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

Using SPM 12’s Second-Level Bayesian Inference Procedure for fMRI Analysis: Practical Guidelines for End Users

PubMed Central

Han, Hyemin; Park, Joonsuk

2018-01-01

Recent debates about the conventional traditional threshold used in the fields of neuroscience and psychology, namely P < 0.05, have spurred researchers to consider alternative ways to analyze fMRI data. A group of methodologists and statisticians have considered Bayesian inference as a candidate methodology. However, few previous studies have attempted to provide end users of fMRI analysis tools, such as SPM 12, with practical guidelines about how to conduct Bayesian inference. In the present study, we aim to demonstrate how to utilize Bayesian inference, Bayesian second-level inference in particular, implemented in SPM 12 by analyzing fMRI data available to public via NeuroVault. In addition, to help end users understand how Bayesian inference actually works in SPM 12, we examine outcomes from Bayesian second-level inference implemented in SPM 12 by comparing them with those from classical second-level inference. Finally, we provide practical guidelines about how to set the parameters for Bayesian inference and how to interpret the results, such as Bayes factors, from the inference. We also discuss the practical and philosophical benefits of Bayesian inference and directions for future research. PMID:29456498

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.

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.

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

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.

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

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.

Inference of Time-Evolving Coupled Dynamical Systems in the Presence of Noise

NASA Astrophysics Data System (ADS)

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

2012-07-01

A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips and enables the evolution of the coupling functions and other parameters to be followed. It is based on phase dynamics, with Bayesian inference of the time-evolving parameters achieved by shaping the prior densities to incorporate knowledge of previous samples. The method is tested numerically and applied to reveal and quantify the time-varying nature of cardiorespiratory interactions.

Using Alien Coins to Test Whether Simple Inference Is Bayesian

ERIC Educational Resources Information Center

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

2016-01-01

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

Bayesian 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.

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.

Dynamical inference: where phase synchronization and generalized synchronization meet.

PubMed

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

2014-06-01

Synchronization is a widespread phenomenon that occurs among interacting oscillatory systems. It facilitates their temporal coordination and can lead to the emergence of spontaneous order. The detection of synchronization from the time series of such systems is of great importance for the understanding and prediction of their dynamics, and several methods for doing so have been introduced. However, the common case where the interacting systems have time-variable characteristic frequencies and coupling parameters, and may also be subject to continuous external perturbation and noise, still presents a major challenge. Here we apply recent developments in dynamical Bayesian inference to tackle these problems. In particular, we discuss how to detect phase slips and the existence of deterministic coupling from measured data, and we unify the concepts of phase synchronization and general synchronization. Starting from phase or state observables, we present methods for the detection of both phase and generalized synchronization. The consistency and equivalence of phase and generalized synchronization are further demonstrated, by the analysis of time series from analog electronic simulations of coupled nonautonomous van der Pol oscillators. We demonstrate that the detection methods work equally well on numerically simulated chaotic systems. In all the cases considered, we show that dynamical Bayesian inference can clearly identify noise-induced phase slips and distinguish coherence from intrinsic coupling-induced synchronization.

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

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

NASA Astrophysics Data System (ADS)

Rajabi, Mohammad Mahdi; Ataie-Ashtiani, Behzad

2016-05-01

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

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

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.

Fundamentals and Recent Developments in Approximate Bayesian Computation

PubMed Central

Lintusaari, Jarno; Gutmann, Michael U.; Dutta, Ritabrata; Kaski, Samuel; Corander, Jukka

2017-01-01

Abstract Bayesian inference plays an important role in phylogenetics, evolutionary biology, and in many other branches of science. It provides a principled framework for dealing with uncertainty and quantifying how it changes in the light of new evidence. For many complex models and inference problems, however, only approximate quantitative answers are obtainable. Approximate Bayesian computation (ABC) refers to a family of algorithms for approximate inference that makes a minimal set of assumptions by only requiring that sampling from a model is possible. We explain here the fundamentals of ABC, review the classical algorithms, and highlight recent developments. [ABC; approximate Bayesian computation; Bayesian inference; likelihood-free inference; phylogenetics; simulator-based models; stochastic simulation models; tree-based models.] PMID:28175922

Variations on Bayesian Prediction and Inference

DTIC Science & Technology

2016-05-09

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

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.

Quantum-Like Representation of Non-Bayesian Inference

NASA Astrophysics Data System (ADS)

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

2013-01-01

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

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Two Approaches to Calibration in Metrology

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

Campanelli, Mark

2014-04-01

Inferring mathematical relationships with quantified uncertainty from measurement data is common to computational science and metrology. Sufficient knowledge of measurement process noise enables Bayesian inference. Otherwise, an alternative approach is required, here termed compartmentalized inference, because collection of uncertain data and model inference occur independently. Bayesian parameterized model inference is compared to a Bayesian-compatible compartmentalized approach for ISO-GUM compliant calibration problems in renewable energy metrology. In either approach, model evidence can help reduce model discrepancy.

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 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.

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 multimodel inference for dose-response studies

USGS Publications Warehouse

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

2007-01-01

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

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

Time-varying nonstationary multivariate risk analysis using a dynamic Bayesian copula

NASA Astrophysics Data System (ADS)

Sarhadi, Ali; Burn, Donald H.; Concepción Ausín, María.; Wiper, Michael P.

2016-03-01

A time-varying risk analysis is proposed for an adaptive design framework in nonstationary conditions arising from climate change. A Bayesian, dynamic conditional copula is developed for modeling the time-varying dependence structure between mixed continuous and discrete multiattributes of multidimensional hydrometeorological phenomena. Joint Bayesian inference is carried out to fit the marginals and copula in an illustrative example using an adaptive, Gibbs Markov Chain Monte Carlo (MCMC) sampler. Posterior mean estimates and credible intervals are provided for the model parameters and the Deviance Information Criterion (DIC) is used to select the model that best captures different forms of nonstationarity over time. This study also introduces a fully Bayesian, time-varying joint return period for multivariate time-dependent risk analysis in nonstationary environments. The results demonstrate that the nature and the risk of extreme-climate multidimensional processes are changed over time under the impact of climate change, and accordingly the long-term decision making strategies should be updated based on the anomalies of the nonstationary environment.

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.

Ultrafast current imaging by Bayesian inversion

DOE Data Explorer

Somnath, Suhas; Law, Kody J. H.; Morozovska, Anna; Maksymovych, Petro; Kim, Yunseok; Lu, Xiaoli; Alexe, Marin; Archibald, Richard K; Kalinin, Sergei V; Jesse, Stephen; Vasudevan, Rama K

2016-01-01

Spectroscopic measurements of current-voltage curves in scanning probe microscopy is the earliest and one of the most common methods for characterizing local energy-dependent electronic properties, providing insight into superconductive, semiconductor, and memristive behaviors. However, the quasistatic nature of these measurements renders them extremely slow. Here, we demonstrate a fundamentally new approach for dynamic spectroscopic current imaging via full information capture and Bayesian inference analysis. This "general-mode I-V"method allows three orders of magnitude faster rates than presently possible. The technique is demonstrated by acquiring I-V curves in ferroelectric nanocapacitors, yielding >100,000 I-V curves in <20 minutes. This allows detection of switching currents in the nanoscale capacitors, as well as determination of dielectric constant. These experiments show the potential for the use of full information capture and Bayesian inference towards extracting physics from rapid I-V measurements, and can be used for transport measurements in both atomic force and scanning tunneling microscopy. The data was analyzed using pycroscopy - an open-source python package available at https://github.com/pycroscopy/pycroscopy

Pan-Antarctic analysis aggregating spatial estimates of Adélie penguin abundance reveals robust dynamics despite stochastic noise.

PubMed

Che-Castaldo, Christian; Jenouvrier, Stephanie; Youngflesh, Casey; Shoemaker, Kevin T; Humphries, Grant; McDowall, Philip; Landrum, Laura; Holland, Marika M; Li, Yun; Ji, Rubao; Lynch, Heather J

2017-10-10

Colonially-breeding seabirds have long served as indicator species for the health of the oceans on which they depend. Abundance and breeding data are repeatedly collected at fixed study sites in the hopes that changes in abundance and productivity may be useful for adaptive management of marine resources, but their suitability for this purpose is often unknown. To address this, we fit a Bayesian population dynamics model that includes process and observation error to all known Adélie penguin abundance data (1982-2015) in the Antarctic, covering >95% of their population globally. We find that process error exceeds observation error in this system, and that continent-wide "year effects" strongly influence population growth rates. Our findings have important implications for the use of Adélie penguins in Southern Ocean feedback management, and suggest that aggregating abundance across space provides the fastest reliable signal of true population change for species whose dynamics are driven by stochastic processes.Adélie penguins are a key Antarctic indicator species, but data patchiness has challenged efforts to link population dynamics to key drivers. Che-Castaldo et al. resolve this issue using a pan-Antarctic Bayesian model to infer missing data, and show that spatial aggregation leads to more robust inference regarding dynamics.

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.

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

NASA Astrophysics Data System (ADS)

Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

2016-04-01

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

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.

Hierarchical modeling and inference in ecology: The analysis of data from populations, metapopulations and communities

USGS Publications Warehouse

Royle, J. Andrew; Dorazio, Robert M.

2008-01-01

A guide to data collection, modeling and inference strategies for biological survey data using Bayesian and classical statistical methods. This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical models, with a strict focus on the use of probability models and parametric inference. Hierarchical models represent a paradigm shift in the application of statistics to ecological inference problems because they combine explicit models of ecological system structure or dynamics with models of how ecological systems are observed. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community, and metacommunity systems. The book provides the first synthetic treatment of many recent methodological advances in ecological modeling and unifies disparate methods and procedures. The authors apply principles of hierarchical modeling to ecological problems, including * occurrence or occupancy models for estimating species distribution * abundance models based on many sampling protocols, including distance sampling * capture-recapture models with individual effects * spatial capture-recapture models based on camera trapping and related methods * population and metapopulation dynamic models * models of biodiversity, community structure and dynamics.

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.

Bayesian inference of the groundwater depth threshold in a vegetation dynamic model: a case study, lower reach, Tarim River

USDA-ARS?s Scientific Manuscript database

The responses of eco-hydrological systems to anthropogenic and natural disturbances have attracted much attention in recent years. The coupling and simulating feedback between hydrological and ecological components have been realized in several recently developed eco-hydrological models. However, li...

Bayesian state space models for dynamic genetic network construction across multiple tissues.

PubMed

Liang, Yulan; Kelemen, Arpad

2016-08-01

Construction of gene-gene interaction networks and potential pathways is a challenging and important problem in genomic research for complex diseases while estimating the dynamic changes of the temporal correlations and non-stationarity are the keys in this process. In this paper, we develop dynamic state space models with hierarchical Bayesian settings to tackle this challenge for inferring the dynamic profiles and genetic networks associated with disease treatments. We treat both the stochastic transition matrix and the observation matrix time-variant and include temporal correlation structures in the covariance matrix estimations in the multivariate Bayesian state space models. The unevenly spaced short time courses with unseen time points are treated as hidden state variables. Hierarchical Bayesian approaches with various prior and hyper-prior models with Monte Carlo Markov Chain and Gibbs sampling algorithms are used to estimate the model parameters and the hidden state variables. We apply the proposed Hierarchical Bayesian state space models to multiple tissues (liver, skeletal muscle, and kidney) Affymetrix time course data sets following corticosteroid (CS) drug administration. Both simulation and real data analysis results show that the genomic changes over time and gene-gene interaction in response to CS treatment can be well captured by the proposed models. The proposed dynamic Hierarchical Bayesian state space modeling approaches could be expanded and applied to other large scale genomic data, such as next generation sequence (NGS) combined with real time and time varying electronic health record (EHR) for more comprehensive and robust systematic and network based analysis in order to transform big biomedical data into predictions and diagnostics for precision medicine and personalized healthcare with better decision making and patient outcomes.

Computational Approaches to Spatial Orientation: From Transfer Functions to Dynamic Bayesian Inference

PubMed Central

MacNeilage, Paul R.; Ganesan, Narayan; Angelaki, Dora E.

2008-01-01

Spatial orientation is the sense of body orientation and self-motion relative to the stationary environment, fundamental to normal waking behavior and control of everyday motor actions including eye movements, postural control, and locomotion. The brain achieves spatial orientation by integrating visual, vestibular, and somatosensory signals. Over the past years, considerable progress has been made toward understanding how these signals are processed by the brain using multiple computational approaches that include frequency domain analysis, the concept of internal models, observer theory, Bayesian theory, and Kalman filtering. Here we put these approaches in context by examining the specific questions that can be addressed by each technique and some of the scientific insights that have resulted. We conclude with a recent application of particle filtering, a probabilistic simulation technique that aims to generate the most likely state estimates by incorporating internal models of sensor dynamics and physical laws and noise associated with sensory processing as well as prior knowledge or experience. In this framework, priors for low angular velocity and linear acceleration can explain the phenomena of velocity storage and frequency segregation, both of which have been modeled previously using arbitrary low-pass filtering. How Kalman and particle filters may be implemented by the brain is an emerging field. Unlike past neurophysiological research that has aimed to characterize mean responses of single neurons, investigations of dynamic Bayesian inference should attempt to characterize population activities that constitute probabilistic representations of sensory and prior information. PMID:18842952

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 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.

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.

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.

Modeling the Evolution of Beliefs Using an Attentional Focus Mechanism

PubMed Central

Marković, Dimitrije; Gläscher, Jan; Bossaerts, Peter; O’Doherty, John; Kiebel, Stefan J.

2015-01-01

For making decisions in everyday life we often have first to infer the set of environmental features that are relevant for the current task. Here we investigated the computational mechanisms underlying the evolution of beliefs about the relevance of environmental features in a dynamical and noisy environment. For this purpose we designed a probabilistic Wisconsin card sorting task (WCST) with belief solicitation, in which subjects were presented with stimuli composed of multiple visual features. At each moment in time a particular feature was relevant for obtaining reward, and participants had to infer which feature was relevant and report their beliefs accordingly. To test the hypothesis that attentional focus modulates the belief update process, we derived and fitted several probabilistic and non-probabilistic behavioral models, which either incorporate a dynamical model of attentional focus, in the form of a hierarchical winner-take-all neuronal network, or a diffusive model, without attention-like features. We used Bayesian model selection to identify the most likely generative model of subjects’ behavior and found that attention-like features in the behavioral model are essential for explaining subjects’ responses. Furthermore, we demonstrate a method for integrating both connectionist and Bayesian models of decision making within a single framework that allowed us to infer hidden belief processes of human subjects. PMID:26495984

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.

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

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…

Synaptic and nonsynaptic plasticity approximating probabilistic inference

PubMed Central

Tully, Philip J.; Hennig, Matthias H.; Lansner, Anders

2014-01-01

Learning and memory operations in neural circuits are believed to involve molecular cascades of synaptic and nonsynaptic changes that lead to a diverse repertoire of dynamical phenomena at higher levels of processing. Hebbian and homeostatic plasticity, neuromodulation, and intrinsic excitability all conspire to form and maintain memories. But it is still unclear how these seemingly redundant mechanisms could jointly orchestrate learning in a more unified system. To this end, a Hebbian learning rule for spiking neurons inspired by Bayesian statistics is proposed. In this model, synaptic weights and intrinsic currents are adapted on-line upon arrival of single spikes, which initiate a cascade of temporally interacting memory traces that locally estimate probabilities associated with relative neuronal activation levels. Trace dynamics enable synaptic learning to readily demonstrate a spike-timing dependence, stably return to a set-point over long time scales, and remain competitive despite this stability. Beyond unsupervised learning, linking the traces with an external plasticity-modulating signal enables spike-based reinforcement learning. At the postsynaptic neuron, the traces are represented by an activity-dependent ion channel that is shown to regulate the input received by a postsynaptic cell and generate intrinsic graded persistent firing levels. We show how spike-based Hebbian-Bayesian learning can be performed in a simulated inference task using integrate-and-fire (IAF) neurons that are Poisson-firing and background-driven, similar to the preferred regime of cortical neurons. Our results support the view that neurons can represent information in the form of probability distributions, and that probabilistic inference could be a functional by-product of coupled synaptic and nonsynaptic mechanisms operating over several timescales. The model provides a biophysical realization of Bayesian computation by reconciling several observed neural phenomena whose functional effects are only partially understood in concert. PMID:24782758

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

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.

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

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

Constraints on the Dynamical Environments of Supermassive Black-Hole Binaries Using Pulsar-Timing Arrays.

PubMed

Taylor, Stephen R; Simon, Joseph; Sampson, Laura

2017-05-05

We introduce a technique for gravitational-wave analysis, where Gaussian process regression is used to emulate the strain spectrum of a stochastic background by training on population-synthesis simulations. This leads to direct Bayesian inference on astrophysical parameters. For pulsar timing arrays specifically, we interpolate over the parameter space of supermassive black-hole binary environments, including three-body stellar scattering, and evolving orbital eccentricity. We illustrate our approach on mock data, and assess the prospects for inference with data similar to the NANOGrav 9-yr data release.

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.

Computational statistics using the Bayesian Inference Engine

NASA Astrophysics Data System (ADS)

Weinberg, Martin D.

2013-09-01

This paper introduces the Bayesian Inference Engine (BIE), a general parallel, optimized software package for parameter inference and model selection. This package is motivated by the analysis needs of modern astronomical surveys and the need to organize and reuse expensive derived data. The BIE is the first platform for computational statistics designed explicitly to enable Bayesian update and model comparison for astronomical problems. Bayesian update is based on the representation of high-dimensional posterior distributions using metric-ball-tree based kernel density estimation. Among its algorithmic offerings, the BIE emphasizes hybrid tempered Markov chain Monte Carlo schemes that robustly sample multimodal posterior distributions in high-dimensional parameter spaces. Moreover, the BIE implements a full persistence or serialization system that stores the full byte-level image of the running inference and previously characterized posterior distributions for later use. Two new algorithms to compute the marginal likelihood from the posterior distribution, developed for and implemented in the BIE, enable model comparison for complex models and data sets. Finally, the BIE was designed to be a collaborative platform for applying Bayesian methodology to astronomy. It includes an extensible object-oriented and easily extended framework that implements every aspect of the Bayesian inference. By providing a variety of statistical algorithms for all phases of the inference problem, a scientist may explore a variety of approaches with a single model and data implementation. Additional technical details and download details are available from http://www.astro.umass.edu/bie. The BIE is distributed under the GNU General Public License.

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.

Stochastic inference with spiking neurons in the high-conductance state

NASA Astrophysics Data System (ADS)

Petrovici, Mihai A.; Bill, Johannes; Bytschok, Ilja; Schemmel, Johannes; Meier, Karlheinz

2016-10-01

The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro. Based on a propagation of the membrane autocorrelation across spike bursts, we provide an analytical derivation of the neural activation function that holds for a large parameter space, including the high-conductance state. On this basis, we show how an ensemble of leaky integrate-and-fire neurons with conductance-based synapses embedded in a spiking environment can attain the correct firing statistics for sampling from a well-defined target distribution. For recurrent networks, we examine convergence toward stationarity in computer simulations and demonstrate sample-based Bayesian inference in a mixed graphical model. This points to a new computational role of high-conductance states and establishes a rigorous link between deterministic neuron models and functional stochastic dynamics on the network level.

A parametric interpretation of Bayesian Nonparametric Inference from Gene Genealogies: Linking ecological, population genetics and evolutionary processes.

PubMed

Ponciano, José Miguel

2017-11-22

Using a nonparametric Bayesian approach Palacios and Minin (2013) dramatically improved the accuracy, precision of Bayesian inference of population size trajectories from gene genealogies. These authors proposed an extension of a Gaussian Process (GP) nonparametric inferential method for the intensity function of non-homogeneous Poisson processes. They found that not only the statistical properties of the estimators were improved with their method, but also, that key aspects of the demographic histories were recovered. The authors' work represents the first Bayesian nonparametric solution to this inferential problem because they specify a convenient prior belief without a particular functional form on the population trajectory. Their approach works so well and provides such a profound understanding of the biological process, that the question arises as to how truly "biology-free" their approach really is. Using well-known concepts of stochastic population dynamics, here I demonstrate that in fact, Palacios and Minin's GP model can be cast as a parametric population growth model with density dependence and environmental stochasticity. Making this link between population genetics and stochastic population dynamics modeling provides novel insights into eliciting biologically meaningful priors for the trajectory of the effective population size. The results presented here also bring novel understanding of GP as models for the evolution of a trait. Thus, the ecological principles foundation of Palacios and Minin (2013)'s prior adds to the conceptual and scientific value of these authors' inferential approach. I conclude this note by listing a series of insights brought about by this connection with Ecology. Copyright © 2017 The Author. Published by Elsevier Inc. All rights reserved.

