An adaptive Gaussian process-based method for efficient Bayesian experimental design in groundwater contaminant source identification problems: ADAPTIVE GAUSSIAN PROCESS-BASED INVERSION

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

Zhang, Jiangjiang; Li, Weixuan; Zeng, Lingzao

Surrogate models are commonly used in Bayesian approaches such as Markov Chain Monte Carlo (MCMC) to avoid repetitive CPU-demanding model evaluations. However, the approximation error of a surrogate may lead to biased estimations of the posterior distribution. This bias can be corrected by constructing a very accurate surrogate or implementing MCMC in a two-stage manner. Since the two-stage MCMC requires extra original model evaluations, the computational cost is still high. If the information of measurement is incorporated, a locally accurate approximation of the original model can be adaptively constructed with low computational cost. Based on this idea, we propose amore » Gaussian process (GP) surrogate-based Bayesian experimental design and parameter estimation approach for groundwater contaminant source identification problems. A major advantage of the GP surrogate is that it provides a convenient estimation of the approximation error, which can be incorporated in the Bayesian formula to avoid over-confident estimation of the posterior distribution. The proposed approach is tested with a numerical case study. Without sacrificing the estimation accuracy, the new approach achieves about 200 times of speed-up compared to our previous work using two-stage MCMC.« less

Bayesian Computation Emerges in Generic Cortical Microcircuits through Spike-Timing-Dependent Plasticity

PubMed Central

Nessler, Bernhard; Pfeiffer, Michael; Buesing, Lars; Maass, Wolfgang

2013-01-01

The principles by which networks of neurons compute, and how spike-timing dependent plasticity (STDP) of synaptic weights generates and maintains their computational function, are unknown. Preceding work has shown that soft winner-take-all (WTA) circuits, where pyramidal neurons inhibit each other via interneurons, are a common motif of cortical microcircuits. We show through theoretical analysis and computer simulations that Bayesian computation is induced in these network motifs through STDP in combination with activity-dependent changes in the excitability of neurons. The fundamental components of this emergent Bayesian computation are priors that result from adaptation of neuronal excitability and implicit generative models for hidden causes that are created in the synaptic weights through STDP. In fact, a surprising result is that STDP is able to approximate a powerful principle for fitting such implicit generative models to high-dimensional spike inputs: Expectation Maximization. Our results suggest that the experimentally observed spontaneous activity and trial-to-trial variability of cortical neurons are essential features of their information processing capability, since their functional role is to represent probability distributions rather than static neural codes. Furthermore it suggests networks of Bayesian computation modules as a new model for distributed information processing in the cortex. PMID:23633941

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

PubMed Central

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

2017-01-01

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

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

PubMed

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

2017-06-07

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

Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models

NASA Astrophysics Data System (ADS)

Vakilzadeh, Majid K.; Huang, Yong; Beck, James L.; Abrahamsson, Thomas

2017-02-01

A new multi-level Markov Chain Monte Carlo algorithm for Approximate Bayesian Computation, ABC-SubSim, has recently appeared that exploits the Subset Simulation method for efficient rare-event simulation. ABC-SubSim adaptively creates a nested decreasing sequence of data-approximating regions in the output space that correspond to increasingly closer approximations of the observed output vector in this output space. At each level, multiple samples of the model parameter vector are generated by a component-wise Metropolis algorithm so that the predicted output corresponding to each parameter value falls in the current data-approximating region. Theoretically, if continued to the limit, the sequence of data-approximating regions would converge on to the observed output vector and the approximate posterior distributions, which are conditional on the data-approximation region, would become exact, but this is not practically feasible. In this paper we study the performance of the ABC-SubSim algorithm for Bayesian updating of the parameters of dynamical systems using a general hierarchical state-space model. We note that the ABC methodology gives an approximate posterior distribution that actually corresponds to an exact posterior where a uniformly distributed combined measurement and modeling error is added. We also note that ABC algorithms have a problem with learning the uncertain error variances in a stochastic state-space model and so we treat them as nuisance parameters and analytically integrate them out of the posterior distribution. In addition, the statistical efficiency of the original ABC-SubSim algorithm is improved by developing a novel strategy to regulate the proposal variance for the component-wise Metropolis algorithm at each level. We demonstrate that Self-regulated ABC-SubSim is well suited for Bayesian system identification by first applying it successfully to model updating of a two degree-of-freedom linear structure for three cases: globally, locally and un-identifiable model classes, and then to model updating of a two degree-of-freedom nonlinear structure with Duffing nonlinearities in its interstory force-deflection relationship.

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.

Autonomic Closure for Turbulent Flows Using Approximate Bayesian Computation

NASA Astrophysics Data System (ADS)

Doronina, Olga; Christopher, Jason; Hamlington, Peter; Dahm, Werner

2017-11-01

Autonomic closure is a new technique for achieving fully adaptive and physically accurate closure of coarse-grained turbulent flow governing equations, such as those solved in large eddy simulations (LES). Although autonomic closure has been shown in recent a priori tests to more accurately represent unclosed terms than do dynamic versions of traditional LES models, the computational cost of the approach makes it challenging to implement for simulations of practical turbulent flows at realistically high Reynolds numbers. The optimization step used in the approach introduces large matrices that must be inverted and is highly memory intensive. In order to reduce memory requirements, here we propose to use approximate Bayesian computation (ABC) in place of the optimization step, thereby yielding a computationally-efficient implementation of autonomic closure that trades memory-intensive for processor-intensive computations. The latter challenge can be overcome as co-processors such as general purpose graphical processing units become increasingly available on current generation petascale and exascale supercomputers. In this work, we outline the formulation of ABC-enabled autonomic closure and present initial results demonstrating the accuracy and computational cost of the approach.

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

COSMOABC: Likelihood-free inference via Population Monte Carlo Approximate Bayesian Computation

NASA Astrophysics Data System (ADS)

Ishida, E. E. O.; Vitenti, S. D. P.; Penna-Lima, M.; Cisewski, J.; de Souza, R. S.; Trindade, A. M. M.; Cameron, E.; Busti, V. C.; COIN Collaboration

2015-11-01

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 catalogues. Here we present COSMOABC, a Python ABC sampler featuring a Population Monte Carlo variation of the original ABC algorithm, which uses an adaptive importance sampling scheme. The code is very flexible and can be easily coupled to an external simulator, while allowing to incorporate arbitrary distance and prior functions. As an example of practical application, we coupled COSMOABC with the NUMCOSMO library and demonstrate how it can be used to estimate posterior probability distributions over cosmological parameters based on measurements of galaxy clusters number counts without computing the likelihood function. COSMOABC is published under the GPLv3 license on PyPI and GitHub and documentation is available at http://goo.gl/SmB8EX.

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

PubMed

Fisher, Charles K; Mehta, Pankaj

2015-06-01

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

Approximate likelihood calculation on a phylogeny for Bayesian estimation of divergence times.

