to quantify the resolving power and associated uncertainties using only teleseismic body waves in a Bayesian framework to infer the slip history for a synthetic case and two earthquakes: the 2011 Mw 7.1 Van, east Turkey, earthquake and the 2010 Mw 7.2 El Mayor–Cucapah, Baja California, earthquake. In implementing the Bayesian method, we further present two distinct solutions to investigate the uncertainties by performing the inversion with and without velocity structure perturbations. We find that the posterior ensemble becomes broader when including velocity structure variability and introduces a spatial smearing of slip. Using the Bayesian framework solely on teleseismic body waves, we find rake is poorly constrained by the observations and rise time is poorly resolved when slip amplitude is low.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Detection of cylinder unbalance from Bayesian inference combining cylinder pressure and vibration block measurement in a Diesel engine

NASA Astrophysics Data System (ADS)

Nguyen, Emmanuel; Antoni, Jerome; Grondin, Olivier

2009-12-01

In the automotive industry, the necessary reduction of pollutant emission for new Diesel engines requires the control of combustion events. This control is efficient provided combustion parameters such as combustion occurrence and combustion energy are relevant. Combustion parameters are traditionally measured from cylinder pressure sensors. However this kind of sensor is expensive and has a limited lifetime. Thus this paper proposes to use only one cylinder pressure on a multi-cylinder engine and to extract combustion parameters from the other cylinders with low cost knock sensors. Knock sensors measure the vibration circulating on the engine block, hence they do not all contain the information on the combustion processes, but they are also contaminated by other mechanical noises that disorder the signal. The question is how to combine the information coming from one cylinder pressure and knock sensors to obtain the most relevant combustion parameters in all engine cylinders. In this paper, the issue is addressed trough the Bayesian inference formalism. In that cylinder where a cylinder pressure sensor is mounted, combustion parameters will be measured directly. In the other cylinders, they will be measured indirectly from Bayesian inference. Experimental results obtained on a four cylinder Diesel engine demonstrate the effectiveness of the proposed algorithm toward that purpose.

Action understanding as inverse planning.

PubMed

Baker, Chris L; Saxe, Rebecca; Tenenbaum, Joshua B

2009-12-01

Humans are adept at inferring the mental states underlying other agents' actions, such as goals, beliefs, desires, emotions and other thoughts. We propose a computational framework based on Bayesian inverse planning for modeling human action understanding. The framework represents an intuitive theory of intentional agents' behavior based on the principle of rationality: the expectation that agents will plan approximately rationally to achieve their goals, given their beliefs about the world. The mental states that caused an agent's behavior are inferred by inverting this model of rational planning using Bayesian inference, integrating the likelihood of the observed actions with the prior over mental states. This approach formalizes in precise probabilistic terms the essence of previous qualitative approaches to action understanding based on an "intentional stance" [Dennett, D. C. (1987). The intentional stance. Cambridge, MA: MIT Press] or a "teleological stance" [Gergely, G., Nádasdy, Z., Csibra, G., & Biró, S. (1995). Taking the intentional stance at 12 months of age. Cognition, 56, 165-193]. In three psychophysical experiments using animated stimuli of agents moving in simple mazes, we assess how well different inverse planning models based on different goal priors can predict human goal inferences. The results provide quantitative evidence for an approximately rational inference mechanism in human goal inference within our simplified stimulus paradigm, and for the flexible nature of goal representations that human observers can adopt. We discuss the implications of our experimental results for human action understanding in real-world contexts, and suggest how our framework might be extended to capture other kinds of mental state inferences, such as inferences about beliefs, or inferring whether an entity is an intentional agent.

Evidence cross-validation and Bayesian inference of MAST plasma equilibria

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

Nessi, G. T. von; Hole, M. J.; Svensson, J.

2012-01-15

In this paper, current profiles for plasma discharges on the mega-ampere spherical tokamak are directly calculated from pickup coil, flux loop, and motional-Stark effect observations via methods based in the statistical theory of Bayesian analysis. By representing toroidal plasma current as a series of axisymmetric current beams with rectangular cross-section and inferring the current for each one of these beams, flux-surface geometry and q-profiles are subsequently calculated by elementary application of Biot-Savart's law. The use of this plasma model in the context of Bayesian analysis was pioneered by Svensson and Werner on the joint-European tokamak [Svensson and Werner,Plasma Phys. Controlledmore » Fusion 50(8), 085002 (2008)]. In this framework, linear forward models are used to generate diagnostic predictions, and the probability distribution for the currents in the collection of plasma beams was subsequently calculated directly via application of Bayes' formula. In this work, we introduce a new diagnostic technique to identify and remove outlier observations associated with diagnostics falling out of calibration or suffering from an unidentified malfunction. These modifications enable a good agreement between Bayesian inference of the last-closed flux-surface with other corroborating data, such as that from force balance considerations using EFIT++[Appel et al., ''A unified approach to equilibrium reconstruction'' Proceedings of the 33rd EPS Conference on Plasma Physics (Rome, Italy, 2006)]. In addition, this analysis also yields errors on the plasma current profile and flux-surface geometry as well as directly predicting the Shafranov shift of the plasma core.« 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.

FuncPatch: a web server for the fast Bayesian inference of conserved functional patches in protein 3D structures.

PubMed

Huang, Yi-Fei; Golding, G Brian

2015-02-15

A number of statistical phylogenetic methods have been developed to infer conserved functional sites or regions in proteins. Many methods, e.g. Rate4Site, apply the standard phylogenetic models to infer site-specific substitution rates and totally ignore the spatial correlation of substitution rates in protein tertiary structures, which may reduce their power to identify conserved functional patches in protein tertiary structures when the sequences used in the analysis are highly similar. The 3D sliding window method has been proposed to infer conserved functional patches in protein tertiary structures, but the window size, which reflects the strength of the spatial correlation, must be predefined and is not inferred from data. We recently developed GP4Rate to solve these problems under the Bayesian framework. Unfortunately, GP4Rate is computationally slow. Here, we present an intuitive web server, FuncPatch, to perform a fast approximate Bayesian inference of conserved functional patches in protein tertiary structures. Both simulations and four case studies based on empirical data suggest that FuncPatch is a good approximation to GP4Rate. However, FuncPatch is orders of magnitudes faster than GP4Rate. In addition, simulations suggest that FuncPatch is potentially a useful tool complementary to Rate4Site, but the 3D sliding window method is less powerful than FuncPatch and Rate4Site. The functional patches predicted by FuncPatch in the four case studies are supported by experimental evidence, which corroborates the usefulness of FuncPatch. The software FuncPatch is freely available at the web site, http://info.mcmaster.ca/yifei/FuncPatch golding@mcmaster.ca Supplementary data are available at Bioinformatics online. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

A Test by Any Other Name: P Values, Bayes Factors, and Statistical Inference.

PubMed

Stern, Hal S

2016-01-01

Procedures used for statistical inference are receiving increased scrutiny as the scientific community studies the factors associated with insuring reproducible research. This note addresses recent negative attention directed at p values, the relationship of confidence intervals and tests, and the role of Bayesian inference and Bayes factors, with an eye toward better understanding these different strategies for statistical inference. We argue that researchers and data analysts too often resort to binary decisions (e.g., whether to reject or accept the null hypothesis) in settings where this may not be required.

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

Understanding the Uncertainty of an Effectiveness-Cost Ratio in Educational Resource Allocation: A Bayesian Approach

ERIC Educational Resources Information Center

Pan, Yilin

2016-01-01

Given the necessity to bridge the gap between what happened and what is likely to happen, this paper aims to explore how to apply Bayesian inference to cost-effectiveness analysis so as to capture the uncertainty of a ratio-type efficiency measure. The first part of the paper summarizes the characteristics of the evaluation data that are commonly…

Assimilating multi-source uncertainties of a parsimonious conceptual hydrological model using hierarchical Bayesian modeling

Treesearch

Wei Wu; James Clark; James Vose

2010-01-01

Hierarchical Bayesian (HB) modeling allows for multiple sources of uncertainty by factoring complex relationships into conditional distributions that can be used to draw inference and make predictions. We applied an HB model to estimate the parameters and state variables of a parsimonious hydrological model – GR4J – by coherently assimilating the uncertainties from the...

Efficient Effects-Based Military Planning Final Report

DTIC Science & Technology

2010-11-13

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

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…

Automated Bayesian model development for frequency detection in biological time series.

PubMed

Granqvist, Emma; Oldroyd, Giles E D; Morris, Richard J

2011-06-24

A first step in building a mathematical model of a biological system is often the analysis of the temporal behaviour of key quantities. Mathematical relationships between the time and frequency domain, such as Fourier Transforms and wavelets, are commonly used to extract information about the underlying signal from a given time series. This one-to-one mapping from time points to frequencies inherently assumes that both domains contain the complete knowledge of the system. However, for truncated, noisy time series with background trends this unique mapping breaks down and the question reduces to an inference problem of identifying the most probable frequencies. In this paper we build on the method of Bayesian Spectrum Analysis and demonstrate its advantages over conventional methods by applying it to a number of test cases, including two types of biological time series. Firstly, oscillations of calcium in plant root cells in response to microbial symbionts are non-stationary and noisy, posing challenges to data analysis. Secondly, circadian rhythms in gene expression measured over only two cycles highlights the problem of time series with limited length. The results show that the Bayesian frequency detection approach can provide useful results in specific areas where Fourier analysis can be uninformative or misleading. We demonstrate further benefits of the Bayesian approach for time series analysis, such as direct comparison of different hypotheses, inherent estimation of noise levels and parameter precision, and a flexible framework for modelling the data without pre-processing. Modelling in systems biology often builds on the study of time-dependent phenomena. Fourier Transforms are a convenient tool for analysing the frequency domain of time series. However, there are well-known limitations of this method, such as the introduction of spurious frequencies when handling short and noisy time series, and the requirement for uniformly sampled data. Biological time series often deviate significantly from the requirements of optimality for Fourier transformation. In this paper we present an alternative approach based on Bayesian inference. We show the value of placing spectral analysis in the framework of Bayesian inference and demonstrate how model comparison can automate this procedure.

Automated Bayesian model development for frequency detection in biological time series

PubMed Central

2011-01-01

Background A first step in building a mathematical model of a biological system is often the analysis of the temporal behaviour of key quantities. Mathematical relationships between the time and frequency domain, such as Fourier Transforms and wavelets, are commonly used to extract information about the underlying signal from a given time series. This one-to-one mapping from time points to frequencies inherently assumes that both domains contain the complete knowledge of the system. However, for truncated, noisy time series with background trends this unique mapping breaks down and the question reduces to an inference problem of identifying the most probable frequencies. Results In this paper we build on the method of Bayesian Spectrum Analysis and demonstrate its advantages over conventional methods by applying it to a number of test cases, including two types of biological time series. Firstly, oscillations of calcium in plant root cells in response to microbial symbionts are non-stationary and noisy, posing challenges to data analysis. Secondly, circadian rhythms in gene expression measured over only two cycles highlights the problem of time series with limited length. The results show that the Bayesian frequency detection approach can provide useful results in specific areas where Fourier analysis can be uninformative or misleading. We demonstrate further benefits of the Bayesian approach for time series analysis, such as direct comparison of different hypotheses, inherent estimation of noise levels and parameter precision, and a flexible framework for modelling the data without pre-processing. Conclusions Modelling in systems biology often builds on the study of time-dependent phenomena. Fourier Transforms are a convenient tool for analysing the frequency domain of time series. However, there are well-known limitations of this method, such as the introduction of spurious frequencies when handling short and noisy time series, and the requirement for uniformly sampled data. Biological time series often deviate significantly from the requirements of optimality for Fourier transformation. In this paper we present an alternative approach based on Bayesian inference. We show the value of placing spectral analysis in the framework of Bayesian inference and demonstrate how model comparison can automate this procedure. PMID:21702910

The anatomy of choice: active inference and agency.

PubMed

Friston, Karl; Schwartenbeck, Philipp; Fitzgerald, Thomas; Moutoussis, Michael; Behrens, Timothy; Dolan, Raymond J

2013-01-01

This paper considers agency in the setting of embodied or active inference. In brief, we associate a sense of agency with prior beliefs about action and ask what sorts of beliefs underlie optimal behavior. In particular, we consider prior beliefs that action minimizes the Kullback-Leibler (KL) divergence between desired states and attainable states in the future. This allows one to formulate bounded rationality as approximate Bayesian inference that optimizes a free energy bound on model evidence. We show that constructs like expected utility, exploration bonuses, softmax choice rules and optimism bias emerge as natural consequences of this formulation. Previous accounts of active inference have focused on predictive coding and Bayesian filtering schemes for minimizing free energy. Here, we consider variational Bayes as an alternative scheme that provides formal constraints on the computational anatomy of inference and action-constraints that are remarkably consistent with neuroanatomy. Furthermore, this scheme contextualizes optimal decision theory and economic (utilitarian) formulations as pure inference problems. For example, expected utility theory emerges as a special case of free energy minimization, where the sensitivity or inverse temperature (of softmax functions and quantal response equilibria) has a unique and Bayes-optimal solution-that minimizes free energy. This sensitivity corresponds to the precision of beliefs about behavior, such that attainable goals are afforded a higher precision or confidence. In turn, this means that optimal behavior entails a representation of confidence about outcomes that are under an agent's control.

Bayesian or Laplacien inference, entropy and information theory and information geometry in data and signal processing

NASA Astrophysics Data System (ADS)

Mohammad-Djafari, Ali

2015-01-01

The main object of this tutorial article is first to review the main inference tools using Bayesian approach, Entropy, Information theory and their corresponding geometries. This review is focused mainly on the ways these tools have been used in data, signal and image processing. After a short introduction of the different quantities related to the Bayes rule, the entropy and the Maximum Entropy Principle (MEP), relative entropy and the Kullback-Leibler divergence, Fisher information, we will study their use in different fields of data and signal processing such as: entropy in source separation, Fisher information in model order selection, different Maximum Entropy based methods in time series spectral estimation and finally, general linear inverse problems.

Bayesian analysis of non-linear differential equation models with application to a gut microbial ecosystem.

PubMed

Lawson, Daniel J; Holtrop, Grietje; Flint, Harry

2011-07-01

Process models specified by non-linear dynamic differential equations contain many parameters, which often must be inferred from a limited amount of data. We discuss a hierarchical Bayesian approach combining data from multiple related experiments in a meaningful way, which permits more powerful inference than treating each experiment as independent. The approach is illustrated with a simulation study and example data from experiments replicating the aspects of the human gut microbial ecosystem. A predictive model is obtained that contains prediction uncertainty caused by uncertainty in the parameters, and we extend the model to capture situations of interest that cannot easily be studied experimentally. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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.

Efficient inference for genetic association studies with multiple outcomes.

PubMed

Ruffieux, Helene; Davison, Anthony C; Hager, Jorg; Irincheeva, Irina

2017-10-01

Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single clinical outcome on many genetic variants one by one, but there is an increasing demand for joint analysis of many molecular outcomes and genetic variants in order to unravel functional interactions. Unfortunately, most existing approaches to joint modeling are either too simplistic to be powerful or are impracticable for computational reasons. Inspired by Richardson and others (2010, Bayesian Statistics 9), we consider a sparse multivariate regression model that allows simultaneous selection of predictors and associated responses. As Markov chain Monte Carlo (MCMC) inference on such models can be prohibitively slow when the number of genetic variants exceeds a few thousand, we propose a variational inference approach which produces posterior information very close to that of MCMC inference, at a much reduced computational cost. Extensive numerical experiments show that our approach outperforms popular variable selection methods and tailored Bayesian procedures, dealing within hours with problems involving hundreds of thousands of genetic variants and tens to hundreds of clinical or molecular outcomes. © The Author 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

The probabilistic convolution tree: efficient exact Bayesian inference for faster LC-MS/MS protein inference.

PubMed

Serang, Oliver

2014-01-01

Exact Bayesian inference can sometimes be performed efficiently for special cases where a function has commutative and associative symmetry of its inputs (called "causal independence"). For this reason, it is desirable to exploit such symmetry on big data sets. Here we present a method to exploit a general form of this symmetry on probabilistic adder nodes by transforming those probabilistic adder nodes into a probabilistic convolution tree with which dynamic programming computes exact probabilities. A substantial speedup is demonstrated using an illustration example that can arise when identifying splice forms with bottom-up mass spectrometry-based proteomics. On this example, even state-of-the-art exact inference algorithms require a runtime more than exponential in the number of splice forms considered. By using the probabilistic convolution tree, we reduce the runtime to O(k log(k)2) and the space to O(k log(k)) where k is the number of variables joined by an additive or cardinal operator. This approach, which can also be used with junction tree inference, is applicable to graphs with arbitrary dependency on counting variables or cardinalities and can be used on diverse problems and fields like forward error correcting codes, elemental decomposition, and spectral demixing. The approach also trivially generalizes to multiple dimensions.

The Probabilistic Convolution Tree: Efficient Exact Bayesian Inference for Faster LC-MS/MS Protein Inference

PubMed Central

Serang, Oliver

2014-01-01

Exact Bayesian inference can sometimes be performed efficiently for special cases where a function has commutative and associative symmetry of its inputs (called “causal independence”). For this reason, it is desirable to exploit such symmetry on big data sets. Here we present a method to exploit a general form of this symmetry on probabilistic adder nodes by transforming those probabilistic adder nodes into a probabilistic convolution tree with which dynamic programming computes exact probabilities. A substantial speedup is demonstrated using an illustration example that can arise when identifying splice forms with bottom-up mass spectrometry-based proteomics. On this example, even state-of-the-art exact inference algorithms require a runtime more than exponential in the number of splice forms considered. By using the probabilistic convolution tree, we reduce the runtime to and the space to where is the number of variables joined by an additive or cardinal operator. This approach, which can also be used with junction tree inference, is applicable to graphs with arbitrary dependency on counting variables or cardinalities and can be used on diverse problems and fields like forward error correcting codes, elemental decomposition, and spectral demixing. The approach also trivially generalizes to multiple dimensions. PMID:24626234

Visual shape perception as Bayesian inference of 3D object-centered shape representations.

PubMed

Erdogan, Goker; Jacobs, Robert A

2017-11-01

Despite decades of research, little is known about how people visually perceive object shape. We hypothesize that a promising approach to shape perception is provided by a "visual perception as Bayesian inference" framework which augments an emphasis on visual representation with an emphasis on the idea that shape perception is a form of statistical inference. Our hypothesis claims that shape perception of unfamiliar objects can be characterized as statistical inference of 3D shape in an object-centered coordinate system. We describe a computational model based on our theoretical framework, and provide evidence for the model along two lines. First, we show that, counterintuitively, the model accounts for viewpoint-dependency of object recognition, traditionally regarded as evidence against people's use of 3D object-centered shape representations. Second, we report the results of an experiment using a shape similarity task, and present an extensive evaluation of existing models' abilities to account for the experimental data. We find that our shape inference model captures subjects' behaviors better than competing models. Taken as a whole, our experimental and computational results illustrate the promise of our approach and suggest that people's shape representations of unfamiliar objects are probabilistic, 3D, and object-centered. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Hierarchical Bayesian Modeling of Fluid-Induced Seismicity

NASA Astrophysics Data System (ADS)

Broccardo, M.; Mignan, A.; Wiemer, S.; Stojadinovic, B.; Giardini, D.

2017-11-01

In this study, we present a Bayesian hierarchical framework to model fluid-induced seismicity. The framework is based on a nonhomogeneous Poisson process with a fluid-induced seismicity rate proportional to the rate of injected fluid. The fluid-induced seismicity rate model depends upon a set of physically meaningful parameters and has been validated for six fluid-induced case studies. In line with the vision of hierarchical Bayesian modeling, the rate parameters are considered as random variables. We develop both the Bayesian inference and updating rules, which are used to develop a probabilistic forecasting model. We tested the Basel 2006 fluid-induced seismic case study to prove that the hierarchical Bayesian model offers a suitable framework to coherently encode both epistemic uncertainty and aleatory variability. Moreover, it provides a robust and consistent short-term seismic forecasting model suitable for online risk quantification and mitigation.