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

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

NASA Astrophysics Data System (ADS)

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

2015-09-01

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

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

The Neural Correlates of Hierarchical Predictions for Perceptual Decisions.

PubMed

Weilnhammer, Veith A; Stuke, Heiner; Sterzer, Philipp; Schmack, Katharina

2018-05-23

Sensory information is inherently noisy, sparse, and ambiguous. In contrast, visual experience is usually clear, detailed, and stable. Bayesian theories of perception resolve this discrepancy by assuming that prior knowledge about the causes underlying sensory stimulation actively shapes perceptual decisions. The CNS is believed to entertain a generative model aligned to dynamic changes in the hierarchical states of our volatile sensory environment. Here, we used model-based fMRI to study the neural correlates of the dynamic updating of hierarchically structured predictions in male and female human observers. We devised a crossmodal associative learning task with covertly interspersed ambiguous trials in which participants engaged in hierarchical learning based on changing contingencies between auditory cues and visual targets. By inverting a Bayesian model of perceptual inference, we estimated individual hierarchical predictions, which significantly biased perceptual decisions under ambiguity. Although "high-level" predictions about the cue-target contingency correlated with activity in supramodal regions such as orbitofrontal cortex and hippocampus, dynamic "low-level" predictions about the conditional target probabilities were associated with activity in retinotopic visual cortex. Our results suggest that our CNS updates distinct representations of hierarchical predictions that continuously affect perceptual decisions in a dynamically changing environment. SIGNIFICANCE STATEMENT Bayesian theories posit that our brain entertains a generative model to provide hierarchical predictions regarding the causes of sensory information. Here, we use behavioral modeling and fMRI to study the neural underpinnings of such hierarchical predictions. We show that "high-level" predictions about the strength of dynamic cue-target contingencies during crossmodal associative learning correlate with activity in orbitofrontal cortex and the hippocampus, whereas "low-level" conditional target probabilities were reflected in retinotopic visual cortex. Our findings empirically corroborate theorizations on the role of hierarchical predictions in visual perception and contribute substantially to a longstanding debate on the link between sensory predictions and orbitofrontal or hippocampal activity. Our work fundamentally advances the mechanistic understanding of perceptual inference in the human brain. Copyright © 2018 the authors 0270-6474/18/385008-14$15.00/0.

Bayesian integration of position and orientation cues in perception of biological and non-biological forms.

PubMed

Thurman, Steven M; Lu, Hongjing

2014-01-01

Visual form analysis is fundamental to shape perception and likely plays a central role in perception of more complex dynamic shapes, such as moving objects or biological motion. Two primary form-based cues serve to represent the overall shape of an object: the spatial position and the orientation of locations along the boundary of the object. However, it is unclear how the visual system integrates these two sources of information in dynamic form analysis, and in particular how the brain resolves ambiguities due to sensory uncertainty and/or cue conflict. In the current study, we created animations of sparsely-sampled dynamic objects (human walkers or rotating squares) comprised of oriented Gabor patches in which orientation could either coincide or conflict with information provided by position cues. When the cues were incongruent, we found a characteristic trade-off between position and orientation information whereby position cues increasingly dominated perception as the relative uncertainty of orientation increased and vice versa. Furthermore, we found no evidence for differences in the visual processing of biological and non-biological objects, casting doubt on the claim that biological motion may be specialized in the human brain, at least in specific terms of form analysis. To explain these behavioral results quantitatively, we adopt a probabilistic template-matching model that uses Bayesian inference within local modules to estimate object shape separately from either spatial position or orientation signals. The outputs of the two modules are integrated with weights that reflect individual estimates of subjective cue reliability, and integrated over time to produce a decision about the perceived dynamics of the input data. Results of this model provided a close fit to the behavioral data, suggesting a mechanism in the human visual system that approximates rational Bayesian inference to integrate position and orientation signals in dynamic form analysis.

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.

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.

Inference of time-delayed gene regulatory networks based on dynamic Bayesian network hybrid learning method

PubMed Central

Yu, Bin; Xu, Jia-Meng; Li, Shan; Chen, Cheng; Chen, Rui-Xin; Wang, Lei; Zhang, Yan; Wang, Ming-Hui

2017-01-01

Gene regulatory networks (GRNs) research reveals complex life phenomena from the perspective of gene interaction, which is an important research field in systems biology. Traditional Bayesian networks have a high computational complexity, and the network structure scoring model has a single feature. Information-based approaches cannot identify the direction of regulation. In order to make up for the shortcomings of the above methods, this paper presents a novel hybrid learning method (DBNCS) based on dynamic Bayesian network (DBN) to construct the multiple time-delayed GRNs for the first time, combining the comprehensive score (CS) with the DBN model. DBNCS algorithm first uses CMI2NI (conditional mutual inclusive information-based network inference) algorithm for network structure profiles learning, namely the construction of search space. Then the redundant regulations are removed by using the recursive optimization algorithm (RO), thereby reduce the false positive rate. Secondly, the network structure profiles are decomposed into a set of cliques without loss, which can significantly reduce the computational complexity. Finally, DBN model is used to identify the direction of gene regulation within the cliques and search for the optimal network structure. The performance of DBNCS algorithm is evaluated by the benchmark GRN datasets from DREAM challenge as well as the SOS DNA repair network in Escherichia coli, and compared with other state-of-the-art methods. The experimental results show the rationality of the algorithm design and the outstanding performance of the GRNs. PMID:29113310

Inference of time-delayed gene regulatory networks based on dynamic Bayesian network hybrid learning method.

PubMed

Yu, Bin; Xu, Jia-Meng; Li, Shan; Chen, Cheng; Chen, Rui-Xin; Wang, Lei; Zhang, Yan; Wang, Ming-Hui

2017-10-06

Gene regulatory networks (GRNs) research reveals complex life phenomena from the perspective of gene interaction, which is an important research field in systems biology. Traditional Bayesian networks have a high computational complexity, and the network structure scoring model has a single feature. Information-based approaches cannot identify the direction of regulation. In order to make up for the shortcomings of the above methods, this paper presents a novel hybrid learning method (DBNCS) based on dynamic Bayesian network (DBN) to construct the multiple time-delayed GRNs for the first time, combining the comprehensive score (CS) with the DBN model. DBNCS algorithm first uses CMI2NI (conditional mutual inclusive information-based network inference) algorithm for network structure profiles learning, namely the construction of search space. Then the redundant regulations are removed by using the recursive optimization algorithm (RO), thereby reduce the false positive rate. Secondly, the network structure profiles are decomposed into a set of cliques without loss, which can significantly reduce the computational complexity. Finally, DBN model is used to identify the direction of gene regulation within the cliques and search for the optimal network structure. The performance of DBNCS algorithm is evaluated by the benchmark GRN datasets from DREAM challenge as well as the SOS DNA repair network in Escherichia coli , and compared with other state-of-the-art methods. The experimental results show the rationality of the algorithm design and the outstanding performance of the GRNs.

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.

Information-Decay Pursuit of Dynamic Parameters in Student Models

DTIC Science & Technology

1994-04-01

simple worked-through example). Commercially available computer programs for structuring and using Bayesian inference include ERGO ( Noetic Systems...Tukey, J.W. (1977). Data analysis and Regression: A second course in statistics. Reading, MA: Addison-Wesley. Noetic Systems, Inc. (1991). ERGO...Naval Academy Division of Educational Studies Annapolis MD 21402-5002 Elmory Univerity Dr Janice Gifford 210 Fiabburne Bldg University of

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.

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.

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.

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.

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.

Bayesian inference of ice thickness from remote-sensing data

NASA Astrophysics Data System (ADS)

Werder, Mauro A.; Huss, Matthias

2017-04-01

Knowledge about ice thickness and volume is indispensable for studying ice dynamics, future sea-level rise due to glacier melt or their contribution to regional hydrology. Accurate measurements of glacier thickness require on-site work, usually employing radar techniques. However, these field measurements are time consuming, expensive and sometime downright impossible. Conversely, measurements of the ice surface, namely elevation and flow velocity, are becoming available world-wide through remote sensing. The model of Farinotti et al. (2009) calculates ice thicknesses based on a mass conservation approach paired with shallow ice physics using estimates of the surface mass balance. The presented work applies a Bayesian inference approach to estimate the parameters of a modified version of this forward model by fitting it to both measurements of surface flow speed and of ice thickness. The inverse model outputs ice thickness as well the distribution of the error. We fit the model to ten test glaciers and ice caps and quantify the improvements of thickness estimates through the usage of surface ice flow measurements.

Bayesian inference of radiation belt loss timescales.

NASA Astrophysics Data System (ADS)

Camporeale, E.; Chandorkar, M.

2017-12-01

Electron fluxes in the Earth's radiation belts are routinely studied using the classical quasi-linear radial diffusion model. Although this simplified linear equation has proven to be an indispensable tool in understanding the dynamics of the radiation belt, it requires specification of quantities such as the diffusion coefficient and electron loss timescales that are never directly measured. Researchers have so far assumed a-priori parameterisations for radiation belt quantities and derived the best fit using satellite data. The state of the art in this domain lacks a coherent formulation of this problem in a probabilistic framework. We present some recent progress that we have made in performing Bayesian inference of radial diffusion parameters. We achieve this by making extensive use of the theory connecting Gaussian Processes and linear partial differential equations, and performing Markov Chain Monte Carlo sampling of radial diffusion parameters. These results are important for understanding the role and the propagation of uncertainties in radiation belt simulations and, eventually, for providing a probabilistic forecast of energetic electron fluxes in a Space Weather context.

Understanding Past Population Dynamics: Bayesian Coalescent-Based Modeling with Covariates

PubMed Central

Gill, Mandev S.; Lemey, Philippe; Bennett, Shannon N.; Biek, Roman; Suchard, Marc A.

2016-01-01

Effective population size characterizes the genetic variability in a population and is a parameter of paramount importance in population genetics and evolutionary biology. Kingman’s coalescent process enables inference of past population dynamics directly from molecular sequence data, and researchers have developed a number of flexible coalescent-based models for Bayesian nonparametric estimation of the effective population size as a function of time. Major goals of demographic reconstruction include identifying driving factors of effective population size, and understanding the association between the effective population size and such factors. Building upon Bayesian nonparametric coalescent-based approaches, we introduce a flexible framework that incorporates time-varying covariates that exploit Gaussian Markov random fields to achieve temporal smoothing of effective population size trajectories. To approximate the posterior distribution, we adapt efficient Markov chain Monte Carlo algorithms designed for highly structured Gaussian models. Incorporating covariates into the demographic inference framework enables the modeling of associations between the effective population size and covariates while accounting for uncertainty in population histories. Furthermore, it can lead to more precise estimates of population dynamics. We apply our model to four examples. We reconstruct the demographic history of raccoon rabies in North America and find a significant association with the spatiotemporal spread of the outbreak. Next, we examine the effective population size trajectory of the DENV-4 virus in Puerto Rico along with viral isolate count data and find similar cyclic patterns. We compare the population history of the HIV-1 CRF02_AG clade in Cameroon with HIV incidence and prevalence data and find that the effective population size is more reflective of incidence rate. Finally, we explore the hypothesis that the population dynamics of musk ox during the Late Quaternary period were related to climate change. [Coalescent; effective population size; Gaussian Markov random fields; phylodynamics; phylogenetics; population genetics. PMID:27368344

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.

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…

Optimal modeling of 1D azimuth correlations in the context of Bayesian inference

NASA Astrophysics Data System (ADS)

De Kock, Michiel B.; Eggers, Hans C.; Trainor, Thomas A.

2015-09-01

Analysis and interpretation of spectrum and correlation data from high-energy nuclear collisions is currently controversial because two opposing physics narratives derive contradictory implications from the same data, one narrative claiming collision dynamics is dominated by dijet production and projectile-nucleon fragmentation, the other claiming collision dynamics is dominated by a dense, flowing QCD medium. Opposing interpretations seem to be supported by alternative data models, and current model-comparison schemes are unable to distinguish between them. There is clearly need for a convincing new methodology to break the deadlock. In this study we introduce Bayesian inference (BI) methods applied to angular correlation data as a basis to evaluate competing data models. For simplicity the data considered are projections of two-dimensional (2D) angular correlations onto a 1D azimuth from three centrality classes of 200-GeV Au-Au collisions. We consider several data models typical of current model choices, including Fourier series (FS) and a Gaussian plus various combinations of individual cosine components. We evaluate model performance with BI methods and with power-spectrum analysis. We find that FS-only models are rejected in all cases by Bayesian analysis, which always prefers a Gaussian. A cylindrical quadrupole cos(2 ϕ ) is required in some cases but rejected for 0%-5%-central Au-Au collisions. Given a Gaussian centered at the azimuth origin, "higher harmonics" cos(m ϕ ) for m >2 are rejected. A model consisting of Gaussian +dipole cos(ϕ )+quadrupole cos(2 ϕ ) provides good 1D data descriptions in all cases.

Advancing understanding of affect labeling with dynamic causal modeling

PubMed Central

Torrisi, Salvatore J.; Lieberman, Matthew D.; Bookheimer, Susan Y.; Altshuler, Lori L.

2013-01-01

Mechanistic understandings of forms of incidental emotion regulation have implications for basic and translational research in the affective sciences. In this study we applied Dynamic Causal Modeling (DCM) for fMRI to a common paradigm of labeling facial affect to elucidate prefrontal to subcortical influences. Four brain regions were used to model affect labeling, including right ventrolateral prefrontal cortex (vlPFC), amygdala and Broca’s area. 64 models were compared, for each of 45 healthy subjects. Family level inference split the model space to a likely driving input and Bayesian Model Selection within the winning family of 32 models revealed a strong pattern of endogenous network connectivity. Modulatory effects of labeling were most prominently observed following Bayesian Model Averaging, with the dampening influence on amygdala originating from Broca’s area but much more strongly from right vlPFC. These results solidify and extend previous correlation and regression-based estimations of negative corticolimbic coupling. PMID:23774393

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.

Time-varying Concurrent Risk of Extreme Droughts and Heatwaves in California

NASA Astrophysics Data System (ADS)

Sarhadi, A.; Diffenbaugh, N. S.; Ausin, M. C.

2016-12-01

Anthropogenic global warming has changed the nature and the risk of extreme climate phenomena such as droughts and heatwaves. The concurrent of these nature-changing climatic extremes may result in intensifying undesirable consequences in terms of human health and destructive effects in water resources. The present study assesses the risk of concurrent extreme droughts and heatwaves under dynamic nonstationary conditions arising from climate change in California. For doing so, a generalized fully Bayesian time-varying multivariate risk framework is proposed evolving through time under dynamic human-induced environment. In this methodology, an extreme, Bayesian, dynamic copula (Gumbel) is developed to model the time-varying dependence structure between the two different climate extremes. The time-varying extreme marginals are previously modeled using a Generalized Extreme Value (GEV) distribution. Bayesian Markov Chain Monte Carlo (MCMC) inference is integrated to estimate parameters of the nonstationary marginals and copula using a Gibbs sampling method. Modelled marginals and copula are then used to develop a fully Bayesian, time-varying joint return period concept for the estimation of concurrent risk. Here we argue that climate change has increased the chance of concurrent droughts and heatwaves over decades in California. It is also demonstrated that a time-varying multivariate perspective should be incorporated to assess realistic concurrent risk of the extremes for water resources planning and management in a changing climate in this area. The proposed generalized methodology can be applied for other stochastic nature-changing compound climate extremes that are under the influence of climate change.

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

Quantum-Like Bayesian Networks for Modeling Decision Making

PubMed Central

Moreira, Catarina; Wichert, Andreas

2016-01-01

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

Astrocytic tracer dynamics estimated from [1-¹¹C]-acetate PET measurements.

PubMed

Arnold, Andrea; Calvetti, Daniela; Gjedde, Albert; Iversen, Peter; Somersalo, Erkki

2015-12-01

We address the problem of estimating the unknown parameters of a model of tracer kinetics from sequences of positron emission tomography (PET) scan data using a statistical sequential algorithm for the inference of magnitudes of dynamic parameters. The method, based on Bayesian statistical inference, is a modification of a recently proposed particle filtering and sequential Monte Carlo algorithm, where instead of preassigning the accuracy in the propagation of each particle, we fix the time step and account for the numerical errors in the innovation term. We apply the algorithm to PET images of [1-¹¹C]-acetate-derived tracer accumulation, estimating the transport rates in a three-compartment model of astrocytic uptake and metabolism of the tracer for a cohort of 18 volunteers from 3 groups, corresponding to healthy control individuals, cirrhotic liver and hepatic encephalopathy patients. The distribution of the parameters for the individuals and for the groups presented within the Bayesian framework support the hypothesis that the parameters for the hepatic encephalopathy group follow a significantly different distribution than the other two groups. The biological implications of the findings are also discussed. © The Authors 2014. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

An accessible method for implementing hierarchical models with spatio-temporal abundance data

USGS Publications Warehouse

Ross, Beth E.; Hooten, Melvin B.; Koons, David N.

2012-01-01

A common goal in ecology and wildlife management is to determine the causes of variation in population dynamics over long periods of time and across large spatial scales. Many assumptions must nevertheless be overcome to make appropriate inference about spatio-temporal variation in population dynamics, such as autocorrelation among data points, excess zeros, and observation error in count data. To address these issues, many scientists and statisticians have recommended the use of Bayesian hierarchical models. Unfortunately, hierarchical statistical models remain somewhat difficult to use because of the necessary quantitative background needed to implement them, or because of the computational demands of using Markov Chain Monte Carlo algorithms to estimate parameters. Fortunately, new tools have recently been developed that make it more feasible for wildlife biologists to fit sophisticated hierarchical Bayesian models (i.e., Integrated Nested Laplace Approximation, ‘INLA’). We present a case study using two important game species in North America, the lesser and greater scaup, to demonstrate how INLA can be used to estimate the parameters in a hierarchical model that decouples observation error from process variation, and accounts for unknown sources of excess zeros as well as spatial and temporal dependence in the data. Ultimately, our goal was to make unbiased inference about spatial variation in population trends over time.

Does History Repeat Itself? Wavelets and the Phylodynamics of Influenza A

PubMed Central

Tom, Jennifer A.; Sinsheimer, Janet S.; Suchard, Marc A.

2012-01-01

Unprecedented global surveillance of viruses will result in massive sequence data sets that require new statistical methods. These data sets press the limits of Bayesian phylogenetics as the high-dimensional parameters that comprise a phylogenetic tree increase the already sizable computational burden of these techniques. This burden often results in partitioning the data set, for example, by gene, and inferring the evolutionary dynamics of each partition independently, a compromise that results in stratified analyses that depend only on data within a given partition. However, parameter estimates inferred from these stratified models are likely strongly correlated, considering they rely on data from a single data set. To overcome this shortfall, we exploit the existing Monte Carlo realizations from stratified Bayesian analyses to efficiently estimate a nonparametric hierarchical wavelet-based model and learn about the time-varying parameters of effective population size that reflect levels of genetic diversity across all partitions simultaneously. Our methods are applied to complete genome influenza A sequences that span 13 years. We find that broad peaks and trends, as opposed to seasonal spikes, in the effective population size history distinguish individual segments from the complete genome. We also address hypotheses regarding intersegment dynamics within a formal statistical framework that accounts for correlation between segment-specific parameters. PMID:22160768

Filtering in Hybrid Dynamic Bayesian Networks

NASA Technical Reports Server (NTRS)

Andersen, Morten Nonboe; Andersen, Rasmus Orum; Wheeler, Kevin

2000-01-01

We implement a 2-time slice dynamic Bayesian network (2T-DBN) framework and make a 1-D state estimation simulation, an extension of the experiment in (v.d. Merwe et al., 2000) and compare different filtering techniques. Furthermore, we demonstrate experimentally that inference in a complex hybrid DBN is possible by simulating fault detection in a watertank system, an extension of the experiment in (Koller & Lerner, 2000) using a hybrid 2T-DBN. In both experiments, we perform approximate inference using standard filtering techniques, Monte Carlo methods and combinations of these. In the watertank simulation, we also demonstrate the use of 'non-strict' Rao-Blackwellisation. We show that the unscented Kalman filter (UKF) and UKF in a particle filtering framework outperform the generic particle filter, the extended Kalman filter (EKF) and EKF in a particle filtering framework with respect to accuracy in terms of estimation RMSE and sensitivity with respect to choice of network structure. Especially we demonstrate the superiority of UKF in a PF framework when our beliefs of how data was generated are wrong. Furthermore, we investigate the influence of data noise in the watertank simulation using UKF and PFUKD and show that the algorithms are more sensitive to changes in the measurement noise level that the process noise level. Theory and implementation is based on (v.d. Merwe et al., 2000).