PubMed

dos Reis, Mario; Yang, Ziheng

2011-07-01

The molecular clock provides a powerful way to estimate species divergence times. If information on some species divergence times is available from the fossil or geological record, it can be used to calibrate a phylogeny and estimate divergence times for all nodes in the tree. The Bayesian method provides a natural framework to incorporate different sources of information concerning divergence times, such as information in the fossil and molecular data. Current models of sequence evolution are intractable in a Bayesian setting, and Markov chain Monte Carlo (MCMC) is used to generate the posterior distribution of divergence times and evolutionary rates. This method is computationally expensive, as it involves the repeated calculation of the likelihood function. Here, we explore the use of Taylor expansion to approximate the likelihood during MCMC iteration. The approximation is much faster than conventional likelihood calculation. However, the approximation is expected to be poor when the proposed parameters are far from the likelihood peak. We explore the use of parameter transforms (square root, logarithm, and arcsine) to improve the approximation to the likelihood curve. We found that the new methods, particularly the arcsine-based transform, provided very good approximations under relaxed clock models and also under the global clock model when the global clock is not seriously violated. The approximation is poorer for analysis under the global clock when the global clock is seriously wrong and should thus not be used. The results suggest that the approximate method may be useful for Bayesian dating analysis using large data sets.

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

Application of the Approximate Bayesian Computation methods in the stochastic estimation of atmospheric contamination parameters for mobile sources

NASA Astrophysics Data System (ADS)

Kopka, Piotr; Wawrzynczak, Anna; Borysiewicz, Mieczyslaw

2016-11-01

In this paper the Bayesian methodology, known as Approximate Bayesian Computation (ABC), is applied to the problem of the atmospheric contamination source identification. The algorithm input data are on-line arriving concentrations of the released substance registered by the distributed sensors network. This paper presents the Sequential ABC algorithm in detail and tests its efficiency in estimation of probabilistic distributions of atmospheric release parameters of a mobile contamination source. The developed algorithms are tested using the data from Over-Land Atmospheric Diffusion (OLAD) field tracer experiment. The paper demonstrates estimation of seven parameters characterizing the contamination source, i.e.: contamination source starting position (x,y), the direction of the motion of the source (d), its velocity (v), release rate (q), start time of release (ts) and its duration (td). The online-arriving new concentrations dynamically update the probability distributions of search parameters. The atmospheric dispersion Second-order Closure Integrated PUFF (SCIPUFF) Model is used as the forward model to predict the concentrations at the sensors locations.

Parameter Estimation for a Turbulent Buoyant Jet Using Approximate Bayesian Computation

NASA Astrophysics Data System (ADS)

Christopher, Jason D.; Wimer, Nicholas T.; Hayden, Torrey R. S.; Lapointe, Caelan; Grooms, Ian; Rieker, Gregory B.; Hamlington, Peter E.

2016-11-01

Approximate Bayesian Computation (ABC) is a powerful tool that allows sparse experimental or other "truth" data to be used for the prediction of unknown model parameters in numerical simulations of real-world engineering systems. In this presentation, we introduce the ABC approach and then use ABC to predict unknown inflow conditions in simulations of a two-dimensional (2D) turbulent, high-temperature buoyant jet. For this test case, truth data are obtained from a simulation with known boundary conditions and problem parameters. Using spatially-sparse temperature statistics from the 2D buoyant jet truth simulation, we show that the ABC method provides accurate predictions of the true jet inflow temperature. The success of the ABC approach in the present test suggests that ABC is a useful and versatile tool for engineering fluid dynamics research.

Approximate Bayesian computation for forward modeling in cosmology

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

Akeret, Joël; Refregier, Alexandre; Amara, Adam

Bayesian inference is often used in cosmology and astrophysics to derive constraints on model parameters from observations. This approach relies on the ability to compute the likelihood of the data given a choice of model parameters. In many practical situations, the likelihood function may however be unavailable or intractable due to non-gaussian errors, non-linear measurements processes, or complex data formats such as catalogs and maps. In these cases, the simulation of mock data sets can often be made through forward modeling. We discuss how Approximate Bayesian Computation (ABC) can be used in these cases to derive an approximation to themore » posterior constraints using simulated data sets. This technique relies on the sampling of the parameter set, a distance metric to quantify the difference between the observation and the simulations and summary statistics to compress the information in the data. We first review the principles of ABC and discuss its implementation using a Population Monte-Carlo (PMC) algorithm and the Mahalanobis distance metric. We test the performance of the implementation using a Gaussian toy model. We then apply the ABC technique to the practical case of the calibration of image simulations for wide field cosmological surveys. We find that the ABC analysis is able to provide reliable parameter constraints for this problem and is therefore a promising technique for other applications in cosmology and astrophysics. Our implementation of the ABC PMC method is made available via a public code release.« less

Optical characterization limits of nanoparticle aggregates at different wavelengths using approximate Bayesian computation

NASA Astrophysics Data System (ADS)

Eriçok, Ozan Burak; Ertürk, Hakan

2018-07-01

Optical characterization of nanoparticle aggregates is a complex inverse problem that can be solved by deterministic or statistical methods. Previous studies showed that there exists a different lower size limit of reliable characterization, corresponding to the wavelength of light source used. In this study, these characterization limits are determined considering a light source wavelength range changing from ultraviolet to near infrared (266-1064 nm) relying on numerical light scattering experiments. Two different measurement ensembles are considered. Collection of well separated aggregates made up of same sized particles and that of having particle size distribution. Filippov's cluster-cluster algorithm is used to generate the aggregates and the light scattering behavior is calculated by discrete dipole approximation. A likelihood-free Approximate Bayesian Computation, relying on Adaptive Population Monte Carlo method, is used for characterization. It is found that when the wavelength range of 266-1064 nm is used, successful characterization limit changes from 21-62 nm effective radius for monodisperse and polydisperse soot aggregates.

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

PubMed

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

2009-11-01

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

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

PubMed

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

2017-01-01

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

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

PubMed

Norris, Dennis

2006-04-01

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

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.

Iterative updating of model error for Bayesian inversion

NASA Astrophysics Data System (ADS)

Calvetti, Daniela; Dunlop, Matthew; Somersalo, Erkki; Stuart, Andrew

2018-02-01

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when optimization algorithms are used to find a single estimate, or to speed up Markov chain Monte Carlo (MCMC) calculations in the Bayesian framework. The use of an approximate model introduces a discrepancy, or modeling error, that may have a detrimental effect on the solution of the ill-posed inverse problem, or it may severely distort the estimate of the posterior distribution. In the Bayesian paradigm, the modeling error can be considered as a random variable, and by using an estimate of the probability distribution of the unknown, one may estimate the probability distribution of the modeling error and incorporate it into the inversion. We introduce an algorithm which iterates this idea to update the distribution of the model error, leading to a sequence of posterior distributions that are demonstrated empirically to capture the underlying truth with increasing accuracy. Since the algorithm is not based on rejections, it requires only limited full model evaluations. We show analytically that, in the linear Gaussian case, the algorithm converges geometrically fast with respect to the number of iterations when the data is finite dimensional. For more general models, we introduce particle approximations of the iteratively generated sequence of distributions; we also prove that each element of the sequence converges in the large particle limit under a simplifying assumption. We show numerically that, as in the linear case, rapid convergence occurs with respect to the number of iterations. Additionally, we show through computed examples that point estimates obtained from this iterative algorithm are superior to those obtained by neglecting the model error.

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.

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.

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.

Bayesian methods in reliability

NASA Astrophysics Data System (ADS)

Sander, P.; Badoux, R.

1991-11-01

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

Bayesian Inference and Online Learning in Poisson Neuronal Networks.