Bayesian performance metrics and small system integration in recent homeland security and defense applications

NASA Astrophysics Data System (ADS)

Jannson, Tomasz; Kostrzewski, Andrew; Patton, Edward; Pradhan, Ranjit; Shih, Min-Yi; Walter, Kevin; Savant, Gajendra; Shie, Rick; Forrester, Thomas

2010-04-01

In this paper, Bayesian inference is applied to performance metrics definition of the important class of recent Homeland Security and defense systems called binary sensors, including both (internal) system performance and (external) CONOPS. The medical analogy is used to define the PPV (Positive Predictive Value), the basic Bayesian metrics parameter of the binary sensors. Also, Small System Integration (SSI) is discussed in the context of recent Homeland Security and defense applications, emphasizing a highly multi-technological approach, within the broad range of clusters ("nexus") of electronics, optics, X-ray physics, γ-ray physics, and other disciplines.

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].

Bayes and blickets: Effects of knowledge on causal induction in children and adults

PubMed Central

Griffiths, Thomas L.; Sobel, David M.; Tenenbaum, Joshua B.; Gopnik, Alison

2011-01-01

People are adept at inferring novel causal relations, even from only a few observations. Prior knowledge about the probability of encountering causal relations of various types and the nature of the mechanisms relating causes and effects plays a crucial role in these inferences. We test a formal account of how this knowledge can be used and acquired, based on analyzing causal induction as Bayesian inference. Five studies explored the predictions of this account with adults and 4-year-olds, using tasks in which participants learned about the causal properties of a set of objects. The studies varied the two factors that our Bayesian approach predicted should be relevant to causal induction: the prior probability with which causal relations exist, and the assumption of a deterministic or a probabilistic relation between cause and effect. Adults’ judgments (Experiments 1, 2, and 4) were in close correspondence with the quantitative predictions of the model, and children’s judgments (Experiments 3 and 5) agreed qualitatively with this account. PMID:21972897

Data analysis using scale-space filtering and Bayesian probabilistic reasoning

NASA Technical Reports Server (NTRS)

Kulkarni, Deepak; Kutulakos, Kiriakos; Robinson, Peter

1991-01-01

This paper describes a program for analysis of output curves from Differential Thermal Analyzer (DTA). The program first extracts probabilistic qualitative features from a DTA curve of a soil sample, and then uses Bayesian probabilistic reasoning to infer the mineral in the soil. The qualifier module employs a simple and efficient extension of scale-space filtering suitable for handling DTA data. We have observed that points can vanish from contours in the scale-space image when filtering operations are not highly accurate. To handle the problem of vanishing points, perceptual organizations heuristics are used to group the points into lines. Next, these lines are grouped into contours by using additional heuristics. Probabilities are associated with these contours using domain-specific correlations. A Bayes tree classifier processes probabilistic features to infer the presence of different minerals in the soil. Experiments show that the algorithm that uses domain-specific correlation to infer qualitative features outperforms a domain-independent algorithm that does not.

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.

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

NASA Astrophysics Data System (ADS)

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

2009-05-01

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

Bayesian 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 approach for three-dimensional aquifer characterization at the Hanford 300 Area

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

Murakami, Haruko; Chen, X.; Hahn, Melanie S.

2010-10-21

This study presents a stochastic, three-dimensional characterization of a heterogeneous hydraulic conductivity field within DOE's Hanford 300 Area site, Washington, by assimilating large-scale, constant-rate injection test data with small-scale, three-dimensional electromagnetic borehole flowmeter (EBF) measurement data. We first inverted the injection test data to estimate the transmissivity field, using zeroth-order temporal moments of pressure buildup curves. We applied a newly developed Bayesian geostatistical inversion framework, the method of anchored distributions (MAD), to obtain a joint posterior distribution of geostatistical parameters and local log-transmissivities at multiple locations. The unique aspects of MAD that make it suitable for this purpose are itsmore » ability to integrate multi-scale, multi-type data within a Bayesian framework and to compute a nonparametric posterior distribution. After we combined the distribution of transmissivities with depth-discrete relative-conductivity profile from EBF data, we inferred the three-dimensional geostatistical parameters of the log-conductivity field, using the Bayesian model-based geostatistics. Such consistent use of the Bayesian approach throughout the procedure enabled us to systematically incorporate data uncertainty into the final posterior distribution. The method was tested in a synthetic study and validated using the actual data that was not part of the estimation. Results showed broader and skewed posterior distributions of geostatistical parameters except for the mean, which suggests the importance of inferring the entire distribution to quantify the parameter uncertainty.« less

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.

Identifiability of sorption parameters in stirred flow-through reactor experiments and their identification with a Bayesian approach.

PubMed

Nicoulaud-Gouin, V; Garcia-Sanchez, L; Giacalone, M; Attard, J C; Martin-Garin, A; Bois, F Y

2016-10-01

This paper addresses the methodological conditions -particularly experimental design and statistical inference- ensuring the identifiability of sorption parameters from breakthrough curves measured during stirred flow-through reactor experiments also known as continuous flow stirred-tank reactor (CSTR) experiments. The equilibrium-kinetic (EK) sorption model was selected as nonequilibrium parameterization embedding the K d approach. Parameter identifiability was studied formally on the equations governing outlet concentrations. It was also studied numerically on 6 simulated CSTR experiments on a soil with known equilibrium-kinetic sorption parameters. EK sorption parameters can not be identified from a single breakthrough curve of a CSTR experiment, because K d,1 and k - were diagnosed collinear. For pairs of CSTR experiments, Bayesian inference allowed to select the correct models of sorption and error among sorption alternatives. Bayesian inference was conducted with SAMCAT software (Sensitivity Analysis and Markov Chain simulations Applied to Transfer models) which launched the simulations through the embedded simulation engine GNU-MCSim, and automated their configuration and post-processing. Experimental designs consisting in varying flow rates between experiments reaching equilibrium at contamination stage were found optimal, because they simultaneously gave accurate sorption parameters and predictions. Bayesian results were comparable to maximum likehood method but they avoided convergence problems, the marginal likelihood allowed to compare all models, and credible interval gave directly the uncertainty of sorption parameters θ. Although these findings are limited to the specific conditions studied here, in particular the considered sorption model, the chosen parameter values and error structure, they help in the conception and analysis of future CSTR experiments with radionuclides whose kinetic behaviour is suspected. Copyright © 2016 Elsevier Ltd. All rights reserved.

Montblanc1: GPU accelerated radio interferometer measurement equations in support of Bayesian inference for radio observations

NASA Astrophysics Data System (ADS)

Perkins, S. J.; Marais, P. C.; Zwart, J. T. L.; Natarajan, I.; Tasse, C.; Smirnov, O.

2015-09-01

We present Montblanc, a GPU implementation of the Radio interferometer measurement equation (RIME) in support of the Bayesian inference for radio observations (BIRO) technique. BIRO uses Bayesian inference to select sky models that best match the visibilities observed by a radio interferometer. To accomplish this, BIRO evaluates the RIME multiple times, varying sky model parameters to produce multiple model visibilities. χ2 values computed from the model and observed visibilities are used as likelihood values to drive the Bayesian sampling process and select the best sky model. As most of the elements of the RIME and χ2 calculation are independent of one another, they are highly amenable to parallel computation. Additionally, Montblanc caters for iterative RIME evaluation to produce multiple χ2 values. Modified model parameters are transferred to the GPU between each iteration. We implemented Montblanc as a Python package based upon NVIDIA's CUDA architecture. As such, it is easy to extend and implement different pipelines. At present, Montblanc supports point and Gaussian morphologies, but is designed for easy addition of new source profiles. Montblanc's RIME implementation is performant: On an NVIDIA K40, it is approximately 250 times faster than MEQTREES on a dual hexacore Intel E5-2620v2 CPU. Compared to the OSKAR simulator's GPU-implemented RIME components it is 7.7 and 12 times faster on the same K40 for single and double-precision floating point respectively. However, OSKAR's RIME implementation is more general than Montblanc's BIRO-tailored RIME. Theoretical analysis of Montblanc's dominant CUDA kernel suggests that it is memory bound. In practice, profiling shows that is balanced between compute and memory, as much of the data required by the problem is retained in L1 and L2 caches.

Bayesian Inference for Signal-Based Seismic Monitoring

NASA Astrophysics Data System (ADS)

Moore, D.

2015-12-01

Traditional seismic monitoring systems rely on discrete detections produced by station processing software, discarding significant information present in the original recorded signal. SIG-VISA (Signal-based Vertically Integrated Seismic Analysis) is a system for global seismic monitoring through Bayesian inference on seismic signals. By modeling signals directly, our forward model is able to incorporate a rich representation of the physics underlying the signal generation process, including source mechanisms, wave propagation, and station response. This allows inference in the model to recover the qualitative behavior of recent geophysical methods including waveform matching and double-differencing, all as part of a unified Bayesian monitoring system that simultaneously detects and locates events from a global network of stations. We demonstrate recent progress in scaling up SIG-VISA to efficiently process the data stream of global signals recorded by the International Monitoring System (IMS), including comparisons against existing processing methods that show increased sensitivity from our signal-based model and in particular the ability to locate events (including aftershock sequences that can tax analyst processing) precisely from waveform correlation effects. We also provide a Bayesian analysis of an alleged low-magnitude event near the DPRK test site in May 2010 [1] [2], investigating whether such an event could plausibly be detected through automated processing in a signal-based monitoring system. [1] Zhang, Miao and Wen, Lianxing. "Seismological Evidence for a Low-Yield Nuclear Test on 12 May 2010 in North Korea". Seismological Research Letters, January/February 2015. [2] Richards, Paul. "A Seismic Event in North Korea on 12 May 2010". CTBTO SnT 2015 oral presentation, video at https://video-archive.ctbto.org/index.php/kmc/preview/partner_id/103/uiconf_id/4421629/entry_id/0_ymmtpps0/delivery/http

Estimation of white matter fiber parameters from compressed multiresolution diffusion MRI using sparse Bayesian learning.

PubMed

Pisharady, Pramod Kumar; Sotiropoulos, Stamatios N; Duarte-Carvajalino, Julio M; Sapiro, Guillermo; Lenglet, Christophe

2018-02-15

We present a sparse Bayesian unmixing algorithm BusineX: Bayesian Unmixing for Sparse Inference-based Estimation of Fiber Crossings (X), for estimation of white matter fiber parameters from compressed (under-sampled) diffusion MRI (dMRI) data. BusineX combines compressive sensing with linear unmixing and introduces sparsity to the previously proposed multiresolution data fusion algorithm RubiX, resulting in a method for improved reconstruction, especially from data with lower number of diffusion gradients. We formulate the estimation of fiber parameters as a sparse signal recovery problem and propose a linear unmixing framework with sparse Bayesian learning for the recovery of sparse signals, the fiber orientations and volume fractions. The data is modeled using a parametric spherical deconvolution approach and represented using a dictionary created with the exponential decay components along different possible diffusion directions. Volume fractions of fibers along these directions define the dictionary weights. The proposed sparse inference, which is based on the dictionary representation, considers the sparsity of fiber populations and exploits the spatial redundancy in data representation, thereby facilitating inference from under-sampled q-space. The algorithm improves parameter estimation from dMRI through data-dependent local learning of hyperparameters, at each voxel and for each possible fiber orientation, that moderate the strength of priors governing the parameter variances. Experimental results on synthetic and in-vivo data show improved accuracy with a lower uncertainty in fiber parameter estimates. BusineX resolves a higher number of second and third fiber crossings. For under-sampled data, the algorithm is also shown to produce more reliable estimates. Copyright © 2017 Elsevier Inc. All rights reserved.

Bayesian inferences suggest that Amazon Yunga Natives diverged from Andeans less than 5000 ybp: implications for South American prehistory.

PubMed

Scliar, Marilia O; Gouveia, Mateus H; Benazzo, Andrea; Ghirotto, Silvia; Fagundes, Nelson J R; Leal, Thiago P; Magalhães, Wagner C S; Pereira, Latife; Rodrigues, Maira R; Soares-Souza, Giordano B; Cabrera, Lilia; Berg, Douglas E; Gilman, Robert H; Bertorelle, Giorgio; Tarazona-Santos, Eduardo

2014-09-30

Archaeology reports millenary cultural contacts between Peruvian Coast-Andes and the Amazon Yunga, a rainforest transitional region between Andes and Lower Amazonia. To clarify the relationships between cultural and biological evolution of these populations, in particular between Amazon Yungas and Andeans, we used DNA-sequence data, a model-based Bayesian approach and several statistical validations to infer a set of demographic parameters. We found that the genetic diversity of the Shimaa (an Amazon Yunga population) is a subset of that of Quechuas from Central-Andes. Using the Isolation-with-Migration population genetics model, we inferred that the Shimaa ancestors were a small subgroup that split less than 5300 years ago (after the development of complex societies) from an ancestral Andean population. After the split, the most plausible scenario compatible with our results is that the ancestors of Shimaas moved toward the Peruvian Amazon Yunga and incorporated the culture and language of some of their neighbors, but not a substantial amount of their genes. We validated our results using Approximate Bayesian Computations, posterior predictive tests and the analysis of pseudo-observed datasets. We presented a case study in which model-based Bayesian approaches, combined with necessary statistical validations, shed light into the prehistoric demographic relationship between Andeans and a population from the Amazon Yunga. Our results offer a testable model for the peopling of this large transitional environmental region between the Andes and the Lower Amazonia. However, studies on larger samples and involving more populations of these regions are necessary to confirm if the predominant Andean biological origin of the Shimaas is the rule, and not the exception.

Variational Bayesian Learning for Wavelet Independent Component Analysis

NASA Astrophysics Data System (ADS)

Roussos, E.; Roberts, S.; Daubechies, I.

2005-11-01

In an exploratory approach to data analysis, it is often useful to consider the observations as generated from a set of latent generators or "sources" via a generally unknown mapping. For the noisy overcomplete case, where we have more sources than observations, the problem becomes extremely ill-posed. Solutions to such inverse problems can, in many cases, be achieved by incorporating prior knowledge about the problem, captured in the form of constraints. This setting is a natural candidate for the application of the Bayesian methodology, allowing us to incorporate "soft" constraints in a natural manner. The work described in this paper is mainly driven by problems in functional magnetic resonance imaging of the brain, for the neuro-scientific goal of extracting relevant "maps" from the data. This can be stated as a `blind' source separation problem. Recent experiments in the field of neuroscience show that these maps are sparse, in some appropriate sense. The separation problem can be solved by independent component analysis (ICA), viewed as a technique for seeking sparse components, assuming appropriate distributions for the sources. We derive a hybrid wavelet-ICA model, transforming the signals into a domain where the modeling assumption of sparsity of the coefficients with respect to a dictionary is natural. We follow a graphical modeling formalism, viewing ICA as a probabilistic generative model. We use hierarchical source and mixing models and apply Bayesian inference to the problem. This allows us to perform model selection in order to infer the complexity of the representation, as well as automatic denoising. Since exact inference and learning in such a model is intractable, we follow a variational Bayesian mean-field approach in the conjugate-exponential family of distributions, for efficient unsupervised learning in multi-dimensional settings. The performance of the proposed algorithm is demonstrated on some representative experiments.

On parametrized cold dense matter equation-of-state inference

NASA Astrophysics Data System (ADS)

Riley, Thomas E.; Raaijmakers, Geert; Watts, Anna L.

2018-07-01

Constraining the equation of state of cold dense matter in compact stars is a major science goal for observing programmes being conducted using X-ray, radio, and gravitational wave telescopes. We discuss Bayesian hierarchical inference of parametrized dense matter equations of state. In particular, we generalize and examine two inference paradigms from the literature: (i) direct posterior equation-of-state parameter estimation, conditioned on observations of a set of rotating compact stars; and (ii) indirect parameter estimation, via transformation of an intermediary joint posterior distribution of exterior spacetime parameters (such as gravitational masses and coordinate equatorial radii). We conclude that the former paradigm is not only tractable for large-scale analyses, but is principled and flexible from a Bayesian perspective while the latter paradigm is not. The thematic problem of Bayesian prior definition emerges as the crux of the difference between these paradigms. The second paradigm should in general only be considered as an ill-defined approach to the problem of utilizing archival posterior constraints on exterior spacetime parameters; we advocate for an alternative approach whereby such information is repurposed as an approximative likelihood function. We also discuss why conditioning on a piecewise-polytropic equation-of-state model - currently standard in the field of dense matter study - can easily violate conditions required for transformation of a probability density distribution between spaces of exterior (spacetime) and interior (source matter) parameters.

On parametrised cold dense matter equation of state inference

NASA Astrophysics Data System (ADS)

Riley, Thomas E.; Raaijmakers, Geert; Watts, Anna L.

2018-04-01

Constraining the equation of state of cold dense matter in compact stars is a major science goal for observing programmes being conducted using X-ray, radio, and gravitational wave telescopes. We discuss Bayesian hierarchical inference of parametrised dense matter equations of state. In particular we generalise and examine two inference paradigms from the literature: (i) direct posterior equation of state parameter estimation, conditioned on observations of a set of rotating compact stars; and (ii) indirect parameter estimation, via transformation of an intermediary joint posterior distribution of exterior spacetime parameters (such as gravitational masses and coordinate equatorial radii). We conclude that the former paradigm is not only tractable for large-scale analyses, but is principled and flexible from a Bayesian perspective whilst the latter paradigm is not. The thematic problem of Bayesian prior definition emerges as the crux of the difference between these paradigms. The second paradigm should in general only be considered as an ill-defined approach to the problem of utilising archival posterior constraints on exterior spacetime parameters; we advocate for an alternative approach whereby such information is repurposed as an approximative likelihood function. We also discuss why conditioning on a piecewise-polytropic equation of state model - currently standard in the field of dense matter study - can easily violate conditions required for transformation of a probability density distribution between spaces of exterior (spacetime) and interior (source matter) parameters.

Active inference and cognitive-emotional interactions in the brain.

PubMed

Pezzulo, Giovanni; Barca, Laura; Friston, Karl J

2015-01-01

All organisms must integrate cognition, emotion, and motivation to guide action toward valuable (goal) states, as described by active inference. Within this framework, cognition, emotion, and motivation interact through the (Bayesian) fusion of exteroceptive, proprioceptive, and interoceptive signals, the precision-weighting of prediction errors, and the "affective tuning" of neuronal representations. Crucially, misregulation of these processes may have profound psychopathological consequences.

Comparing Trend and Gap Statistics across Tests: Distributional Change Using Ordinal Methods and Bayesian Inference

ERIC Educational Resources Information Center

Denbleyker, John Nickolas

2012-01-01

The shortcomings of the proportion above cut (PAC) statistic used so prominently in the educational landscape renders it a very problematic measure for making correct inferences with student test data. The limitations of PAC-based statistics are more pronounced with cross-test comparisons due to their dependency on cut-score locations. A better…

MULTINEST: an efficient and robust Bayesian inference tool for cosmology and particle physics

NASA Astrophysics Data System (ADS)

Feroz, F.; Hobson, M. P.; Bridges, M.

2009-10-01

We present further development and the first public release of our multimodal nested sampling algorithm, called MULTINEST. This Bayesian inference tool calculates the evidence, with an associated error estimate, and produces posterior samples from distributions that may contain multiple modes and pronounced (curving) degeneracies in high dimensions. The developments presented here lead to further substantial improvements in sampling efficiency and robustness, as compared to the original algorithm presented in Feroz & Hobson, which itself significantly outperformed existing Markov chain Monte Carlo techniques in a wide range of astrophysical inference problems. The accuracy and economy of the MULTINEST algorithm are demonstrated by application to two toy problems and to a cosmological inference problem focusing on the extension of the vanilla Λ cold dark matter model to include spatial curvature and a varying equation of state for dark energy. The MULTINEST software, which is fully parallelized using MPI and includes an interface to COSMOMC, is available at http://www.mrao.cam.ac.uk/software/multinest/. It will also be released as part of the SUPERBAYES package, for the analysis of supersymmetric theories of particle physics, at http://www.superbayes.org.

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.

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

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.

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

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

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.

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

USGS Publications Warehouse

Love, Jeffrey J.