Bayesian model calibration of computational models in velocimetry diagnosed dynamic compression experiments.

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

Brown, Justin; Hund, Lauren

2017-02-01

Dynamic compression experiments are being performed on complicated materials using increasingly complex drivers. The data produced in these experiments are beginning to reach a regime where traditional analysis techniques break down; requiring the solution of an inverse problem. A common measurement in dynamic experiments is an interface velocity as a function of time, and often this functional output can be simulated using a hydrodynamics code. Bayesian model calibration is a statistical framework to estimate inputs into a computational model in the presence of multiple uncertainties, making it well suited to measurements of this type. In this article, we apply Bayesianmore » model calibration to high pressure (250 GPa) ramp compression measurements in tantalum. We address several issues speci c to this calibration including the functional nature of the output as well as parameter and model discrepancy identi ability. Speci cally, we propose scaling the likelihood function by an e ective sample size rather than modeling the autocorrelation function to accommodate the functional output and propose sensitivity analyses using the notion of `modularization' to assess the impact of experiment-speci c nuisance input parameters on estimates of material properties. We conclude that the proposed Bayesian model calibration procedure results in simple, fast, and valid inferences on the equation of state parameters for tantalum.« less

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

PubMed Central

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

2016-01-01

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

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.

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.

Inferring phenomenological models of Markov processes from data

NASA Astrophysics Data System (ADS)

Rivera, Catalina; Nemenman, Ilya

Microscopically accurate modeling of stochastic dynamics of biochemical networks is hard due to the extremely high dimensionality of the state space of such networks. Here we propose an algorithm for inference of phenomenological, coarse-grained models of Markov processes describing the network dynamics directly from data, without the intermediate step of microscopically accurate modeling. The approach relies on the linear nature of the Chemical Master Equation and uses Bayesian Model Selection for identification of parsimonious models that fit the data. When applied to synthetic data from the Kinetic Proofreading process (KPR), a common mechanism used by cells for increasing specificity of molecular assembly, the algorithm successfully uncovers the known coarse-grained description of the process. This phenomenological description has been notice previously, but this time it is derived in an automated manner by the algorithm. James S. McDonnell Foundation Grant No. 220020321.

Using simulation to interpret experimental data in terms of protein conformational ensembles.

PubMed

Allison, Jane R

2017-04-01

In their biological environment, proteins are dynamic molecules, necessitating an ensemble structural description. Molecular dynamics simulations and solution-state experiments provide complimentary information in the form of atomically detailed coordinates and averaged or distributions of structural properties or related quantities. Recently, increases in the temporal and spatial scale of conformational sampling and comparison of the more diverse conformational ensembles thus generated have revealed the importance of sampling rare events. Excitingly, new methods based on maximum entropy and Bayesian inference are promising to provide a statistically sound mechanism for combining experimental data with molecular dynamics simulations. Copyright © 2016 Elsevier Ltd. All rights reserved.

Integrating dynamic and distributed compressive sensing techniques to enhance image quality of the compressive line sensing system for unmanned aerial vehicles application

NASA Astrophysics Data System (ADS)

Ouyang, Bing; Hou, Weilin; Caimi, Frank M.; Dalgleish, Fraser R.; Vuorenkoski, Anni K.; Gong, Cuiling

2017-07-01

The compressive line sensing imaging system adopts distributed compressive sensing (CS) to acquire data and reconstruct images. Dynamic CS uses Bayesian inference to capture the correlated nature of the adjacent lines. An image reconstruction technique that incorporates dynamic CS in the distributed CS framework was developed to improve the quality of reconstructed images. The effectiveness of the technique was validated using experimental data acquired in an underwater imaging test facility. Results that demonstrate contrast and resolution improvements will be presented. The improved efficiency is desirable for unmanned aerial vehicles conducting long-duration missions.

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

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.

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.

Exploring complex dynamics in multi agent-based intelligent systems: Theoretical and experimental approaches using the Multi Agent-based Behavioral Economic Landscape (MABEL) model

NASA Astrophysics Data System (ADS)

Alexandridis, Konstantinos T.

This dissertation adopts a holistic and detailed approach to modeling spatially explicit agent-based artificial intelligent systems, using the Multi Agent-based Behavioral Economic Landscape (MABEL) model. The research questions that addresses stem from the need to understand and analyze the real-world patterns and dynamics of land use change from a coupled human-environmental systems perspective. Describes the systemic, mathematical, statistical, socio-economic and spatial dynamics of the MABEL modeling framework, and provides a wide array of cross-disciplinary modeling applications within the research, decision-making and policy domains. Establishes the symbolic properties of the MABEL model as a Markov decision process, analyzes the decision-theoretic utility and optimization attributes of agents towards comprising statistically and spatially optimal policies and actions, and explores the probabilogic character of the agents' decision-making and inference mechanisms via the use of Bayesian belief and decision networks. Develops and describes a Monte Carlo methodology for experimental replications of agent's decisions regarding complex spatial parcel acquisition and learning. Recognizes the gap on spatially-explicit accuracy assessment techniques for complex spatial models, and proposes an ensemble of statistical tools designed to address this problem. Advanced information assessment techniques such as the Receiver-Operator Characteristic curve, the impurity entropy and Gini functions, and the Bayesian classification functions are proposed. The theoretical foundation for modular Bayesian inference in spatially-explicit multi-agent artificial intelligent systems, and the ensembles of cognitive and scenario assessment modular tools build for the MABEL model are provided. Emphasizes the modularity and robustness as valuable qualitative modeling attributes, and examines the role of robust intelligent modeling as a tool for improving policy-decisions related to land use change. Finally, the major contributions to the science are presented along with valuable directions for future research.

Exact calculation of distributions on integers, with application to sequence alignment.

PubMed

Newberg, Lee A; Lawrence, Charles E

2009-01-01

Computational biology is replete with high-dimensional discrete prediction and inference problems. Dynamic programming recursions can be applied to several of the most important of these, including sequence alignment, RNA secondary-structure prediction, phylogenetic inference, and motif finding. In these problems, attention is frequently focused on some scalar quantity of interest, a score, such as an alignment score or the free energy of an RNA secondary structure. In many cases, score is naturally defined on integers, such as a count of the number of pairing differences between two sequence alignments, or else an integer score has been adopted for computational reasons, such as in the test of significance of motif scores. The probability distribution of the score under an appropriate probabilistic model is of interest, such as in tests of significance of motif scores, or in calculation of Bayesian confidence limits around an alignment. Here we present three algorithms for calculating the exact distribution of a score of this type; then, in the context of pairwise local sequence alignments, we apply the approach so as to find the alignment score distribution and Bayesian confidence limits.

Multiple player tracking in sports video: a dual-mode two-way bayesian inference approach with progressive observation modeling.

PubMed

Xing, Junliang; Ai, Haizhou; Liu, Liwei; Lao, Shihong

2011-06-01

Multiple object tracking (MOT) is a very challenging task yet of fundamental importance for many practical applications. In this paper, we focus on the problem of tracking multiple players in sports video which is even more difficult due to the abrupt movements of players and their complex interactions. To handle the difficulties in this problem, we present a new MOT algorithm which contributes both in the observation modeling level and in the tracking strategy level. For the observation modeling, we develop a progressive observation modeling process that is able to provide strong tracking observations and greatly facilitate the tracking task. For the tracking strategy, we propose a dual-mode two-way Bayesian inference approach which dynamically switches between an offline general model and an online dedicated model to deal with single isolated object tracking and multiple occluded object tracking integrally by forward filtering and backward smoothing. Extensive experiments on different kinds of sports videos, including football, basketball, as well as hockey, demonstrate the effectiveness and efficiency of the proposed method.

Attention in a Bayesian Framework

PubMed Central

Whiteley, Louise; Sahani, Maneesh

2012-01-01

The behavioral phenomena of sensory attention are thought to reflect the allocation of a limited processing resource, but there is little consensus on the nature of the resource or why it should be limited. Here we argue that a fundamental bottleneck emerges naturally within Bayesian models of perception, and use this observation to frame a new computational account of the need for, and action of, attention – unifying diverse attentional phenomena in a way that goes beyond previous inferential, probabilistic and Bayesian models. Attentional effects are most evident in cluttered environments, and include both selective phenomena, where attention is invoked by cues that point to particular stimuli, and integrative phenomena, where attention is invoked dynamically by endogenous processing. However, most previous Bayesian accounts of attention have focused on describing relatively simple experimental settings, where cues shape expectations about a small number of upcoming stimuli and thus convey “prior” information about clearly defined objects. While operationally consistent with the experiments it seeks to describe, this view of attention as prior seems to miss many essential elements of both its selective and integrative roles, and thus cannot be easily extended to complex environments. We suggest that the resource bottleneck stems from the computational intractability of exact perceptual inference in complex settings, and that attention reflects an evolved mechanism for approximate inference which can be shaped to refine the local accuracy of perception. We show that this approach extends the simple picture of attention as prior, so as to provide a unified and computationally driven account of both selective and integrative attentional phenomena. PMID:22712010

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

Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation.

PubMed

Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

2016-04-01

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact, and very efficient approach for generating posterior parameter distributions for stochastic differential equation models calibrated to measured time series. The algorithm is inspired by reinterpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for one-dimensional problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.

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.

Parameter Estimation of Partial Differential Equation Models.

PubMed

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

2013-01-01

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

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.

Inferring Ice Thickness from a Glacier Dynamics Model and Multiple Surface Datasets.

NASA Astrophysics Data System (ADS)

Guan, Y.; Haran, M.; Pollard, D.

2017-12-01

The future behavior of the West Antarctic Ice Sheet (WAIS) may have a major impact on future climate. For instance, ice sheet melt may contribute significantly to global sea level rise. Understanding the current state of WAIS is therefore of great interest. WAIS is drained by fast-flowing glaciers which are major contributors to ice loss. Hence, understanding the stability and dynamics of glaciers is critical for predicting the future of the ice sheet. Glacier dynamics are driven by the interplay between the topography, temperature and basal conditions beneath the ice. A glacier dynamics model describes the interactions between these processes. We develop a hierarchical Bayesian model that integrates multiple ice sheet surface data sets with a glacier dynamics model. Our approach allows us to (1) infer important parameters describing the glacier dynamics, (2) learn about ice sheet thickness, and (3) account for errors in the observations and the model. Because we have relatively dense and accurate ice thickness data from the Thwaites Glacier in West Antarctica, we use these data to validate the proposed approach. The long-term goal of this work is to have a general model that may be used to study multiple glaciers in the Antarctic.

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.

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.

Parameter and Structure Inference for Nonlinear Dynamical Systems

NASA Technical Reports Server (NTRS)

Morris, Robin D.; Smelyanskiy, Vadim N.; Millonas, Mark

2006-01-01

A great many systems can be modeled in the non-linear dynamical systems framework, as x = f(x) + xi(t), where f() is the potential function for the system, and xi is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications.

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…

Inferring Fault Frictional and Reservoir Hydraulic Properties From Injection-Induced Seismicity

NASA Astrophysics Data System (ADS)

Jagalur-Mohan, Jayanth; Jha, Birendra; Wang, Zheng; Juanes, Ruben; Marzouk, Youssef

2018-02-01

Characterizing the rheological properties of faults and the evolution of fault friction during seismic slip are fundamental problems in geology and seismology. Recent increases in the frequency of induced earthquakes have intensified the need for robust methods to estimate fault properties. Here we present a novel approach for estimation of aquifer and fault properties, which combines coupled multiphysics simulation of injection-induced seismicity with adaptive surrogate-based Bayesian inversion. In a synthetic 2-D model, we use aquifer pressure, ground displacements, and fault slip measurements during fluid injection to estimate the dynamic fault friction, the critical slip distance, and the aquifer permeability. Our forward model allows us to observe nonmonotonic evolutions of shear traction and slip on the fault resulting from the interplay of several physical mechanisms, including injection-induced aquifer expansion, stress transfer along the fault, and slip-induced stress relaxation. This interplay provides the basis for a successful joint inversion of induced seismicity, yielding well-informed Bayesian posterior distributions of dynamic friction and critical slip. We uncover an inverse relationship between dynamic friction and critical slip distance, which is in agreement with the small dynamic friction and large critical slip reported during seismicity on mature faults.

A Parallel and Incremental Approach for Data-Intensive Learning of Bayesian Networks.

PubMed

Yue, Kun; Fang, Qiyu; Wang, Xiaoling; Li, Jin; Liu, Weiyi

2015-12-01

Bayesian network (BN) has been adopted as the underlying model for representing and inferring uncertain knowledge. As the basis of realistic applications centered on probabilistic inferences, learning a BN from data is a critical subject of machine learning, artificial intelligence, and big data paradigms. Currently, it is necessary to extend the classical methods for learning BNs with respect to data-intensive computing or in cloud environments. In this paper, we propose a parallel and incremental approach for data-intensive learning of BNs from massive, distributed, and dynamically changing data by extending the classical scoring and search algorithm and using MapReduce. First, we adopt the minimum description length as the scoring metric and give the two-pass MapReduce-based algorithms for computing the required marginal probabilities and scoring the candidate graphical model from sample data. Then, we give the corresponding strategy for extending the classical hill-climbing algorithm to obtain the optimal structure, as well as that for storing a BN by pairs. Further, in view of the dynamic characteristics of the changing data, we give the concept of influence degree to measure the coincidence of the current BN with new data, and then propose the corresponding two-pass MapReduce-based algorithms for BNs incremental learning. Experimental results show the efficiency, scalability, and effectiveness of our methods.

Specificity and timescales of cortical adaptation as inferences about natural movie statistics.

PubMed

Snow, Michoel; Coen-Cagli, Ruben; Schwartz, Odelia

2016-10-01

Adaptation is a phenomenological umbrella term under which a variety of temporal contextual effects are grouped. Previous models have shown that some aspects of visual adaptation reflect optimal processing of dynamic visual inputs, suggesting that adaptation should be tuned to the properties of natural visual inputs. However, the link between natural dynamic inputs and adaptation is poorly understood. Here, we extend a previously developed Bayesian modeling framework for spatial contextual effects to the temporal domain. The model learns temporal statistical regularities of natural movies and links these statistics to adaptation in primary visual cortex via divisive normalization, a ubiquitous neural computation. In particular, the model divisively normalizes the present visual input by the past visual inputs only to the degree that these are inferred to be statistically dependent. We show that this flexible form of normalization reproduces classical findings on how brief adaptation affects neuronal selectivity. Furthermore, prior knowledge acquired by the Bayesian model from natural movies can be modified by prolonged exposure to novel visual stimuli. We show that this updating can explain classical results on contrast adaptation. We also simulate the recent finding that adaptation maintains population homeostasis, namely, a balanced level of activity across a population of neurons with different orientation preferences. Consistent with previous disparate observations, our work further clarifies the influence of stimulus-specific and neuronal-specific normalization signals in adaptation.

Specificity and timescales of cortical adaptation as inferences about natural movie statistics

PubMed Central

Snow, Michoel; Coen-Cagli, Ruben; Schwartz, Odelia

2016-01-01

Adaptation is a phenomenological umbrella term under which a variety of temporal contextual effects are grouped. Previous models have shown that some aspects of visual adaptation reflect optimal processing of dynamic visual inputs, suggesting that adaptation should be tuned to the properties of natural visual inputs. However, the link between natural dynamic inputs and adaptation is poorly understood. Here, we extend a previously developed Bayesian modeling framework for spatial contextual effects to the temporal domain. The model learns temporal statistical regularities of natural movies and links these statistics to adaptation in primary visual cortex via divisive normalization, a ubiquitous neural computation. In particular, the model divisively normalizes the present visual input by the past visual inputs only to the degree that these are inferred to be statistically dependent. We show that this flexible form of normalization reproduces classical findings on how brief adaptation affects neuronal selectivity. Furthermore, prior knowledge acquired by the Bayesian model from natural movies can be modified by prolonged exposure to novel visual stimuli. We show that this updating can explain classical results on contrast adaptation. We also simulate the recent finding that adaptation maintains population homeostasis, namely, a balanced level of activity across a population of neurons with different orientation preferences. Consistent with previous disparate observations, our work further clarifies the influence of stimulus-specific and neuronal-specific normalization signals in adaptation. PMID:27699416

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.

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.

Cortical Coupling Reflects Bayesian Belief Updating in the Deployment of Spatial Attention.

PubMed

Vossel, Simone; Mathys, Christoph; Stephan, Klaas E; Friston, Karl J

2015-08-19

The deployment of visuospatial attention and the programming of saccades are governed by the inferred likelihood of events. In the present study, we combined computational modeling of psychophysical data with fMRI to characterize the computational and neural mechanisms underlying this flexible attentional control. Sixteen healthy human subjects performed a modified version of Posner's location-cueing paradigm in which the percentage of cue validity varied in time and the targets required saccadic responses. Trialwise estimates of the certainty (precision) of the prediction that the target would appear at the cued location were derived from a hierarchical Bayesian model fitted to individual trialwise saccadic response speeds. Trial-specific model parameters then entered analyses of fMRI data as parametric regressors. Moreover, dynamic causal modeling (DCM) was performed to identify the most likely functional architecture of the attentional reorienting network and its modulation by (Bayes-optimal) precision-dependent attention. While the frontal eye fields (FEFs), intraparietal sulcus, and temporoparietal junction (TPJ) of both hemispheres showed higher activity on invalid relative to valid trials, reorienting responses in right FEF, TPJ, and the putamen were significantly modulated by precision-dependent attention. Our DCM results suggested that the precision of predictability underlies the attentional modulation of the coupling of TPJ with FEF and the putamen. Our results shed new light on the computational architecture and neuronal network dynamics underlying the context-sensitive deployment of visuospatial attention. Spatial attention and its neural correlates in the human brain have been studied extensively with the help of fMRI and cueing paradigms in which the location of targets is pre-cued on a trial-by-trial basis. One aspect that has so far been neglected concerns the question of how the brain forms attentional expectancies when no a priori probability information is available but needs to be inferred from observations. This study elucidates the computational and neural mechanisms under which probabilistic inference governs attentional deployment. Our results show that Bayesian belief updating explains changes in cortical connectivity; in that directional influences from the temporoparietal junction on the frontal eye fields and the putamen were modulated by (Bayes-optimal) updates. Copyright © 2015 Vossel et al.

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.

Bayesian analysis of the dynamic cosmic web in the SDSS galaxy survey

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

Leclercq, Florent; Wandelt, Benjamin; Jasche, Jens, E-mail: florent.leclercq@polytechnique.org, E-mail: jasche@iap.fr, E-mail: wandelt@iap.fr

Recent application of the Bayesian algorithm \\textsc(borg) to the Sloan Digital Sky Survey (SDSS) main sample galaxies resulted in the physical inference of the formation history of the observed large-scale structure from its origin to the present epoch. In this work, we use these inferences as inputs for a detailed probabilistic cosmic web-type analysis. To do so, we generate a large set of data-constrained realizations of the large-scale structure using a fast, fully non-linear gravitational model. We then perform a dynamic classification of the cosmic web into four distinct components (voids, sheets, filaments, and clusters) on the basis of themore » tidal field. Our inference framework automatically and self-consistently propagates typical observational uncertainties to web-type classification. As a result, this study produces accurate cosmographic classification of large-scale structure elements in the SDSS volume. By also providing the history of these structure maps, the approach allows an analysis of the origin and growth of the early traces of the cosmic web present in the initial density field and of the evolution of global quantities such as the volume and mass filling fractions of different structures. For the problem of web-type classification, the results described in this work constitute the first connection between theory and observations at non-linear scales including a physical model of structure formation and the demonstrated capability of uncertainty quantification. A connection between cosmology and information theory using real data also naturally emerges from our probabilistic approach. Our results constitute quantitative chrono-cosmography of the complex web-like patterns underlying the observed galaxy distribution.« less

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

Gaussian process-based Bayesian nonparametric inference of population size trajectories from gene genealogies.