PubMed

Huang, Yanping; Rao, Rajesh P N

2016-08-01

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

Model selection on solid ground: Rigorous comparison of nine ways to evaluate Bayesian model evidence

PubMed Central

Schöniger, Anneli; Wöhling, Thomas; Samaniego, Luis; Nowak, Wolfgang

2014-01-01

Bayesian model selection or averaging objectively ranks a number of plausible, competing conceptual models based on Bayes' theorem. It implicitly performs an optimal trade-off between performance in fitting available data and minimum model complexity. The procedure requires determining Bayesian model evidence (BME), which is the likelihood of the observed data integrated over each model's parameter space. The computation of this integral is highly challenging because it is as high-dimensional as the number of model parameters. Three classes of techniques to compute BME are available, each with its own challenges and limitations: (1) Exact and fast analytical solutions are limited by strong assumptions. (2) Numerical evaluation quickly becomes unfeasible for expensive models. (3) Approximations known as information criteria (ICs) such as the AIC, BIC, or KIC (Akaike, Bayesian, or Kashyap information criterion, respectively) yield contradicting results with regard to model ranking. Our study features a theory-based intercomparison of these techniques. We further assess their accuracy in a simplistic synthetic example where for some scenarios an exact analytical solution exists. In more challenging scenarios, we use a brute-force Monte Carlo integration method as reference. We continue this analysis with a real-world application of hydrological model selection. This is a first-time benchmarking of the various methods for BME evaluation against true solutions. Results show that BME values from ICs are often heavily biased and that the choice of approximation method substantially influences the accuracy of model ranking. For reliable model selection, bias-free numerical methods should be preferred over ICs whenever computationally feasible. PMID:25745272

al3c: high-performance software for parameter inference using Approximate Bayesian Computation.

PubMed

Stram, Alexander H; Marjoram, Paul; Chen, Gary K

2015-11-01

The development of Approximate Bayesian Computation (ABC) algorithms for parameter inference which are both computationally efficient and scalable in parallel computing environments is an important area of research. Monte Carlo rejection sampling, a fundamental component of ABC algorithms, is trivial to distribute over multiple processors but is inherently inefficient. While development of algorithms such as ABC Sequential Monte Carlo (ABC-SMC) help address the inherent inefficiencies of rejection sampling, such approaches are not as easily scaled on multiple processors. As a result, current Bayesian inference software offerings that use ABC-SMC lack the ability to scale in parallel computing environments. We present al3c, a C++ framework for implementing ABC-SMC in parallel. By requiring only that users define essential functions such as the simulation model and prior distribution function, al3c abstracts the user from both the complexities of parallel programming and the details of the ABC-SMC algorithm. By using the al3c framework, the user is able to scale the ABC-SMC algorithm in parallel computing environments for his or her specific application, with minimal programming overhead. al3c is offered as a static binary for Linux and OS-X computing environments. The user completes an XML configuration file and C++ plug-in template for the specific application, which are used by al3c to obtain the desired results. Users can download the static binaries, source code, reference documentation and examples (including those in this article) by visiting https://github.com/ahstram/al3c. astram@usc.edu Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation.

PubMed

Cornuet, Jean-Marie; Santos, Filipe; Beaumont, Mark A; Robert, Christian P; Marin, Jean-Michel; Balding, David J; Guillemaud, Thomas; Estoup, Arnaud

2008-12-01

Genetic data obtained on population samples convey information about their evolutionary history. Inference methods can extract part of this information but they require sophisticated statistical techniques that have been made available to the biologist community (through computer programs) only for simple and standard situations typically involving a small number of samples. We propose here a computer program (DIY ABC) for inference based on approximate Bayesian computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number of populations and samples. Such scenarios involve any combination of population divergences, admixtures and population size changes. DIY ABC can be used to compare competing scenarios, estimate parameters for one or more scenarios and compute bias and precision measures for a given scenario and known values of parameters (the current version applies to unlinked microsatellite data). This article describes key methods used in the program and provides its main features. The analysis of one simulated and one real dataset, both with complex evolutionary scenarios, illustrates the main possibilities of DIY ABC. The software DIY ABC is freely available at http://www.montpellier.inra.fr/CBGP/diyabc.

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

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

Marzouk, Youssef

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

Assessing system reliability and allocating resources: a bayesian approach that integrates multi-level data

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

Graves, Todd L; Hamada, Michael S

2008-01-01

Good estimates of the reliability of a system make use of test data and expert knowledge at all available levels. Furthermore, by integrating all these information sources, one can determine how best to allocate scarce testing resources to reduce uncertainty. Both of these goals are facilitated by modern Bayesian computational methods. We apply these tools to examples that were previously solvable only through the use of ingenious approximations, and use genetic algorithms to guide resource allocation.

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

PubMed Central

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

2017-01-01

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

Bayesian experimental design for models with intractable likelihoods.

PubMed

Drovandi, Christopher C; Pettitt, Anthony N

2013-12-01

In this paper we present a methodology for designing experiments for efficiently estimating the parameters of models with computationally intractable likelihoods. The approach combines a commonly used methodology for robust experimental design, based on Markov chain Monte Carlo sampling, with approximate Bayesian computation (ABC) to ensure that no likelihood evaluations are required. The utility function considered for precise parameter estimation is based upon the precision of the ABC posterior distribution, which we form efficiently via the ABC rejection algorithm based on pre-computed model simulations. Our focus is on stochastic models and, in particular, we investigate the methodology for Markov process models of epidemics and macroparasite population evolution. The macroparasite example involves a multivariate process and we assess the loss of information from not observing all variables. © 2013, The International Biometric Society.

Taking error into account when fitting models using Approximate Bayesian Computation.

PubMed

van der Vaart, Elske; Prangle, Dennis; Sibly, Richard M

2018-03-01

Stochastic computer simulations are often the only practical way of answering questions relating to ecological management. However, due to their complexity, such models are difficult to calibrate and evaluate. Approximate Bayesian Computation (ABC) offers an increasingly popular approach to this problem, widely applied across a variety of fields. However, ensuring the accuracy of ABC's estimates has been difficult. Here, we obtain more accurate estimates by incorporating estimation of error into the ABC protocol. We show how this can be done where the data consist of repeated measures of the same quantity and errors may be assumed to be normally distributed and independent. We then derive the correct acceptance probabilities for a probabilistic ABC algorithm, and update the coverage test with which accuracy is assessed. We apply this method, which we call error-calibrated ABC, to a toy example and a realistic 14-parameter simulation model of earthworms that is used in environmental risk assessment. A comparison with exact methods and the diagnostic coverage test show that our approach improves estimation of parameter values and their credible intervals for both models. © 2017 by the Ecological Society of America.

Hamiltonian Monte Carlo acceleration using surrogate functions with random bases.

PubMed

Zhang, Cheng; Shahbaba, Babak; Zhao, Hongkai

2017-11-01

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov chain Monte Carlo methods, namely, Hamiltonian Monte Carlo. The key idea is to explore and exploit the structure and regularity in parameter space for the underlying probabilistic model to construct an effective approximation of its geometric properties. To this end, we build a surrogate function to approximate the target distribution using properly chosen random bases and an efficient optimization process. The resulting method provides a flexible, scalable, and efficient sampling algorithm, which converges to the correct target distribution. We show that by choosing the basis functions and optimization process differently, our method can be related to other approaches for the construction of surrogate functions such as generalized additive models or Gaussian process models. Experiments based on simulated and real data show that our approach leads to substantially more efficient sampling algorithms compared to existing state-of-the-art methods.