2012-01-01

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

A Hierarchical Bayesian Model for Crowd Emotions

PubMed Central

Urizar, Oscar J.; Baig, Mirza S.; Barakova, Emilia I.; Regazzoni, Carlo S.; Marcenaro, Lucio; Rauterberg, Matthias

2016-01-01

Estimation of emotions is an essential aspect in developing intelligent systems intended for crowded environments. However, emotion estimation in crowds remains a challenging problem due to the complexity in which human emotions are manifested and the capability of a system to perceive them in such conditions. This paper proposes a hierarchical Bayesian model to learn in unsupervised manner the behavior of individuals and of the crowd as a single entity, and explore the relation between behavior and emotions to infer emotional states. Information about the motion patterns of individuals are described using a self-organizing map, and a hierarchical Bayesian network builds probabilistic models to identify behaviors and infer the emotional state of individuals and the crowd. This model is trained and tested using data produced from simulated scenarios that resemble real-life environments. The conducted experiments tested the efficiency of our method to learn, detect and associate behaviors with emotional states yielding accuracy levels of 74% for individuals and 81% for the crowd, similar in performance with existing methods for pedestrian behavior detection but with novel concepts regarding the analysis of crowds. PMID:27458366

Variational dynamic background model for keyword spotting in handwritten documents

NASA Astrophysics Data System (ADS)

Kumar, Gaurav; Wshah, Safwan; Govindaraju, Venu

2013-12-01

We propose a bayesian framework for keyword spotting in handwritten documents. This work is an extension to our previous work where we proposed dynamic background model, DBM for keyword spotting that takes into account the local character level scores and global word level scores to learn a logistic regression classifier to separate keywords from non-keywords. In this work, we add a bayesian layer on top of the DBM called the variational dynamic background model, VDBM. The logistic regression classifier uses the sigmoid function to separate keywords from non-keywords. The sigmoid function being neither convex nor concave, exact inference of VDBM becomes intractable. An expectation maximization step is proposed to do approximate inference. The advantage of VDBM over the DBM is multi-fold. Firstly, being bayesian, it prevents over-fitting of data. Secondly, it provides better modeling of data and an improved prediction of unseen data. VDBM is evaluated on the IAM dataset and the results prove that it outperforms our prior work and other state of the art line based word spotting system.

Bayesian Techniques for Comparing Time-dependent GRMHD Simulations to Variable Event Horizon Telescope Observations

NASA Astrophysics Data System (ADS)

Kim, Junhan; Marrone, Daniel P.; Chan, Chi-Kwan; Medeiros, Lia; Özel, Feryal; Psaltis, Dimitrios

2016-12-01

The Event Horizon Telescope (EHT) is a millimeter-wavelength, very-long-baseline interferometry (VLBI) experiment that is capable of observing black holes with horizon-scale resolution. Early observations have revealed variable horizon-scale emission in the Galactic Center black hole, Sagittarius A* (Sgr A*). Comparing such observations to time-dependent general relativistic magnetohydrodynamic (GRMHD) simulations requires statistical tools that explicitly consider the variability in both the data and the models. We develop here a Bayesian method to compare time-resolved simulation images to variable VLBI data, in order to infer model parameters and perform model comparisons. We use mock EHT data based on GRMHD simulations to explore the robustness of this Bayesian method and contrast it to approaches that do not consider the effects of variability. We find that time-independent models lead to offset values of the inferred parameters with artificially reduced uncertainties. Moreover, neglecting the variability in the data and the models often leads to erroneous model selections. We finally apply our method to the early EHT data on Sgr A*.

BAYESIAN TECHNIQUES FOR COMPARING TIME-DEPENDENT GRMHD SIMULATIONS TO VARIABLE EVENT HORIZON TELESCOPE OBSERVATIONS

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

Kim, Junhan; Marrone, Daniel P.; Chan, Chi-Kwan

2016-12-01

The Event Horizon Telescope (EHT) is a millimeter-wavelength, very-long-baseline interferometry (VLBI) experiment that is capable of observing black holes with horizon-scale resolution. Early observations have revealed variable horizon-scale emission in the Galactic Center black hole, Sagittarius A* (Sgr A*). Comparing such observations to time-dependent general relativistic magnetohydrodynamic (GRMHD) simulations requires statistical tools that explicitly consider the variability in both the data and the models. We develop here a Bayesian method to compare time-resolved simulation images to variable VLBI data, in order to infer model parameters and perform model comparisons. We use mock EHT data based on GRMHD simulations to explore themore » robustness of this Bayesian method and contrast it to approaches that do not consider the effects of variability. We find that time-independent models lead to offset values of the inferred parameters with artificially reduced uncertainties. Moreover, neglecting the variability in the data and the models often leads to erroneous model selections. We finally apply our method to the early EHT data on Sgr A*.« less

Impact of petrophysical uncertainty on Bayesian hydrogeophysical inversion and model selection

NASA Astrophysics Data System (ADS)

Brunetti, Carlotta; Linde, Niklas

2018-01-01

Quantitative hydrogeophysical studies rely heavily on petrophysical relationships that link geophysical properties to hydrogeological properties and state variables. Coupled inversion studies are frequently based on the questionable assumption that these relationships are perfect (i.e., no scatter). Using synthetic examples and crosshole ground-penetrating radar (GPR) data from the South Oyster Bacterial Transport Site in Virginia, USA, we investigate the impact of spatially-correlated petrophysical uncertainty on inferred posterior porosity and hydraulic conductivity distributions and on Bayes factors used in Bayesian model selection. Our study shows that accounting for petrophysical uncertainty in the inversion (I) decreases bias of the inferred variance of hydrogeological subsurface properties, (II) provides more realistic uncertainty assessment and (III) reduces the overconfidence in the ability of geophysical data to falsify conceptual hydrogeological models.

Bayesian Inference of Natural Rankings in Incomplete Competition Networks

PubMed Central

Park, Juyong; Yook, Soon-Hyung

2014-01-01

Competition between a complex system's constituents and a corresponding reward mechanism based on it have profound influence on the functioning, stability, and evolution of the system. But determining the dominance hierarchy or ranking among the constituent parts from the strongest to the weakest – essential in determining reward and penalty – is frequently an ambiguous task due to the incomplete (partially filled) nature of competition networks. Here we introduce the “Natural Ranking,” an unambiguous ranking method applicable to a round robin tournament, and formulate an analytical model based on the Bayesian formula for inferring the expected mean and error of the natural ranking of nodes from an incomplete network. We investigate its potential and uses in resolving important issues of ranking by applying it to real-world competition networks. PMID:25163528

Uncertain deduction and conditional reasoning.

PubMed

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

2015-01-01

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

Bayesian inference to identify parameters in viscoelasticity

NASA Astrophysics Data System (ADS)

Rappel, Hussein; Beex, Lars A. A.; Bordas, Stéphane P. A.

2017-08-01

This contribution discusses Bayesian inference (BI) as an approach to identify parameters in viscoelasticity. The aims are: (i) to show that the prior has a substantial influence for viscoelasticity, (ii) to show that this influence decreases for an increasing number of measurements and (iii) to show how different types of experiments influence the identified parameters and their uncertainties. The standard linear solid model is the material description of interest and a relaxation test, a constant strain-rate test and a creep test are the tensile experiments focused on. The experimental data are artificially created, allowing us to make a one-to-one comparison between the input parameters and the identified parameter values. Besides dealing with the aforementioned issues, we believe that this contribution forms a comprehensible start for those interested in applying BI in viscoelasticity.

On an adaptive preconditioned Crank-Nicolson MCMC algorithm for infinite dimensional Bayesian inference

NASA Astrophysics Data System (ADS)

Hu, Zixi; Yao, Zhewei; Li, Jinglai

2017-03-01

Many scientific and engineering problems require to perform Bayesian inference for unknowns of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary slow under the mesh refinement, which is referred to as being dimension dependent. To this end, a family of dimensional independent MCMC algorithms, known as the preconditioned Crank-Nicolson (pCN) methods, were proposed to sample the infinite dimensional parameters. In this work we develop an adaptive version of the pCN algorithm, where the covariance operator of the proposal distribution is adjusted based on sampling history to improve the simulation efficiency. We show that the proposed algorithm satisfies an important ergodicity condition under some mild assumptions. Finally we provide numerical examples to demonstrate the performance of the proposed method.

Data set for phylogenetic tree and RAMPAGE Ramachandran plot analysis of SODs in Gossypium raimondii and G. arboreum.

PubMed

Wang, Wei; Xia, Minxuan; Chen, Jie; Deng, Fenni; Yuan, Rui; Zhang, Xiaopei; Shen, Fafu

2016-12-01

The data presented in this paper is supporting the research article "Genome-Wide Analysis of Superoxide Dismutase Gene Family in Gossypium raimondii and G. arboreum" [1]. In this data article, we present phylogenetic tree showing dichotomy with two different clusters of SODs inferred by the Bayesian method of MrBayes (version 3.2.4), "Bayesian phylogenetic inference under mixed models" [2], Ramachandran plots of G. raimondii and G. arboreum SODs, the protein sequence used to generate 3D sructure of proteins and the template accession via SWISS-MODEL server, "SWISS-MODEL: modelling protein tertiary and quaternary structure using evolutionary information." [3] and motif sequences of SODs identified by InterProScan (version 4.8) with the Pfam database, "Pfam: the protein families database" [4].

Multi-Objective data analysis using Bayesian Inference for MagLIF experiments

NASA Astrophysics Data System (ADS)

Knapp, Patrick; Glinksy, Michael; Evans, Matthew; Gom, Matth; Han, Stephanie; Harding, Eric; Slutz, Steve; Hahn, Kelly; Harvey-Thompson, Adam; Geissel, Matthias; Ampleford, David; Jennings, Christopher; Schmit, Paul; Smith, Ian; Schwarz, Jens; Peterson, Kyle; Jones, Brent; Rochau, Gregory; Sinars, Daniel

2017-10-01

The MagLIF concept has recently demonstrated Gbar pressures and confinement of charged fusion products at stagnation. We present a new analysis methodology that allows for integration of multiple diagnostics including nuclear, x-ray imaging, and x-ray power to determine the temperature, pressure, liner areal density, and mix fraction. A simplified hot-spot model is used with a Bayesian inference network to determine the most probable model parameters that describe the observations while simultaneously revealing the principal uncertainties in the analysis. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525.

Bayesian Inference of Natural Rankings in Incomplete Competition Networks

NASA Astrophysics Data System (ADS)

Park, Juyong; Yook, Soon-Hyung

2014-08-01

Competition between a complex system's constituents and a corresponding reward mechanism based on it have profound influence on the functioning, stability, and evolution of the system. But determining the dominance hierarchy or ranking among the constituent parts from the strongest to the weakest - essential in determining reward and penalty - is frequently an ambiguous task due to the incomplete (partially filled) nature of competition networks. Here we introduce the ``Natural Ranking,'' an unambiguous ranking method applicable to a round robin tournament, and formulate an analytical model based on the Bayesian formula for inferring the expected mean and error of the natural ranking of nodes from an incomplete network. We investigate its potential and uses in resolving important issues of ranking by applying it to real-world competition networks.

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

PubMed

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

2016-01-15

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

Greenhouse Gas Source Attribution: Measurements Modeling and Uncertainty Quantification

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

Liu, Zhen; Safta, Cosmin; Sargsyan, Khachik

2014-09-01

In this project we have developed atmospheric measurement capabilities and a suite of atmospheric modeling and analysis tools that are well suited for verifying emissions of green- house gases (GHGs) on an urban-through-regional scale. We have for the first time applied the Community Multiscale Air Quality (CMAQ) model to simulate atmospheric CO 2 . This will allow for the examination of regional-scale transport and distribution of CO 2 along with air pollutants traditionally studied using CMAQ at relatively high spatial and temporal resolution with the goal of leveraging emissions verification efforts for both air quality and climate. We have developedmore » a bias-enhanced Bayesian inference approach that can remedy the well-known problem of transport model errors in atmospheric CO 2 inversions. We have tested the approach using data and model outputs from the TransCom3 global CO 2 inversion comparison project. We have also performed two prototyping studies on inversion approaches in the generalized convection-diffusion context. One of these studies employed Polynomial Chaos Expansion to accelerate the evaluation of a regional transport model and enable efficient Markov Chain Monte Carlo sampling of the posterior for Bayesian inference. The other approach uses de- terministic inversion of a convection-diffusion-reaction system in the presence of uncertainty. These approaches should, in principle, be applicable to realistic atmospheric problems with moderate adaptation. We outline a regional greenhouse gas source inference system that integrates (1) two ap- proaches of atmospheric dispersion simulation and (2) a class of Bayesian inference and un- certainty quantification algorithms. We use two different and complementary approaches to simulate atmospheric dispersion. Specifically, we use a Eulerian chemical transport model CMAQ and a Lagrangian Particle Dispersion Model - FLEXPART-WRF. These two models share the same WRF assimilated meteorology fields, making it possible to perform a hybrid simulation, in which the Eulerian model (CMAQ) can be used to compute the initial condi- tion needed by the Lagrangian model, while the source-receptor relationships for a large state vector can be efficiently computed using the Lagrangian model in its backward mode. In ad- dition, CMAQ has a complete treatment of atmospheric chemistry of a suite of traditional air pollutants, many of which could help attribute GHGs from different sources. The inference of emissions sources using atmospheric observations is cast as a Bayesian model calibration problem, which is solved using a variety of Bayesian techniques, such as the bias-enhanced Bayesian inference algorithm, which accounts for the intrinsic model deficiency, Polynomial Chaos Expansion to accelerate model evaluation and Markov Chain Monte Carlo sampling, and Karhunen-Lo %60 eve (KL) Expansion to reduce the dimensionality of the state space. We have established an atmospheric measurement site in Livermore, CA and are collect- ing continuous measurements of CO 2 , CH 4 and other species that are typically co-emitted with these GHGs. Measurements of co-emitted species can assist in attributing the GHGs to different emissions sectors. Automatic calibrations using traceable standards are performed routinely for the gas-phase measurements. We are also collecting standard meteorological data at the Livermore site as well as planetary boundary height measurements using a ceilometer. The location of the measurement site is well suited to sample air transported between the San Francisco Bay area and the California Central Valley.« less

Dynamical simulation priors for human motion tracking.

PubMed

Vondrak, Marek; Sigal, Leonid; Jenkins, Odest Chadwicke

2013-01-01

We propose a simulation-based dynamical motion prior for tracking human motion from video in presence of physical ground-person interactions. Most tracking approaches to date have focused on efficient inference algorithms and/or learning of prior kinematic motion models; however, few can explicitly account for the physical plausibility of recovered motion. Here, we aim to recover physically plausible motion of a single articulated human subject. Toward this end, we propose a full-body 3D physical simulation-based prior that explicitly incorporates a model of human dynamics into the Bayesian filtering framework. We consider the motion of the subject to be generated by a feedback “control loop” in which Newtonian physics approximates the rigid-body motion dynamics of the human and the environment through the application and integration of interaction forces, motor forces, and gravity. Interaction forces prevent physically impossible hypotheses, enable more appropriate reactions to the environment (e.g., ground contacts), and are produced from detected human-environment collisions. Motor forces actuate the body, ensure that proposed pose transitions are physically feasible, and are generated using a motion controller. For efficient inference in the resulting high-dimensional state space, we utilize an exemplar-based control strategy that reduces the effective search space of motor forces. As a result, we are able to recover physically plausible motion of human subjects from monocular and multiview video. We show, both quantitatively and qualitatively, that our approach performs favorably with respect to Bayesian filtering methods with standard motion priors.

DETECTING UNSPECIFIED STRUCTURE IN LOW-COUNT IMAGES

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

Stein, Nathan M.; Dyk, David A. van; Kashyap, Vinay L.

Unexpected structure in images of astronomical sources often presents itself upon visual inspection of the image, but such apparent structure may either correspond to true features in the source or be due to noise in the data. This paper presents a method for testing whether inferred structure in an image with Poisson noise represents a significant departure from a baseline (null) model of the image. To infer image structure, we conduct a Bayesian analysis of a full model that uses a multiscale component to allow flexible departures from the posited null model. As a test statistic, we use a tailmore » probability of the posterior distribution under the full model. This choice of test statistic allows us to estimate a computationally efficient upper bound on a p-value that enables us to draw strong conclusions even when there are limited computational resources that can be devoted to simulations under the null model. We demonstrate the statistical performance of our method on simulated images. Applying our method to an X-ray image of the quasar 0730+257, we find significant evidence against the null model of a single point source and uniform background, lending support to the claim of an X-ray jet.« less

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

A Systematic Bayesian Integration of Epidemiological and Genetic Data

PubMed Central

Lau, Max S. Y.; Marion, Glenn; Streftaris, George; Gibson, Gavin

2015-01-01

Genetic sequence data on pathogens have great potential to inform inference of their transmission dynamics ultimately leading to better disease control. Where genetic change and disease transmission occur on comparable timescales additional information can be inferred via the joint analysis of such genetic sequence data and epidemiological observations based on clinical symptoms and diagnostic tests. Although recently introduced approaches represent substantial progress, for computational reasons they approximate genuine joint inference of disease dynamics and genetic change in the pathogen population, capturing partially the joint epidemiological-evolutionary dynamics. Improved methods are needed to fully integrate such genetic data with epidemiological observations, for achieving a more robust inference of the transmission tree and other key epidemiological parameters such as latent periods. Here, building on current literature, a novel Bayesian framework is proposed that infers simultaneously and explicitly the transmission tree and unobserved transmitted pathogen sequences. Our framework facilitates the use of realistic likelihood functions and enables systematic and genuine joint inference of the epidemiological-evolutionary process from partially observed outbreaks. Using simulated data it is shown that this approach is able to infer accurately joint epidemiological-evolutionary dynamics, even when pathogen sequences and epidemiological data are incomplete, and when sequences are available for only a fraction of exposures. These results also characterise and quantify the value of incomplete and partial sequence data, which has important implications for sampling design, and demonstrate the abilities of the introduced method to identify multiple clusters within an outbreak. The framework is used to analyse an outbreak of foot-and-mouth disease in the UK, enhancing current understanding of its transmission dynamics and evolutionary process. PMID:26599399

A Bayesian account of ‘hysteria’

PubMed Central

Adams, Rick A.; Brown, Harriet; Pareés, Isabel; Friston, Karl J.

2012-01-01

This article provides a neurobiological account of symptoms that have been called ‘hysterical’, ‘psychogenic’ or ‘medically unexplained’, which we will call functional motor and sensory symptoms. We use a neurobiologically informed model of hierarchical Bayesian inference in the brain to explain functional motor and sensory symptoms in terms of perception and action arising from inference based on prior beliefs and sensory information. This explanation exploits the key balance between prior beliefs and sensory evidence that is mediated by (body focused) attention, symptom expectations, physical and emotional experiences and beliefs about illness. Crucially, this furnishes an explanation at three different levels: (i) underlying neuromodulatory (synaptic) mechanisms; (ii) cognitive and experiential processes (attention and attribution of agency); and (iii) formal computations that underlie perceptual inference (representation of uncertainty or precision). Our explanation involves primary and secondary failures of inference; the primary failure is the (autonomous) emergence of a percept or belief that is held with undue certainty (precision) following top-down attentional modulation of synaptic gain. This belief can constitute a sensory percept (or its absence) or induce movement (or its absence). The secondary failure of inference is when the ensuing percept (and any somatosensory consequences) is falsely inferred to be a symptom to explain why its content was not predicted by the source of attentional modulation. This account accommodates several fundamental observations about functional motor and sensory symptoms, including: (i) their induction and maintenance by attention; (ii) their modification by expectation, prior experience and cultural beliefs and (iii) their involuntary and symptomatic nature. PMID:22641838

The anatomy of choice: active inference and agency

PubMed Central

Friston, Karl; Schwartenbeck, Philipp; FitzGerald, Thomas; Moutoussis, Michael; Behrens, Timothy; Dolan, Raymond J.