PubMed

Palacios, Julia A; Minin, Vladimir N

2013-03-01

Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past population dynamics from genomic data. We start with a standard framework based on the coalescent, a stochastic process that generates genealogies connecting randomly sampled individuals from the population of interest. These genealogies serve as a glue between the population demographic history and genomic sequences. It turns out that only the times of genealogical lineage coalescences contain information about population size dynamics. Viewing these coalescent times as a point process, estimating population size trajectories is equivalent to estimating a conditional intensity of this point process. Therefore, our inverse problem is similar to estimating an inhomogeneous Poisson process intensity function. We demonstrate how recent advances in Gaussian process-based nonparametric inference for Poisson processes can be extended to Bayesian nonparametric estimation of population size dynamics under the coalescent. We compare our Gaussian process (GP) approach to one of the state-of-the-art Gaussian Markov random field (GMRF) methods for estimating population trajectories. Using simulated data, we demonstrate that our method has better accuracy and precision. Next, we analyze two genealogies reconstructed from real sequences of hepatitis C and human Influenza A viruses. In both cases, we recover more believed aspects of the viral demographic histories than the GMRF approach. We also find that our GP method produces more reasonable uncertainty estimates than the GMRF method. Copyright © 2013, The International Biometric Society.

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

Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology

NASA Astrophysics Data System (ADS)

Alsing, Justin; Wandelt, Benjamin; Feeney, Stephen

2018-07-01

Many statistical models in cosmology can be simulated forwards but have intractable likelihood functions. Likelihood-free inference methods allow us to perform Bayesian inference from these models using only forward simulations, free from any likelihood assumptions or approximations. Likelihood-free inference generically involves simulating mock data and comparing to the observed data; this comparison in data space suffers from the curse of dimensionality and requires compression of the data to a small number of summary statistics to be tractable. In this paper, we use massive asymptotically optimal data compression to reduce the dimensionality of the data space to just one number per parameter, providing a natural and optimal framework for summary statistic choice for likelihood-free inference. Secondly, we present the first cosmological application of Density Estimation Likelihood-Free Inference (DELFI), which learns a parametrized model for joint distribution of data and parameters, yielding both the parameter posterior and the model evidence. This approach is conceptually simple, requires less tuning than traditional Approximate Bayesian Computation approaches to likelihood-free inference and can give high-fidelity posteriors from orders of magnitude fewer forward simulations. As an additional bonus, it enables parameter inference and Bayesian model comparison simultaneously. We demonstrate DELFI with massive data compression on an analysis of the joint light-curve analysis supernova data, as a simple validation case study. We show that high-fidelity posterior inference is possible for full-scale cosmological data analyses with as few as ˜104 simulations, with substantial scope for further improvement, demonstrating the scalability of likelihood-free inference to large and complex cosmological data sets.

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.

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

PubMed

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

2013-12-01

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

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…

Application of dynamic uncertain causality graph in spacecraft fault diagnosis: Logic cycle

NASA Astrophysics Data System (ADS)

Yao, Quanying; Zhang, Qin; Liu, Peng; Yang, Ping; Zhu, Ma; Wang, Xiaochen

2017-04-01

Intelligent diagnosis system are applied to fault diagnosis in spacecraft. Dynamic Uncertain Causality Graph (DUCG) is a new probability graphic model with many advantages. In the knowledge expression of spacecraft fault diagnosis, feedback among variables is frequently encountered, which may cause directed cyclic graphs (DCGs). Probabilistic graphical models (PGMs) such as bayesian network (BN) have been widely applied in uncertain causality representation and probabilistic reasoning, but BN does not allow DCGs. In this paper, DUGG is applied to fault diagnosis in spacecraft: introducing the inference algorithm for the DUCG to deal with feedback. Now, DUCG has been tested in 16 typical faults with 100% diagnosis accuracy.

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.

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

PubMed Central

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

2013-01-01

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

Bayesian refinement of protein structures and ensembles against SAXS data using molecular dynamics

PubMed Central

Shevchuk, Roman; Hub, Jochen S.

2017-01-01

Small-angle X-ray scattering is an increasingly popular technique used to detect protein structures and ensembles in solution. However, the refinement of structures and ensembles against SAXS data is often ambiguous due to the low information content of SAXS data, unknown systematic errors, and unknown scattering contributions from the solvent. We offer a solution to such problems by combining Bayesian inference with all-atom molecular dynamics simulations and explicit-solvent SAXS calculations. The Bayesian formulation correctly weights the SAXS data versus prior physical knowledge, it quantifies the precision or ambiguity of fitted structures and ensembles, and it accounts for unknown systematic errors due to poor buffer matching. The method further provides a probabilistic criterion for identifying the number of states required to explain the SAXS data. The method is validated by refining ensembles of a periplasmic binding protein against calculated SAXS curves. Subsequently, we derive the solution ensembles of the eukaryotic chaperone heat shock protein 90 (Hsp90) against experimental SAXS data. We find that the SAXS data of the apo state of Hsp90 is compatible with a single wide-open conformation, whereas the SAXS data of Hsp90 bound to ATP or to an ATP-analogue strongly suggest heterogenous ensembles of a closed and a wide-open state. PMID:29045407

EEG-fMRI Bayesian framework for neural activity estimation: a simulation study

NASA Astrophysics Data System (ADS)

Croce, Pierpaolo; Basti, Alessio; Marzetti, Laura; Zappasodi, Filippo; Del Gratta, Cosimo

2016-12-01

Objective. Due to the complementary nature of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI), and given the possibility of simultaneous acquisition, the joint data analysis can afford a better understanding of the underlying neural activity estimation. In this simulation study we want to show the benefit of the joint EEG-fMRI neural activity estimation in a Bayesian framework. Approach. We built a dynamic Bayesian framework in order to perform joint EEG-fMRI neural activity time course estimation. The neural activity is originated by a given brain area and detected by means of both measurement techniques. We have chosen a resting state neural activity situation to address the worst case in terms of the signal-to-noise ratio. To infer information by EEG and fMRI concurrently we used a tool belonging to the sequential Monte Carlo (SMC) methods: the particle filter (PF). Main results. First, despite a high computational cost, we showed the feasibility of such an approach. Second, we obtained an improvement in neural activity reconstruction when using both EEG and fMRI measurements. Significance. The proposed simulation shows the improvements in neural activity reconstruction with EEG-fMRI simultaneous data. The application of such an approach to real data allows a better comprehension of the neural dynamics.

EEG-fMRI Bayesian framework for neural activity estimation: a simulation study.

PubMed

Croce, Pierpaolo; Basti, Alessio; Marzetti, Laura; Zappasodi, Filippo; Gratta, Cosimo Del

2016-12-01

Due to the complementary nature of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI), and given the possibility of simultaneous acquisition, the joint data analysis can afford a better understanding of the underlying neural activity estimation. In this simulation study we want to show the benefit of the joint EEG-fMRI neural activity estimation in a Bayesian framework. We built a dynamic Bayesian framework in order to perform joint EEG-fMRI neural activity time course estimation. The neural activity is originated by a given brain area and detected by means of both measurement techniques. We have chosen a resting state neural activity situation to address the worst case in terms of the signal-to-noise ratio. To infer information by EEG and fMRI concurrently we used a tool belonging to the sequential Monte Carlo (SMC) methods: the particle filter (PF). First, despite a high computational cost, we showed the feasibility of such an approach. Second, we obtained an improvement in neural activity reconstruction when using both EEG and fMRI measurements. The proposed simulation shows the improvements in neural activity reconstruction with EEG-fMRI simultaneous data. The application of such an approach to real data allows a better comprehension of the neural dynamics.

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.

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

Technical Note: Approximate Bayesian parameterization of a complex tropical forest model

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2013-08-01

Inverse parameter estimation of process-based models is a long-standing problem in ecology and evolution. A key problem of inverse parameter estimation is to define a metric that quantifies how well model predictions fit to the data. Such a metric can be expressed by general cost or objective functions, but statistical inversion approaches are based on a particular metric, the probability of observing the data given the model, known as the likelihood. Deriving likelihoods for dynamic models requires making assumptions about the probability for observations to deviate from mean model predictions. For technical reasons, these assumptions are usually derived without explicit consideration of the processes in the simulation. Only in recent years have new methods become available that allow generating likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional MCMC, performs well in retrieving known parameter values from virtual field data generated by the forest model. We analyze the results of the parameter estimation, examine the sensitivity towards the choice and aggregation of model outputs and observed data (summary statistics), and show results from using this method to fit the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss differences of this approach to Approximate Bayesian Computing (ABC), another commonly used method to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can successfully be applied to process-based models of high complexity. The methodology is particularly suited to heterogeneous and complex data structures and can easily be adjusted to other model types, including most stochastic population and individual-based models. Our study therefore provides a blueprint for a fairly general approach to parameter estimation of stochastic process-based models in ecology and evolution.

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.

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

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.

Dynamic social networks based on movement

USGS Publications Warehouse

Scharf, Henry; Hooten, Mevin B.; Fosdick, Bailey K.; Johnson, Devin S.; London, Joshua M.; Durban, John W.

2016-01-01

Network modeling techniques provide a means for quantifying social structure in populations of individuals. Data used to define social connectivity are often expensive to collect and based on case-specific, ad hoc criteria. Moreover, in applications involving animal social networks, collection of these data is often opportunistic and can be invasive. Frequently, the social network of interest for a given population is closely related to the way individuals move. Thus, telemetry data, which are minimally invasive and relatively inexpensive to collect, present an alternative source of information. We develop a framework for using telemetry data to infer social relationships among animals. To achieve this, we propose a Bayesian hierarchical model with an underlying dynamic social network controlling movement of individuals via two mechanisms: an attractive effect and an aligning effect. We demonstrate the model and its ability to accurately identify complex social behavior in simulation, and apply our model to telemetry data arising from killer whales. Using auxiliary information about the study population, we investigate model validity and find the inferred dynamic social network is consistent with killer whale ecology and expert knowledge.

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

Bayesian selection of Markov models for symbol sequences: application to microsaccadic eye movements.

PubMed

Bettenbühl, Mario; Rusconi, Marco; Engbert, Ralf; Holschneider, Matthias

2012-01-01

Complex biological dynamics often generate sequences of discrete events which can be described as a Markov process. The order of the underlying Markovian stochastic process is fundamental for characterizing statistical dependencies within sequences. As an example for this class of biological systems, we investigate the Markov order of sequences of microsaccadic eye movements from human observers. We calculate the integrated likelihood of a given sequence for various orders of the Markov process and use this in a Bayesian framework for statistical inference on the Markov order. Our analysis shows that data from most participants are best explained by a first-order Markov process. This is compatible with recent findings of a statistical coupling of subsequent microsaccade orientations. Our method might prove to be useful for a broad class of biological systems.

A Bayesian approach for calibrating probability judgments

NASA Astrophysics Data System (ADS)

Firmino, Paulo Renato A.; Santana, Nielson A.

2012-10-01

Eliciting experts' opinions has been one of the main alternatives for addressing paucity of data. In the vanguard of this area is the development of calibration models (CMs). CMs are models dedicated to overcome miscalibration, i.e. judgment biases reflecting deficient strategies of reasoning adopted by the expert when inferring about an unknown. One of the main challenges of CMs is to determine how and when to intervene against miscalibration, in order to enhance the tradeoff between costs (time spent with calibration processes) and accuracy of the resulting models. The current paper dedicates special attention to this issue by presenting a dynamic Bayesian framework for monitoring, diagnosing, and handling miscalibration patterns. The framework is based on Beta-, Uniform, or Triangular-Bernoulli models and classes of judgmental calibration theories. Issues regarding the usefulness of the proposed framework are discussed and illustrated via simulation studies.

Perception of the dynamic visual vertical during sinusoidal linear motion.

PubMed

Pomante, A; Selen, L P J; Medendorp, W P

2017-10-01

The vestibular system provides information for spatial orientation. However, this information is ambiguous: because the otoliths sense the gravitoinertial force, they cannot distinguish gravitational and inertial components. As a consequence, prolonged linear acceleration of the head can be interpreted as tilt, referred to as the somatogravic effect. Previous modeling work suggests that the brain disambiguates the otolith signal according to the rules of Bayesian inference, combining noisy canal cues with the a priori assumption that prolonged linear accelerations are unlikely. Within this modeling framework the noise of the vestibular signals affects the dynamic characteristics of the tilt percept during linear whole-body motion. To test this prediction, we devised a novel paradigm to psychometrically characterize the dynamic visual vertical-as a proxy for the tilt percept-during passive sinusoidal linear motion along the interaural axis (0.33 Hz motion frequency, 1.75 m/s 2 peak acceleration, 80 cm displacement). While subjects ( n =10) kept fixation on a central body-fixed light, a line was briefly flashed (5 ms) at different phases of the motion, the orientation of which had to be judged relative to gravity. Consistent with the model's prediction, subjects showed a phase-dependent modulation of the dynamic visual vertical, with a subject-specific phase shift with respect to the imposed acceleration signal. The magnitude of this modulation was smaller than predicted, suggesting a contribution of nonvestibular signals to the dynamic visual vertical. Despite their dampening effect, our findings may point to a link between the noise components in the vestibular system and the characteristics of dynamic visual vertical. NEW & NOTEWORTHY A fundamental question in neuroscience is how the brain processes vestibular signals to infer the orientation of the body and objects in space. We show that, under sinusoidal linear motion, systematic error patterns appear in the disambiguation of linear acceleration and spatial orientation. We discuss the dynamics of these illusory percepts in terms of a dynamic Bayesian model that combines uncertainty in the vestibular signals with priors based on the natural statistics of head motion. Copyright © 2017 the American Physiological Society.

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.

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.

Comparison of two integration methods for dynamic causal modeling of electrophysiological data.

PubMed

Lemaréchal, Jean-Didier; George, Nathalie; David, Olivier

2018-06-01

Dynamic causal modeling (DCM) is a methodological approach to study effective connectivity among brain regions. Based on a set of observations and a biophysical model of brain interactions, DCM uses a Bayesian framework to estimate the posterior distribution of the free parameters of the model (e.g. modulation of connectivity) and infer architectural properties of the most plausible model (i.e. model selection). When modeling electrophysiological event-related responses, the estimation of the model relies on the integration of the system of delay differential equations (DDEs) that describe the dynamics of the system. In this technical note, we compared two numerical schemes for the integration of DDEs. The first, and standard, scheme approximates the DDEs (more precisely, the state of the system, with respect to conduction delays among brain regions) using ordinary differential equations (ODEs) and solves it with a fixed step size. The second scheme uses a dedicated DDEs solver with adaptive step sizes to control error, making it theoretically more accurate. To highlight the effects of the approximation used by the first integration scheme in regard to parameter estimation and Bayesian model selection, we performed simulations of local field potentials using first, a simple model comprising 2 regions and second, a more complex model comprising 6 regions. In these simulations, the second integration scheme served as the standard to which the first one was compared. Then, the performances of the two integration schemes were directly compared by fitting a public mismatch negativity EEG dataset with different models. The simulations revealed that the use of the standard DCM integration scheme was acceptable for Bayesian model selection but underestimated the connectivity parameters and did not allow an accurate estimation of conduction delays. Fitting to empirical data showed that the models systematically obtained an increased accuracy when using the second integration scheme. We conclude that inference on connectivity strength and delay based on DCM for EEG/MEG requires an accurate integration scheme. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

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).

Dynamic Uncertain Causality Graph for Knowledge Representation and Reasoning: Utilization of Statistical Data and Domain Knowledge in Complex Cases.

PubMed

Zhang, Qin; Yao, Quanying

2018-05-01

The dynamic uncertain causality graph (DUCG) is a newly presented framework for uncertain causality representation and probabilistic reasoning. It has been successfully applied to online fault diagnoses of large, complex industrial systems, and decease diagnoses. This paper extends the DUCG to model more complex cases than what could be previously modeled, e.g., the case in which statistical data are in different groups with or without overlap, and some domain knowledge and actions (new variables with uncertain causalities) are introduced. In other words, this paper proposes to use -mode, -mode, and -mode of the DUCG to model such complex cases and then transform them into either the standard -mode or the standard -mode. In the former situation, if no directed cyclic graph is involved, the transformed result is simply a Bayesian network (BN), and existing inference methods for BNs can be applied. In the latter situation, an inference method based on the DUCG is proposed. Examples are provided to illustrate the methodology.

Empirical intrinsic geometry for nonlinear modeling and time series filtering.

PubMed

Talmon, Ronen; Coifman, Ronald R

2013-07-30

In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.

Masses of Kepler-46b, c from Transit Timing Variations

NASA Astrophysics Data System (ADS)

Saad-Olivera, Ximena; Nesvorný, David; Kipping, David M.; Roig, Fernando

2017-04-01

We use 16 quarters of the Kepler mission data to analyze the transit timing variations (TTVs) of the extrasolar planet Kepler-46b (KOI-872). Our dynamical fits confirm that the TTVs of this planet (period P={33.648}-0.005+0.004 days) are produced by a non-transiting planet Kepler-46c (P={57.325}-0.098+0.116 days). The Bayesian inference tool MultiNest is used to infer the dynamical parameters of Kepler-46b and Kepler-46c. We find that the two planets have nearly coplanar and circular orbits, with eccentricities ≃ 0.03 somewhat higher than previously estimated. The masses of the two planets are found to be {M}b={0.885}-0.343+0.374 and {M}c={0.362}-0.016+0.016 Jupiter masses, with M b being determined here from TTVs for the first time. Due to the precession of its orbital plane, Kepler-46c should start transiting its host star a few decades from now.

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.

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 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.

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 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.

Bayesian model calibration of ramp compression experiments on Z

NASA Astrophysics Data System (ADS)

Brown, Justin; Hund, Lauren

2017-06-01

Bayesian model calibration (BMC) is a statistical framework to estimate inputs for a computational model in the presence of multiple uncertainties, making it well suited to dynamic experiments which must be coupled with numerical simulations to interpret the results. Often, dynamic experiments are diagnosed using velocimetry and this output can be modeled using a hydrocode. Several calibration issues unique to this type of scenario including the functional nature of the output, uncertainty of nuisance parameters within the simulation, and model discrepancy identifiability are addressed, and a novel BMC process is proposed. As a proof of concept, we examine experiments conducted on Sandia National Laboratories' Z-machine which ramp compressed tantalum to peak stresses of 250 GPa. The proposed BMC framework is used to calibrate the cold curve of Ta (with uncertainty), and we conclude that the procedure results in simple, fast, and valid inferences. Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

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.

Uncertainty quantification for PZT bimorph actuators

NASA Astrophysics Data System (ADS)

Bravo, Nikolas; Smith, Ralph C.; Crews, John

2018-03-01

In this paper, we discuss the development of a high fidelity model for a PZT bimorph actuator used for micro-air vehicles, which includes the Robobee. We developed a high-fidelity model for the actuator using the homogenized energy model (HEM) framework, which quantifies the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in dynamic operating regimes. We then discussed an inverse problem on the model. We included local and global sensitivity analysis of the parameters in the high-fidelity model. Finally, we will discuss the results of Bayesian inference and uncertainty quantification on the HEM.

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.

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…

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.

A comparison of Monte Carlo-based Bayesian parameter estimation methods for stochastic models of genetic networks

PubMed Central

Zaikin, Alexey; Míguez, Joaquín

2017-01-01

We compare three state-of-the-art Bayesian inference methods for the estimation of the unknown parameters in a stochastic model of a genetic network. In particular, we introduce a stochastic version of the paradigmatic synthetic multicellular clock model proposed by Ullner et al., 2007. By introducing dynamical noise in the model and assuming that the partial observations of the system are contaminated by additive noise, we enable a principled mechanism to represent experimental uncertainties in the synthesis of the multicellular system and pave the way for the design of probabilistic methods for the estimation of any unknowns in the model. Within this setup, we tackle the Bayesian estimation of a subset of the model parameters. Specifically, we compare three Monte Carlo based numerical methods for the approximation of the posterior probability density function of the unknown parameters given a set of partial and noisy observations of the system. The schemes we assess are the particle Metropolis-Hastings (PMH) algorithm, the nonlinear population Monte Carlo (NPMC) method and the approximate Bayesian computation sequential Monte Carlo (ABC-SMC) scheme. We present an extensive numerical simulation study, which shows that while the three techniques can effectively solve the problem there are significant differences both in estimation accuracy and computational efficiency. PMID:28797087

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.

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.

Of bugs and birds: Markov Chain Monte Carlo for hierarchical modeling in wildlife research

USGS Publications Warehouse

Link, W.A.; Cam, E.; Nichols, J.D.; Cooch, E.G.