Automating approximate Bayesian computation by local linear regression.

PubMed

Thornton, Kevin R

2009-07-07

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

A computer program for estimation from incomplete multinomial data

NASA Technical Reports Server (NTRS)

Credeur, K. R.

1978-01-01

Coding is given for maximum likelihood and Bayesian estimation of the vector p of multinomial cell probabilities from incomplete data. Also included is coding to calculate and approximate elements of the posterior mean and covariance matrices. The program is written in FORTRAN 4 language for the Control Data CYBER 170 series digital computer system with network operating system (NOS) 1.1. The program requires approximately 44000 octal locations of core storage. A typical case requires from 72 seconds to 92 seconds on CYBER 175 depending on the value of the prior parameter.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Low-rank separated representation surrogates of high-dimensional stochastic functions: Application in Bayesian inference

NASA Astrophysics Data System (ADS)

Validi, AbdoulAhad

2014-03-01

This study introduces a non-intrusive approach in the context of low-rank separated representation to construct a surrogate of high-dimensional stochastic functions, e.g., PDEs/ODEs, in order to decrease the computational cost of Markov Chain Monte Carlo simulations in Bayesian inference. The surrogate model is constructed via a regularized alternative least-square regression with Tikhonov regularization using a roughening matrix computing the gradient of the solution, in conjunction with a perturbation-based error indicator to detect optimal model complexities. The model approximates a vector of a continuous solution at discrete values of a physical variable. The required number of random realizations to achieve a successful approximation linearly depends on the function dimensionality. The computational cost of the model construction is quadratic in the number of random inputs, which potentially tackles the curse of dimensionality in high-dimensional stochastic functions. Furthermore, this vector-valued separated representation-based model, in comparison to the available scalar-valued case, leads to a significant reduction in the cost of approximation by an order of magnitude equal to the vector size. The performance of the method is studied through its application to three numerical examples including a 41-dimensional elliptic PDE and a 21-dimensional cavity flow.

Exemplar Models as a Mechanism for Performing Bayesian Inference

DTIC Science & Technology

2010-01-01

Feldman Department of Cognitive and Linguistic Sciences Brown University Adam N. Sanborn Gatsby Computational Neuroscience Unit University College London...problem. As noted above, particle filters are another instance of a rational process model, but the great diversity of efficient approximation algorithms

Identification of transmissivity fields using a Bayesian strategy and perturbative approach

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Decentralized Bayesian search using approximate dynamic programming methods.

PubMed

Zhao, Yijia; Patek, Stephen D; Beling, Peter A

2008-08-01

We consider decentralized Bayesian search problems that involve a team of multiple autonomous agents searching for targets on a network of search points operating under the following constraints: 1) interagent communication is limited; 2) the agents do not have the opportunity to agree in advance on how to resolve equivalent but incompatible strategies; and 3) each agent lacks the ability to control or predict with certainty the actions of the other agents. We formulate the multiagent search-path-planning problem as a decentralized optimal control problem and introduce approximate dynamic heuristics that can be implemented in a decentralized fashion. After establishing some analytical properties of the heuristics, we present computational results for a search problem involving two agents on a 5 x 5 grid.

Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation

PubMed Central

Cornuet, Jean-Marie; Santos, Filipe; Beaumont, Mark A.; Robert, Christian P.; Marin, Jean-Michel; Balding, David J.; Guillemaud, Thomas; Estoup, Arnaud

2008-01-01

Summary: Genetic data obtained on population samples convey information about their evolutionary history. Inference methods can extract part of this information but they require sophisticated statistical techniques that have been made available to the biologist community (through computer programs) only for simple and standard situations typically involving a small number of samples. We propose here a computer program (DIY ABC) for inference based on approximate Bayesian computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number of populations and samples. Such scenarios involve any combination of population divergences, admixtures and population size changes. DIY ABC can be used to compare competing scenarios, estimate parameters for one or more scenarios and compute bias and precision measures for a given scenario and known values of parameters (the current version applies to unlinked microsatellite data). This article describes key methods used in the program and provides its main features. The analysis of one simulated and one real dataset, both with complex evolutionary scenarios, illustrates the main possibilities of DIY ABC. Availability: The software DIY ABC is freely available at http://www.montpellier.inra.fr/CBGP/diyabc. Contact: j.cornuet@imperial.ac.uk Supplementary information: Supplementary data are also available at http://www.montpellier.inra.fr/CBGP/diyabc PMID:18842597

Initialization and Restart in Stochastic Local Search: Computing a Most Probable Explanation in Bayesian Networks

NASA Technical Reports Server (NTRS)

Mengshoel, Ole J.; Wilkins, David C.; Roth, Dan

2010-01-01

For hard computational problems, stochastic local search has proven to be a competitive approach to finding optimal or approximately optimal problem solutions. Two key research questions for stochastic local search algorithms are: Which algorithms are effective for initialization? When should the search process be restarted? In the present work we investigate these research questions in the context of approximate computation of most probable explanations (MPEs) in Bayesian networks (BNs). We introduce a novel approach, based on the Viterbi algorithm, to explanation initialization in BNs. While the Viterbi algorithm works on sequences and trees, our approach works on BNs with arbitrary topologies. We also give a novel formalization of stochastic local search, with focus on initialization and restart, using probability theory and mixture models. Experimentally, we apply our methods to the problem of MPE computation, using a stochastic local search algorithm known as Stochastic Greedy Search. By carefully optimizing both initialization and restart, we reduce the MPE search time for application BNs by several orders of magnitude compared to using uniform at random initialization without restart. On several BNs from applications, the performance of Stochastic Greedy Search is competitive with clique tree clustering, a state-of-the-art exact algorithm used for MPE computation in BNs.

Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain

NASA Astrophysics Data System (ADS)

Beck, Joakim; Dia, Ben Mansour; Espath, Luis F. R.; Long, Quan; Tempone, Raúl

2018-06-01

In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. These drawbacks can be avoided by using an importance sampling approach. We present a computationally efficient method for optimal Bayesian experimental design that introduces importance sampling based on the Laplace method to the inner loop. We derive the optimal values for the method parameters in which the average computational cost is minimized according to the desired error tolerance. We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a more recent single-loop Monte Carlo method that uses the Laplace method as an approximation of the return value of the inner loop. The first example is a scalar problem that is linear in the uncertain parameter. The second example is a nonlinear scalar problem. The third example deals with the optimal sensor placement for an electrical impedance tomography experiment to recover the fiber orientation in laminate composites.

Parameter Estimation for a Pulsating Turbulent Buoyant Jet Using Approximate Bayesian Computation

NASA Astrophysics Data System (ADS)

Christopher, Jason; Wimer, Nicholas; Lapointe, Caelan; Hayden, Torrey; Grooms, Ian; Rieker, Greg; Hamlington, Peter

2017-11-01

Approximate Bayesian Computation (ABC) is a powerful tool that allows sparse experimental or other ``truth'' data to be used for the prediction of unknown parameters, such as flow properties and boundary conditions, in numerical simulations of real-world engineering systems. Here we introduce the ABC approach and then use ABC to predict unknown inflow conditions in simulations of a two-dimensional (2D) turbulent, high-temperature buoyant jet. For this test case, truth data are obtained from a direct numerical simulation (DNS) with known boundary conditions and problem parameters, while the ABC procedure utilizes lower fidelity large eddy simulations. Using spatially-sparse statistics from the 2D buoyant jet DNS, we show that the ABC method provides accurate predictions of true jet inflow parameters. The success of the ABC approach in the present test suggests that ABC is a useful and versatile tool for predicting flow information, such as boundary conditions, that can be difficult to determine experimentally.