2013-01-01

This paper considers agency in the setting of embodied or active inference. In brief, we associate a sense of agency with prior beliefs about action and ask what sorts of beliefs underlie optimal behavior. In particular, we consider prior beliefs that action minimizes the Kullback–Leibler (KL) divergence between desired states and attainable states in the future. This allows one to formulate bounded rationality as approximate Bayesian inference that optimizes a free energy bound on model evidence. We show that constructs like expected utility, exploration bonuses, softmax choice rules and optimism bias emerge as natural consequences of this formulation. Previous accounts of active inference have focused on predictive coding and Bayesian filtering schemes for minimizing free energy. Here, we consider variational Bayes as an alternative scheme that provides formal constraints on the computational anatomy of inference and action—constraints that are remarkably consistent with neuroanatomy. Furthermore, this scheme contextualizes optimal decision theory and economic (utilitarian) formulations as pure inference problems. For example, expected utility theory emerges as a special case of free energy minimization, where the sensitivity or inverse temperature (of softmax functions and quantal response equilibria) has a unique and Bayes-optimal solution—that minimizes free energy. This sensitivity corresponds to the precision of beliefs about behavior, such that attainable goals are afforded a higher precision or confidence. In turn, this means that optimal behavior entails a representation of confidence about outcomes that are under an agent's control. PMID:24093015

Do people reason rationally about causally related events? Markov violations, weak inferences, and failures of explaining away.

PubMed

Rottman, Benjamin M; Hastie, Reid

2016-06-01

Making judgments by relying on beliefs about the causal relationships between events is a fundamental capacity of everyday cognition. In the last decade, Causal Bayesian Networks have been proposed as a framework for modeling causal reasoning. Two experiments were conducted to provide comprehensive data sets with which to evaluate a variety of different types of judgments in comparison to the standard Bayesian networks calculations. Participants were introduced to a fictional system of three events and observed a set of learning trials that instantiated the multivariate distribution relating the three variables. We tested inferences on chains X1→Y→X2, common cause structures X1←Y→X2, and common effect structures X1→Y←X2, on binary and numerical variables, and with high and intermediate causal strengths. We tested transitive inferences, inferences when one variable is irrelevant because it is blocked by an intervening variable (Markov Assumption), inferences from two variables to a middle variable, and inferences about the presence of one cause when the alternative cause was known to have occurred (the normative "explaining away" pattern). Compared to the normative account, in general, when the judgments should change, they change in the normative direction. However, we also discuss a few persistent violations of the standard normative model. In addition, we evaluate the relative success of 12 theoretical explanations for these deviations. Copyright © 2016 Elsevier Inc. All rights reserved.

Efficient Bayesian inference for natural time series using ARFIMA processes

NASA Astrophysics Data System (ADS)

Graves, Timothy; Gramacy, Robert; Franzke, Christian; Watkins, Nicholas

2016-04-01

Many geophysical quantities, such as atmospheric temperature, water levels in rivers, and wind speeds, have shown evidence of long memory (LM). LM implies that these quantities experience non-trivial temporal memory, which potentially not only enhances their predictability, but also hampers the detection of externally forced trends. Thus, it is important to reliably identify whether or not a system exhibits LM. We present a modern and systematic approach to the inference of LM. We use the flexible autoregressive fractional integrated moving average (ARFIMA) model, which is widely used in time series analysis, and of increasing interest in climate science. Unlike most previous work on the inference of LM, which is frequentist in nature, we provide a systematic treatment of Bayesian inference. In particular, we provide a new approximate likelihood for efficient parameter inference, and show how nuisance parameters (e.g., short-memory effects) can be integrated over in order to focus on long-memory parameters and hypothesis testing more directly. We illustrate our new methodology on the Nile water level data and the central England temperature (CET) time series, with favorable comparison to the standard estimators [1]. In addition we show how the method can be used to perform joint inference of the stability exponent and the memory parameter when ARFIMA is extended to allow for alpha-stable innovations. Such models can be used to study systems where heavy tails and long range memory coexist. [1] Graves et al, Nonlin. Processes Geophys., 22, 679-700, 2015; doi:10.5194/npg-22-679-2015.

Bayesian inversion of a CRN depth profile to infer Quaternary erosion of the northwestern Campine Plateau (NE Belgium)

NASA Astrophysics Data System (ADS)

Laloy, Eric; Beerten, Koen; Vanacker, Veerle; Christl, Marcus; Rogiers, Bart; Wouters, Laurent

2017-07-01

The rate at which low-lying sandy areas in temperate regions, such as the Campine Plateau (NE Belgium), have been eroding during the Quaternary is a matter of debate. Current knowledge on the average pace of landscape evolution in the Campine area is largely based on geological inferences and modern analogies. We performed a Bayesian inversion of an in situ-produced 10Be concentration depth profile to infer the average long-term erosion rate together with two other parameters: the surface exposure age and the inherited 10Be concentration. Compared to the latest advances in probabilistic inversion of cosmogenic radionuclide (CRN) data, our approach has the following two innovative components: it (1) uses Markov chain Monte Carlo (MCMC) sampling and (2) accounts (under certain assumptions) for the contribution of model errors to posterior uncertainty. To investigate to what extent our approach differs from the state of the art in practice, a comparison against the Bayesian inversion method implemented in the CRONUScalc program is made. Both approaches identify similar maximum a posteriori (MAP) parameter values, but posterior parameter and predictive uncertainty derived using the method taken in CRONUScalc is moderately underestimated. A simple way for producing more consistent uncertainty estimates with the CRONUScalc-like method in the presence of model errors is therefore suggested. Our inferred erosion rate of 39 ± 8. 9 mm kyr-1 (1σ) is relatively large in comparison with landforms that erode under comparable (paleo-)climates elsewhere in the world. We evaluate this value in the light of the erodibility of the substrate and sudden base level lowering during the Middle Pleistocene. A denser sampling scheme of a two-nuclide concentration depth profile would allow for better inferred erosion rate resolution, and including more uncertain parameters in the MCMC inversion.

Network inference from multimodal data: A review of approaches from infectious disease transmission.

PubMed

Ray, Bisakha; Ghedin, Elodie; Chunara, Rumi

2016-12-01

Networks inference problems are commonly found in multiple biomedical subfields such as genomics, metagenomics, neuroscience, and epidemiology. Networks are useful for representing a wide range of complex interactions ranging from those between molecular biomarkers, neurons, and microbial communities, to those found in human or animal populations. Recent technological advances have resulted in an increasing amount of healthcare data in multiple modalities, increasing the preponderance of network inference problems. Multi-domain data can now be used to improve the robustness and reliability of recovered networks from unimodal data. For infectious diseases in particular, there is a body of knowledge that has been focused on combining multiple pieces of linked information. Combining or analyzing disparate modalities in concert has demonstrated greater insight into disease transmission than could be obtained from any single modality in isolation. This has been particularly helpful in understanding incidence and transmission at early stages of infections that have pandemic potential. Novel pieces of linked information in the form of spatial, temporal, and other covariates including high-throughput sequence data, clinical visits, social network information, pharmaceutical prescriptions, and clinical symptoms (reported as free-text data) also encourage further investigation of these methods. The purpose of this review is to provide an in-depth analysis of multimodal infectious disease transmission network inference methods with a specific focus on Bayesian inference. We focus on analytical Bayesian inference-based methods as this enables recovering multiple parameters simultaneously, for example, not just the disease transmission network, but also parameters of epidemic dynamics. Our review studies their assumptions, key inference parameters and limitations, and ultimately provides insights about improving future network inference methods in multiple applications. Copyright © 2016 Elsevier Inc. All rights reserved.

IZI: INFERRING THE GAS PHASE METALLICITY (Z) AND IONIZATION PARAMETER (q) OF IONIZED NEBULAE USING BAYESIAN STATISTICS

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

Blanc, Guillermo A.; Kewley, Lisa; Vogt, Frédéric P. A.

2015-01-10

We present a new method for inferring the metallicity (Z) and ionization parameter (q) of H II regions and star-forming galaxies using strong nebular emission lines (SELs). We use Bayesian inference to derive the joint and marginalized posterior probability density functions for Z and q given a set of observed line fluxes and an input photoionization model. Our approach allows the use of arbitrary sets of SELs and the inclusion of flux upper limits. The method provides a self-consistent way of determining the physical conditions of ionized nebulae that is not tied to the arbitrary choice of a particular SELmore » diagnostic and uses all the available information. Unlike theoretically calibrated SEL diagnostics, the method is flexible and not tied to a particular photoionization model. We describe our algorithm, validate it against other methods, and present a tool that implements it called IZI. Using a sample of nearby extragalactic H II regions, we assess the performance of commonly used SEL abundance diagnostics. We also use a sample of 22 local H II regions having both direct and recombination line (RL) oxygen abundance measurements in the literature to study discrepancies in the abundance scale between different methods. We find that oxygen abundances derived through Bayesian inference using currently available photoionization models in the literature can be in good (∼30%) agreement with RL abundances, although some models perform significantly better than others. We also confirm that abundances measured using the direct method are typically ∼0.2 dex lower than both RL and photoionization-model-based abundances.« less

Essays on inference in economics, competition, and the rate of profit

NASA Astrophysics Data System (ADS)

Scharfenaker, Ellis S.

This dissertation is comprised of three papers that demonstrate the role of Bayesian methods of inference and Shannon's information theory in classical political economy. The first chapter explores the empirical distribution of profit rate data from North American firms from 1962-2012. This chapter address the fact that existing methods for sample selection from noisy profit rate data in the industrial organization field of economics tends to be conditional on a covariate's value that risks discarding information. Conditioning sample selection instead on the profit rate data's structure by means of a two component (signal and noise) Bayesian mixture model we find the the profit rate sample to be time stationary Laplace distributed, corroborating earlier estimates of cross section distributions. The second chapter compares alternative probabilistic approaches to discrete (quantal) choice analysis and examines the various ways in which they overlap. In particular, the work on individual choice behavior by Duncan Luce and the extension of this work to quantal response problems by game theoreticians is shown to be related both to the rational inattention work of Christopher Sims through Shannon's information theory as well as to the maximum entropy principle of inference proposed physicist Edwin T. Jaynes. In the third chapter I propose a model of ``classically" competitive firms facing informational entropy constraints in their decisions to potentially enter or exit markets based on profit rate differentials. The result is a three parameter logit quantal response distribution for firm entry and exit decisions. Bayesian methods are used for inference into the the distribution of entry and exit decisions conditional on profit rate deviations and firm level data from Compustat is used to test these predictions.

Bayesian inference for disease prevalence using negative binomial group testing

PubMed Central

Pritchard, Nicholas A.; Tebbs, Joshua M.

2011-01-01

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

Bayesian 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.

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.

Stan : A Probabilistic Programming Language

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

Carpenter, Bob; Gelman, Andrew; Hoffman, Matthew D.

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectationmore » propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can also be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.« less

Stan : A Probabilistic Programming Language

DOE PAGES

Carpenter, Bob; Gelman, Andrew; Hoffman, Matthew D.; ...

2017-01-01

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectationmore » propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can also be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.« less

PyClone: statistical inference of clonal population structure in cancer.

PubMed

Roth, Andrew; Khattra, Jaswinder; Yap, Damian; Wan, Adrian; Laks, Emma; Biele, Justina; Ha, Gavin; Aparicio, Samuel; Bouchard-Côté, Alexandre; Shah, Sohrab P

2014-04-01

We introduce PyClone, a statistical model for inference of clonal population structures in cancers. PyClone is a Bayesian clustering method for grouping sets of deeply sequenced somatic mutations into putative clonal clusters while estimating their cellular prevalences and accounting for allelic imbalances introduced by segmental copy-number changes and normal-cell contamination. Single-cell sequencing validation demonstrates PyClone's accuracy.

Bayesian Inference for Source Reconstruction: A Real-World Application

DTIC Science & Technology

2014-09-25

deliberately or acci- dentally . Two examples of operational monitoring sensor networks are the deployment of biological sensor arrays by the Department of...remarkable paper, Cox [16] demonstrated that proba- bility theory, when interpreted as logic, is the only calculus that conforms to a consistent theory...of inference. This demonstration provides the firm logical basis for asserting that probability calculus is the unique quantitative theory of

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

PubMed Central

Ogunsakin, Ropo Ebenezer; Siaka, Lougue

2017-01-01

Background: There has been no previous study to classify malignant breast tumor in details based on Markov Chain Monte Carlo (MCMC) convergence in Western, Nigeria. This study therefore aims to profile patients living with benign and malignant breast tumor in two different hospitals among women of Western Nigeria, with a focus on prognostic factors and MCMC convergence. Materials and Methods: A hospital-based record was used to identify prognostic factors for malignant breast cancer among women of Western Nigeria. This paper describes Bayesian inference and demonstrates its usage to estimation of parameters of the logistic regression via Markov Chain Monte Carlo (MCMC) algorithm. The result of the Bayesian approach is compared with the classical statistics. Results: The mean age of the respondents was 42.2 ±16.6 years with 52% of the women aged between 35-49 years. The results of both techniques suggest that age and women with at least high school education have a significantly higher risk of being diagnosed with malignant breast tumors than benign breast tumors. The results also indicate a reduction of standard errors is associated with the coefficients obtained from the Bayesian approach. In addition, simulation result reveal that women with at least high school are 1.3 times more at risk of having malignant breast lesion in western Nigeria compared to benign breast lesion. Conclusion: We concluded that more efforts are required towards creating awareness and advocacy campaigns on how the prevalence of malignant breast lesions can be reduced, especially among women. The application of Bayesian produces precise estimates for modeling malignant breast cancer. PMID:29072396

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.

Dynamical foundations of the neural circuit for bayesian decision making.

PubMed

Morita, Kenji

2009-07-01

On the basis of accumulating behavioral and neural evidences, it has recently been proposed that the brain neural circuits of humans and animals are equipped with several specific properties, which ensure that perceptual decision making implemented by the circuits can be nearly optimal in terms of Bayesian inference. Here, I introduce the basic ideas of such a proposal and discuss its implications from the standpoint of biophysical modeling developed in the framework of dynamical systems.

Bayesian Covariate Selection in Mixed-Effects Models For Longitudinal Shape Analysis

PubMed Central

Muralidharan, Prasanna; Fishbaugh, James; Kim, Eun Young; Johnson, Hans J.; Paulsen, Jane S.; Gerig, Guido; Fletcher, P. Thomas

2016-01-01

The goal of longitudinal shape analysis is to understand how anatomical shape changes over time, in response to biological processes, including growth, aging, or disease. In many imaging studies, it is also critical to understand how these shape changes are affected by other factors, such as sex, disease diagnosis, IQ, etc. Current approaches to longitudinal shape analysis have focused on modeling age-related shape changes, but have not included the ability to handle covariates. In this paper, we present a novel Bayesian mixed-effects shape model that incorporates simultaneous relationships between longitudinal shape data and multiple predictors or covariates to the model. Moreover, we place an Automatic Relevance Determination (ARD) prior on the parameters, that lets us automatically select which covariates are most relevant to the model based on observed data. We evaluate our proposed model and inference procedure on a longitudinal study of Huntington's disease from PREDICT-HD. We first show the utility of the ARD prior for model selection in a univariate modeling of striatal volume, and next we apply the full high-dimensional longitudinal shape model to putamen shapes. PMID:28090246

Adaptive design optimization: a mutual information-based approach to model discrimination in cognitive science.

PubMed

Cavagnaro, Daniel R; Myung, Jay I; Pitt, Mark A; Kujala, Janne V

2010-04-01

Discriminating among competing statistical models is a pressing issue for many experimentalists in the field of cognitive science. Resolving this issue begins with designing maximally informative experiments. To this end, the problem to be solved in adaptive design optimization is identifying experimental designs under which one can infer the underlying model in the fewest possible steps. When the models under consideration are nonlinear, as is often the case in cognitive science, this problem can be impossible to solve analytically without simplifying assumptions. However, as we show in this letter, a full solution can be found numerically with the help of a Bayesian computational trick derived from the statistics literature, which recasts the problem as a probability density simulation in which the optimal design is the mode of the density. We use a utility function based on mutual information and give three intuitive interpretations of the utility function in terms of Bayesian posterior estimates. As a proof of concept, we offer a simple example application to an experiment on memory retention.

Variational Bayesian Inversion of Quasi-Localized Seismic Attributes for the Spatial Distribution of Geological Facies

NASA Astrophysics Data System (ADS)

Nawaz, Muhammad Atif; Curtis, Andrew

2018-04-01

We introduce a new Bayesian inversion method that estimates the spatial distribution of geological facies from attributes of seismic data, by showing how the usual probabilistic inverse problem can be solved using an optimization framework still providing full probabilistic results. Our mathematical model consists of seismic attributes as observed data, which are assumed to have been generated by the geological facies. The method infers the post-inversion (posterior) probability density of the facies plus some other unknown model parameters, from the seismic attributes and geological prior information. Most previous research in this domain is based on the localized likelihoods assumption, whereby the seismic attributes at a location are assumed to depend on the facies only at that location. Such an assumption is unrealistic because of imperfect seismic data acquisition and processing, and fundamental limitations of seismic imaging methods. In this paper, we relax this assumption: we allow probabilistic dependence between seismic attributes at a location and the facies in any neighbourhood of that location through a spatial filter. We term such likelihoods quasi-localized.

Feasibility study of direct spectra measurements for Thomson scattered signals for KSTAR fusion-grade plasmas

NASA Astrophysics Data System (ADS)

Park, K.-R.; Kim, K.-h.; Kwak, S.; Svensson, J.; Lee, J.; Ghim, Y.-c.

2017-11-01

Feasibility study of direct spectra measurements of Thomson scattered photons for fusion-grade plasmas is performed based on a forward model of the KSTAR Thomson scattering system. Expected spectra in the forward model are calculated based on Selden function including the relativistic polarization correction. Noise in the signal is modeled with photon noise and Gaussian electrical noise. Electron temperature and density are inferred using Bayesian probability theory. Based on bias error, full width at half maximum and entropy of posterior distributions, spectral measurements are found to be feasible. Comparisons between spectrometer-based and polychromator-based Thomson scattering systems are performed with varying quantum efficiency and electrical noise levels.

Analyzing Single-Molecule Time Series via Nonparametric Bayesian Inference

PubMed Central

Hines, Keegan E.; Bankston, John R.; Aldrich, Richard W.

2015-01-01

The ability to measure the properties of proteins at the single-molecule level offers an unparalleled glimpse into biological systems at the molecular scale. The interpretation of single-molecule time series has often been rooted in statistical mechanics and the theory of Markov processes. While existing analysis methods have been useful, they are not without significant limitations including problems of model selection and parameter nonidentifiability. To address these challenges, we introduce the use of nonparametric Bayesian inference for the analysis of single-molecule time series. These methods provide a flexible way to extract structure from data instead of assuming models beforehand. We demonstrate these methods with applications to several diverse settings in single-molecule biophysics. This approach provides a well-constrained and rigorously grounded method for determining the number of biophysical states underlying single-molecule data. PMID:25650922

Uncertain deduction and conditional reasoning

PubMed Central

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

2015-01-01

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

The double slit experiment and the time reversed fire alarm

NASA Astrophysics Data System (ADS)

Halabi, Tarek

2011-03-01

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

A Bayesian method for inferring transmission chains in a partially observed epidemic.

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

Marzouk, Youssef M.; Ray, Jaideep

2008-10-01

We present a Bayesian approach for estimating transmission chains and rates in the Abakaliki smallpox epidemic of 1967. The epidemic affected 30 individuals in a community of 74; only the dates of appearance of symptoms were recorded. Our model assumes stochastic transmission of the infections over a social network. Distinct binomial random graphs model intra- and inter-compound social connections, while disease transmission over each link is treated as a Poisson process. Link probabilities and rate parameters are objects of inference. Dates of infection and recovery comprise the remaining unknowns. Distributions for smallpox incubation and recovery periods are obtained from historicalmore » data. Using Markov chain Monte Carlo, we explore the joint posterior distribution of the scalar parameters and provide an expected connectivity pattern for the social graph and infection pathway.« less

Comparing nonparametric Bayesian tree priors for clonal reconstruction of tumors.