2002-01-01

Markov chain Monte Carlo (MCMC) is a statistical innovation that allows researchers to fit far more complex models to data than is feasible using conventional methods. Despite its widespread use in a variety of scientific fields, MCMC appears to be underutilized in wildlife applications. This may be due to a misconception that MCMC requires the adoption of a subjective Bayesian analysis, or perhaps simply to its lack of familiarity among wildlife researchers. We introduce the basic ideas of MCMC and software BUGS (Bayesian inference using Gibbs sampling), stressing that a simple and satisfactory intuition for MCMC does not require extraordinary mathematical sophistication. We illustrate the use of MCMC with an analysis of the association between latent factors governing individual heterogeneity in breeding and survival rates of kittiwakes (Rissa tridactyla). We conclude with a discussion of the importance of individual heterogeneity for understanding population dynamics and designing management plans.

Extreme-Scale Bayesian Inference for Uncertainty Quantification of Complex Simulations

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

Biros, George

Uncertainty quantification (UQ)—that is, quantifying uncertainties in complex mathematical models and their large-scale computational implementations—is widely viewed as one of the outstanding challenges facing the field of CS&E over the coming decade. The EUREKA project set to address the most difficult class of UQ problems: those for which both the underlying PDE model as well as the uncertain parameters are of extreme scale. In the project we worked on these extreme-scale challenges in the following four areas: 1. Scalable parallel algorithms for sampling and characterizing the posterior distribution that exploit the structure of the underlying PDEs and parameter-to-observable map. Thesemore » include structure-exploiting versions of the randomized maximum likelihood method, which aims to overcome the intractability of employing conventional MCMC methods for solving extreme-scale Bayesian inversion problems by appealing to and adapting ideas from large-scale PDE-constrained optimization, which have been very successful at exploring high-dimensional spaces. 2. Scalable parallel algorithms for construction of prior and likelihood functions based on learning methods and non-parametric density estimation. Constructing problem-specific priors remains a critical challenge in Bayesian inference, and more so in high dimensions. Another challenge is construction of likelihood functions that capture unmodeled couplings between observations and parameters. We will create parallel algorithms for non-parametric density estimation using high dimensional N-body methods and combine them with supervised learning techniques for the construction of priors and likelihood functions. 3. Bayesian inadequacy models, which augment physics models with stochastic models that represent their imperfections. The success of the Bayesian inference framework depends on the ability to represent the uncertainty due to imperfections of the mathematical model of the phenomena of interest. This is a central challenge in UQ, especially for large-scale models. We propose to develop the mathematical tools to address these challenges in the context of extreme-scale problems. 4. Parallel scalable algorithms for Bayesian optimal experimental design (OED). Bayesian inversion yields quantified uncertainties in the model parameters, which can be propagated forward through the model to yield uncertainty in outputs of interest. This opens the way for designing new experiments to reduce the uncertainties in the model parameters and model predictions. Such experimental design problems have been intractable for large-scale problems using conventional methods; we will create OED algorithms that exploit the structure of the PDE model and the parameter-to-output map to overcome these challenges. Parallel algorithms for these four problems were created, analyzed, prototyped, implemented, tuned, and scaled up for leading-edge supercomputers, including UT-Austin’s own 10 petaflops Stampede system, ANL’s Mira system, and ORNL’s Titan system. While our focus is on fundamental mathematical/computational methods and algorithms, we will assess our methods on model problems derived from several DOE mission applications, including multiscale mechanics and ice sheet dynamics.« less

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.

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.

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

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

Basics of Bayesian methods.

PubMed

Ghosh, Sujit K

2010-01-01

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

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

Time-varying coupling functions: Dynamical inference and cause of synchronization transitions

NASA Astrophysics Data System (ADS)

Stankovski, Tomislav

2017-02-01

Interactions in nature can be described by their coupling strength, direction of coupling, and coupling function. The coupling strength and directionality are relatively well understood and studied, at least for two interacting systems; however, there can be a complexity in the interactions uniquely dependent on the coupling functions. Such a special case is studied here: synchronization transition occurs only due to the time variability of the coupling functions, while the net coupling strength is constant throughout the observation time. To motivate the investigation, an example is used to present an analysis of cross-frequency coupling functions between delta and alpha brain waves extracted from the electroencephalography recording of a healthy human subject in a free-running resting state. The results indicate that time-varying coupling functions are a reality for biological interactions. A model of phase oscillators is used to demonstrate and detect the synchronization transition caused by the varying coupling functions during an invariant coupling strength. The ability to detect this phenomenon is discussed with the method of dynamical Bayesian inference, which was able to infer the time-varying coupling functions. The form of the coupling function acts as an additional dimension for the interactions, and it should be taken into account when detecting biological or other interactions from data.

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.

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

A generative model of whole-brain effective connectivity.

PubMed

Frässle, Stefan; Lomakina, Ekaterina I; Kasper, Lars; Manjaly, Zina M; Leff, Alex; Pruessmann, Klaas P; Buhmann, Joachim M; Stephan, Klaas E

2018-05-25

The development of whole-brain models that can infer effective (directed) connection strengths from fMRI data represents a central challenge for computational neuroimaging. A recently introduced generative model of fMRI data, regression dynamic causal modeling (rDCM), moves towards this goal as it scales gracefully to very large networks. However, large-scale networks with thousands of connections are difficult to interpret; additionally, one typically lacks information (data points per free parameter) for precise estimation of all model parameters. This paper introduces sparsity constraints to the variational Bayesian framework of rDCM as a solution to these problems in the domain of task-based fMRI. This sparse rDCM approach enables highly efficient effective connectivity analyses in whole-brain networks and does not require a priori assumptions about the network's connectivity structure but prunes fully (all-to-all) connected networks as part of model inversion. Following the derivation of the variational Bayesian update equations for sparse rDCM, we use both simulated and empirical data to assess the face validity of the model. In particular, we show that it is feasible to infer effective connection strengths from fMRI data using a network with more than 100 regions and 10,000 connections. This demonstrates the feasibility of whole-brain inference on effective connectivity from fMRI data - in single subjects and with a run-time below 1 min when using parallelized code. We anticipate that sparse rDCM may find useful application in connectomics and clinical neuromodeling - for example, for phenotyping individual patients in terms of whole-brain network structure. Copyright © 2018. Published by Elsevier Inc.

Testing Models of Stellar Structure and Evolution I. Comparison with Detached Eclipsing Binaries

NASA Astrophysics Data System (ADS)

del Burgo, C.; Allende Prieto, C.

2018-05-01

We present the results of an analysis aimed at testing the accuracy and precision of the PARSEC v1.2S library of stellar evolution models, combined with a Bayesian approach, to infer stellar parameters. We mainly employ the online DEBCat catalogue by Southworth, a compilation of detached eclipsing binary systems with published measurements of masses and radii to ˜ 2 per cent precision. We select a sample of 318 binary components, with masses between 0.10 and 14.5 solar units, and distances between 1.3 pc and ˜ 8 kpc for Galactic objects and ˜ 44-68 kpc for the extragalactic ones. The Bayesian analysis applied takes on input effective temperature, radius, and [Fe/H], and their uncertainties, returning theoretical predictions for other stellar parameters. From the comparison with dynamical masses, we conclude inferred masses are precisely derived for stars on the main-sequence and in the core-helium-burning phase, with respective uncertainties of 4 per cent and 7 per cent, on average. Subgiants and red giants masses are predicted within 14 per cent, and early asymptotic giant branch stars within 24 per cent. These results are helpful to further improve the models, in particular for advanced evolutionary stages for which our understanding is limited. We obtain distances and ages for the binary systems and compare them, whenever possible, with precise literature estimates, finding excellent agreement. We discuss evolutionary effects and the challenges associated with the inference of stellar ages from evolutionary models. We also provide useful polynomial fittings to theoretical zero-age main-sequence relations.

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.

UniEnt: uniform entropy model for the dynamics of a neuronal population

NASA Astrophysics Data System (ADS)

Hernandez Lahme, Damian; Nemenman, Ilya

Sensory information and motor responses are encoded in the brain in a collective spiking activity of a large number of neurons. Understanding the neural code requires inferring statistical properties of such collective dynamics from multicellular neurophysiological recordings. Questions of whether synchronous activity or silence of multiple neurons carries information about the stimuli or the motor responses are especially interesting. Unfortunately, detection of such high order statistical interactions from data is especially challenging due to the exponentially large dimensionality of the state space of neural collectives. Here we present UniEnt, a method for the inference of strengths of multivariate neural interaction patterns. The method is based on the Bayesian prior that makes no assumptions (uniform a priori expectations) about the value of the entropy of the observed multivariate neural activity, in contrast to popular approaches that maximize this entropy. We then study previously published multi-electrode recordings data from salamander retina, exposing the relevance of higher order neural interaction patterns for information encoding in this system. This work was supported in part by Grants JSMF/220020321 and NSF/IOS/1208126.

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.

A generative inference framework for analysing patterns of cultural change in sparse population data with evidence for fashion trends in LBK culture.

PubMed

Kandler, Anne; Shennan, Stephen

2015-12-06

Cultural change can be quantified by temporal changes in frequency of different cultural artefacts and it is a central question to identify what underlying cultural transmission processes could have caused the observed frequency changes. Observed changes, however, often describe the dynamics in samples of the population of artefacts, whereas transmission processes act on the whole population. Here we develop a modelling framework aimed at addressing this inference problem. To do so, we firstly generate population structures from which the observed sample could have been drawn randomly and then determine theoretical samples at a later time t2 produced under the assumption that changes in frequencies are caused by a specific transmission process. Thereby we also account for the potential effect of time-averaging processes in the generation of the observed sample. Subsequent statistical comparisons (e.g. using Bayesian inference) of the theoretical and observed samples at t2 can establish which processes could have produced the observed frequency data. In this way, we infer underlying transmission processes directly from available data without any equilibrium assumption. We apply this framework to a dataset describing pottery from settlements of some of the first farmers in Europe (the LBK culture) and conclude that the observed frequency dynamic of different types of decorated pottery is consistent with age-dependent selection, a preference for 'young' pottery types which is potentially indicative of fashion trends. © 2015 The Author(s).

Relationships between probabilistic Boolean networks and dynamic Bayesian networks as models of gene regulatory networks

PubMed Central

Lähdesmäki, Harri; Hautaniemi, Sampsa; Shmulevich, Ilya; Yli-Harja, Olli

2006-01-01

A significant amount of attention has recently been focused on modeling of gene regulatory networks. Two frequently used large-scale modeling frameworks are Bayesian networks (BNs) and Boolean networks, the latter one being a special case of its recent stochastic extension, probabilistic Boolean networks (PBNs). PBN is a promising model class that generalizes the standard rule-based interactions of Boolean networks into the stochastic setting. Dynamic Bayesian networks (DBNs) is a general and versatile model class that is able to represent complex temporal stochastic processes and has also been proposed as a model for gene regulatory systems. In this paper, we concentrate on these two model classes and demonstrate that PBNs and a certain subclass of DBNs can represent the same joint probability distribution over their common variables. The major benefit of introducing the relationships between the models is that it opens up the possibility of applying the standard tools of DBNs to PBNs and vice versa. Hence, the standard learning tools of DBNs can be applied in the context of PBNs, and the inference methods give a natural way of handling the missing values in PBNs which are often present in gene expression measurements. Conversely, the tools for controlling the stationary behavior of the networks, tools for projecting networks onto sub-networks, and efficient learning schemes can be used for DBNs. In other words, the introduced relationships between the models extend the collection of analysis tools for both model classes. PMID:17415411

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

Paleoclimate reconstruction through Bayesian data assimilation

NASA Astrophysics Data System (ADS)

Fer, I.; Raiho, A.; Rollinson, C.; Dietze, M.

2017-12-01

Methods of paleoclimate reconstruction from plant-based proxy data rely on assumptions of static vegetation-climate link which is often established between modern climate and vegetation. This approach might result in biased climate constructions as it does not account for vegetation dynamics. Predictive tools such as process-based dynamic vegetation models (DVM) and their Bayesian inversion could be used to construct the link between plant-based proxy data and palaeoclimate more realistically. In other words, given the proxy data, it is possible to infer the climate that could result in that particular vegetation composition, by comparing the DVM outputs to the proxy data within a Bayesian state data assimilation framework. In this study, using fossil pollen data from five sites across the northern hardwood region of the US, we assimilate fractional composition and aboveground biomass into dynamic vegetation models, LINKAGES, LPJ-GUESS and ED2. To do this, starting from 4 Global Climate Model outputs, we generate an ensemble of downscaled meteorological drivers for the period 850-2015. Then, as a first pass, we weigh these ensembles based on their fidelity with independent paleoclimate proxies. Next, we run the models with this ensemble of drivers, and comparing the ensemble model output to the vegetation data, adjust the model state estimates towards the data. At each iteration, we also reweight the climate values that make the model and data consistent, producing a reconstructed climate time-series dataset. We validated the method using present-day datasets, as well as a synthetic dataset, and then assessed the consistency of results across ecosystem models. Our method allows the combination of multiple data types to reconstruct the paleoclimate, with associated uncertainty estimates, based on ecophysiological and ecological processes rather than phenomenological correlations with proxy data.

Coronal loop seismology using damping of standing kink oscillations by mode coupling. II. additional physical effects and Bayesian analysis

NASA Astrophysics Data System (ADS)

Pascoe, D. J.; Anfinogentov, S.; Nisticò, G.; Goddard, C. R.; Nakariakov, V. M.

2017-04-01

Context. The strong damping of kink oscillations of coronal loops can be explained by mode coupling. The damping envelope depends on the transverse density profile of the loop. Observational measurements of the damping envelope have been used to determine the transverse loop structure which is important for understanding other physical processes such as heating. Aims: The general damping envelope describing the mode coupling of kink waves consists of a Gaussian damping regime followed by an exponential damping regime. Recent observational detection of these damping regimes has been employed as a seismological tool. We extend the description of the damping behaviour to account for additional physical effects, namely a time-dependent period of oscillation, the presence of additional longitudinal harmonics, and the decayless regime of standing kink oscillations. Methods: We examine four examples of standing kink oscillations observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). We use forward modelling of the loop position and investigate the dependence on the model parameters using Bayesian inference and Markov chain Monte Carlo (MCMC) sampling. Results: Our improvements to the physical model combined with the use of Bayesian inference and MCMC produce improved estimates of model parameters and their uncertainties. Calculation of the Bayes factor also allows us to compare the suitability of different physical models. We also use a new method based on spline interpolation of the zeroes of the oscillation to accurately describe the background trend of the oscillating loop. Conclusions: This powerful and robust method allows for accurate seismology of coronal loops, in particular the transverse density profile, and potentially reveals additional physical effects.

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.

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

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.

Multi-agent based control of large-scale complex systems employing distributed dynamic inference engine

NASA Astrophysics Data System (ADS)

Zhang, Daili

Increasing societal demand for automation has led to considerable efforts to control large-scale complex systems, especially in the area of autonomous intelligent control methods. The control system of a large-scale complex system needs to satisfy four system level requirements: robustness, flexibility, reusability, and scalability. Corresponding to the four system level requirements, there arise four major challenges. First, it is difficult to get accurate and complete information. Second, the system may be physically highly distributed. Third, the system evolves very quickly. Fourth, emergent global behaviors of the system can be caused by small disturbances at the component level. The Multi-Agent Based Control (MABC) method as an implementation of distributed intelligent control has been the focus of research since the 1970s, in an effort to solve the above-mentioned problems in controlling large-scale complex systems. However, to the author's best knowledge, all MABC systems for large-scale complex systems with significant uncertainties are problem-specific and thus difficult to extend to other domains or larger systems. This situation is partly due to the control architecture of multiple agents being determined by agent to agent coupling and interaction mechanisms. Therefore, the research objective of this dissertation is to develop a comprehensive, generalized framework for the control system design of general large-scale complex systems with significant uncertainties, with the focus on distributed control architecture design and distributed inference engine design. A Hybrid Multi-Agent Based Control (HyMABC) architecture is proposed by combining hierarchical control architecture and module control architecture with logical replication rings. First, it decomposes a complex system hierarchically; second, it combines the components in the same level as a module, and then designs common interfaces for all of the components in the same module; third, replications are made for critical agents and are organized into logical rings. This architecture maintains clear guidelines for complexity decomposition and also increases the robustness of the whole system. Multiple Sectioned Dynamic Bayesian Networks (MSDBNs) as a distributed dynamic probabilistic inference engine, can be embedded into the control architecture to handle uncertainties of general large-scale complex systems. MSDBNs decomposes a large knowledge-based system into many agents. Each agent holds its partial perspective of a large problem domain by representing its knowledge as a Dynamic Bayesian Network (DBN). Each agent accesses local evidence from its corresponding local sensors and communicates with other agents through finite message passing. If the distributed agents can be organized into a tree structure, satisfying the running intersection property and d-sep set requirements, globally consistent inferences are achievable in a distributed way. By using different frequencies for local DBN agent belief updating and global system belief updating, it balances the communication cost with the global consistency of inferences. In this dissertation, a fully factorized Boyen-Koller (BK) approximation algorithm is used for local DBN agent belief updating, and the static Junction Forest Linkage Tree (JFLT) algorithm is used for global system belief updating. MSDBNs assume a static structure and a stable communication network for the whole system. However, for a real system, sub-Bayesian networks as nodes could be lost, and the communication network could be shut down due to partial damage in the system. Therefore, on-line and automatic MSDBNs structure formation is necessary for making robust state estimations and increasing survivability of the whole system. A Distributed Spanning Tree Optimization (DSTO) algorithm, a Distributed D-Sep Set Satisfaction (DDSSS) algorithm, and a Distributed Running Intersection Satisfaction (DRIS) algorithm are proposed in this dissertation. Combining these three distributed algorithms and a Distributed Belief Propagation (DBP) algorithm in MSDBNs makes state estimations robust to partial damage in the whole system. Combining the distributed control architecture design and the distributed inference engine design leads to a process of control system design for a general large-scale complex system. As applications of the proposed methodology, the control system design of a simplified ship chilled water system and a notional ship chilled water system have been demonstrated step by step. Simulation results not only show that the proposed methodology gives a clear guideline for control system design for general large-scale complex systems with dynamic and uncertain environment, but also indicate that the combination of MSDBNs and HyMABC can provide excellent performance for controlling general large-scale complex systems.

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.

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.

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 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.

Neuron’s eye view: Inferring features of complex stimuli from neural responses

PubMed Central

Chen, Xin; Beck, Jeffrey M.

2017-01-01

Experiments that study neural encoding of stimuli at the level of individual neurons typically choose a small set of features present in the world—contrast and luminance for vision, pitch and intensity for sound—and assemble a stimulus set that systematically varies along these dimensions. Subsequent analysis of neural responses to these stimuli typically focuses on regression models, with experimenter-controlled features as predictors and spike counts or firing rates as responses. Unfortunately, this approach requires knowledge in advance about the relevant features coded by a given population of neurons. For domains as complex as social interaction or natural movement, however, the relevant feature space is poorly understood, and an arbitrary a priori choice of features may give rise to confirmation bias. Here, we present a Bayesian model for exploratory data analysis that is capable of automatically identifying the features present in unstructured stimuli based solely on neuronal responses. Our approach is unique within the class of latent state space models of neural activity in that it assumes that firing rates of neurons are sensitive to multiple discrete time-varying features tied to the stimulus, each of which has Markov (or semi-Markov) dynamics. That is, we are modeling neural activity as driven by multiple simultaneous stimulus features rather than intrinsic neural dynamics. We derive a fast variational Bayesian inference algorithm and show that it correctly recovers hidden features in synthetic data, as well as ground-truth stimulus features in a prototypical neural dataset. To demonstrate the utility of the algorithm, we also apply it to cluster neural responses and demonstrate successful recovery of features corresponding to monkeys and faces in the image set. PMID:28827790

[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.

Analysis of Spin Financial Market by GARCH Model

NASA Astrophysics Data System (ADS)

Takaishi, Tetsuya

2013-08-01

A spin model is used for simulations of financial markets. To determine return volatility in the spin financial market we use the GARCH model often used for volatility estimation in empirical finance. We apply the Bayesian inference performed by the Markov Chain Monte Carlo method to the parameter estimation of the GARCH model. It is found that volatility determined by the GARCH model exhibits "volatility clustering" also observed in the real financial markets. Using volatility determined by the GARCH model we examine the mixture-of-distribution hypothesis (MDH) suggested for the asset return dynamics. We find that the returns standardized by volatility are approximately standard normal random variables. Moreover we find that the absolute standardized returns show no significant autocorrelation. These findings are consistent with the view of the MDH for the return dynamics.

Inferring dynamic gene regulatory networks in cardiac differentiation through the integration of multi-dimensional data.