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.

Kernel-density estimation and approximate Bayesian computation for flexible epidemiological model fitting in Python.

PubMed

Irvine, Michael A; Hollingsworth, T Déirdre

2018-05-26

Fitting complex models to epidemiological data is a challenging problem: methodologies can be inaccessible to all but specialists, there may be challenges in adequately describing uncertainty in model fitting, the complex models may take a long time to run, and it can be difficult to fully capture the heterogeneity in the data. We develop an adaptive approximate Bayesian computation scheme to fit a variety of epidemiologically relevant data with minimal hyper-parameter tuning by using an adaptive tolerance scheme. We implement a novel kernel density estimation scheme to capture both dispersed and multi-dimensional data, and directly compare this technique to standard Bayesian approaches. We then apply the procedure to a complex individual-based simulation of lymphatic filariasis, a human parasitic disease. The procedure and examples are released alongside this article as an open access library, with examples to aid researchers to rapidly fit models to data. This demonstrates that an adaptive ABC scheme with a general summary and distance metric is capable of performing model fitting for a variety of epidemiological data. It also does not require significant theoretical background to use and can be made accessible to the diverse epidemiological research community. Copyright © 2018 The Authors. Published by Elsevier B.V. All rights reserved.

Formalizing Neurath's ship: Approximate algorithms for online causal learning.

PubMed

Bramley, Neil R; Dayan, Peter; Griffiths, Thomas L; Lagnado, David A

2017-04-01

Higher-level cognition depends on the ability to learn models of the world. We can characterize this at the computational level as a structure-learning problem with the goal of best identifying the prevailing causal relationships among a set of relata. However, the computational cost of performing exact Bayesian inference over causal models grows rapidly as the number of relata increases. This implies that the cognitive processes underlying causal learning must be substantially approximate. A powerful class of approximations that focuses on the sequential absorption of successive inputs is captured by the Neurath's ship metaphor in philosophy of science, where theory change is cast as a stochastic and gradual process shaped as much by people's limited willingness to abandon their current theory when considering alternatives as by the ground truth they hope to approach. Inspired by this metaphor and by algorithms for approximating Bayesian inference in machine learning, we propose an algorithmic-level model of causal structure learning under which learners represent only a single global hypothesis that they update locally as they gather evidence. We propose a related scheme for understanding how, under these limitations, learners choose informative interventions that manipulate the causal system to help elucidate its workings. We find support for our approach in the analysis of 3 experiments. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

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.

A Gaussian Approximation Approach for Value of Information Analysis.

PubMed

Jalal, Hawre; Alarid-Escudero, Fernando

2018-02-01

Most decisions are associated with uncertainty. Value of information (VOI) analysis quantifies the opportunity loss associated with choosing a suboptimal intervention based on current imperfect information. VOI can inform the value of collecting additional information, resource allocation, research prioritization, and future research designs. However, in practice, VOI remains underused due to many conceptual and computational challenges associated with its application. Expected value of sample information (EVSI) is rooted in Bayesian statistical decision theory and measures the value of information from a finite sample. The past few years have witnessed a dramatic growth in computationally efficient methods to calculate EVSI, including metamodeling. However, little research has been done to simplify the experimental data collection step inherent to all EVSI computations, especially for correlated model parameters. This article proposes a general Gaussian approximation (GA) of the traditional Bayesian updating approach based on the original work by Raiffa and Schlaifer to compute EVSI. The proposed approach uses a single probabilistic sensitivity analysis (PSA) data set and involves 2 steps: 1) a linear metamodel step to compute the EVSI on the preposterior distributions and 2) a GA step to compute the preposterior distribution of the parameters of interest. The proposed approach is efficient and can be applied for a wide range of data collection designs involving multiple non-Gaussian parameters and unbalanced study designs. Our approach is particularly useful when the parameters of an economic evaluation are correlated or interact.

Complementarity of statistical treatments to reconstruct worldwide routes of invasion: The case of the Asian ladybird Harmonia axyridis

USDA-ARS?s Scientific Manuscript database

Technical Abstract. Molecular markers can provide clear insight into the introduction history of invasive species. However, inferences about recent introduction histories remain challenging, because of the stochastic demographic processes often involved. Approximate Bayesian computation (ABC) can he...

Using Approximate Bayesian Computation to Probe Multiple Transiting Planet Systems

NASA Astrophysics Data System (ADS)

Morehead, Robert C.

2015-08-01

The large number of multiple transiting planet systems (MTPS) uncovered with Kepler suggest a population of well-aligned planetary systems. Previously, the distribution of transit duration ratios in MTPSs has been used to place constraints on the distributions of mutual orbital inclinations and orbital eccentricities in these systems. However, degeneracies with the underlying number of planets in these systems pose added challenges and make explicit likelihood functions intractable. Approximate Bayesian computation (ABC) offers an intriguing path forward. In its simplest form, ABC proposes from a prior on the population parameters to produce synthetic datasets via a physically-motivated model. Samples are accepted or rejected based on how close they come to reproducing the actual observed dataset to some tolerance. The accepted samples then form a robust and useful approximation of the true posterior distribution of the underlying population parameters. We will demonstrate the utility of ABC in exoplanet populations by presenting new constraints on the mutual inclination and eccentricity distributions in the Kepler MTPSs. We will also introduce Simple-ABC, a new open-source Python package designed for ease of use and rapid specification of general models, suitable for use in a wide variety of applications in both exoplanet science and astrophysics as a whole.

Statistical Surrogate Modeling of Atmospheric Dispersion Events Using Bayesian Adaptive Splines

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

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

PubMed

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

2017-11-14

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

Bayesian 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.

Asymptotic Normality of Poly-T Densities with Bayesian Applications.

DTIC Science & Technology

1987-10-01

be extended to the case of many t-like factors in a straightforward manner. Obviously, the computational complexity will increase rapidly as the number...York: Marcel-Dekker. Broemeling, L.D. and Abdullah, M.Y. (1984). An approximation to the poly-t distribution. Communciations in Statistics A,11, 1407...Street Center Champaign, IL 61820 Austin, TX 78703 Dr. Steven Hunks Dr. James Krantz Department of Education Computer -based Education University of

a Novel Discrete Optimal Transport Method for Bayesian Inverse Problems

NASA Astrophysics Data System (ADS)

Bui-Thanh, T.; Myers, A.; Wang, K.; Thiery, A.

2017-12-01

We present the Augmented Ensemble Transform (AET) method for generating approximate samples from a high-dimensional posterior distribution as a solution to Bayesian inverse problems. Solving large-scale inverse problems is critical for some of the most relevant and impactful scientific endeavors of our time. Therefore, constructing novel methods for solving the Bayesian inverse problem in more computationally efficient ways can have a profound impact on the science community. This research derives the novel AET method for exploring a posterior by solving a sequence of linear programming problems, resulting in a series of transport maps which map prior samples to posterior samples, allowing for the computation of moments of the posterior. We show both theoretical and numerical results, indicating this method can offer superior computational efficiency when compared to other SMC methods. Most of this efficiency is derived from matrix scaling methods to solve the linear programming problem and derivative-free optimization for particle movement. We use this method to determine inter-well connectivity in a reservoir and the associated uncertainty related to certain parameters. The attached file shows the difference between the true parameter and the AET parameter in an example 3D reservoir problem. The error is within the Morozov discrepancy allowance with lower computational cost than other particle methods.