PubMed

Deshwar, Amit G; Vembu, Shankar; Morris, Quaid

2015-01-01

Statistical machine learning methods, especially nonparametric Bayesian methods, have become increasingly popular to infer clonal population structure of tumors. Here we describe the treeCRP, an extension of the Chinese restaurant process (CRP), a popular construction used in nonparametric mixture models, to infer the phylogeny and genotype of major subclonal lineages represented in the population of cancer cells. We also propose new split-merge updates tailored to the subclonal reconstruction problem that improve the mixing time of Markov chains. In comparisons with the tree-structured stick breaking prior used in PhyloSub, we demonstrate superior mixing and running time using the treeCRP with our new split-merge procedures. We also show that given the same number of samples, TSSB and treeCRP have similar ability to recover the subclonal structure of a tumor…

Sizing aerosolized fractal nanoparticle aggregates through Bayesian analysis of wide-angle light scattering (WALS) data

NASA Astrophysics Data System (ADS)

Huber, Franz J. T.; Will, Stefan; Daun, Kyle J.

2016-11-01

Inferring the size distribution of aerosolized fractal aggregates from the angular distribution of elastically scattered light is a mathematically ill-posed problem. This paper presents a procedure for analyzing Wide-Angle Light Scattering (WALS) data using Bayesian inference. The outcome is probability densities for the recovered size distribution and aggregate morphology parameters. This technique is applied to both synthetic data and experimental data collected on soot-laden aerosols, using a measurement equation derived from Rayleigh-Debye-Gans fractal aggregate (RDG-FA) theory. In the case of experimental data, the recovered aggregate size distribution parameters are generally consistent with TEM-derived values, but the accuracy is impaired by the well-known limited accuracy of RDG-FA theory. Finally, we show how this bias could potentially be avoided using the approximation error technique.

Bayesian inference in geomagnetism

NASA Technical Reports Server (NTRS)

Backus, George E.

1988-01-01

The inverse problem in empirical geomagnetic modeling is investigated, with critical examination of recently published studies. Particular attention is given to the use of Bayesian inference (BI) to select the damping parameter lambda in the uniqueness portion of the inverse problem. The mathematical bases of BI and stochastic inversion are explored, with consideration of bound-softening problems and resolution in linear Gaussian BI. The problem of estimating the radial magnetic field B(r) at the earth core-mantle boundary from surface and satellite measurements is then analyzed in detail, with specific attention to the selection of lambda in the studies of Gubbins (1983) and Gubbins and Bloxham (1985). It is argued that the selection method is inappropriate and leads to lambda values much larger than those that would result if a reasonable bound on the heat flow at the CMB were assumed.

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

NASA Astrophysics Data System (ADS)

Yu, Jianbo

2015-12-01

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

The First Comprehensive Phylogeny of Coptis (Ranunculaceae) and Its Implications for Character Evolution and Classification

PubMed Central

Xiang, Kun-Li; Wu, Sheng-Dan; Yu, Sheng-Xian; Liu, Yang; Jabbour, Florian; Erst, Andrey S.; Zhao, Liang; Wang, Wei; Chen, Zhi-Duan

2016-01-01

Coptis (Ranunculaceae) contains 15 species and is one of the pharmaceutically most important plant genera in eastern Asia. Understanding of the evolution of morphological characters and phylogenetic relationships within the genus is very limited. Here, we present the first comprehensive phylogenetic analysis of the genus based on two plastid and one nuclear markers. The phylogeny was reconstructed using Bayesian inference, as well as maximum parsimony and maximum likelihood methods. The Swofford-Olsen-Waddell-Hillis and Bayesian tests were used to assess the strength of the conflicts between traditional taxonomic units and those suggested by the phylogenetic inferences. Evolution of morphological characters was inferred using Bayesian method to identify synapomorphies for the infrageneric lineages. Our data recognize two strongly supported clades within Coptis. The first clade contains subgenus Coptis and section Japonocoptis of subgenus Metacoptis, supported by morphological characters, such as traits of the central leaflet base, petal color, and petal shape. The second clade consists of section Japonocoptis of subgenus Metacoptis. Coptis morii is not united with C. quinquefolia, in contrast with the view that C. morii is a synonym of C. quinquefolia. Two varieties of C. chinensis do not cluster together. Coptis groenlandica and C. lutescens are reduced to C. trifolia and C. japonica, respectively. Central leaflet base, sepal shape, and petal blade carry a strong phylogenetic signal in Coptis, while leaf type, sepal and petal color, and petal shape exhibit relatively higher levels of evolutionary flexibility. PMID:27044035

Hierarchical Bayesian inference of the initial mass function in composite stellar populations

NASA Astrophysics Data System (ADS)

Dries, M.; Trager, S. C.; Koopmans, L. V. E.; Popping, G.; Somerville, R. S.

2018-03-01

The initial mass function (IMF) is a key ingredient in many studies of galaxy formation and evolution. Although the IMF is often assumed to be universal, there is continuing evidence that it is not universal. Spectroscopic studies that derive the IMF of the unresolved stellar populations of a galaxy often assume that this spectrum can be described by a single stellar population (SSP). To alleviate these limitations, in this paper we have developed a unique hierarchical Bayesian framework for modelling composite stellar populations (CSPs). Within this framework, we use a parametrized IMF prior to regulate a direct inference of the IMF. We use this new framework to determine the number of SSPs that is required to fit a set of realistic CSP mock spectra. The CSP mock spectra that we use are based on semi-analytic models and have an IMF that varies as a function of stellar velocity dispersion of the galaxy. Our results suggest that using a single SSP biases the determination of the IMF slope to a higher value than the true slope, although the trend with stellar velocity dispersion is overall recovered. If we include more SSPs in the fit, the Bayesian evidence increases significantly and the inferred IMF slopes of our mock spectra converge, within the errors, to their true values. Most of the bias is already removed by using two SSPs instead of one. We show that we can reconstruct the variable IMF of our mock spectra for signal-to-noise ratios exceeding ˜75.

Hierarchical models of animal abundance and occurrence

USGS Publications Warehouse

Royle, J. Andrew; Dorazio, R.M.

2006-01-01

Much of animal ecology is devoted to studies of abundance and occurrence of species, based on surveys of spatially referenced sample units. These surveys frequently yield sparse counts that are contaminated by imperfect detection, making direct inference about abundance or occurrence based on observational data infeasible. This article describes a flexible hierarchical modeling framework for estimation and inference about animal abundance and occurrence from survey data that are subject to imperfect detection. Within this framework, we specify models of abundance and detectability of animals at the level of the local populations defined by the sample units. Information at the level of the local population is aggregated by specifying models that describe variation in abundance and detection among sites. We describe likelihood-based and Bayesian methods for estimation and inference under the resulting hierarchical model. We provide two examples of the application of hierarchical models to animal survey data, the first based on removal counts of stream fish and the second based on avian quadrat counts. For both examples, we provide a Bayesian analysis of the models using the software WinBUGS.

Bayesian inference for heterogeneous caprock permeability based on above zone pressure monitoring

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

Namhata, Argha; Small, Mitchell J.; Dilmore, Rober

The presence of faults/ fractures or highly permeable zones in the primary sealing caprock of a CO2 storage reservoir can result in leakage of CO2. Monitoring of leakage requires the capability to detect and resolve the onset, location, and volume of leakage in a systematic and timely manner. Pressure-based monitoring possesses such capabilities. This study demonstrates a basis for monitoring network design based on the characterization of CO2 leakage scenarios through an assessment of the integrity and permeability of the caprock inferred from above zone pressure measurements. Four representative heterogeneous fractured seal types are characterized to demonstrate seal permeability rangingmore » from highly permeable to impermeable. Based on Bayesian classification theory, the probability of each fractured caprock scenario given above zone pressure measurements with measurement error is inferred. The sensitivity to injection rate and caprock thickness is also evaluated and the probability of proper classification is calculated. The time required to distinguish between above zone pressure outcomes and the associated leakage scenarios is also computed.« less

Supernova Cosmology Inference with Probabilistic Photometric Redshifts (SCIPPR)

NASA Astrophysics Data System (ADS)

Peters, Christina; Malz, Alex; Hlozek, Renée

2018-01-01

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

Open-Universe Theory for Bayesian Inference, Decision, and Sensing (OUTBIDS)

DTIC Science & Technology

2014-01-01

using a novel dynamic programming algorithm [6]. The second allows for tensor data, in which observations at a given time step exhibit...unlimited. 5 We developed a dynamical tensor model that gives far better estimation and system- identification results than the standard vectorization...inference. Third, unlike prior work that learns different pieces of the model independently, use matching between 3D models and 2D views and/or voting

Spatially explicit inference for open populations: estimating demographic parameters from camera-trap studies

USGS Publications Warehouse

Gardner, Beth; Reppucci, Juan; Lucherini, Mauro; Royle, J. Andrew

2010-01-01

We develop a hierarchical capture–recapture model for demographically open populations when auxiliary spatial information about location of capture is obtained. Such spatial capture–recapture data arise from studies based on camera trapping, DNA sampling, and other situations in which a spatial array of devices records encounters of unique individuals. We integrate an individual-based formulation of a Jolly-Seber type model with recently developed spatially explicit capture–recapture models to estimate density and demographic parameters for survival and recruitment. We adopt a Bayesian framework for inference under this model using the method of data augmentation which is implemented in the software program WinBUGS. The model was motivated by a camera trapping study of Pampas cats Leopardus colocolo from Argentina, which we present as an illustration of the model in this paper. We provide estimates of density and the first quantitative assessment of vital rates for the Pampas cat in the High Andes. The precision of these estimates is poor due likely to the sparse data set. Unlike conventional inference methods which usually rely on asymptotic arguments, Bayesian inferences are valid in arbitrary sample sizes, and thus the method is ideal for the study of rare or endangered species for which small data sets are typical.

Spatially explicit inference for open populations: estimating demographic parameters from camera-trap studies.

PubMed

Gardner, Beth; Reppucci, Juan; Lucherini, Mauro; Royle, J Andrew

2010-11-01

We develop a hierarchical capture-recapture model for demographically open populations when auxiliary spatial information about location of capture is obtained. Such spatial capture-recapture data arise from studies based on camera trapping, DNA sampling, and other situations in which a spatial array of devices records encounters of unique individuals. We integrate an individual-based formulation of a Jolly-Seber type model with recently developed spatially explicit capture-recapture models to estimate density and demographic parameters for survival and recruitment. We adopt a Bayesian framework for inference under this model using the method of data augmentation which is implemented in the software program WinBUGS. The model was motivated by a camera trapping study of Pampas cats Leopardus colocolo from Argentina, which we present as an illustration of the model in this paper. We provide estimates of density and the first quantitative assessment of vital rates for the Pampas cat in the High Andes. The precision of these estimates is poor due likely to the sparse data set. Unlike conventional inference methods which usually rely on asymptotic arguments, Bayesian inferences are valid in arbitrary sample sizes, and thus the method is ideal for the study of rare or endangered species for which small data sets are typical.

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

On Bayesian Testing of Additive Conjoint Measurement Axioms Using Synthetic Likelihood.

PubMed

Karabatsos, George

2018-06-01

This article introduces a Bayesian method for testing the axioms of additive conjoint measurement. The method is based on an importance sampling algorithm that performs likelihood-free, approximate Bayesian inference using a synthetic likelihood to overcome the analytical intractability of this testing problem. This new method improves upon previous methods because it provides an omnibus test of the entire hierarchy of cancellation axioms, beyond double cancellation. It does so while accounting for the posterior uncertainty that is inherent in the empirical orderings that are implied by these axioms, together. The new method is illustrated through a test of the cancellation axioms on a classic survey data set, and through the analysis of simulated data.

Bayesian non-parametric inference for stochastic epidemic models using Gaussian Processes.

PubMed

Xu, Xiaoguang; Kypraios, Theodore; O'Neill, Philip D

2016-10-01

This paper considers novel Bayesian non-parametric methods for stochastic epidemic models. Many standard modeling and data analysis methods use underlying assumptions (e.g. concerning the rate at which new cases of disease will occur) which are rarely challenged or tested in practice. To relax these assumptions, we develop a Bayesian non-parametric approach using Gaussian Processes, specifically to estimate the infection process. The methods are illustrated with both simulated and real data sets, the former illustrating that the methods can recover the true infection process quite well in practice, and the latter illustrating that the methods can be successfully applied in different settings. © The Author 2016. Published by Oxford University Press.

Exploiting Cross-sensitivity by Bayesian Decoding of Mixed Potential Sensor Arrays

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

Kreller, Cortney

LANL mixed-potential electrochemical sensor (MPES) device arrays were coupled with advanced Bayesian inference treatment of the physical model of relevant sensor-analyte interactions. We demonstrated that our approach could be used to uniquely discriminate the composition of ternary gas sensors with three discreet MPES sensors with an average error of less than 2%. We also observed that the MPES exhibited excellent stability over a year of operation at elevated temperatures in the presence of test gases.

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.

Bayesian inference of a historical bottleneck in a heavily exploited marine mammal.

PubMed

Hoffman, J I; Grant, S M; Forcada, J; Phillips, C D

2011-10-01

Emerging Bayesian analytical approaches offer increasingly sophisticated means of reconstructing historical population dynamics from genetic data, but have been little applied to scenarios involving demographic bottlenecks. Consequently, we analysed a large mitochondrial and microsatellite dataset from the Antarctic fur seal Arctocephalus gazella, a species subjected to one of the most extreme examples of uncontrolled exploitation in history when it was reduced to the brink of extinction by the sealing industry during the late eighteenth and nineteenth centuries. Classical bottleneck tests, which exploit the fact that rare alleles are rapidly lost during demographic reduction, yielded ambiguous results. In contrast, a strong signal of recent demographic decline was detected using both Bayesian skyline plots and Approximate Bayesian Computation, the latter also allowing derivation of posterior parameter estimates that were remarkably consistent with historical observations. This was achieved using only contemporary samples, further emphasizing the potential of Bayesian approaches to address important problems in conservation and evolutionary biology. © 2011 Blackwell Publishing Ltd.

A Bayesian state-space approach for damage detection and classification

NASA Astrophysics Data System (ADS)

Dzunic, Zoran; Chen, Justin G.; Mobahi, Hossein; Büyüköztürk, Oral; Fisher, John W.

2017-11-01

The problem of automatic damage detection in civil structures is complex and requires a system that can interpret collected sensor data into meaningful information. We apply our recently developed switching Bayesian model for dependency analysis to the problems of damage detection and classification. The model relies on a state-space approach that accounts for noisy measurement processes and missing data, which also infers the statistical temporal dependency between measurement locations signifying the potential flow of information within the structure. A Gibbs sampling algorithm is used to simultaneously infer the latent states, parameters of the state dynamics, the dependence graph, and any changes in behavior. By employing a fully Bayesian approach, we are able to characterize uncertainty in these variables via their posterior distribution and provide probabilistic estimates of the occurrence of damage or a specific damage scenario. We also implement a single class classification method which is more realistic for most real world situations where training data for a damaged structure is not available. We demonstrate the methodology with experimental test data from a laboratory model structure and accelerometer data from a real world structure during different environmental and excitation conditions.

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.

Bayesian ensemble refinement by replica simulations and reweighting.

PubMed

Hummer, Gerhard; Köfinger, Jürgen

2015-12-28

We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be characterized by integrating a wide range of experimental data, including measurements of ensemble-averaged observables. We start from a Bayesian formulation in which the posterior is a functional that ranks different configuration space distributions. By maximizing this posterior, we derive an optimal Bayesian ensemble distribution. For discrete configurations, this optimal distribution is identical to that obtained by the maximum entropy "ensemble refinement of SAXS" (EROS) formulation. Bayesian replica ensemble refinement enhances the sampling of relevant configurations by imposing restraints on averages of observables in coupled replica molecular dynamics simulations. We show that the strength of the restraints should scale linearly with the number of replicas to ensure convergence to the optimal Bayesian result in the limit of infinitely many replicas. In the "Bayesian inference of ensembles" method, we combine the replica and EROS approaches to accelerate the convergence. An adaptive algorithm can be used to sample directly from the optimal ensemble, without replicas. We discuss the incorporation of single-molecule measurements and dynamic observables such as relaxation parameters. The theoretical analysis of different Bayesian ensemble refinement approaches provides a basis for practical applications and a starting point for further investigations.

Daniel Goodman’s empirical approach to Bayesian statistics

USGS Publications Warehouse

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

2016-01-01

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

Bayesian ensemble refinement by replica simulations and reweighting

NASA Astrophysics Data System (ADS)

Hummer, Gerhard; Köfinger, Jürgen

2015-12-01

We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be characterized by integrating a wide range of experimental data, including measurements of ensemble-averaged observables. We start from a Bayesian formulation in which the posterior is a functional that ranks different configuration space distributions. By maximizing this posterior, we derive an optimal Bayesian ensemble distribution. For discrete configurations, this optimal distribution is identical to that obtained by the maximum entropy "ensemble refinement of SAXS" (EROS) formulation. Bayesian replica ensemble refinement enhances the sampling of relevant configurations by imposing restraints on averages of observables in coupled replica molecular dynamics simulations. We show that the strength of the restraints should scale linearly with the number of replicas to ensure convergence to the optimal Bayesian result in the limit of infinitely many replicas. In the "Bayesian inference of ensembles" method, we combine the replica and EROS approaches to accelerate the convergence. An adaptive algorithm can be used to sample directly from the optimal ensemble, without replicas. We discuss the incorporation of single-molecule measurements and dynamic observables such as relaxation parameters. The theoretical analysis of different Bayesian ensemble refinement approaches provides a basis for practical applications and a starting point for further investigations.

Active Inference, homeostatic regulation and adaptive behavioural control

PubMed Central

Pezzulo, Giovanni; Rigoli, Francesco; Friston, Karl

2015-01-01

We review a theory of homeostatic regulation and adaptive behavioural control within the Active Inference framework. Our aim is to connect two research streams that are usually considered independently; namely, Active Inference and associative learning theories of animal behaviour. The former uses a probabilistic (Bayesian) formulation of perception and action, while the latter calls on multiple (Pavlovian, habitual, goal-directed) processes for homeostatic and behavioural control. We offer a synthesis these classical processes and cast them as successive hierarchical contextualisations of sensorimotor constructs, using the generative models that underpin Active Inference. This dissolves any apparent mechanistic distinction between the optimization processes that mediate classical control or learning. Furthermore, we generalize the scope of Active Inference by emphasizing interoceptive inference and homeostatic regulation. The ensuing homeostatic (or allostatic) perspective provides an intuitive explanation for how priors act as drives or goals to enslave action, and emphasises the embodied nature of inference. PMID:26365173

Use of genetic data to infer population-specific ecological and phenotypic traits from mixed aggregations

USGS Publications Warehouse

Moran, Paul; Bromaghin, Jeffrey F.; Masuda, Michele

2014-01-01

Many applications in ecological genetics involve sampling individuals from a mixture of multiple biological populations and subsequently associating those individuals with the populations from which they arose. Analytical methods that assign individuals to their putative population of origin have utility in both basic and applied research, providing information about population-specific life history and habitat use, ecotoxins, pathogen and parasite loads, and many other non-genetic ecological, or phenotypic traits. Although the question is initially directed at the origin of individuals, in most cases the ultimate desire is to investigate the distribution of some trait among populations. Current practice is to assign individuals to a population of origin and study properties of the trait among individuals within population strata as if they constituted independent samples. It seemed that approach might bias population-specific trait inference. In this study we made trait inferences directly through modeling, bypassing individual assignment. We extended a Bayesian model for population mixture analysis to incorporate parameters for the phenotypic trait and compared its performance to that of individual assignment with a minimum probability threshold for assignment. The Bayesian mixture model outperformed individual assignment under some trait inference conditions. However, by discarding individuals whose origins are most uncertain, the individual assignment method provided a less complex analytical technique whose performance may be adequate for some common trait inference problems. Our results provide specific guidance for method selection under various genetic relationships among populations with different trait distributions.