PubMed

Gong, Wuming; Koyano-Nakagawa, Naoko; Li, Tongbin; Garry, Daniel J

2015-03-07

Decoding the temporal control of gene expression patterns is key to the understanding of the complex mechanisms that govern developmental decisions during heart development. High-throughput methods have been employed to systematically study the dynamic and coordinated nature of cardiac differentiation at the global level with multiple dimensions. Therefore, there is a pressing need to develop a systems approach to integrate these data from individual studies and infer the dynamic regulatory networks in an unbiased fashion. We developed a two-step strategy to integrate data from (1) temporal RNA-seq, (2) temporal histone modification ChIP-seq, (3) transcription factor (TF) ChIP-seq and (4) gene perturbation experiments to reconstruct the dynamic network during heart development. First, we trained a logistic regression model to predict the probability (LR score) of any base being bound by 543 TFs with known positional weight matrices. Second, four dimensions of data were combined using a time-varying dynamic Bayesian network model to infer the dynamic networks at four developmental stages in the mouse [mouse embryonic stem cells (ESCs), mesoderm (MES), cardiac progenitors (CP) and cardiomyocytes (CM)]. Our method not only infers the time-varying networks between different stages of heart development, but it also identifies the TF binding sites associated with promoter or enhancers of downstream genes. The LR scores of experimentally verified ESCs and heart enhancers were significantly higher than random regions (p <10(-100)), suggesting that a high LR score is a reliable indicator for functional TF binding sites. Our network inference model identified a region with an elevated LR score approximately -9400 bp upstream of the transcriptional start site of Nkx2-5, which overlapped with a previously reported enhancer region (-9435 to -8922 bp). TFs such as Tead1, Gata4, Msx2, and Tgif1 were predicted to bind to this region and participate in the regulation of Nkx2-5 gene expression. Our model also predicted the key regulatory networks for the ESC-MES, MES-CP and CP-CM transitions. We report a novel method to systematically integrate multi-dimensional -omics data and reconstruct the gene regulatory networks. This method will allow one to rapidly determine the cis-modules that regulate key genes during cardiac differentiation.

Predicting gene regulatory networks by combining spatial and temporal gene expression data in Arabidopsis root stem cells

PubMed Central

de Luis Balaguer, Maria Angels; Fisher, Adam P.; Clark, Natalie M.; Fernandez-Espinosa, Maria Guadalupe; Möller, Barbara K.; Weijers, Dolf; Williams, Cranos; Lorenzo, Oscar; Sozzani, Rosangela

2017-01-01

Identifying the transcription factors (TFs) and associated networks involved in stem cell regulation is essential for understanding the initiation and growth of plant tissues and organs. Although many TFs have been shown to have a role in the Arabidopsis root stem cells, a comprehensive view of the transcriptional signature of the stem cells is lacking. In this work, we used spatial and temporal transcriptomic data to predict interactions among the genes involved in stem cell regulation. To accomplish this, we transcriptionally profiled several stem cell populations and developed a gene regulatory network inference algorithm that combines clustering with dynamic Bayesian network inference. We leveraged the topology of our networks to infer potential major regulators. Specifically, through mathematical modeling and experimental validation, we identified PERIANTHIA (PAN) as an important molecular regulator of quiescent center function. The results presented in this work show that our combination of molecular biology, computational biology, and mathematical modeling is an efficient approach to identify candidate factors that function in the stem cells. PMID:28827319

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…

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.

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.

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.

Modelling Odor Decoding in the Antennal Lobe by Combining Sequential Firing Rate Models with Bayesian Inference

PubMed Central

Cuevas Rivera, Dario; Bitzer, Sebastian; Kiebel, Stefan J.

2015-01-01

The olfactory information that is received by the insect brain is encoded in the form of spatiotemporal patterns in the projection neurons of the antennal lobe. These dense and overlapping patterns are transformed into a sparse code in Kenyon cells in the mushroom body. Although it is clear that this sparse code is the basis for rapid categorization of odors, it is yet unclear how the sparse code in Kenyon cells is computed and what information it represents. Here we show that this computation can be modeled by sequential firing rate patterns using Lotka-Volterra equations and Bayesian online inference. This new model can be understood as an ‘intelligent coincidence detector’, which robustly and dynamically encodes the presence of specific odor features. We found that the model is able to qualitatively reproduce experimentally observed activity in both the projection neurons and the Kenyon cells. In particular, the model explains mechanistically how sparse activity in the Kenyon cells arises from the dense code in the projection neurons. The odor classification performance of the model proved to be robust against noise and time jitter in the observed input sequences. As in recent experimental results, we found that recognition of an odor happened very early during stimulus presentation in the model. Critically, by using the model, we found surprising but simple computational explanations for several experimental phenomena. PMID:26451888

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.

Using Stan for Item Response Theory Models

ERIC Educational Resources Information Center

Ames, Allison J.; Au, Chi Hang

2018-01-01

Stan is a flexible probabilistic programming language providing full Bayesian inference through Hamiltonian Monte Carlo algorithms. The benefits of Hamiltonian Monte Carlo include improved efficiency and faster inference, when compared to other MCMC software implementations. Users can interface with Stan through a variety of computing…

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

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.

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

Bayesian dynamic regression models for interval censored survival data with application to children dental health.

PubMed

Wang, Xiaojing; Chen, Ming-Hui; Yan, Jun

2013-07-01

Cox models with time-varying coefficients offer great flexibility in capturing the temporal dynamics of covariate effects on event times, which could be hidden from a Cox proportional hazards model. Methodology development for varying coefficient Cox models, however, has been largely limited to right censored data; only limited work on interval censored data has been done. In most existing methods for varying coefficient models, analysts need to specify which covariate coefficients are time-varying and which are not at the time of fitting. We propose a dynamic Cox regression model for interval censored data in a Bayesian framework, where the coefficient curves are piecewise constant but the number of pieces and the jump points are covariate specific and estimated from the data. The model automatically determines the extent to which the temporal dynamics is needed for each covariate, resulting in smoother and more stable curve estimates. The posterior computation is carried out via an efficient reversible jump Markov chain Monte Carlo algorithm. Inference of each coefficient is based on an average of models with different number of pieces and jump points. A simulation study with three covariates, each with a coefficient of different degree in temporal dynamics, confirmed that the dynamic model is preferred to the existing time-varying model in terms of model comparison criteria through conditional predictive ordinate. When applied to a dental health data of children with age between 7 and 12 years, the dynamic model reveals that the relative risk of emergence of permanent tooth 24 between children with and without an infected primary predecessor is the highest at around age 7.5, and that it gradually reduces to one after age 11. These findings were not seen from the existing studies with Cox proportional hazards models.

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

PubMed

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

2016-03-01

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

Team performance and collective efficacy in the dynamic psychology of competitive team: a Bayesian network analysis.

PubMed

Fuster-Parra, P; García-Mas, A; Ponseti, F J; Leo, F M

2015-04-01

The purpose of this paper was to discover the relationships among 22 relevant psychological features in semi-professional football players in order to study team's performance and collective efficacy via a Bayesian network (BN). The paper includes optimization of team's performance and collective efficacy using intercausal reasoning pattern which constitutes a very common pattern in human reasoning. The BN is used to make inferences regarding our problem, and therefore we obtain some conclusions; among them: maximizing the team's performance causes a decrease in collective efficacy and when team's performance achieves the minimum value it causes an increase in moderate/high values of collective efficacy. Similarly, we may reason optimizing team collective efficacy instead. It also allows us to determine the features that have the strongest influence on performance and which on collective efficacy. From the BN two different coaching styles were differentiated taking into account the local Markov property: training leadership and autocratic leadership. Copyright © 2014 Elsevier B.V. All rights reserved.

The Iquique earthquake sequence of April 2014: Bayesian modeling accounting for prediction uncertainty

USGS Publications Warehouse

Duputel, Zacharie; Jiang, Junle; Jolivet, Romain; Simons, Mark; Rivera, Luis; Ampuero, Jean-Paul; Riel, Bryan; Owen, Susan E; Moore, Angelyn W; Samsonov, Sergey V; Ortega Culaciati, Francisco; Minson, Sarah E.

2016-01-01

The subduction zone in northern Chile is a well-identified seismic gap that last ruptured in 1877. On 1 April 2014, this region was struck by a large earthquake following a two week long series of foreshocks. This study combines a wide range of observations, including geodetic, tsunami, and seismic data, to produce a reliable kinematic slip model of the Mw=8.1 main shock and a static slip model of the Mw=7.7 aftershock. We use a novel Bayesian modeling approach that accounts for uncertainty in the Green's functions, both static and dynamic, while avoiding nonphysical regularization. The results reveal a sharp slip zone, more compact than previously thought, located downdip of the foreshock sequence and updip of high-frequency sources inferred by back-projection analysis. Both the main shock and the Mw=7.7 aftershock did not rupture to the trench and left most of the seismic gap unbroken, leaving the possibility of a future large earthquake in the region.

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

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.

Bayesian inference of the lung alveolar spatial model for the identification of alveolar mechanics associated with acute respiratory distress syndrome

NASA Astrophysics Data System (ADS)

Christley, Scott; Emr, Bryanna; Ghosh, Auyon; Satalin, Josh; Gatto, Louis; Vodovotz, Yoram; Nieman, Gary F.; An, Gary

2013-06-01

Acute respiratory distress syndrome (ARDS) is acute lung failure secondary to severe systemic inflammation, resulting in a derangement of alveolar mechanics (i.e. the dynamic change in alveolar size and shape during tidal ventilation), leading to alveolar instability that can cause further damage to the pulmonary parenchyma. Mechanical ventilation is a mainstay in the treatment of ARDS, but may induce mechano-physical stresses on unstable alveoli, which can paradoxically propagate the cellular and molecular processes exacerbating ARDS pathology. This phenomenon is called ventilator induced lung injury (VILI), and plays a significant role in morbidity and mortality associated with ARDS. In order to identify optimal ventilation strategies to limit VILI and treat ARDS, it is necessary to understand the complex interplay between biological and physical mechanisms of VILI, first at the alveolar level, and then in aggregate at the whole-lung level. Since there is no current consensus about the underlying dynamics of alveolar mechanics, as an initial step we investigate the ventilatory dynamics of an alveolar sac (AS) with the lung alveolar spatial model (LASM), a 3D spatial biomechanical representation of the AS and its interaction with airflow pressure and the surface tension effects of pulmonary surfactant. We use the LASM to identify the mechanical ramifications of alveolar dynamics associated with ARDS. Using graphical processing unit parallel algorithms, we perform Bayesian inference on the model parameters using experimental data from rat lung under control and Tween-induced ARDS conditions. Our results provide two plausible models that recapitulate two fundamental hypotheses about volume change at the alveolar level: (1) increase in alveolar size through isotropic volume change, or (2) minimal change in AS radius with primary expansion of the mouth of the AS, with the implication that the majority of change in lung volume during the respiratory cycle occurs in the alveolar ducts. These two model solutions correspond to significantly different mechanical properties of the tissue, and we discuss the implications of these different properties and the requirements for new experimental data to discriminate between the hypotheses.

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…

XID+: Next generation XID development

NASA Astrophysics Data System (ADS)

Hurley, Peter

2017-04-01

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

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…

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.

A Smoluchowski model of crystallization dynamics of small colloidal clusters

NASA Astrophysics Data System (ADS)

Beltran-Villegas, Daniel J.; Sehgal, Ray M.; Maroudas, Dimitrios; Ford, David M.; Bevan, Michael A.

2011-10-01

We investigate the dynamics of colloidal crystallization in a 32-particle system at a fixed value of interparticle depletion attraction that produces coexisting fluid and solid phases. Free energy landscapes (FELs) and diffusivity landscapes (DLs) are obtained as coefficients of 1D Smoluchowski equations using as order parameters either the radius of gyration or the average crystallinity. FELs and DLs are estimated by fitting the Smoluchowski equations to Brownian dynamics (BD) simulations using either linear fits to locally initiated trajectories or global fits to unbiased trajectories using Bayesian inference. The resulting FELs are compared to Monte Carlo Umbrella Sampling results. The accuracy of the FELs and DLs for modeling colloidal crystallization dynamics is evaluated by comparing mean first-passage times from BD simulations with analytical predictions using the FEL and DL models. While the 1D models accurately capture dynamics near the free energy minimum fluid and crystal configurations, predictions near the transition region are not quantitatively accurate. A preliminary investigation of ensemble averaged 2D order parameter trajectories suggests that 2D models are required to capture crystallization dynamics in the transition region.

Bayesian analysis of time-series data under case-crossover designs: posterior equivalence and inference.

PubMed

Li, Shi; Mukherjee, Bhramar; Batterman, Stuart; Ghosh, Malay

2013-12-01

Case-crossover designs are widely used to study short-term exposure effects on the risk of acute adverse health events. While the frequentist literature on this topic is vast, there is no Bayesian work in this general area. The contribution of this paper is twofold. First, the paper establishes Bayesian equivalence results that require characterization of the set of priors under which the posterior distributions of the risk ratio parameters based on a case-crossover and time-series analysis are identical. Second, the paper studies inferential issues under case-crossover designs in a Bayesian framework. Traditionally, a conditional logistic regression is used for inference on risk-ratio parameters in case-crossover studies. We consider instead a more general full likelihood-based approach which makes less restrictive assumptions on the risk functions. Formulation of a full likelihood leads to growth in the number of parameters proportional to the sample size. We propose a semi-parametric Bayesian approach using a Dirichlet process prior to handle the random nuisance parameters that appear in a full likelihood formulation. We carry out a simulation study to compare the Bayesian methods based on full and conditional likelihood with the standard frequentist approaches for case-crossover and time-series analysis. The proposed methods are illustrated through the Detroit Asthma Morbidity, Air Quality and Traffic study, which examines the association between acute asthma risk and ambient air pollutant concentrations. © 2013, The International Biometric Society.

A Bayesian Alternative for Multi-objective Ecohydrological Model Specification

NASA Astrophysics Data System (ADS)

Tang, Y.; Marshall, L. A.; Sharma, A.; Ajami, H.

2015-12-01

Process-based ecohydrological models combine the study of hydrological, physical, biogeochemical and ecological processes of the catchments, which are usually more complex and parametric than conceptual hydrological models. Thus, appropriate calibration objectives and model uncertainty analysis are essential for ecohydrological modeling. In recent years, Bayesian inference has become one of the most popular tools for quantifying the uncertainties in hydrological modeling with the development of Markov Chain Monte Carlo (MCMC) techniques. Our study aims to develop appropriate prior distributions and likelihood functions that minimize the model uncertainties and bias within a Bayesian ecohydrological framework. In our study, a formal Bayesian approach is implemented in an ecohydrological model which combines a hydrological model (HyMOD) and a dynamic vegetation model (DVM). Simulations focused on one objective likelihood (Streamflow/LAI) and multi-objective likelihoods (Streamflow and LAI) with different weights are compared. Uniform, weakly informative and strongly informative prior distributions are used in different simulations. The Kullback-leibler divergence (KLD) is used to measure the dis(similarity) between different priors and corresponding posterior distributions to examine the parameter sensitivity. Results show that different prior distributions can strongly influence posterior distributions for parameters, especially when the available data is limited or parameters are insensitive to the available data. We demonstrate differences in optimized parameters and uncertainty limits in different cases based on multi-objective likelihoods vs. single objective likelihoods. We also demonstrate the importance of appropriately defining the weights of objectives in multi-objective calibration according to different data types.

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.

Conditional adaptive Bayesian spectral analysis of nonstationary biomedical time series.

PubMed

Bruce, Scott A; Hall, Martica H; Buysse, Daniel J; Krafty, Robert T

2018-03-01

Many studies of biomedical time series signals aim to measure the association between frequency-domain properties of time series and clinical and behavioral covariates. However, the time-varying dynamics of these associations are largely ignored due to a lack of methods that can assess the changing nature of the relationship through time. This article introduces a method for the simultaneous and automatic analysis of the association between the time-varying power spectrum and covariates, which we refer to as conditional adaptive Bayesian spectrum analysis (CABS). The procedure adaptively partitions the grid of time and covariate values into an unknown number of approximately stationary blocks and nonparametrically estimates local spectra within blocks through penalized splines. CABS is formulated in a fully Bayesian framework, in which the number and locations of partition points are random, and fit using reversible jump Markov chain Monte Carlo techniques. Estimation and inference averaged over the distribution of partitions allows for the accurate analysis of spectra with both smooth and abrupt changes. The proposed methodology is used to analyze the association between the time-varying spectrum of heart rate variability and self-reported sleep quality in a study of older adults serving as the primary caregiver for their ill spouse. © 2017, The International Biometric Society.

Profile-Based LC-MS Data Alignment—A Bayesian Approach

PubMed Central

Tsai, Tsung-Heng; Tadesse, Mahlet G.; Wang, Yue; Ressom, Habtom W.

2014-01-01

A Bayesian alignment model (BAM) is proposed for alignment of liquid chromatography-mass spectrometry (LC-MS) data. BAM belongs to the category of profile-based approaches, which are composed of two major components: a prototype function and a set of mapping functions. Appropriate estimation of these functions is crucial for good alignment results. BAM uses Markov chain Monte Carlo (MCMC) methods to draw inference on the model parameters and improves on existing MCMC-based alignment methods through 1) the implementation of an efficient MCMC sampler and 2) an adaptive selection of knots. A block Metropolis-Hastings algorithm that mitigates the problem of the MCMC sampler getting stuck at local modes of the posterior distribution is used for the update of the mapping function coefficients. In addition, a stochastic search variable selection (SSVS) methodology is used to determine the number and positions of knots. We applied BAM to a simulated data set, an LC-MS proteomic data set, and two LC-MS metabolomic data sets, and compared its performance with the Bayesian hierarchical curve registration (BHCR) model, the dynamic time-warping (DTW) model, and the continuous profile model (CPM). The advantage of applying appropriate profile-based retention time correction prior to performing a feature-based approach is also demonstrated through the metabolomic data sets. PMID:23929872

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.

Inference and forecast of H7N9 influenza in China, 2013 to 2015.

PubMed

Li, Ruiyun; Bai, Yuqi; Heaney, Alex; Kandula, Sasikiran; Cai, Jun; Zhao, Xuyi; Xu, Bing; Shaman, Jeffrey

2017-02-16

The recent emergence of A(H7N9) avian influenza poses a significant challenge to public health in China and around the world; however, understanding of the transmission dynamics and progression of influenza A(H7N9) infection in domestic poultry, as well as spillover transmission to humans, remains limited. Here, we develop a mathematical model-Bayesian inference system which combines a simple epidemic model and data assimilation method, and use it in conjunction with data on observed human influenza A(H7N9) cases from 19 February 2013 to 19 September 2015 to estimate key epidemiological parameters and to forecast infection in both poultry and humans. Our findings indicate a high outbreak attack rate of 33% among poultry but a low rate of chicken-to-human spillover transmission. In addition, we generated accurate forecasts of the peak timing and magnitude of human influenza A(H7N9) cases. This work demonstrates that transmission dynamics within an avian reservoir can be estimated and that real-time forecast of spillover avian influenza in humans is possible. This article is copyright of The Authors, 2017.

Impact of environmental inputs on reverse-engineering approach to network structures.

PubMed

Wu, Jianhua; Sinfield, James L; Buchanan-Wollaston, Vicky; Feng, Jianfeng

2009-12-04

Uncovering complex network structures from a biological system is one of the main topic in system biology. The network structures can be inferred by the dynamical Bayesian network or Granger causality, but neither techniques have seriously taken into account the impact of environmental inputs. With considerations of natural rhythmic dynamics of biological data, we propose a system biology approach to reveal the impact of environmental inputs on network structures. We first represent the environmental inputs by a harmonic oscillator and combine them with Granger causality to identify environmental inputs and then uncover the causal network structures. We also generalize it to multiple harmonic oscillators to represent various exogenous influences. This system approach is extensively tested with toy models and successfully applied to a real biological network of microarray data of the flowering genes of the model plant Arabidopsis Thaliana. The aim is to identify those genes that are directly affected by the presence of the sunlight and uncover the interactive network structures associating with flowering metabolism. We demonstrate that environmental inputs are crucial for correctly inferring network structures. Harmonic causal method is proved to be a powerful technique to detect environment inputs and uncover network structures, especially when the biological data exhibit periodic oscillations.