How Recent History Affects Perception: The Normative Approach and Its Heuristic Approximation

PubMed Central

Raviv, Ofri; Ahissar, Merav; Loewenstein, Yonatan

2012-01-01

There is accumulating evidence that prior knowledge about expectations plays an important role in perception. The Bayesian framework is the standard computational approach to explain how prior knowledge about the distribution of expected stimuli is incorporated with noisy observations in order to improve performance. However, it is unclear what information about the prior distribution is acquired by the perceptual system over short periods of time and how this information is utilized in the process of perceptual decision making. Here we address this question using a simple two-tone discrimination task. We find that the “contraction bias”, in which small magnitudes are overestimated and large magnitudes are underestimated, dominates the pattern of responses of human participants. This contraction bias is consistent with the Bayesian hypothesis in which the true prior information is available to the decision-maker. However, a trial-by-trial analysis of the pattern of responses reveals that the contribution of most recent trials to performance is overweighted compared with the predictions of a standard Bayesian model. Moreover, we study participants' performance in a-typical distributions of stimuli and demonstrate substantial deviations from the ideal Bayesian detector, suggesting that the brain utilizes a heuristic approximation of the Bayesian inference. We propose a biologically plausible model, in which decision in the two-tone discrimination task is based on a comparison between the second tone and an exponentially-decaying average of the first tone and past tones. We show that this model accounts for both the contraction bias and the deviations from the ideal Bayesian detector hypothesis. These findings demonstrate the power of Bayesian-like heuristics in the brain, as well as their limitations in their failure to fully adapt to novel environments. PMID:23133343

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.

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.

Of bits and wows: A Bayesian theory of surprise with applications to attention.

PubMed

Baldi, Pierre; Itti, Laurent

2010-06-01

The amount of information contained in a piece of data can be measured by the effect this data has on its observer. Fundamentally, this effect is to transform the observer's prior beliefs into posterior beliefs, according to Bayes theorem. Thus the amount of information can be measured in a natural way by the distance (relative entropy) between the prior and posterior distributions of the observer over the available space of hypotheses. This facet of information, termed "surprise", is important in dynamic situations where beliefs change, in particular during learning and adaptation. Surprise can often be computed analytically, for instance in the case of distributions from the exponential family, or it can be numerically approximated. During sequential Bayesian learning, surprise decreases as the inverse of the number of training examples. Theoretical properties of surprise are discussed, in particular how it differs and complements Shannon's definition of information. A computer vision neural network architecture is then presented capable of computing surprise over images and video stimuli. Hypothesizing that surprising data ought to attract natural or artificial attention systems, the output of this architecture is used in a psychophysical experiment to analyze human eye movements in the presence of natural video stimuli. Surprise is found to yield robust performance at predicting human gaze (ROC-like ordinal dominance score approximately 0.7 compared to approximately 0.8 for human inter-observer repeatability, approximately 0.6 for simpler intensity contrast-based predictor, and 0.5 for chance). The resulting theory of surprise is applicable across different spatio-temporal scales, modalities, and levels of abstraction. Copyright 2010 Elsevier Ltd. All rights reserved.

Efficient Posterior Probability Mapping Using Savage-Dickey Ratios

PubMed Central

Penny, William D.; Ridgway, Gerard R.

2013-01-01

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

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.

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

NASA Astrophysics Data System (ADS)

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

2013-10-01

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

Invasion and transmission of Salmonella Kentucky in an adult dairy herd using approximate Bayesian computation

USDA-ARS?s Scientific Manuscript database

An outbreak of Salmonella Kentucky followed by a high level of sustained endemic prevalence was recently observed in a US adult dairy herd enrolled in a longitudinal study involving intensive fecal sampling. To understand the invasion ability and transmission dynamics of Salmonella Kentucky in dairy...

Specialist and generalist symbionts show counterintuitive levels of genetic diversity and discordant demographic histories along the Florida Reef Tract

NASA Astrophysics Data System (ADS)

Titus, Benjamin M.; Daly, Marymegan

2017-03-01

Specialist and generalist life histories are expected to result in contrasting levels of genetic diversity at the population level, and symbioses are expected to lead to patterns that reflect a shared biogeographic history and co-diversification. We test these assumptions using mtDNA sequencing and a comparative phylogeographic approach for six co-occurring crustacean species that are symbiotic with sea anemones on western Atlantic coral reefs, yet vary in their host specificities: four are host specialists and two are host generalists. We first conducted species discovery analyses to delimit cryptic lineages, followed by classic population genetic diversity analyses for each delimited taxon, and then reconstructed the demographic history for each taxon using traditional summary statistics, Bayesian skyline plots, and approximate Bayesian computation to test for signatures of recent and concerted population expansion. The genetic diversity values recovered here contravene the expectations of the specialist-generalist variation hypothesis and classic population genetics theory; all specialist lineages had greater genetic diversity than generalists. Demography suggests recent population expansions in all taxa, although Bayesian skyline plots and approximate Bayesian computation suggest the timing and magnitude of these events were idiosyncratic. These results do not meet the a priori expectation of concordance among symbiotic taxa and suggest that intrinsic aspects of species biology may contribute more to phylogeographic history than extrinsic forces that shape whole communities. The recovery of two cryptic specialist lineages adds an additional layer of biodiversity to this symbiosis and contributes to an emerging pattern of cryptic speciation in the specialist taxa. Our results underscore the differences in the evolutionary processes acting on marine systems from the terrestrial processes that often drive theory. Finally, we continue to highlight the Florida Reef Tract as an important biodiversity hotspot.

Inference of reaction rate parameters based on summary statistics from experiments

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

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

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

Inference of reaction rate parameters based on summary statistics from experiments

DOE PAGES

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

2016-10-15

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

Bayesian cross-validation for model evaluation and selection, with application to the North American Breeding Bird Survey

USGS Publications Warehouse

Link, William; Sauer, John R.

2016-01-01

The analysis of ecological data has changed in two important ways over the last 15 years. The development and easy availability of Bayesian computational methods has allowed and encouraged the fitting of complex hierarchical models. At the same time, there has been increasing emphasis on acknowledging and accounting for model uncertainty. Unfortunately, the ability to fit complex models has outstripped the development of tools for model selection and model evaluation: familiar model selection tools such as Akaike's information criterion and the deviance information criterion are widely known to be inadequate for hierarchical models. In addition, little attention has been paid to the evaluation of model adequacy in context of hierarchical modeling, i.e., to the evaluation of fit for a single model. In this paper, we describe Bayesian cross-validation, which provides tools for model selection and evaluation. We describe the Bayesian predictive information criterion and a Bayesian approximation to the BPIC known as the Watanabe-Akaike information criterion. We illustrate the use of these tools for model selection, and the use of Bayesian cross-validation as a tool for model evaluation, using three large data sets from the North American Breeding Bird Survey.

Variational Gaussian approximation for Poisson data

NASA Astrophysics Data System (ADS)

Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

2018-02-01

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

Approximate, computationally efficient online learning in Bayesian spiking neurons.