Use of Genetic Data to Infer Population-Specific Ecological and Phenotypic Traits from Mixed Aggregations

PubMed Central

Moran, Paul; Bromaghin, Jeffrey F.; Masuda, Michele

2014-01-01

Many applications in ecological genetics involve sampling individuals from a mixture of multiple biological populations and subsequently associating those individuals with the populations from which they arose. Analytical methods that assign individuals to their putative population of origin have utility in both basic and applied research, providing information about population-specific life history and habitat use, ecotoxins, pathogen and parasite loads, and many other non-genetic ecological, or phenotypic traits. Although the question is initially directed at the origin of individuals, in most cases the ultimate desire is to investigate the distribution of some trait among populations. Current practice is to assign individuals to a population of origin and study properties of the trait among individuals within population strata as if they constituted independent samples. It seemed that approach might bias population-specific trait inference. In this study we made trait inferences directly through modeling, bypassing individual assignment. We extended a Bayesian model for population mixture analysis to incorporate parameters for the phenotypic trait and compared its performance to that of individual assignment with a minimum probability threshold for assignment. The Bayesian mixture model outperformed individual assignment under some trait inference conditions. However, by discarding individuals whose origins are most uncertain, the individual assignment method provided a less complex analytical technique whose performance may be adequate for some common trait inference problems. Our results provide specific guidance for method selection under various genetic relationships among populations with different trait distributions. PMID:24905464

Causal learning with local computations.

PubMed

Fernbach, Philip M; Sloman, Steven A

2009-05-01

The authors proposed and tested a psychological theory of causal structure learning based on local computations. Local computations simplify complex learning problems via cues available on individual trials to update a single causal structure hypothesis. Structural inferences from local computations make minimal demands on memory, require relatively small amounts of data, and need not respect normative prescriptions as inferences that are principled locally may violate those principles when combined. Over a series of 3 experiments, the authors found (a) systematic inferences from small amounts of data; (b) systematic inference of extraneous causal links; (c) influence of data presentation order on inferences; and (d) error reduction through pretraining. Without pretraining, a model based on local computations fitted data better than a Bayesian structural inference model. The data suggest that local computations serve as a heuristic for learning causal structure. Copyright 2009 APA, all rights reserved.

Bayesian models: A statistical primer for ecologists

USGS Publications Warehouse

Hobbs, N. Thompson; Hooten, Mevin B.

2015-01-01

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

A probabilistic model framework for evaluating year-to-year variation in crop productivity

NASA Astrophysics Data System (ADS)

Yokozawa, M.; Iizumi, T.; Tao, F.

2008-12-01

Most models describing the relation between crop productivity and weather condition have so far been focused on mean changes of crop yield. For keeping stable food supply against abnormal weather as well as climate change, evaluating the year-to-year variations in crop productivity rather than the mean changes is more essential. We here propose a new framework of probabilistic model based on Bayesian inference and Monte Carlo simulation. As an example, we firstly introduce a model on paddy rice production in Japan. It is called PRYSBI (Process- based Regional rice Yield Simulator with Bayesian Inference; Iizumi et al., 2008). The model structure is the same as that of SIMRIW, which was developed and used widely in Japan. The model includes three sub- models describing phenological development, biomass accumulation and maturing of rice crop. These processes are formulated to include response nature of rice plant to weather condition. This model inherently was developed to predict rice growth and yield at plot paddy scale. We applied it to evaluate the large scale rice production with keeping the same model structure. Alternatively, we assumed the parameters as stochastic variables. In order to let the model catch up actual yield at larger scale, model parameters were determined based on agricultural statistical data of each prefecture of Japan together with weather data averaged over the region. The posterior probability distribution functions (PDFs) of parameters included in the model were obtained using Bayesian inference. The MCMC (Markov Chain Monte Carlo) algorithm was conducted to numerically solve the Bayesian theorem. For evaluating the year-to-year changes in rice growth/yield under this framework, we firstly iterate simulations with set of parameter values sampled from the estimated posterior PDF of each parameter and then take the ensemble mean weighted with the posterior PDFs. We will also present another example for maize productivity in China. The framework proposed here provides us information on uncertainties, possibilities and limitations on future improvements in crop model as well.

An adaptive sparse-grid high-order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling

NASA Astrophysics Data System (ADS)

Zhang, Guannan; Lu, Dan; Ye, Ming; Gunzburger, Max; Webster, Clayton

2013-10-01

Bayesian analysis has become vital to uncertainty quantification in groundwater modeling, but its application has been hindered by the computational cost associated with numerous model executions required by exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, a new approach is developed to improve the computational efficiency of Bayesian inference by constructing a surrogate of the PPDF, using an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, this paper utilizes a compactly supported higher-order hierarchical basis to construct the surrogate system, resulting in a significant reduction in the number of required model executions. In addition, using the hierarchical surplus as an error indicator allows locally adaptive refinement of sparse grids in the parameter space, which further improves computational efficiency. To efficiently build the surrogate system for the PPDF with multiple significant modes, optimization techniques are used to identify the modes, for which high-probability regions are defined and components of the aSG-hSC approximation are constructed. After the surrogate is determined, the PPDF can be evaluated by sampling the surrogate system directly without model execution, resulting in improved efficiency of the surrogate-based MCMC compared with conventional MCMC. The developed method is evaluated using two synthetic groundwater reactive transport models. The first example involves coupled linear reactions and demonstrates the accuracy of our high-order hierarchical basis approach in approximating high-dimensional posteriori distribution. The second example is highly nonlinear because of the reactions of uranium surface complexation, and demonstrates how the iterative aSG-hSC method is able to capture multimodal and non-Gaussian features of PPDF caused by model nonlinearity. Both experiments show that aSG-hSC is an effective and efficient tool for Bayesian inference.

SOMBI: Bayesian identification of parameter relations in unstructured cosmological data

NASA Astrophysics Data System (ADS)

Frank, Philipp; Jasche, Jens; Enßlin, Torsten A.

2016-11-01

This work describes the implementation and application of a correlation determination method based on self organizing maps and Bayesian inference (SOMBI). SOMBI aims to automatically identify relations between different observed parameters in unstructured cosmological or astrophysical surveys by automatically identifying data clusters in high-dimensional datasets via the self organizing map neural network algorithm. Parameter relations are then revealed by means of a Bayesian inference within respective identified data clusters. Specifically such relations are assumed to be parametrized as a polynomial of unknown order. The Bayesian approach results in a posterior probability distribution function for respective polynomial coefficients. To decide which polynomial order suffices to describe correlation structures in data, we include a method for model selection, the Bayesian information criterion, to the analysis. The performance of the SOMBI algorithm is tested with mock data. As illustration we also provide applications of our method to cosmological data. In particular, we present results of a correlation analysis between galaxy and active galactic nucleus (AGN) properties provided by the SDSS catalog with the cosmic large-scale-structure (LSS). The results indicate that the combined galaxy and LSS dataset indeed is clustered into several sub-samples of data with different average properties (for example different stellar masses or web-type classifications). The majority of data clusters appear to have a similar correlation structure between galaxy properties and the LSS. In particular we revealed a positive and linear dependency between the stellar mass, the absolute magnitude and the color of a galaxy with the corresponding cosmic density field. A remaining subset of data shows inverted correlations, which might be an artifact of non-linear redshift distortions.

Doctor, what does my positive test mean? From Bayesian textbook tasks to personalized risk communication

PubMed Central

Navarrete, Gorka; Correia, Rut; Sirota, Miroslav; Juanchich, Marie; Huepe, David

2015-01-01

Most of the research on Bayesian reasoning aims to answer theoretical questions about the extent to which people are able to update their beliefs according to Bayes' Theorem, about the evolutionary nature of Bayesian inference, or about the role of cognitive abilities in Bayesian inference. Few studies aim to answer practical, mainly health-related questions, such as, “What does it mean to have a positive test in a context of cancer screening?” or “What is the best way to communicate a medical test result so a patient will understand it?”. This type of research aims to translate empirical findings into effective ways of providing risk information. In addition, the applied research often adopts the paradigms and methods of the theoretically-motivated research. But sometimes it works the other way around, and the theoretical research borrows the importance of the practical question in the medical context. The study of Bayesian reasoning is relevant to risk communication in that, to be as useful as possible, applied research should employ specifically tailored methods and contexts specific to the recipients of the risk information. In this paper, we concentrate on the communication of the result of medical tests and outline the epidemiological and test parameters that affect the predictive power of a test—whether it is correct or not. Building on this, we draw up recommendations for better practice to convey the results of medical tests that could inform health policy makers (What are the drawbacks of mass screenings?), be used by health practitioners and, in turn, help patients to make better and more informed decisions. PMID:26441711

Bias in logistic regression due to imperfect diagnostic test results and practical correction approaches.

PubMed

Valle, Denis; Lima, Joanna M Tucker; Millar, Justin; Amratia, Punam; Haque, Ubydul

2015-11-04

Logistic regression is a statistical model widely used in cross-sectional and cohort studies to identify and quantify the effects of potential disease risk factors. However, the impact of imperfect tests on adjusted odds ratios (and thus on the identification of risk factors) is under-appreciated. The purpose of this article is to draw attention to the problem associated with modelling imperfect diagnostic tests, and propose simple Bayesian models to adequately address this issue. A systematic literature review was conducted to determine the proportion of malaria studies that appropriately accounted for false-negatives/false-positives in a logistic regression setting. Inference from the standard logistic regression was also compared with that from three proposed Bayesian models using simulations and malaria data from the western Brazilian Amazon. A systematic literature review suggests that malaria epidemiologists are largely unaware of the problem of using logistic regression to model imperfect diagnostic test results. Simulation results reveal that statistical inference can be substantially improved when using the proposed Bayesian models versus the standard logistic regression. Finally, analysis of original malaria data with one of the proposed Bayesian models reveals that microscopy sensitivity is strongly influenced by how long people have lived in the study region, and an important risk factor (i.e., participation in forest extractivism) is identified that would have been missed by standard logistic regression. Given the numerous diagnostic methods employed by malaria researchers and the ubiquitous use of logistic regression to model the results of these diagnostic tests, this paper provides critical guidelines to improve data analysis practice in the presence of misclassification error. Easy-to-use code that can be readily adapted to WinBUGS is provided, enabling straightforward implementation of the proposed Bayesian models.

Understanding the Scalability of Bayesian Network Inference Using Clique Tree Growth Curves

NASA Technical Reports Server (NTRS)

Mengshoel, Ole J.

2010-01-01

One of the main approaches to performing computation in Bayesian networks (BNs) is clique tree clustering and propagation. The clique tree approach consists of propagation in a clique tree compiled from a Bayesian network, and while it was introduced in the 1980s, there is still a lack of understanding of how clique tree computation time depends on variations in BN size and structure. In this article, we improve this understanding by developing an approach to characterizing clique tree growth as a function of parameters that can be computed in polynomial time from BNs, specifically: (i) the ratio of the number of a BN s non-root nodes to the number of root nodes, and (ii) the expected number of moral edges in their moral graphs. Analytically, we partition the set of cliques in a clique tree into different sets, and introduce a growth curve for the total size of each set. For the special case of bipartite BNs, there are two sets and two growth curves, a mixed clique growth curve and a root clique growth curve. In experiments, where random bipartite BNs generated using the BPART algorithm are studied, we systematically increase the out-degree of the root nodes in bipartite Bayesian networks, by increasing the number of leaf nodes. Surprisingly, root clique growth is well-approximated by Gompertz growth curves, an S-shaped family of curves that has previously been used to describe growth processes in biology, medicine, and neuroscience. We believe that this research improves the understanding of the scaling behavior of clique tree clustering for a certain class of Bayesian networks; presents an aid for trade-off studies of clique tree clustering using growth curves; and ultimately provides a foundation for benchmarking and developing improved BN inference and machine learning algorithms.

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.

Effective Bayesian Transfer Learning

DTIC Science & Technology

2010-03-01

reasonable value of k , defined by the task B training set size. Transfer Regret 1 Regret = 100 * G AB B No Transfer With Transfer AB...a. REPORT U b . ABSTRACT U c. THIS PAGE U 19b. TELEPHONE NUMBER (Include area code) N/A Standard Form 298 (Rev. 8-98) Prescribed...rule set given the prior and developed staged approximate inference strategy, in which data from observed tasks 1 to k are used to infer general rule

Automatic inference of multicellular regulatory networks using informative priors.

PubMed

Sun, Xiaoyun; Hong, Pengyu

2009-01-01

To fully understand the mechanisms governing animal development, computational models and algorithms are needed to enable quantitative studies of the underlying regulatory networks. We developed a mathematical model based on dynamic Bayesian networks to model multicellular regulatory networks that govern cell differentiation processes. A machine-learning method was developed to automatically infer such a model from heterogeneous data. We show that the model inference procedure can be greatly improved by incorporating interaction data across species. The proposed approach was applied to C. elegans vulval induction to reconstruct a model capable of simulating C. elegans vulval induction under 73 different genetic conditions.

Cardiovascular oscillations: in search of a nonlinear parametric model

NASA Astrophysics Data System (ADS)

Bandrivskyy, Andriy; Luchinsky, Dmitry; McClintock, Peter V.; Smelyanskiy, Vadim; Stefanovska, Aneta; Timucin, Dogan

2003-05-01

We suggest a fresh approach to the modeling of the human cardiovascular system. Taking advantage of a new Bayesian inference technique, able to deal with stochastic nonlinear systems, we show that one can estimate parameters for models of the cardiovascular system directly from measured time series. We present preliminary results of inference of parameters of a model of coupled oscillators from measured cardiovascular data addressing cardiorespiratory interaction. We argue that the inference technique offers a very promising tool for the modeling, able to contribute significantly towards the solution of a long standing challenge -- development of new diagnostic techniques based on noninvasive measurements.

Judd-Ofelt Parameters via Bayesian Inference

NASA Astrophysics Data System (ADS)

Silva, Valdeir A.; Silva, José W.; de Morais, Paulo C.; Dantas, Noelio O.

2018-04-01

Bayesian inference was used as a new approach to calculate of rare earth (RE) ion spectroscopic parameters within the Judd-Ofelt theory using the Li2O-B2O3-Al2O3 glass system doped with Nd2O3 and TiO2. This system was synthesized by the fusion method, and the physical properties of the as-synthesized material were investigated. Optical absorption, photoluminescence, micro-Raman, mass density, refractive index, and radiative lifetime calcuations were performed. We investigated the effects of crystal field changes on Nd3+-ions caused due to co-doping with increasing TiO2 content. We observed that co-doping with TiO2 altered the radiative transition rates A( J, J '), favored symmetry enhancement around the Nd3+-ions, and promoted the onset of vibrational modes, contributed to the attenuation of O-H bonds, and substantially increased the spectroscopic quality, χ.

Hypothesis-Testing Demands Trustworthy Data—A Simulation Approach to Inferential Statistics Advocating the Research Program Strategy

PubMed Central

Krefeld-Schwalb, Antonia; Witte, Erich H.; Zenker, Frank

2018-01-01

In psychology as elsewhere, the main statistical inference strategy to establish empirical effects is null-hypothesis significance testing (NHST). The recent failure to replicate allegedly well-established NHST-results, however, implies that such results lack sufficient statistical power, and thus feature unacceptably high error-rates. Using data-simulation to estimate the error-rates of NHST-results, we advocate the research program strategy (RPS) as a superior methodology. RPS integrates Frequentist with Bayesian inference elements, and leads from a preliminary discovery against a (random) H0-hypothesis to a statistical H1-verification. Not only do RPS-results feature significantly lower error-rates than NHST-results, RPS also addresses key-deficits of a “pure” Frequentist and a standard Bayesian approach. In particular, RPS aggregates underpowered results safely. RPS therefore provides a tool to regain the trust the discipline had lost during the ongoing replicability-crisis. PMID:29740363

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

NASA Astrophysics Data System (ADS)

Wang, Hongqiao; Lin, Guang; Li, Jinglai

2016-05-01

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

Hypothesis-Testing Demands Trustworthy Data-A Simulation Approach to Inferential Statistics Advocating the Research Program Strategy.

PubMed

Krefeld-Schwalb, Antonia; Witte, Erich H; Zenker, Frank

2018-01-01

In psychology as elsewhere, the main statistical inference strategy to establish empirical effects is null-hypothesis significance testing (NHST). The recent failure to replicate allegedly well-established NHST-results, however, implies that such results lack sufficient statistical power, and thus feature unacceptably high error-rates. Using data-simulation to estimate the error-rates of NHST-results, we advocate the research program strategy (RPS) as a superior methodology. RPS integrates Frequentist with Bayesian inference elements, and leads from a preliminary discovery against a (random) H 0 -hypothesis to a statistical H 1 -verification. Not only do RPS-results feature significantly lower error-rates than NHST-results, RPS also addresses key-deficits of a "pure" Frequentist and a standard Bayesian approach. In particular, RPS aggregates underpowered results safely. RPS therefore provides a tool to regain the trust the discipline had lost during the ongoing replicability-crisis.

Annealed Importance Sampling for Neural Mass Models

PubMed Central

Penny, Will; Sengupta, Biswa

2016-01-01

Neural Mass Models provide a compact description of the dynamical activity of cell populations in neocortical regions. Moreover, models of regional activity can be connected together into networks, and inferences made about the strength of connections, using M/EEG data and Bayesian inference. To date, however, Bayesian methods have been largely restricted to the Variational Laplace (VL) algorithm which assumes that the posterior distribution is Gaussian and finds model parameters that are only locally optimal. This paper explores the use of Annealed Importance Sampling (AIS) to address these restrictions. We implement AIS using proposals derived from Langevin Monte Carlo (LMC) which uses local gradient and curvature information for efficient exploration of parameter space. In terms of the estimation of Bayes factors, VL and AIS agree about which model is best but report different degrees of belief. Additionally, AIS finds better model parameters and we find evidence of non-Gaussianity in their posterior distribution. PMID:26942606

Selectivity curves of the capture of mangrove crab (Ucides cordatus) on the northern coast of Brazil using bayesian inference.

PubMed

Furtado-Junior, I; Abrunhosa, F A; Holanda, F C A F; Tavares, M C S

2016-06-01

Fishing selectivity of the mangrove crab Ucides cordatus in the north coast of Brazil can be defined as the fisherman's ability to capture and select individuals from a certain size or sex (or a combination of these factors) which suggests an empirical selectivity. Considering this hypothesis, we calculated the selectivity curves for males and females crabs using the logit function of the logistic model in the formulation. The Bayesian inference consisted of obtaining the posterior distribution by applying the Markov chain Monte Carlo (MCMC) method to software R using the OpenBUGS, BRugs, and R2WinBUGS libraries. The estimated results of width average carapace selection for males and females compared with previous studies reporting the average width of the carapace of sexual maturity allow us to confirm the hypothesis that most mature individuals do not suffer from fishing pressure; thus, ensuring their sustainability.

Fast Bayesian Inference of Copy Number Variants using Hidden Markov Models with Wavelet Compression

PubMed Central

Wiedenhoeft, John; Brugel, Eric; Schliep, Alexander

2016-01-01

By integrating Haar wavelets with Hidden Markov Models, we achieve drastically reduced running times for Bayesian inference using Forward-Backward Gibbs sampling. We show that this improves detection of genomic copy number variants (CNV) in array CGH experiments compared to the state-of-the-art, including standard Gibbs sampling. The method concentrates computational effort on chromosomal segments which are difficult to call, by dynamically and adaptively recomputing consecutive blocks of observations likely to share a copy number. This makes routine diagnostic use and re-analysis of legacy data collections feasible; to this end, we also propose an effective automatic prior. An open source software implementation of our method is available at http://schlieplab.org/Software/HaMMLET/ (DOI: 10.5281/zenodo.46262). This paper was selected for oral presentation at RECOMB 2016, and an abstract is published in the conference proceedings. PMID:27177143

Bayesian Analysis of Biogeography when the Number of Areas is Large

PubMed Central

Landis, Michael J.; Matzke, Nicholas J.; Moore, Brian R.; Huelsenbeck, John P.