Technical Note: Approximate Bayesian parameterization of a process-based tropical forest model

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2014-02-01

Inverse parameter estimation of process-based models is a long-standing problem in many scientific disciplines. A key question for inverse parameter estimation is how to define the metric that quantifies how well model predictions fit to the data. This metric can be expressed by general cost or objective functions, but statistical inversion methods require a particular metric, the probability of observing the data given the model parameters, known as the likelihood. For technical and computational reasons, likelihoods for process-based stochastic models are usually based on general assumptions about variability in the observed data, and not on the stochasticity generated by the model. Only in recent years have new methods become available that allow the generation of likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional Markov chain Monte Carlo (MCMC) sampler, performs well in retrieving known parameter values from virtual inventory data generated by the forest model. We analyze the results of the parameter estimation, examine its sensitivity to the choice and aggregation of model outputs and observed data (summary statistics), and demonstrate the application of this method by fitting the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss how this approach differs from approximate Bayesian computation (ABC), another method commonly used to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can be successfully applied to process-based models of high complexity. The methodology is particularly suitable for heterogeneous and complex data structures and can easily be adjusted to other model types, including most stochastic population and individual-based models. Our study therefore provides a blueprint for a fairly general approach to parameter estimation of stochastic process-based models.

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

Bayesian Inference on the Effect of Density Dependence and Weather on a Guanaco Population from Chile

PubMed Central

Zubillaga, María; Skewes, Oscar; Soto, Nicolás; Rabinovich, Jorge E.; Colchero, Fernando

2014-01-01

Understanding the mechanisms that drive population dynamics is fundamental for management of wild populations. The guanaco (Lama guanicoe) is one of two wild camelid species in South America. We evaluated the effects of density dependence and weather variables on population regulation based on a time series of 36 years of population sampling of guanacos in Tierra del Fuego, Chile. The population density varied between 2.7 and 30.7 guanaco/km2, with an apparent monotonic growth during the first 25 years; however, in the last 10 years the population has shown large fluctuations, suggesting that it might have reached its carrying capacity. We used a Bayesian state-space framework and model selection to determine the effect of density and environmental variables on guanaco population dynamics. Our results show that the population is under density dependent regulation and that it is currently fluctuating around an average carrying capacity of 45,000 guanacos. We also found a significant positive effect of previous winter temperature while sheep density has a strong negative effect on the guanaco population growth. We conclude that there are significant density dependent processes and that climate as well as competition with domestic species have important effects determining the population size of guanacos, with important implications for management and conservation. PMID:25514510

Bayesian inference on the effect of density dependence and weather on a guanaco population from Chile.

PubMed

Zubillaga, María; Skewes, Oscar; Soto, Nicolás; Rabinovich, Jorge E; Colchero, Fernando

2014-01-01

Understanding the mechanisms that drive population dynamics is fundamental for management of wild populations. The guanaco (Lama guanicoe) is one of two wild camelid species in South America. We evaluated the effects of density dependence and weather variables on population regulation based on a time series of 36 years of population sampling of guanacos in Tierra del Fuego, Chile. The population density varied between 2.7 and 30.7 guanaco/km2, with an apparent monotonic growth during the first 25 years; however, in the last 10 years the population has shown large fluctuations, suggesting that it might have reached its carrying capacity. We used a Bayesian state-space framework and model selection to determine the effect of density and environmental variables on guanaco population dynamics. Our results show that the population is under density dependent regulation and that it is currently fluctuating around an average carrying capacity of 45,000 guanacos. We also found a significant positive effect of previous winter temperature while sheep density has a strong negative effect on the guanaco population growth. We conclude that there are significant density dependent processes and that climate as well as competition with domestic species have important effects determining the population size of guanacos, with important implications for management and conservation.

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.

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.

Observation uncertainty in reversible Markov chains.

PubMed

Metzner, Philipp; Weber, Marcus; Schütte, Christof

2010-09-01

In many applications one is interested in finding a simplified model which captures the essential dynamical behavior of a real life process. If the essential dynamics can be assumed to be (approximately) memoryless then a reasonable choice for a model is a Markov model whose parameters are estimated by means of Bayesian inference from an observed time series. We propose an efficient Monte Carlo Markov chain framework to assess the uncertainty of the Markov model and related observables. The derived Gibbs sampler allows for sampling distributions of transition matrices subject to reversibility and/or sparsity constraints. The performance of the suggested sampling scheme is demonstrated and discussed for a variety of model examples. The uncertainty analysis of functions of the Markov model under investigation is discussed in application to the identification of conformations of the trialanine molecule via Robust Perron Cluster Analysis (PCCA+) .

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.

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

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.

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 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

Mean Field Variational Bayesian Data Assimilation

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

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.

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.

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

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.

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.

A Statistical Description of Neural Ensemble Dynamics

PubMed Central

Long, John D.; Carmena, Jose M.

2011-01-01

The growing use of multi-channel neural recording techniques in behaving animals has produced rich datasets that hold immense potential for advancing our understanding of how the brain mediates behavior. One limitation of these techniques is they do not provide important information about the underlying anatomical connections among the recorded neurons within an ensemble. Inferring these connections is often intractable because the set of possible interactions grows exponentially with ensemble size. This is a fundamental challenge one confronts when interpreting these data. Unfortunately, the combination of expert knowledge and ensemble data is often insufficient for selecting a unique model of these interactions. Our approach shifts away from modeling the network diagram of the ensemble toward analyzing changes in the dynamics of the ensemble as they relate to behavior. Our contribution consists of adapting techniques from signal processing and Bayesian statistics to track the dynamics of ensemble data on time-scales comparable with behavior. We employ a Bayesian estimator to weigh prior information against the available ensemble data, and use an adaptive quantization technique to aggregate poorly estimated regions of the ensemble data space. Importantly, our method is capable of detecting changes in both the magnitude and structure of correlations among neurons missed by firing rate metrics. We show that this method is scalable across a wide range of time-scales and ensemble sizes. Lastly, the performance of this method on both simulated and real ensemble data is used to demonstrate its utility. PMID:22319486

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.

Development of dynamic Bayesian models for web application test management

NASA Astrophysics Data System (ADS)

Azarnova, T. V.; Polukhin, P. V.; Bondarenko, Yu V.; Kashirina, I. L.

2018-03-01

The mathematical apparatus of dynamic Bayesian networks is an effective and technically proven tool that can be used to model complex stochastic dynamic processes. According to the results of the research, mathematical models and methods of dynamic Bayesian networks provide a high coverage of stochastic tasks associated with error testing in multiuser software products operated in a dynamically changing environment. Formalized representation of the discrete test process as a dynamic Bayesian model allows us to organize the logical connection between individual test assets for multiple time slices. This approach gives an opportunity to present testing as a discrete process with set structural components responsible for the generation of test assets. Dynamic Bayesian network-based models allow us to combine in one management area individual units and testing components with different functionalities and a direct influence on each other in the process of comprehensive testing of various groups of computer bugs. The application of the proposed models provides an opportunity to use a consistent approach to formalize test principles and procedures, methods used to treat situational error signs, and methods used to produce analytical conclusions based on test results.

Inverse Ising problem in continuous time: A latent variable approach

NASA Astrophysics Data System (ADS)

Donner, Christian; Opper, Manfred

2017-12-01

We consider the inverse Ising problem: the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form which allows for simple iterative inference algorithms with analytical updates. The variables are (1) Poisson variables to linearize an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.

Bayesian inference for dynamic transcriptional regulation; the Hes1 system as a case study.

PubMed

Heron, Elizabeth A; Finkenstädt, Bärbel; Rand, David A

2007-10-01

In this study, we address the problem of estimating the parameters of regulatory networks and provide the first application of Markov chain Monte Carlo (MCMC) methods to experimental data. As a case study, we consider a stochastic model of the Hes1 system expressed in terms of stochastic differential equations (SDEs) to which rigorous likelihood methods of inference can be applied. When fitting continuous-time stochastic models to discretely observed time series the lengths of the sampling intervals are important, and much of our study addresses the problem when the data are sparse. We estimate the parameters of an autoregulatory network providing results both for simulated and real experimental data from the Hes1 system. We develop an estimation algorithm using MCMC techniques which are flexible enough to allow for the imputation of latent data on a finer time scale and the presence of prior information about parameters which may be informed from other experiments as well as additional measurement error.

Holarctic genetic structure and range dynamics in the woolly mammoth

PubMed Central

Palkopoulou, Eleftheria; Dalén, Love; Lister, Adrian M.; Vartanyan, Sergey; Sablin, Mikhail; Sher, Andrei; Edmark, Veronica Nyström; Brandström, Mikael D.; Germonpré, Mietje; Barnes, Ian; Thomas, Jessica A.

2013-01-01

Ancient DNA analyses have provided enhanced resolution of population histories in many Pleistocene taxa. However, most studies are spatially restricted, making inference of species-level biogeographic histories difficult. Here, we analyse mitochondrial DNA (mtDNA) variation in the woolly mammoth from across its Holarctic range to reconstruct its history over the last 200 thousand years (kyr). We identify a previously undocumented major mtDNA lineage in Europe, which was replaced by another major mtDNA lineage 32–34 kyr before present (BP). Coalescent simulations provide support for demographic expansions at approximately 121 kyr BP, suggesting that the previous interglacial was an important driver for demography and intraspecific genetic divergence. Furthermore, our results suggest an expansion into Eurasia from America around 66 kyr BP, coinciding with the first exposure of the Bering Land Bridge during the Late Pleistocene. Bayesian inference indicates Late Pleistocene demographic stability until 20–15 kyr BP, when a severe population size decline occurred. PMID:24026825

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

Machine Learning

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

Chikkagoudar, Satish; Chatterjee, Samrat; Thomas, Dennis G.

The absence of a robust and unified theory of cyber dynamics presents challenges and opportunities for using machine learning based data-driven approaches to further the understanding of the behavior of such complex systems. Analysts can also use machine learning approaches to gain operational insights. In order to be operationally beneficial, cybersecurity machine learning based models need to have the ability to: (1) represent a real-world system, (2) infer system properties, and (3) learn and adapt based on expert knowledge and observations. Probabilistic models and Probabilistic graphical models provide these necessary properties and are further explored in this chapter. Bayesian Networksmore » and Hidden Markov Models are introduced as an example of a widely used data driven classification/modeling strategy.« less

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.

Inference of Transmission Network Structure from HIV Phylogenetic Trees

DOE PAGES

Giardina, Federica; Romero-Severson, Ethan Obie; Albert, Jan; ...

2017-01-13

Phylogenetic inference is an attractive means to reconstruct transmission histories and epidemics. However, there is not a perfect correspondence between transmission history and virus phylogeny. Both node height and topological differences may occur, depending on the interaction between within-host evolutionary dynamics and between-host transmission patterns. To investigate these interactions, we added a within-host evolutionary model in epidemiological simulations and examined if the resulting phylogeny could recover different types of contact networks. To further improve realism, we also introduced patient-specific differences in infectivity across disease stages, and on the epidemic level we considered incomplete sampling and the age of the epidemic.more » Second, we implemented an inference method based on approximate Bayesian computation (ABC) to discriminate among three well-studied network models and jointly estimate both network parameters and key epidemiological quantities such as the infection rate. Our ABC framework used both topological and distance-based tree statistics for comparison between simulated and observed trees. Overall, our simulations showed that a virus time-scaled phylogeny (genealogy) may be substantially different from the between-host transmission tree. This has important implications for the interpretation of what a phylogeny reveals about the underlying epidemic contact network. In particular, we found that while the within-host evolutionary process obscures the transmission tree, the diversification process and infectivity dynamics also add discriminatory power to differentiate between different types of contact networks. We also found that the possibility to differentiate contact networks depends on how far an epidemic has progressed, where distance-based tree statistics have more power early in an epidemic. Finally, we applied our ABC inference on two different outbreaks from the Swedish HIV-1 epidemic.« less

Inference of Transmission Network Structure from HIV Phylogenetic Trees

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

Giardina, Federica; Romero-Severson, Ethan Obie; Albert, Jan

Phylogenetic inference is an attractive means to reconstruct transmission histories and epidemics. However, there is not a perfect correspondence between transmission history and virus phylogeny. Both node height and topological differences may occur, depending on the interaction between within-host evolutionary dynamics and between-host transmission patterns. To investigate these interactions, we added a within-host evolutionary model in epidemiological simulations and examined if the resulting phylogeny could recover different types of contact networks. To further improve realism, we also introduced patient-specific differences in infectivity across disease stages, and on the epidemic level we considered incomplete sampling and the age of the epidemic.more » Second, we implemented an inference method based on approximate Bayesian computation (ABC) to discriminate among three well-studied network models and jointly estimate both network parameters and key epidemiological quantities such as the infection rate. Our ABC framework used both topological and distance-based tree statistics for comparison between simulated and observed trees. Overall, our simulations showed that a virus time-scaled phylogeny (genealogy) may be substantially different from the between-host transmission tree. This has important implications for the interpretation of what a phylogeny reveals about the underlying epidemic contact network. In particular, we found that while the within-host evolutionary process obscures the transmission tree, the diversification process and infectivity dynamics also add discriminatory power to differentiate between different types of contact networks. We also found that the possibility to differentiate contact networks depends on how far an epidemic has progressed, where distance-based tree statistics have more power early in an epidemic. Finally, we applied our ABC inference on two different outbreaks from the Swedish HIV-1 epidemic.« less

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.

Inverse stochastic-dynamic models for high-resolution Greenland ice core records

NASA Astrophysics Data System (ADS)

Boers, Niklas; Chekroun, Mickael D.; Liu, Honghu; Kondrashov, Dmitri; Rousseau, Denis-Didier; Svensson, Anders; Bigler, Matthias; Ghil, Michael

2017-12-01

Proxy records from Greenland ice cores have been studied for several decades, yet many open questions remain regarding the climate variability encoded therein. Here, we use a Bayesian framework for inferring inverse, stochastic-dynamic models from δ18O and dust records of unprecedented, subdecadal temporal resolution. The records stem from the North Greenland Ice Core Project (NGRIP), and we focus on the time interval 59-22 ka b2k. Our model reproduces the dynamical characteristics of both the δ18O and dust proxy records, including the millennial-scale Dansgaard-Oeschger variability, as well as statistical properties such as probability density functions, waiting times and power spectra, with no need for any external forcing. The crucial ingredients for capturing these properties are (i) high-resolution training data, (ii) cubic drift terms, (iii) nonlinear coupling terms between the δ18O and dust time series, and (iv) non-Markovian contributions that represent short-term memory effects.

Modeling Dynamic Contrast-Enhanced MRI Data with a Constrained Local AIF.

PubMed

Duan, Chong; Kallehauge, Jesper F; Pérez-Torres, Carlos J; Bretthorst, G Larry; Beeman, Scott C; Tanderup, Kari; Ackerman, Joseph J H; Garbow, Joel R

2018-02-01

This study aims to develop a constrained local arterial input function (cL-AIF) to improve quantitative analysis of dynamic contrast-enhanced (DCE)-magnetic resonance imaging (MRI) data by accounting for the contrast-agent bolus amplitude error in the voxel-specific AIF. Bayesian probability theory-based parameter estimation and model selection were used to compare tracer kinetic modeling employing either the measured remote-AIF (R-AIF, i.e., the traditional approach) or an inferred cL-AIF against both in silico DCE-MRI data and clinical, cervical cancer DCE-MRI data. When the data model included the cL-AIF, tracer kinetic parameters were correctly estimated from in silico data under contrast-to-noise conditions typical of clinical DCE-MRI experiments. Considering the clinical cervical cancer data, Bayesian model selection was performed for all tumor voxels of the 16 patients (35,602 voxels in total). Among those voxels, a tracer kinetic model that employed the voxel-specific cL-AIF was preferred (i.e., had a higher posterior probability) in 80 % of the voxels compared to the direct use of a single R-AIF. Maps of spatial variation in voxel-specific AIF bolus amplitude and arrival time for heterogeneous tissues, such as cervical cancer, are accessible with the cL-AIF approach. The cL-AIF method, which estimates unique local-AIF amplitude and arrival time for each voxel within the tissue of interest, provides better modeling of DCE-MRI data than the use of a single, measured R-AIF. The Bayesian-based data analysis described herein affords estimates of uncertainties for each model parameter, via posterior probability density functions, and voxel-wise comparison across methods/models, via model selection in data modeling.

Model Selection in Historical Research Using Approximate Bayesian Computation

PubMed Central

Rubio-Campillo, Xavier

2016-01-01

Formal Models and History Computational models are increasingly being used to study historical dynamics. This new trend, which could be named Model-Based History, makes use of recently published datasets and innovative quantitative methods to improve our understanding of past societies based on their written sources. The extensive use of formal models allows historians to re-evaluate hypotheses formulated decades ago and still subject to debate due to the lack of an adequate quantitative framework. The initiative has the potential to transform the discipline if it solves the challenges posed by the study of historical dynamics. These difficulties are based on the complexities of modelling social interaction, and the methodological issues raised by the evaluation of formal models against data with low sample size, high variance and strong fragmentation. Case Study This work examines an alternate approach to this evaluation based on a Bayesian-inspired model selection method. The validity of the classical Lanchester’s laws of combat is examined against a dataset comprising over a thousand battles spanning 300 years. Four variations of the basic equations are discussed, including the three most common formulations (linear, squared, and logarithmic) and a new variant introducing fatigue. Approximate Bayesian Computation is then used to infer both parameter values and model selection via Bayes Factors. Impact Results indicate decisive evidence favouring the new fatigue model. The interpretation of both parameter estimations and model selection provides new insights into the factors guiding the evolution of warfare. At a methodological level, the case study shows how model selection methods can be used to guide historical research through the comparison between existing hypotheses and empirical evidence. PMID:26730953

Tracing the spatio-temporal dynamics of endangered fin whales (Balaenoptera physalus) within baleen whale (Mysticeti) lineages: a mitogenomic perspective.

PubMed

Yu, Jihyun; Nam, Bo-Hye; Yoon, Joon; Kim, Eun Bae; Park, Jung Youn; Kim, Heebal; Yoon, Sook Hee

2017-12-01

To explore the spatio-temporal dynamics of endangered fin whales (Balaenoptera physalus) within the baleen whale (Mysticeti) lineages, we analyzed 148 published mitochondrial genome sequences of baleen whales. We used a Bayesian coalescent approach as well as Bayesian inferences and maximum likelihood methods. The results showed that the fin whales had a single maternal origin, and that there is a significant correlation between geographic location and evolution of global fin whales. The most recent common female ancestor of this species lived approximately 9.88 million years ago (Mya). Here, North Pacific fin whales first appeared about 7.48 Mya, followed by a subsequent divergence in Southern Hemisphere approximately 6.63 Mya and North Atlantic about 4.42 Mya. Relatively recently, approximately 1.76 and 1.42 Mya, there were two additional occurrences of North Pacific populations; one originated from the Southern Hemisphere and the other from an uncertain location. The evolutionary rate of this species was 1.002 × 10 -3 substitutions/site/My. Our Bayesian skyline plot illustrates that the fin whale population has the rapid expansion event since ~ 2.5 Mya, during the Quaternary glaciation stage. Additionally, this study indicates that the fin whale has a sister group relationship with humpback whale (Meganoptera novaeangliae) within the baleen whale lineages. Of the 16 genomic regions, NADH5 showed the most powerful signal for baleen whale phylogenetics. Interestingly, fin whales have 16 species-specific amino acid residues in eight mitochondrial genes: NADH2, COX2, COX3, ATPase6, ATPase8, NADH4, NADH5, and Cytb.

Stochastic modelling, Bayesian inference, and new in vivo measurements elucidate the debated mtDNA bottleneck mechanism

PubMed Central

Johnston, Iain G; Burgstaller, Joerg P; Havlicek, Vitezslav; Kolbe, Thomas; Rülicke, Thomas; Brem, Gottfried; Poulton, Jo; Jones, Nick S

2015-01-01

Dangerous damage to mitochondrial DNA (mtDNA) can be ameliorated during mammalian development through a highly debated mechanism called the mtDNA bottleneck. Uncertainty surrounding this process limits our ability to address inherited mtDNA diseases. We produce a new, physically motivated, generalisable theoretical model for mtDNA populations during development, allowing the first statistical comparison of proposed bottleneck mechanisms. Using approximate Bayesian computation and mouse data, we find most statistical support for a combination of binomial partitioning of mtDNAs at cell divisions and random mtDNA turnover, meaning that the debated exact magnitude of mtDNA copy number depletion is flexible. New experimental measurements from a wild-derived mtDNA pairing in mice confirm the theoretical predictions of this model. We analytically solve a mathematical description of this mechanism, computing probabilities of mtDNA disease onset, efficacy of clinical sampling strategies, and effects of potential dynamic interventions, thus developing a quantitative and experimentally-supported stochastic theory of the bottleneck. DOI: http://dx.doi.org/10.7554/eLife.07464.001 PMID:26035426

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.