PubMed

Kuhlmann, Levin; Hauser-Raspe, Michael; Manton, Jonathan H; Grayden, David B; Tapson, Jonathan; van Schaik, André

2014-03-01

Bayesian spiking neurons (BSNs) provide a probabilistic interpretation of how neurons perform inference and learning. Online learning in BSNs typically involves parameter estimation based on maximum-likelihood expectation-maximization (ML-EM) which is computationally slow and limits the potential of studying networks of BSNs. An online learning algorithm, fast learning (FL), is presented that is more computationally efficient than the benchmark ML-EM for a fixed number of time steps as the number of inputs to a BSN increases (e.g., 16.5 times faster run times for 20 inputs). Although ML-EM appears to converge 2.0 to 3.6 times faster than FL, the computational cost of ML-EM means that ML-EM takes longer to simulate to convergence than FL. FL also provides reasonable convergence performance that is robust to initialization of parameter estimates that are far from the true parameter values. However, parameter estimation depends on the range of true parameter values. Nevertheless, for a physiologically meaningful range of parameter values, FL gives very good average estimation accuracy, despite its approximate nature. The FL algorithm therefore provides an efficient tool, complementary to ML-EM, for exploring BSN networks in more detail in order to better understand their biological relevance. Moreover, the simplicity of the FL algorithm means it can be easily implemented in neuromorphic VLSI such that one can take advantage of the energy-efficient spike coding of BSNs.

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

PubMed

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

2013-05-01

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

The discounting model selector: Statistical software for delay discounting applications.

PubMed

Gilroy, Shawn P; Franck, Christopher T; Hantula, Donald A

2017-05-01

Original, open-source computer software was developed and validated against established delay discounting methods in the literature. The software executed approximate Bayesian model selection methods from user-supplied temporal discounting data and computed the effective delay 50 (ED50) from the best performing model. Software was custom-designed to enable behavior analysts to conveniently apply recent statistical methods to temporal discounting data with the aid of a graphical user interface (GUI). The results of independent validation of the approximate Bayesian model selection methods indicated that the program provided results identical to that of the original source paper and its methods. Monte Carlo simulation (n = 50,000) confirmed that true model was selected most often in each setting. Simulation code and data for this study were posted to an online repository for use by other researchers. The model selection approach was applied to three existing delay discounting data sets from the literature in addition to the data from the source paper. Comparisons of model selected ED50 were consistent with traditional indices of discounting. Conceptual issues related to the development and use of computer software by behavior analysts and the opportunities afforded by free and open-sourced software are discussed and a review of possible expansions of this software are provided. © 2017 Society for the Experimental Analysis of Behavior.

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

PubMed Central

Liu, Yihai

2018-01-01

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

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.

Inferring the origin of populations introduced from a genetically structured native range by approximate Bayesian computation: case study of the invasive ladybird Harmonia axyridis

USDA-ARS?s Scientific Manuscript database

The correct identification of the source population of an invasive species is a prerequisite for defining and testing different hypotheses concerning the environmental and evolutionary factors responsible for biological invasions. The native area of invasive species may be large, barely known and/or...

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

NASA Technical Reports Server (NTRS)

Mengshoel, Ole J.

2010-01-01

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

Evolution of the cerebellum as a neuronal machine for Bayesian state estimation

NASA Astrophysics Data System (ADS)

Paulin, M. G.

2005-09-01

The cerebellum evolved in association with the electric sense and vestibular sense of the earliest vertebrates. Accurate information provided by these sensory systems would have been essential for precise control of orienting behavior in predation. A simple model shows that individual spikes in electrosensory primary afferent neurons can be interpreted as measurements of prey location. Using this result, I construct a computational neural model in which the spatial distribution of spikes in a secondary electrosensory map forms a Monte Carlo approximation to the Bayesian posterior distribution of prey locations given the sense data. The neural circuit that emerges naturally to perform this task resembles the cerebellar-like hindbrain electrosensory filtering circuitry of sharks and other electrosensory vertebrates. The optimal filtering mechanism can be extended to handle dynamical targets observed from a dynamical platform; that is, to construct an optimal dynamical state estimator using spiking neurons. This may provide a generic model of cerebellar computation. Vertebrate motion-sensing neurons have specific fractional-order dynamical characteristics that allow Bayesian state estimators to be implemented elegantly and efficiently, using simple operations with asynchronous pulses, i.e. spikes. The computational neural models described in this paper represent a novel kind of particle filter, using spikes as particles. The models are specific and make testable predictions about computational mechanisms in cerebellar circuitry, while providing a plausible explanation of cerebellar contributions to aspects of motor control, perception and cognition.

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

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.

Comparing hierarchical models via the marginalized deviance information criterion.

PubMed

Quintero, Adrian; Lesaffre, Emmanuel

2018-07-20

Hierarchical models are extensively used in pharmacokinetics and longitudinal studies. When the estimation is performed from a Bayesian approach, model comparison is often based on the deviance information criterion (DIC). In hierarchical models with latent variables, there are several versions of this statistic: the conditional DIC (cDIC) that incorporates the latent variables in the focus of the analysis and the marginalized DIC (mDIC) that integrates them out. Regardless of the asymptotic and coherency difficulties of cDIC, this alternative is usually used in Markov chain Monte Carlo (MCMC) methods for hierarchical models because of practical convenience. The mDIC criterion is more appropriate in most cases but requires integration of the likelihood, which is computationally demanding and not implemented in Bayesian software. Therefore, we consider a method to compute mDIC by generating replicate samples of the latent variables that need to be integrated out. This alternative can be easily conducted from the MCMC output of Bayesian packages and is widely applicable to hierarchical models in general. Additionally, we propose some approximations in order to reduce the computational complexity for large-sample situations. The method is illustrated with simulated data sets and 2 medical studies, evidencing that cDIC may be misleading whilst mDIC appears pertinent. Copyright © 2018 John Wiley & Sons, Ltd.

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

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

NASA Technical Reports Server (NTRS)

Mengshoel, Ole Jakob

2009-01-01

Bayesian networks (BNs) are used to represent and efficiently compute with multi-variate probability distributions in a wide range of disciplines. One of the main approaches to perform computation in BNs is clique tree clustering and propagation. In this approach, BN computation consists of propagation in a clique tree compiled from a Bayesian network. There is a lack of understanding of how clique tree computation time, and BN computation time in more general, depends on variations in BN size and structure. On the one hand, complexity results tell us that many interesting BN queries are NP-hard or worse to answer, and it is not hard to find application BNs where the clique tree approach in practice cannot be used. On the other hand, it is well-known that tree-structured BNs can be used to answer probabilistic queries in polynomial time. In this article, we develop an approach to characterizing clique tree growth as a function of parameters that can be computed in polynomial time from BNs, specifically: (i) the ratio of the number of a BN's non-root nodes to the number of root nodes, or (ii) the expected number of moral edges in their moral graphs. Our approach is based on combining analytical and experimental results. Analytically, we partition the set of cliques in a clique tree into different sets, and introduce a growth curve for each set. For the special case of bipartite BNs, we consequently have two growth curves, a mixed clique growth curve and a root clique growth curve. In experiments, we systematically increase the degree of the root nodes in bipartite Bayesian networks, and find that root clique growth is well-approximated by Gompertz growth curves. It is believed that this research improves the understanding of the scaling behavior of clique tree clustering, provides a foundation for benchmarking and developing improved BN inference and machine learning algorithms, and presents an aid for analytical trade-off studies of clique tree clustering using growth curves.