2013-01-01

Historical biogeography is increasingly studied from an explicitly statistical perspective, using stochastic models to describe the evolution of species range as a continuous-time Markov process of dispersal between and extinction within a set of discrete geographic areas. The main constraint of these methods is the computational limit on the number of areas that can be specified. We propose a Bayesian approach for inferring biogeographic history that extends the application of biogeographic models to the analysis of more realistic problems that involve a large number of areas. Our solution is based on a “data-augmentation” approach, in which we first populate the tree with a history of biogeographic events that is consistent with the observed species ranges at the tips of the tree. We then calculate the likelihood of a given history by adopting a mechanistic interpretation of the instantaneous-rate matrix, which specifies both the exponential waiting times between biogeographic events and the relative probabilities of each biogeographic change. We develop this approach in a Bayesian framework, marginalizing over all possible biogeographic histories using Markov chain Monte Carlo (MCMC). Besides dramatically increasing the number of areas that can be accommodated in a biogeographic analysis, our method allows the parameters of a given biogeographic model to be estimated and different biogeographic models to be objectively compared. Our approach is implemented in the program, BayArea. [ancestral area analysis; Bayesian biogeographic inference; data augmentation; historical biogeography; Markov chain Monte Carlo.] PMID:23736102

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

NASA Astrophysics Data System (ADS)

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

2013-08-01

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

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

PubMed

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

2013-08-01

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

bnstruct: an R package for Bayesian Network structure learning in the presence of missing data.

PubMed

Franzin, Alberto; Sambo, Francesco; Di Camillo, Barbara

2017-04-15

A Bayesian Network is a probabilistic graphical model that encodes probabilistic dependencies between a set of random variables. We introduce bnstruct, an open source R package to (i) learn the structure and the parameters of a Bayesian Network from data in the presence of missing values and (ii) perform reasoning and inference on the learned Bayesian Networks. To the best of our knowledge, there is no other open source software that provides methods for all of these tasks, particularly the manipulation of missing data, which is a common situation in practice. The software is implemented in R and C and is available on CRAN under a GPL licence. francesco.sambo@unipd.it. Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Using Bayesian Networks for Candidate Generation in Consistency-based Diagnosis

NASA Technical Reports Server (NTRS)

Narasimhan, Sriram; Mengshoel, Ole

2008-01-01

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

IMNN: Information Maximizing Neural Networks

NASA Astrophysics Data System (ADS)

Charnock, Tom; Lavaux, Guilhem; Wandelt, Benjamin D.

2018-04-01

This software trains artificial neural networks to find non-linear functionals of data that maximize Fisher information: information maximizing neural networks (IMNNs). As compressing large data sets vastly simplifies both frequentist and Bayesian inference, important information may be inadvertently missed. Likelihood-free inference based on automatically derived IMNN summaries produces summaries that are good approximations to sufficient statistics. IMNNs are robustly capable of automatically finding optimal, non-linear summaries of the data even in cases where linear compression fails: inferring the variance of Gaussian signal in the presence of noise, inferring cosmological parameters from mock simulations of the Lyman-α forest in quasar spectra, and inferring frequency-domain parameters from LISA-like detections of gravitational waveforms. In this final case, the IMNN summary outperforms linear data compression by avoiding the introduction of spurious likelihood maxima.

Bayesian inference with historical data-based informative priors improves detection of differentially expressed genes

PubMed Central

Li, Ben; Sun, Zhaonan; He, Qing; Zhu, Yu; Qin, Zhaohui S.

2016-01-01

Motivation: Modern high-throughput biotechnologies such as microarray are capable of producing a massive amount of information for each sample. However, in a typical high-throughput experiment, only limited number of samples were assayed, thus the classical ‘large p, small n’ problem. On the other hand, rapid propagation of these high-throughput technologies has resulted in a substantial collection of data, often carried out on the same platform and using the same protocol. It is highly desirable to utilize the existing data when performing analysis and inference on a new dataset. Results: Utilizing existing data can be carried out in a straightforward fashion under the Bayesian framework in which the repository of historical data can be exploited to build informative priors and used in new data analysis. In this work, using microarray data, we investigate the feasibility and effectiveness of deriving informative priors from historical data and using them in the problem of detecting differentially expressed genes. Through simulation and real data analysis, we show that the proposed strategy significantly outperforms existing methods including the popular and state-of-the-art Bayesian hierarchical model-based approaches. Our work illustrates the feasibility and benefits of exploiting the increasingly available genomics big data in statistical inference and presents a promising practical strategy for dealing with the ‘large p, small n’ problem. Availability and implementation: Our method is implemented in R package IPBT, which is freely available from https://github.com/benliemory/IPBT. Contact: yuzhu@purdue.edu; zhaohui.qin@emory.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:26519502

Towards Breaking the Histone Code – Bayesian Graphical Models for Histone Modifications

PubMed Central

Mitra, Riten; Müller, Peter; Liang, Shoudan; Xu, Yanxun; Ji, Yuan

2013-01-01

Background Histones are proteins that wrap DNA around in small spherical structures called nucleosomes. Histone modifications (HMs) refer to the post-translational modifications to the histone tails. At a particular genomic locus, each of these HMs can either be present or absent, and the combinatory patterns of the presence or absence of multiple HMs, or the ‘histone codes,’ are believed to co-regulate important biological processes. We aim to use raw data on HM markers at different genomic loci to (1) decode the complex biological network of HMs in a single region and (2) demonstrate how the HM networks differ in different regulatory regions. We suggest that these differences in network attributes form a significant link between histones and genomic functions. Methods and Results We develop a powerful graphical model under Bayesian paradigm. Posterior inference is fully probabilistic, allowing us to compute the probabilities of distinct dependence patterns of the HMs using graphs. Furthermore, our model-based framework allows for easy but important extensions for inference on differential networks under various conditions, such as the different annotations of the genomic locations (e.g., promoters versus insulators). We applied these models to ChIP-Seq data based on CD4+ T lymphocytes. The results confirmed many existing findings and provided a unified tool to generate various promising hypotheses. Differential network analyses revealed new insights on co-regulation of HMs of transcriptional activities in different genomic regions. Conclusions The use of Bayesian graphical models and borrowing strength across different conditions provide high power to infer histone networks and their differences. PMID:23748248

A full-spectral Bayesian reconstruction approach based on the material decomposition model applied in dual-energy computed tomography.

PubMed

Cai, C; Rodet, T; Legoupil, S; Mohammad-Djafari, A

2013-11-01

Dual-energy computed tomography (DECT) makes it possible to get two fractions of basis materials without segmentation. One is the soft-tissue equivalent water fraction and the other is the hard-matter equivalent bone fraction. Practical DECT measurements are usually obtained with polychromatic x-ray beams. Existing reconstruction approaches based on linear forward models without counting the beam polychromaticity fail to estimate the correct decomposition fractions and result in beam-hardening artifacts (BHA). The existing BHA correction approaches either need to refer to calibration measurements or suffer from the noise amplification caused by the negative-log preprocessing and the ill-conditioned water and bone separation problem. To overcome these problems, statistical DECT reconstruction approaches based on nonlinear forward models counting the beam polychromaticity show great potential for giving accurate fraction images. This work proposes a full-spectral Bayesian reconstruction approach which allows the reconstruction of high quality fraction images from ordinary polychromatic measurements. This approach is based on a Gaussian noise model with unknown variance assigned directly to the projections without taking negative-log. Referring to Bayesian inferences, the decomposition fractions and observation variance are estimated by using the joint maximum a posteriori (MAP) estimation method. Subject to an adaptive prior model assigned to the variance, the joint estimation problem is then simplified into a single estimation problem. It transforms the joint MAP estimation problem into a minimization problem with a nonquadratic cost function. To solve it, the use of a monotone conjugate gradient algorithm with suboptimal descent steps is proposed. The performance of the proposed approach is analyzed with both simulated and experimental data. The results show that the proposed Bayesian approach is robust to noise and materials. It is also necessary to have the accurate spectrum information about the source-detector system. When dealing with experimental data, the spectrum can be predicted by a Monte Carlo simulator. For the materials between water and bone, less than 5% separation errors are observed on the estimated decomposition fractions. The proposed approach is a statistical reconstruction approach based on a nonlinear forward model counting the full beam polychromaticity and applied directly to the projections without taking negative-log. Compared to the approaches based on linear forward models and the BHA correction approaches, it has advantages in noise robustness and reconstruction accuracy.

Bayesian paradox in homeland security and homeland defense

NASA Astrophysics Data System (ADS)

Jannson, Tomasz; Forrester, Thomas; Wang, Wenjian

2011-06-01

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

BANYAN_Sigma: Bayesian classifier for members of young stellar associations

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Bayesian 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.

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.

INFERENCE FOR INDIVIDUAL-LEVEL MODELS OF INFECTIOUS DISEASES IN LARGE POPULATIONS.

PubMed

Deardon, Rob; Brooks, Stephen P; Grenfell, Bryan T; Keeling, Matthew J; Tildesley, Michael J; Savill, Nicholas J; Shaw, Darren J; Woolhouse, Mark E J

2010-01-01

Individual Level Models (ILMs), a new class of models, are being applied to infectious epidemic data to aid in the understanding of the spatio-temporal dynamics of infectious diseases. These models are highly flexible and intuitive, and can be parameterised under a Bayesian framework via Markov chain Monte Carlo (MCMC) methods. Unfortunately, this parameterisation can be difficult to implement due to intense computational requirements when calculating the full posterior for large, or even moderately large, susceptible populations, or when missing data are present. Here we detail a methodology that can be used to estimate parameters for such large, and/or incomplete, data sets. This is done in the context of a study of the UK 2001 foot-and-mouth disease (FMD) epidemic.

Exact Bayesian Inference for Phylogenetic Birth-Death Models.

PubMed

Parag, K V; Pybus, O G

2018-04-26

Inferring the rates of change of a population from a reconstructed phylogeny of genetic sequences is a central problem in macro-evolutionary biology, epidemiology, and many other disciplines. A popular solution involves estimating the parameters of a birth-death process (BDP), which links the shape of the phylogeny to its birth and death rates. Modern BDP estimators rely on random Markov chain Monte Carlo (MCMC) sampling to infer these rates. Such methods, while powerful and scalable, cannot be guaranteed to converge, leading to results that may be hard to replicate or difficult to validate. We present a conceptually and computationally different parametric BDP inference approach using flexible and easy to implement Snyder filter (SF) algorithms. This method is deterministic so its results are provable, guaranteed, and reproducible. We validate the SF on constant rate BDPs and find that it solves BDP likelihoods known to produce robust estimates. We then examine more complex BDPs with time-varying rates. Our estimates compare well with a recently developed parametric MCMC inference method. Lastly, we performmodel selection on an empirical Agamid species phylogeny, obtaining results consistent with the literature. The SF makes no approximations, beyond those required for parameter quantisation and numerical integration, and directly computes the posterior distribution of model parameters. It is a promising alternative inference algorithm that may serve either as a standalone Bayesian estimator or as a useful diagnostic reference for validating more involved MCMC strategies. The Snyder filter is implemented in Matlab and the time-varying BDP models are simulated in R. The source code and data are freely available at https://github.com/kpzoo/snyder-birth-death-code. kris.parag@zoo.ox.ac.uk. Supplementary material is available at Bioinformatics online.

Generative models for discovering sparse distributed representations.

PubMed Central

Hinton, G E; Ghahramani, Z

1997-01-01

We describe a hierarchical, generative model that can be viewed as a nonlinear generalization of factor analysis and can be implemented in a neural network. The model uses bottom-up, top-down and lateral connections to perform Bayesian perceptual inference correctly. Once perceptual inference has been performed the connection strengths can be updated using a very simple learning rule that only requires locally available information. We demonstrate that the network learns to extract sparse, distributed, hierarchical representations. PMID:9304685

Post-Boreotropical dispersals explain the pantropical disjunction in Paederia (Rubiaceae)

PubMed Central

Nie, Ze-Long; Deng, Tao; Meng, Ying; Sun, Hang; Wen, Jun

2013-01-01

Background and Aims Pantropical intercontinental disjunction is a common biogeographical pattern in flowering plants exhibiting a discontinuous distribution primarily in tropical Asia, Africa and the Americas. Only a few plant groups with this pattern have been investigated at the generic level with molecular phylogenetic and biogeographical methods. Paederia (Rubiaceae) is a pantropical genus of 31 species of woody lianas, with the greatest species diversity in continental Asia and Madagascar and only two species from tropical America. The aim of this study was to reconstruct the biogeographical history of Paederia based on phylogenetic analyses to explore how the genus attained its pantropical distribution. Methods Maximum parsimony and Bayesian inference were used for phylogenetic analyses using sequences of five plastid markers (the rbcL gene, rps16 intron, trnT-F region, atpB-rbcL spacer and psbA-trnH spacer). Biogeographical inferences were based on a Bayesian uncorrelated lognormal relaxed molecular clock together with both Bayesian and likelihood ancestral area reconstructions. Key Results The data suggest an early diverged Asian lineage sister to the clade of the remaining species consisting of a predominantly Asian sub-clade and a primarily Malagasy sub-clade. Paederia is inferred to have originated in the Oligocene in tropical continental Asia. It then reached Africa in the early to middle Miocene, most probably via long-distance dispersal across the Indian Ocean. The two Neotropical species are inferred to have derived independently in the late Miocene from ancestors of Asia and East Africa, respectively. Conclusions The results demonstrate the importance of post-Boreotropical long-distance dispersals (across three major oceans) in shaping the global pantropical disjunction in some plants, such as Paederia, with small, winged diaspores adapted to long-distance dispersal by various agents including wind, ocean currents or birds. Overland migration is less likely to explain its palaeotropical disjunction between Asia and Africa. PMID:23478944

Phylogenetic analysis of honey bee behavioral evolution.

PubMed

Raffiudin, Rika; Crozier, Ross H

2007-05-01

DNA sequences from three mitochondrial (rrnL, cox2, nad2) and one nuclear gene (itpr) from all 9 known honey bee species (Apis), a 10th possible species, Apis dorsata binghami, and three outgroup species (Bombus terrestris, Melipona bicolor and Trigona fimbriata) were used to infer Apis phylogenetic relationships using Bayesian analysis. The dwarf honey bees were confirmed as basal, and the giant and cavity-nesting species to be monophyletic. All nodes were strongly supported except that grouping Apis cerana with A. nigrocincta. Two thousand post-burnin trees from the phylogenetic analysis were used in a Bayesian comparative analysis to explore the evolution of dance type, nest structure, comb structure and dance sound within Apis. The ancestral honey bee species was inferred with high support to have nested in the open, and to have more likely than not had a silent vertical waggle dance and a single comb. The common ancestor of the giant and cavity-dwelling bees is strongly inferred to have had a buzzing vertical directional dance. All pairwise combinations of characters showed strong association, but the multiple comparisons problem reduces the ability to infer associations between states between characters. Nevertheless, a buzzing dance is significantly associated with cavity-nesting, several vertical combs, and dancing vertically, a horizontal dance is significantly associated with a nest with a single comb wrapped around the support, and open nesting with a single pendant comb and a silent waggle dance.

Nonparametric Bayesian inference for mean residual life functions in survival analysis.

PubMed

Poynor, Valerie; Kottas, Athanasios

2018-01-19

Modeling and inference for survival analysis problems typically revolves around different functions related to the survival distribution. Here, we focus on the mean residual life (MRL) function, which provides the expected remaining lifetime given that a subject has survived (i.e. is event-free) up to a particular time. This function is of direct interest in reliability, medical, and actuarial fields. In addition to its practical interpretation, the MRL function characterizes the survival distribution. We develop general Bayesian nonparametric inference for MRL functions built from a Dirichlet process mixture model for the associated survival distribution. The resulting model for the MRL function admits a representation as a mixture of the kernel MRL functions with time-dependent mixture weights. This model structure allows for a wide range of shapes for the MRL function. Particular emphasis is placed on the selection of the mixture kernel, taken to be a gamma distribution, to obtain desirable properties for the MRL function arising from the mixture model. The inference method is illustrated with a data set of two experimental groups and a data set involving right censoring. The supplementary material available at Biostatistics online provides further results on empirical performance of the model, using simulated data examples. © The Author 2018. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

A Bayesian model for time-to-event data with informative censoring

PubMed Central

Kaciroti, Niko A.; Raghunathan, Trivellore E.; Taylor, Jeremy M. G.; Julius, Stevo

2012-01-01

Randomized trials with dropouts or censored data and discrete time-to-event type outcomes are frequently analyzed using the Kaplan–Meier or product limit (PL) estimation method. However, the PL method assumes that the censoring mechanism is noninformative and when this assumption is violated, the inferences may not be valid. We propose an expanded PL method using a Bayesian framework to incorporate informative censoring mechanism and perform sensitivity analysis on estimates of the cumulative incidence curves. The expanded method uses a model, which can be viewed as a pattern mixture model, where odds for having an event during the follow-up interval (tk−1,tk], conditional on being at risk at tk−1, differ across the patterns of missing data. The sensitivity parameters relate the odds of an event, between subjects from a missing-data pattern with the observed subjects for each interval. The large number of the sensitivity parameters is reduced by considering them as random and assumed to follow a log-normal distribution with prespecified mean and variance. Then we vary the mean and variance to explore sensitivity of inferences. The missing at random (MAR) mechanism is a special case of the expanded model, thus allowing exploration of the sensitivity to inferences as departures from the inferences under the MAR assumption. The proposed approach is applied to data from the TRial Of Preventing HYpertension. PMID:22223746

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

PubMed

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

2015-01-01

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

A Bayesian Developmental Approach to Robotic Goal-Based Imitation Learning

PubMed Central

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

2015-01-01

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

Boosting probabilistic graphical model inference by incorporating prior knowledge from multiple sources.

PubMed

Praveen, Paurush; Fröhlich, Holger

2013-01-01

Inferring regulatory networks from experimental data via probabilistic graphical models is a popular framework to gain insights into biological systems. However, the inherent noise in experimental data coupled with a limited sample size reduces the performance of network reverse engineering. Prior knowledge from existing sources of biological information can address this low signal to noise problem by biasing the network inference towards biologically plausible network structures. Although integrating various sources of information is desirable, their heterogeneous nature makes this task challenging. We propose two computational methods to incorporate various information sources into a probabilistic consensus structure prior to be used in graphical model inference. Our first model, called Latent Factor Model (LFM), assumes a high degree of correlation among external information sources and reconstructs a hidden variable as a common source in a Bayesian manner. The second model, a Noisy-OR, picks up the strongest support for an interaction among information sources in a probabilistic fashion. Our extensive computational studies on KEGG signaling pathways as well as on gene expression data from breast cancer and yeast heat shock response reveal that both approaches can significantly enhance the reconstruction accuracy of Bayesian Networks compared to other competing methods as well as to the situation without any prior. Our framework allows for using diverse information sources, like pathway databases, GO terms and protein domain data, etc. and is flexible enough to integrate new sources, if available.

Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation.

PubMed

Cornuet, Jean-Marie; Santos, Filipe; Beaumont, Mark A; Robert, Christian P; Marin, Jean-Michel; Balding, David J; Guillemaud, Thomas; Estoup, Arnaud

2008-12-01

Genetic data obtained on population samples convey information about their evolutionary history. Inference methods can extract part of this information but they require sophisticated statistical techniques that have been made available to the biologist community (through computer programs) only for simple and standard situations typically involving a small number of samples. We propose here a computer program (DIY ABC) for inference based on approximate Bayesian computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number of populations and samples. Such scenarios involve any combination of population divergences, admixtures and population size changes. DIY ABC can be used to compare competing scenarios, estimate parameters for one or more scenarios and compute bias and precision measures for a given scenario and known values of parameters (the current version applies to unlinked microsatellite data). This article describes key methods used in the program and provides its main features. The analysis of one simulated and one real dataset, both with complex evolutionary scenarios, illustrates the main possibilities of DIY ABC. The software DIY ABC is freely available at http://www.montpellier.inra.fr/CBGP/diyabc.

Recursive algorithms for phylogenetic tree counting.