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.

Dynamic Bayesian Network Modeling of Game Based Diagnostic Assessments. CRESST Report 837

ERIC Educational Resources Information Center

Levy, Roy

2014-01-01

Digital games offer an appealing environment for assessing student proficiencies, including skills and misconceptions in a diagnostic setting. This paper proposes a dynamic Bayesian network modeling approach for observations of student performance from an educational video game. A Bayesian approach to model construction, calibration, and use in…

Approximation and inference methods for stochastic biochemical kinetics—a tutorial review

NASA Astrophysics Data System (ADS)

Schnoerr, David; Sanguinetti, Guido; Grima, Ramon

2017-03-01

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the chemical master equation. Despite its simple structure, no analytic solutions to the chemical master equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.

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].

Dynamic classification of fetal heart rates by hierarchical Dirichlet process mixture models.

PubMed

Yu, Kezi; Quirk, J Gerald; Djurić, Petar M

2017-01-01

In this paper, we propose an application of non-parametric Bayesian (NPB) models for classification of fetal heart rate (FHR) recordings. More specifically, we propose models that are used to differentiate between FHR recordings that are from fetuses with or without adverse outcomes. In our work, we rely on models based on hierarchical Dirichlet processes (HDP) and the Chinese restaurant process with finite capacity (CRFC). Two mixture models were inferred from real recordings, one that represents healthy and another, non-healthy fetuses. The models were then used to classify new recordings and provide the probability of the fetus being healthy. First, we compared the classification performance of the HDP models with that of support vector machines on real data and concluded that the HDP models achieved better performance. Then we demonstrated the use of mixture models based on CRFC for dynamic classification of the performance of (FHR) recordings in a real-time setting.

Don't Fear Optimality: Sampling for Probabilistic-Logic Sequence Models

NASA Astrophysics Data System (ADS)

Thon, Ingo

One of the current challenges in artificial intelligence is modeling dynamic environments that change due to the actions or activities undertaken by people or agents. The task of inferring hidden states, e.g. the activities or intentions of people, based on observations is called filtering. Standard probabilistic models such as Dynamic Bayesian Networks are able to solve this task efficiently using approximative methods such as particle filters. However, these models do not support logical or relational representations. The key contribution of this paper is the upgrade of a particle filter algorithm for use with a probabilistic logical representation through the definition of a proposal distribution. The performance of the algorithm depends largely on how well this distribution fits the target distribution. We adopt the idea of logical compilation into Binary Decision Diagrams for sampling. This allows us to use the optimal proposal distribution which is normally prohibitively slow.

Dynamic classification of fetal heart rates by hierarchical Dirichlet process mixture models

PubMed Central

Yu, Kezi; Quirk, J. Gerald

2017-01-01

In this paper, we propose an application of non-parametric Bayesian (NPB) models for classification of fetal heart rate (FHR) recordings. More specifically, we propose models that are used to differentiate between FHR recordings that are from fetuses with or without adverse outcomes. In our work, we rely on models based on hierarchical Dirichlet processes (HDP) and the Chinese restaurant process with finite capacity (CRFC). Two mixture models were inferred from real recordings, one that represents healthy and another, non-healthy fetuses. The models were then used to classify new recordings and provide the probability of the fetus being healthy. First, we compared the classification performance of the HDP models with that of support vector machines on real data and concluded that the HDP models achieved better performance. Then we demonstrated the use of mixture models based on CRFC for dynamic classification of the performance of (FHR) recordings in a real-time setting. PMID:28953927

Dynamic Bayesian network modeling for longitudinal brain morphometry

PubMed Central

Chen, Rong; Resnick, Susan M; Davatzikos, Christos; Herskovits, Edward H

2011-01-01

Identifying interactions among brain regions from structural magnetic-resonance images presents one of the major challenges in computational neuroanatomy. We propose a Bayesian data-mining approach to the detection of longitudinal morphological changes in the human brain. Our method uses a dynamic Bayesian network to represent evolving inter-regional dependencies. The major advantage of dynamic Bayesian network modeling is that it can represent complicated interactions among temporal processes. We validated our approach by analyzing a simulated atrophy study, and found that this approach requires only a small number of samples to detect the ground-truth temporal model. We further applied dynamic Bayesian network modeling to a longitudinal study of normal aging and mild cognitive impairment — the Baltimore Longitudinal Study of Aging. We found that interactions among regional volume-change rates for the mild cognitive impairment group are different from those for the normal-aging group. PMID:21963916

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.

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.

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.

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 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.

In silico model-based inference: a contemporary approach for hypothesis testing in network biology

PubMed Central

Klinke, David J.

2014-01-01

Inductive inference plays a central role in the study of biological systems where one aims to increase their understanding of the system by reasoning backwards from uncertain observations to identify causal relationships among components of the system. These causal relationships are postulated from prior knowledge as a hypothesis or simply a model. Experiments are designed to test the model. Inferential statistics are used to establish a level of confidence in how well our postulated model explains the acquired data. This iterative process, commonly referred to as the scientific method, either improves our confidence in a model or suggests that we revisit our prior knowledge to develop a new model. Advances in technology impact how we use prior knowledge and data to formulate models of biological networks and how we observe cellular behavior. However, the approach for model-based inference has remained largely unchanged since Fisher, Neyman and Pearson developed the ideas in the early 1900’s that gave rise to what is now known as classical statistical hypothesis (model) testing. Here, I will summarize conventional methods for model-based inference and suggest a contemporary approach to aid in our quest to discover how cells dynamically interpret and transmit information for therapeutic aims that integrates ideas drawn from high performance computing, Bayesian statistics, and chemical kinetics. PMID:25139179

In silico model-based inference: a contemporary approach for hypothesis testing in network biology.

PubMed

Klinke, David J

2014-01-01

Inductive inference plays a central role in the study of biological systems where one aims to increase their understanding of the system by reasoning backwards from uncertain observations to identify causal relationships among components of the system. These causal relationships are postulated from prior knowledge as a hypothesis or simply a model. Experiments are designed to test the model. Inferential statistics are used to establish a level of confidence in how well our postulated model explains the acquired data. This iterative process, commonly referred to as the scientific method, either improves our confidence in a model or suggests that we revisit our prior knowledge to develop a new model. Advances in technology impact how we use prior knowledge and data to formulate models of biological networks and how we observe cellular behavior. However, the approach for model-based inference has remained largely unchanged since Fisher, Neyman and Pearson developed the ideas in the early 1900s that gave rise to what is now known as classical statistical hypothesis (model) testing. Here, I will summarize conventional methods for model-based inference and suggest a contemporary approach to aid in our quest to discover how cells dynamically interpret and transmit information for therapeutic aims that integrates ideas drawn from high performance computing, Bayesian statistics, and chemical kinetics. © 2014 American Institute of Chemical Engineers.

A note on probabilistic models over strings: the linear algebra approach.

PubMed

Bouchard-Côté, Alexandre

2013-12-01

Probabilistic models over strings have played a key role in developing methods that take into consideration indels as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do inference on these probabilistic models, in which an important theoretical question is the complexity of computing the normalization of a class of string-valued graphical models. This question has been investigated using tools from combinatorics, dynamic programming, and graph theory, and has practical applications in Bayesian phylogenetics. In this work, we revisit this theoretical question from a different point of view, based on linear algebra. The main contribution is a set of results based on this linear algebra view that facilitate the analysis and design of inference algorithms on string-valued graphical models. As an illustration, we use this method to give a new elementary proof of a known result on the complexity of inference on the "TKF91" model, a well-known probabilistic model over strings. Compared to previous work, our proving method is easier to extend to other models, since it relies on a novel weak condition, triangular transducers, which is easy to establish in practice. The linear algebra view provides a concise way of describing transducer algorithms and their compositions, opens the possibility of transferring fast linear algebra libraries (for example, based on GPUs), as well as low rank matrix approximation methods, to string-valued inference problems.

Stochasticity of convection in Giga-LES data

NASA Astrophysics Data System (ADS)

De La Chevrotière, Michèle; Khouider, Boualem; Majda, Andrew J.

2016-09-01

The poor representation of tropical convection in general circulation models (GCMs) is believed to be responsible for much of the uncertainty in the predictions of weather and climate in the tropics. The stochastic multicloud model (SMCM) was recently developed by Khouider et al. (Commun Math Sci 8(1):187-216, 2010) to represent the missing variability in GCMs due to unresolved features of organized tropical convection. The SMCM is based on three cloud types (congestus, deep and stratiform), and transitions between these cloud types are formalized in terms of probability rules that are functions of the large-scale environment convective state and a set of seven arbitrary cloud timescale parameters. Here, a statistical inference method based on the Bayesian paradigm is applied to estimate these key cloud timescales from the Giga-LES dataset, a 24-h large-eddy simulation (LES) of deep tropical convection (Khairoutdinov et al. in J Adv Model Earth Syst 1(12), 2009) over a domain comparable to a GCM gridbox. A sequential learning strategy is used where the Giga-LES domain is partitioned into a few subdomains, and atmospheric time series obtained on each subdomain are used to train the Bayesian procedure incrementally. Convergence of the marginal posterior densities for all seven parameters is demonstrated for two different grid partitions, and sensitivity tests to other model parameters are also presented. A single column model simulation using the SMCM parameterization with the Giga-LES inferred parameters reproduces many important statistical features of the Giga-LES run, without any further tuning. In particular it exhibits intermittent dynamical behavior in both the stochastic cloud fractions and the large scale dynamics, with periods of dry phases followed by a coherent sequence of congestus, deep, and stratiform convection, varying on timescales of a few hours consistent with the Giga-LES time series. The chaotic variations of the cloud area fractions were captured fairly well both qualitatively and quantitatively demonstrating the stochastic nature of convection in the Giga-LES simulation.

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.

From Birdsong to Human Speech Recognition: Bayesian Inference on a Hierarchy of Nonlinear Dynamical Systems

PubMed Central

Yildiz, Izzet B.; von Kriegstein, Katharina; Kiebel, Stefan J.

2013-01-01

Our knowledge about the computational mechanisms underlying human learning and recognition of sound sequences, especially speech, is still very limited. One difficulty in deciphering the exact means by which humans recognize speech is that there are scarce experimental findings at a neuronal, microscopic level. Here, we show that our neuronal-computational understanding of speech learning and recognition may be vastly improved by looking at an animal model, i.e., the songbird, which faces the same challenge as humans: to learn and decode complex auditory input, in an online fashion. Motivated by striking similarities between the human and songbird neural recognition systems at the macroscopic level, we assumed that the human brain uses the same computational principles at a microscopic level and translated a birdsong model into a novel human sound learning and recognition model with an emphasis on speech. We show that the resulting Bayesian model with a hierarchy of nonlinear dynamical systems can learn speech samples such as words rapidly and recognize them robustly, even in adverse conditions. In addition, we show that recognition can be performed even when words are spoken by different speakers and with different accents—an everyday situation in which current state-of-the-art speech recognition models often fail. The model can also be used to qualitatively explain behavioral data on human speech learning and derive predictions for future experiments. PMID:24068902

Network discovery with DCM

PubMed Central

Friston, Karl J.; Li, Baojuan; Daunizeau, Jean; Stephan, Klaas E.

2011-01-01

This paper is about inferring or discovering the functional architecture of distributed systems using Dynamic Causal Modelling (DCM). We describe a scheme that recovers the (dynamic) Bayesian dependency graph (connections in a network) using observed network activity. This network discovery uses Bayesian model selection to identify the sparsity structure (absence of edges or connections) in a graph that best explains observed time-series. The implicit adjacency matrix specifies the form of the network (e.g., cyclic or acyclic) and its graph-theoretical attributes (e.g., degree distribution). The scheme is illustrated using functional magnetic resonance imaging (fMRI) time series to discover functional brain networks. Crucially, it can be applied to experimentally evoked responses (activation studies) or endogenous activity in task-free (resting state) fMRI studies. Unlike conventional approaches to network discovery, DCM permits the analysis of directed and cyclic graphs. Furthermore, it eschews (implausible) Markovian assumptions about the serial independence of random fluctuations. The scheme furnishes a network description of distributed activity in the brain that is optimal in the sense of having the greatest conditional probability, relative to other networks. The networks are characterised in terms of their connectivity or adjacency matrices and conditional distributions over the directed (and reciprocal) effective connectivity between connected nodes or regions. We envisage that this approach will provide a useful complement to current analyses of functional connectivity for both activation and resting-state studies. PMID:21182971

From birdsong to human speech recognition: bayesian inference on a hierarchy of nonlinear dynamical systems.

PubMed

Yildiz, Izzet B; von Kriegstein, Katharina; Kiebel, Stefan J

2013-01-01

Our knowledge about the computational mechanisms underlying human learning and recognition of sound sequences, especially speech, is still very limited. One difficulty in deciphering the exact means by which humans recognize speech is that there are scarce experimental findings at a neuronal, microscopic level. Here, we show that our neuronal-computational understanding of speech learning and recognition may be vastly improved by looking at an animal model, i.e., the songbird, which faces the same challenge as humans: to learn and decode complex auditory input, in an online fashion. Motivated by striking similarities between the human and songbird neural recognition systems at the macroscopic level, we assumed that the human brain uses the same computational principles at a microscopic level and translated a birdsong model into a novel human sound learning and recognition model with an emphasis on speech. We show that the resulting Bayesian model with a hierarchy of nonlinear dynamical systems can learn speech samples such as words rapidly and recognize them robustly, even in adverse conditions. In addition, we show that recognition can be performed even when words are spoken by different speakers and with different accents-an everyday situation in which current state-of-the-art speech recognition models often fail. The model can also be used to qualitatively explain behavioral data on human speech learning and derive predictions for future experiments.

Bayesian inference in an extended SEIR model with nonparametric disease transmission rate: an application to the Ebola epidemic in Sierra Leone.

PubMed

Frasso, Gianluca; Lambert, Philippe

2016-10-01

SummaryThe 2014 Ebola outbreak in Sierra Leone is analyzed using a susceptible-exposed-infectious-removed (SEIR) epidemic compartmental model. The discrete time-stochastic model for the epidemic evolution is coupled to a set of ordinary differential equations describing the dynamics of the expected proportions of subjects in each epidemic state. The unknown parameters are estimated in a Bayesian framework by combining data on the number of new (laboratory confirmed) Ebola cases reported by the Ministry of Health and prior distributions for the transition rates elicited using information collected by the WHO during the follow-up of specific Ebola cases. The time-varying disease transmission rate is modeled in a flexible way using penalized B-splines. Our framework represents a valuable stochastic tool for the study of an epidemic dynamic even when only irregularly observed and possibly aggregated data are available. Simulations and the analysis of the 2014 Sierra Leone Ebola data highlight the merits of the proposed methodology. In particular, the flexible modeling of the disease transmission rate makes the estimation of the effective reproduction number robust to the misspecification of the initial epidemic states and to underreporting of the infectious cases. © The Author 2016. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Probabilistic inference of ecohydrological parameters using observations from point to satellite scales

NASA Astrophysics Data System (ADS)

Bassiouni, Maoya; Higgins, Chad W.; Still, Christopher J.; Good, Stephen P.

2018-06-01

Vegetation controls on soil moisture dynamics are challenging to measure and translate into scale- and site-specific ecohydrological parameters for simple soil water balance models. We hypothesize that empirical probability density functions (pdfs) of relative soil moisture or soil saturation encode sufficient information to determine these ecohydrological parameters. Further, these parameters can be estimated through inverse modeling of the analytical equation for soil saturation pdfs, derived from the commonly used stochastic soil water balance framework. We developed a generalizable Bayesian inference framework to estimate ecohydrological parameters consistent with empirical soil saturation pdfs derived from observations at point, footprint, and satellite scales. We applied the inference method to four sites with different land cover and climate assuming (i) an annual rainfall pattern and (ii) a wet season rainfall pattern with a dry season of negligible rainfall. The Nash-Sutcliffe efficiencies of the analytical model's fit to soil observations ranged from 0.89 to 0.99. The coefficient of variation of posterior parameter distributions ranged from < 1 to 15 %. The parameter identifiability was not significantly improved in the more complex seasonal model; however, small differences in parameter values indicate that the annual model may have absorbed dry season dynamics. Parameter estimates were most constrained for scales and locations at which soil water dynamics are more sensitive to the fitted ecohydrological parameters of interest. In these cases, model inversion converged more slowly but ultimately provided better goodness of fit and lower uncertainty. Results were robust using as few as 100 daily observations randomly sampled from the full records, demonstrating the advantage of analyzing soil saturation pdfs instead of time series to estimate ecohydrological parameters from sparse records. Our work combines modeling and empirical approaches in ecohydrology and provides a simple framework to obtain scale- and site-specific analytical descriptions of soil moisture dynamics consistent with soil moisture observations.

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

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.

Internal cycling, not external loading, decides the nutrient limitation in eutrophic lake: A dynamic model with temporal Bayesian hierarchical inference.

PubMed

Wu, Zhen; Liu, Yong; Liang, Zhongyao; Wu, Sifeng; Guo, Huaicheng

2017-06-01

Lake eutrophication is associated with excessive anthropogenic nutrients (mainly nitrogen (N) and phosphorus (P)) and unobserved internal nutrient cycling. Despite the advances in understanding the role of external loadings, the contribution of internal nutrient cycling is still an open question. A dynamic mass-balance model was developed to simulate and measure the contributions of internal cycling and external loading. It was based on the temporal Bayesian Hierarchical Framework (BHM), where we explored the seasonal patterns in the dynamics of nutrient cycling processes and the limitation of N and P on phytoplankton growth in hyper-eutrophic Lake Dianchi, China. The dynamic patterns of the five state variables (Chla, TP, ammonia, nitrate and organic N) were simulated based on the model. Five parameters (algae growth rate, sediment exchange rate of N and P, nitrification rate and denitrification rate) were estimated based on BHM. The model provided a good fit to observations. Our model results highlighted the role of internal cycling of N and P in Lake Dianchi. The internal cycling processes contributed more than external loading to the N and P changes in the water column. Further insights into the nutrient limitation analysis indicated that the sediment exchange of P determined the P limitation. Allowing for the contribution of denitrification to N removal, N was the more limiting nutrient in most of the time, however, P was the more important nutrient for eutrophication management. For Lake Dianchi, it would not be possible to recover solely by reducing the external watershed nutrient load; the mechanisms of internal cycling should also be considered as an approach to inhibit the release of sediments and to enhance denitrification. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

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

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

Uncertainty and inference in the world of paleoecological data

NASA Astrophysics Data System (ADS)

McLachlan, J. S.; Dawson, A.; Dietze, M.; Finley, M.; Hooten, M.; Itter, M.; Jackson, S. T.; Marlon, J. R.; Raiho, A.; Tipton, J.; Williams, J.

2017-12-01

Proxy data in paleoecology and paleoclimatology share a common set of biases and uncertainties: spatiotemporal error associated with the taphonomic processes of deposition, preservation, and dating; calibration error between proxy data and the ecosystem states of interest; and error in the interpolation of calibrated estimates across space and time. Researchers often account for this daunting suite of challenges by applying qualitave expert judgment: inferring the past states of ecosystems and assessing the level of uncertainty in those states subjectively. The effectiveness of this approach can be seen by the extent to which future observations confirm previous assertions. Hierarchical Bayesian (HB) statistical approaches allow an alternative approach to accounting for multiple uncertainties in paleo data. HB estimates of ecosystem state formally account for each of the common uncertainties listed above. HB approaches can readily incorporate additional data, and data of different types into estimates of ecosystem state. And HB estimates of ecosystem state, with associated uncertainty, can be used to constrain forecasts of ecosystem dynamics based on mechanistic ecosystem models using data assimilation. Decisions about how to structure an HB model are also subjective, which creates a parallel framework for deciding how to interpret data from the deep past.Our group, the Paleoecological Observatory Network (PalEON), has applied hierarchical Bayesian statistics to formally account for uncertainties in proxy based estimates of past climate, fire, primary productivity, biomass, and vegetation composition. Our estimates often reveal new patterns of past ecosystem change, which is an unambiguously good thing, but we also often estimate a level of uncertainty that is uncomfortably high for many researchers. High levels of uncertainty are due to several features of the HB approach: spatiotemporal smoothing, the formal aggregation of multiple types of uncertainty, and a coarseness in statistical models of taphonomic process. Each of these features provides useful opportunities for statisticians and data-generating researchers to assess what we know about the signal and the noise in paleo data and to improve inference about past changes in ecosystem state.

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.