PubMed

Gavryushkina, Alexandra; Welch, David; Drummond, Alexei J

2013-10-28

In Bayesian phylogenetic inference we are interested in distributions over a space of trees. The number of trees in a tree space is an important characteristic of the space and is useful for specifying prior distributions. When all samples come from the same time point and no prior information available on divergence times, the tree counting problem is easy. However, when fossil evidence is used in the inference to constrain the tree or data are sampled serially, new tree spaces arise and counting the number of trees is more difficult. We describe an algorithm that is polynomial in the number of sampled individuals for counting of resolutions of a constraint tree assuming that the number of constraints is fixed. We generalise this algorithm to counting resolutions of a fully ranked constraint tree. We describe a quadratic algorithm for counting the number of possible fully ranked trees on n sampled individuals. We introduce a new type of tree, called a fully ranked tree with sampled ancestors, and describe a cubic time algorithm for counting the number of such trees on n sampled individuals. These algorithms should be employed for Bayesian Markov chain Monte Carlo inference when fossil data are included or data are serially sampled.

Bayesian inference in camera trapping studies for a class of spatial capture-recapture models

USGS Publications Warehouse

Royle, J. Andrew; Karanth, K. Ullas; Gopalaswamy, Arjun M.; Kumar, N. Samba

2009-01-01

We develop a class of models for inference about abundance or density using spatial capture-recapture data from studies based on camera trapping and related methods. The model is a hierarchical model composed of two components: a point process model describing the distribution of individuals in space (or their home range centers) and a model describing the observation of individuals in traps. We suppose that trap- and individual-specific capture probabilities are a function of distance between individual home range centers and trap locations. We show that the models can be regarded as generalized linear mixed models, where the individual home range centers are random effects. We adopt a Bayesian framework for inference under these models using a formulation based on data augmentation. We apply the models to camera trapping data on tigers from the Nagarahole Reserve, India, collected over 48 nights in 2006. For this study, 120 camera locations were used, but cameras were only operational at 30 locations during any given sample occasion. Movement of traps is common in many camera-trapping studies and represents an important feature of the observation model that we address explicitly in our application.

The Bayesian group lasso for confounded spatial data

USGS Publications Warehouse

Hefley, Trevor J.; Hooten, Mevin B.; Hanks, Ephraim M.; Russell, Robin E.; Walsh, Daniel P.

2017-01-01

Generalized linear mixed models for spatial processes are widely used in applied statistics. In many applications of the spatial generalized linear mixed model (SGLMM), the goal is to obtain inference about regression coefficients while achieving optimal predictive ability. When implementing the SGLMM, multicollinearity among covariates and the spatial random effects can make computation challenging and influence inference. We present a Bayesian group lasso prior with a single tuning parameter that can be chosen to optimize predictive ability of the SGLMM and jointly regularize the regression coefficients and spatial random effect. We implement the group lasso SGLMM using efficient Markov chain Monte Carlo (MCMC) algorithms and demonstrate how multicollinearity among covariates and the spatial random effect can be monitored as a derived quantity. To test our method, we compared several parameterizations of the SGLMM using simulated data and two examples from plant ecology and disease ecology. In all examples, problematic levels multicollinearity occurred and influenced sampling efficiency and inference. We found that the group lasso prior resulted in roughly twice the effective sample size for MCMC samples of regression coefficients and can have higher and less variable predictive accuracy based on out-of-sample data when compared to the standard SGLMM.

Human Inferences about Sequences: A Minimal Transition Probability Model

PubMed Central

2016-01-01

The brain constantly infers the causes of the inputs it receives and uses these inferences to generate statistical expectations about future observations. Experimental evidence for these expectations and their violations include explicit reports, sequential effects on reaction times, and mismatch or surprise signals recorded in electrophysiology and functional MRI. Here, we explore the hypothesis that the brain acts as a near-optimal inference device that constantly attempts to infer the time-varying matrix of transition probabilities between the stimuli it receives, even when those stimuli are in fact fully unpredictable. This parsimonious Bayesian model, with a single free parameter, accounts for a broad range of findings on surprise signals, sequential effects and the perception of randomness. Notably, it explains the pervasive asymmetry between repetitions and alternations encountered in those studies. Our analysis suggests that a neural machinery for inferring transition probabilities lies at the core of human sequence knowledge. PMID:28030543

Multi-Agent Inference in Social Networks: A Finite Population Learning Approach.

PubMed

Fan, Jianqing; Tong, Xin; Zeng, Yao

When people in a society want to make inference about some parameter, each person may want to use data collected by other people. Information (data) exchange in social networks is usually costly, so to make reliable statistical decisions, people need to trade off the benefits and costs of information acquisition. Conflicts of interests and coordination problems will arise in the process. Classical statistics does not consider people's incentives and interactions in the data collection process. To address this imperfection, this work explores multi-agent Bayesian inference problems with a game theoretic social network model. Motivated by our interest in aggregate inference at the societal level, we propose a new concept, finite population learning , to address whether with high probability, a large fraction of people in a given finite population network can make "good" inference. Serving as a foundation, this concept enables us to study the long run trend of aggregate inference quality as population grows.

Bayesian techniques for analyzing group differences in the Iowa Gambling Task: A case study of intuitive and deliberate decision-makers.

PubMed

Steingroever, Helen; Pachur, Thorsten; Šmíra, Martin; Lee, Michael D

2018-06-01

The Iowa Gambling Task (IGT) is one of the most popular experimental paradigms for comparing complex decision-making across groups. Most commonly, IGT behavior is analyzed using frequentist tests to compare performance across groups, and to compare inferred parameters of cognitive models developed for the IGT. Here, we present a Bayesian alternative based on Bayesian repeated-measures ANOVA for comparing performance, and a suite of three complementary model-based methods for assessing the cognitive processes underlying IGT performance. The three model-based methods involve Bayesian hierarchical parameter estimation, Bayes factor model comparison, and Bayesian latent-mixture modeling. We illustrate these Bayesian methods by applying them to test the extent to which differences in intuitive versus deliberate decision style are associated with differences in IGT performance. The results show that intuitive and deliberate decision-makers behave similarly on the IGT, and the modeling analyses consistently suggest that both groups of decision-makers rely on similar cognitive processes. Our results challenge the notion that individual differences in intuitive and deliberate decision styles have a broad impact on decision-making. They also highlight the advantages of Bayesian methods, especially their ability to quantify evidence in favor of the null hypothesis, and that they allow model-based analyses to incorporate hierarchical and latent-mixture structures.

New insights into galaxy structure from GALPHAT- I. Motivation, methodology and benchmarks for Sérsic models

NASA Astrophysics Data System (ADS)

Yoon, Ilsang; Weinberg, Martin D.; Katz, Neal

2011-06-01

We introduce a new galaxy image decomposition tool, GALPHAT (GALaxy PHotometric ATtributes), which is a front-end application of the Bayesian Inference Engine (BIE), a parallel Markov chain Monte Carlo package, to provide full posterior probability distributions and reliable confidence intervals for all model parameters. The BIE relies on GALPHAT to compute the likelihood function. GALPHAT generates scale-free cumulative image tables for the desired model family with precise error control. Interpolation of this table yields accurate pixellated images with any centre, scale and inclination angle. GALPHAT then rotates the image by position angle using a Fourier shift theorem, yielding high-speed, accurate likelihood computation. We benchmark this approach using an ensemble of simulated Sérsic model galaxies over a wide range of observational conditions: the signal-to-noise ratio S/N, the ratio of galaxy size to the point spread function (PSF) and the image size, and errors in the assumed PSF; and a range of structural parameters: the half-light radius re and the Sérsic index n. We characterize the strength of parameter covariance in the Sérsic model, which increases with S/N and n, and the results strongly motivate the need for the full posterior probability distribution in galaxy morphology analyses and later inferences. The test results for simulated galaxies successfully demonstrate that, with a careful choice of Markov chain Monte Carlo algorithms and fast model image generation, GALPHAT is a powerful analysis tool for reliably inferring morphological parameters from a large ensemble of galaxies over a wide range of different observational conditions.

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

PubMed

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

2013-08-30

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

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.

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.

A Bayesian approach to modeling diffraction profiles and application to ferroelectric materials

DOE PAGES

Iamsasri, Thanakorn; Guerrier, Jonathon; Esteves, Giovanni; ...

2017-02-01

A new statistical approach for modeling diffraction profiles is introduced, using Bayesian inference and a Markov chain Monte Carlo (MCMC) algorithm. This method is demonstrated by modeling the degenerate reflections during application of an electric field to two different ferroelectric materials: thin-film lead zirconate titanate (PZT) of composition PbZr 0.3Ti 0.7O 3and a bulk commercial PZT polycrystalline ferroelectric. Here, the new method offers a unique uncertainty quantification of the model parameters that can be readily propagated into new calculated parameters.

A Bayesian least squares support vector machines based framework for fault diagnosis and failure prognosis

NASA Astrophysics Data System (ADS)

Khawaja, Taimoor Saleem

A high-belief low-overhead Prognostics and Health Management (PHM) system is desired for online real-time monitoring of complex non-linear systems operating in a complex (possibly non-Gaussian) noise environment. This thesis presents a Bayesian Least Squares Support Vector Machine (LS-SVM) based framework for fault diagnosis and failure prognosis in nonlinear non-Gaussian systems. The methodology assumes the availability of real-time process measurements, definition of a set of fault indicators and the existence of empirical knowledge (or historical data) to characterize both nominal and abnormal operating conditions. An efficient yet powerful Least Squares Support Vector Machine (LS-SVM) algorithm, set within a Bayesian Inference framework, not only allows for the development of real-time algorithms for diagnosis and prognosis but also provides a solid theoretical framework to address key concepts related to classification for diagnosis and regression modeling for prognosis. SVM machines are founded on the principle of Structural Risk Minimization (SRM) which tends to find a good trade-off between low empirical risk and small capacity. The key features in SVM are the use of non-linear kernels, the absence of local minima, the sparseness of the solution and the capacity control obtained by optimizing the margin. The Bayesian Inference framework linked with LS-SVMs allows a probabilistic interpretation of the results for diagnosis and prognosis. Additional levels of inference provide the much coveted features of adaptability and tunability of the modeling parameters. The two main modules considered in this research are fault diagnosis and failure prognosis. With the goal of designing an efficient and reliable fault diagnosis scheme, a novel Anomaly Detector is suggested based on the LS-SVM machines. The proposed scheme uses only baseline data to construct a 1-class LS-SVM machine which, when presented with online data is able to distinguish between normal behavior and any abnormal or novel data during real-time operation. The results of the scheme are interpreted as a posterior probability of health (1 - probability of fault). As shown through two case studies in Chapter 3, the scheme is well suited for diagnosing imminent faults in dynamical non-linear systems. Finally, the failure prognosis scheme is based on an incremental weighted Bayesian LS-SVR machine. It is particularly suited for online deployment given the incremental nature of the algorithm and the quick optimization problem solved in the LS-SVR algorithm. By way of kernelization and a Gaussian Mixture Modeling (GMM) scheme, the algorithm can estimate "possibly" non-Gaussian posterior distributions for complex non-linear systems. An efficient regression scheme associated with the more rigorous core algorithm allows for long-term predictions, fault growth estimation with confidence bounds and remaining useful life (RUL) estimation after a fault is detected. The leading contributions of this thesis are (a) the development of a novel Bayesian Anomaly Detector for efficient and reliable Fault Detection and Identification (FDI) based on Least Squares Support Vector Machines, (b) the development of a data-driven real-time architecture for long-term Failure Prognosis using Least Squares Support Vector Machines, (c) Uncertainty representation and management using Bayesian Inference for posterior distribution estimation and hyper-parameter tuning, and finally (d) the statistical characterization of the performance of diagnosis and prognosis algorithms in order to relate the efficiency and reliability of the proposed schemes.

A new probe of the magnetic field power spectrum in cosmic web filaments

NASA Astrophysics Data System (ADS)

Hales, Christopher A.; Greiner, Maksim; Ensslin, Torsten A.

2015-08-01

Establishing the properties of magnetic fields on scales larger than galaxy clusters is critical for resolving the unknown origin and evolution of galactic and cluster magnetism. More generally, observations of magnetic fields on cosmic scales are needed for assessing the impacts of magnetism on cosmology, particle physics, and structure formation over the full history of the Universe. However, firm observational evidence for magnetic fields in large scale structure remains elusive. In an effort to address this problem, we have developed a novel statistical method to infer the magnetic field power spectrum in cosmic web filaments using observation of the two-point correlation of Faraday rotation measures from a dense grid of extragalactic radio sources. Here we describe our approach, which embeds and extends the pioneering work of Kolatt (1998) within the context of Information Field Theory (a statistical theory for Bayesian inference on spatially distributed signals; Enfllin et al., 2009). We describe prospects for observation, for example with forthcoming data from the ultra-deep JVLA CHILES Con Pol survey and future surveys with the SKA.

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

NASA Astrophysics Data System (ADS)

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

2013-04-01

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

Terminal location planning in intermodal transportation with Bayesian inference method.

DOT National Transportation Integrated Search

2014-01-01

In this project, we consider the planning of terminal locations for intermodal transportation systems. For a given number of potential terminals and coexisted multiple service pairs, we find the set of appropriate terminals and their locations that p...

Uncertainty quantification of measured quantities for a HCCI engine: composition or temperatures

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

Petitpas, Guillaume; Whitesides, Russell

UQHCCI_1 computes the measurement uncertainties of a HCCI engine test bench using the pressure trace and the estimated uncertainties of the measured quantities as inputs, then propagating them through Bayesian inference and a mixing model.

Tutorial: Asteroseismic Data Analysis with DIAMONDS

NASA Astrophysics Data System (ADS)

Corsaro, Enrico

Since the advent of the space-based photometric missions such as CoRoT and NASA's Kepler, asteroseismology has acquired a central role in our understanding about stellar physics. The Kepler spacecraft, especially, is still releasing excellent photometric observations that contain a large amount of information not yet investigated. For exploiting the full potential of these data, sophisticated and robust analysis tools are now essential, so that further constraining of stellar structure and evolutionary models can be obtained. In addition, extracting detailed asteroseismic properties for many stars can yield new insights on their correlations to fundamental stellar properties and dynamics. After a brief introduction to the Bayesian notion of probability, I describe the code Diamonds for Bayesian parameter estimation and model comparison by means of the nested sampling Monte Carlo (NSMC) algorithm. NSMC constitutes an efficient and powerful method, in replacement to standard Markov chain Monte Carlo, very suitable for high-dimensional and multimodal problems that are typical of detailed asteroseismic analyses, such as the fitting and mode identification of individual oscillation modes in stars (known as peak-bagging). Diamonds is able to provide robust results for statistical inferences involving tens of individual oscillation modes, while at the same time preserving a considerable computational efficiency for identifying the solution. In the tutorial, I will present the fitting of the stellar background signal and the peak-bagging analysis of the oscillation modes in a red-giant star, providing an example to use Bayesian evidence for assessing the peak significance of the fitted oscillation peaks.

Long-Branch Attraction Bias and Inconsistency in Bayesian Phylogenetics

PubMed Central

Kolaczkowski, Bryan; Thornton, Joseph W.

2009-01-01

Bayesian inference (BI) of phylogenetic relationships uses the same probabilistic models of evolution as its precursor maximum likelihood (ML), so BI has generally been assumed to share ML's desirable statistical properties, such as largely unbiased inference of topology given an accurate model and increasingly reliable inferences as the amount of data increases. Here we show that BI, unlike ML, is biased in favor of topologies that group long branches together, even when the true model and prior distributions of evolutionary parameters over a group of phylogenies are known. Using experimental simulation studies and numerical and mathematical analyses, we show that this bias becomes more severe as more data are analyzed, causing BI to infer an incorrect tree as the maximum a posteriori phylogeny with asymptotically high support as sequence length approaches infinity. BI's long branch attraction bias is relatively weak when the true model is simple but becomes pronounced when sequence sites evolve heterogeneously, even when this complexity is incorporated in the model. This bias—which is apparent under both controlled simulation conditions and in analyses of empirical sequence data—also makes BI less efficient and less robust to the use of an incorrect evolutionary model than ML. Surprisingly, BI's bias is caused by one of the method's stated advantages—that it incorporates uncertainty about branch lengths by integrating over a distribution of possible values instead of estimating them from the data, as ML does. Our findings suggest that trees inferred using BI should be interpreted with caution and that ML may be a more reliable framework for modern phylogenetic analysis. PMID:20011052

Long-branch attraction bias and inconsistency in Bayesian phylogenetics.

PubMed

Kolaczkowski, Bryan; Thornton, Joseph W

2009-12-09

Bayesian inference (BI) of phylogenetic relationships uses the same probabilistic models of evolution as its precursor maximum likelihood (ML), so BI has generally been assumed to share ML's desirable statistical properties, such as largely unbiased inference of topology given an accurate model and increasingly reliable inferences as the amount of data increases. Here we show that BI, unlike ML, is biased in favor of topologies that group long branches together, even when the true model and prior distributions of evolutionary parameters over a group of phylogenies are known. Using experimental simulation studies and numerical and mathematical analyses, we show that this bias becomes more severe as more data are analyzed, causing BI to infer an incorrect tree as the maximum a posteriori phylogeny with asymptotically high support as sequence length approaches infinity. BI's long branch attraction bias is relatively weak when the true model is simple but becomes pronounced when sequence sites evolve heterogeneously, even when this complexity is incorporated in the model. This bias--which is apparent under both controlled simulation conditions and in analyses of empirical sequence data--also makes BI less efficient and less robust to the use of an incorrect evolutionary model than ML. Surprisingly, BI's bias is caused by one of the method's stated advantages--that it incorporates uncertainty about branch lengths by integrating over a distribution of possible values instead of estimating them from the data, as ML does. Our findings suggest that trees inferred using BI should be interpreted with caution and that ML may be a more reliable framework for modern phylogenetic analysis.

Model based inference from microvascular measurements: Combining experimental measurements and model predictions using a Bayesian probabilistic approach

PubMed Central

Rasmussen, Peter M.; Smith, Amy F.; Sakadžić, Sava; Boas, David A.; Pries, Axel R.; Secomb, Timothy W.; Østergaard, Leif

2017-01-01

Objective In vivo imaging of the microcirculation and network-oriented modeling have emerged as powerful means of studying microvascular function and understanding its physiological significance. Network-oriented modeling may provide the means of summarizing vast amounts of data produced by high-throughput imaging techniques in terms of key, physiological indices. To estimate such indices with sufficient certainty, however, network-oriented analysis must be robust to the inevitable presence of uncertainty due to measurement errors as well as model errors. Methods We propose the Bayesian probabilistic data analysis framework as a means of integrating experimental measurements and network model simulations into a combined and statistically coherent analysis. The framework naturally handles noisy measurements and provides posterior distributions of model parameters as well as physiological indices associated with uncertainty. Results We applied the analysis framework to experimental data from three rat mesentery networks and one mouse brain cortex network. We inferred distributions for more than five hundred unknown pressure and hematocrit boundary conditions. Model predictions were consistent with previous analyses, and remained robust when measurements were omitted from model calibration. Conclusion Our Bayesian probabilistic approach may be suitable for optimizing data acquisition and for analyzing and reporting large datasets acquired as part of microvascular imaging studies. PMID:27987383

Maximum Entropy Discrimination Poisson Regression for Software Reliability Modeling.

PubMed

Chatzis, Sotirios P; Andreou, Andreas S

2015-11-01

Reliably predicting software defects is one of the most significant tasks in software engineering. Two of the major components of modern software reliability modeling approaches are: 1) extraction of salient features for software system representation, based on appropriately designed software metrics and 2) development of intricate regression models for count data, to allow effective software reliability data modeling and prediction. Surprisingly, research in the latter frontier of count data regression modeling has been rather limited. More specifically, a lack of simple and efficient algorithms for posterior computation has made the Bayesian approaches appear unattractive, and thus underdeveloped in the context of software reliability modeling. In this paper, we try to address these issues by introducing a novel Bayesian regression model for count data, based on the concept of max-margin data modeling, effected in the context of a fully Bayesian model treatment with simple and efficient posterior distribution updates. Our novel approach yields a more discriminative learning technique, making more effective use of our training data during model inference. In addition, it allows of better handling uncertainty in the modeled data, which can be a significant problem when the training data are limited. We derive elegant inference algorithms for our model under the mean-field paradigm and exhibit its effectiveness using the publicly available benchmark data sets.

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