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.

Application of Bayesian Reliability Concepts to Cruise Missile Electronic Components

DTIC Science & Technology

1989-09-01

and contrast them with the more prevalent classical inference view. 3 II. literature Review Introduction This literature review will consider current ...events on the basis of whatever evidence is currently available. Then if additional evidence is subsequently obtained, the initial probabilities are...Chay contends there is no longer any need to approximate continuous prior distributions through discretization because current computer calculations

Confidence Intervals for the Between-Study Variance in Random Effects Meta-Analysis Using Generalised Cochran Heterogeneity Statistics

ERIC Educational Resources Information Center

Jackson, Dan

2013-01-01

Statistical inference is problematic in the common situation in meta-analysis where the random effects model is fitted to just a handful of studies. In particular, the asymptotic theory of maximum likelihood provides a poor approximation, and Bayesian methods are sensitive to the prior specification. Hence, less efficient, but easily computed and…

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

PubMed

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

2014-03-01

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

Dynamics of attentional selection under conflict: toward a rational Bayesian account.

PubMed

Yu, Angela J; Dayan, Peter; Cohen, Jonathan D

2009-06-01

The brain exhibits remarkable facility in exerting attentional control in most circumstances, but it also suffers apparent limitations in others. The authors' goal is to construct a rational account for why attentional control appears suboptimal under conditions of conflict and what this implies about the underlying computational principles. The formal framework used is based on Bayesian probability theory, which provides a convenient language for delineating the rationale and dynamics of attentional selection. The authors illustrate these issues with the Eriksen flanker task, a classical paradigm that explores the effects of competing sensory inputs on response tendencies. The authors show how 2 distinctly formulated models, based on compatibility bias and spatial uncertainty principles, can account for the behavioral data. They also suggest novel experiments that may differentiate these models. In addition, they elaborate a simplified model that approximates optimal computation and may map more directly onto the underlying neural machinery. This approximate model uses conflict monitoring, putatively mediated by the anterior cingulate cortex, as a proxy for compatibility representation. The authors also consider how this conflict information might be disseminated and used to control processing. (c) 2009 APA, all rights reserved.

Bayesian Ising approximation for learning dictionaries of multispike timing patterns in premotor neurons

NASA Astrophysics Data System (ADS)

Hernandez Lahme, Damian; Sober, Samuel; Nemenman, Ilya

Important questions in computational neuroscience are whether, how much, and how information is encoded in the precise timing of neural action potentials. We recently demonstrated that, in the premotor cortex during vocal control in songbirds, spike timing is far more informative about upcoming behavior than is spike rate (Tang et al, 2014). However, identification of complete dictionaries that relate spike timing patterns with the controled behavior remains an elusive problem. Here we present a computational approach to deciphering such codes for individual neurons in the songbird premotor area RA, an analog of mammalian primary motor cortex. Specifically, we analyze which multispike patterns of neural activity predict features of the upcoming vocalization, and hence are important codewords. We use a recently introduced Bayesian Ising Approximation, which properly accounts for the fact that many codewords overlap and hence are not independent. Our results show which complex, temporally precise multispike combinations are used by individual neurons to control acoustic features of the produced song, and that these code words are different across individual neurons and across different acoustic features. This work was supported, in part, by JSMF Grant 220020321, NSF Grant 1208126, NIH Grant NS084844 and NIH Grant 1 R01 EB022872.

Architectures of Kepler Planet Systems with Approximate Bayesian Computation

NASA Astrophysics Data System (ADS)

Morehead, Robert C.; Ford, Eric B.

2015-12-01

The distribution of period normalized transit duration ratios among Kepler’s multiple transiting planet systems constrains the distributions of mutual orbital inclinations and orbital eccentricities. However, degeneracies in these parameters tied to the underlying number of planets in these systems complicate their interpretation. To untangle the true architecture of planet systems, the mutual inclination, eccentricity, and underlying planet number distributions must be considered simultaneously. The complexities of target selection, transit probability, detection biases, vetting, and follow-up observations make it impractical to write an explicit likelihood function. Approximate Bayesian computation (ABC) offers an intriguing path forward. In its simplest form, ABC generates a sample of trial population parameters from a prior distribution to produce synthetic datasets via a physically-motivated forward model. Samples are then accepted or rejected based on how close they come to reproducing the actual observed dataset to some tolerance. The accepted samples form a robust and useful approximation of the true posterior distribution of the underlying population parameters. We build on the considerable progress from the field of statistics to develop sequential algorithms for performing ABC in an efficient and flexible manner. We demonstrate the utility of ABC in exoplanet populations and present new constraints on the distributions of mutual orbital inclinations, eccentricities, and the relative number of short-period planets per star. We conclude with a discussion of the implications for other planet occurrence rate calculations, such as eta-Earth.

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.

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.

Bayesian Peak Picking for NMR Spectra

PubMed Central

Cheng, Yichen; Gao, Xin; Liang, Faming

2013-01-01

Protein structure determination is a very important topic in structural genomics, which helps people to understand varieties of biological functions such as protein-protein interactions, protein–DNA interactions and so on. Nowadays, nuclear magnetic resonance (NMR) has often been used to determine the three-dimensional structures of protein in vivo. This study aims to automate the peak picking step, the most important and tricky step in NMR structure determination. We propose to model the NMR spectrum by a mixture of bivariate Gaussian densities and use the stochastic approximation Monte Carlo algorithm as the computational tool to solve the problem. Under the Bayesian framework, the peak picking problem is casted as a variable selection problem. The proposed method can automatically distinguish true peaks from false ones without preprocessing the data. To the best of our knowledge, this is the first effort in the literature that tackles the peak picking problem for NMR spectrum data using Bayesian method. PMID:24184964

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

Modelling Trial-by-Trial Changes in the Mismatch Negativity

PubMed Central

Lieder, Falk; Daunizeau, Jean; Garrido, Marta I.; Friston, Karl J.; Stephan, Klaas E.

2013-01-01

The mismatch negativity (MMN) is a differential brain response to violations of learned regularities. It has been used to demonstrate that the brain learns the statistical structure of its environment and predicts future sensory inputs. However, the algorithmic nature of these computations and the underlying neurobiological implementation remain controversial. This article introduces a mathematical framework with which competing ideas about the computational quantities indexed by MMN responses can be formalized and tested against single-trial EEG data. This framework was applied to five major theories of the MMN, comparing their ability to explain trial-by-trial changes in MMN amplitude. Three of these theories (predictive coding, model adjustment, and novelty detection) were formalized by linking the MMN to different manifestations of the same computational mechanism: approximate Bayesian inference according to the free-energy principle. We thereby propose a unifying view on three distinct theories of the MMN. The relative plausibility of each theory was assessed against empirical single-trial MMN amplitudes acquired from eight healthy volunteers in a roving oddball experiment. Models based on the free-energy principle provided more plausible explanations of trial-by-trial changes in MMN amplitude than models representing the two more traditional theories (change detection and adaptation). Our results suggest that the MMN reflects approximate Bayesian learning of sensory regularities, and that the MMN-generating process adjusts a probabilistic model of the environment according to prediction errors. PMID:23436989

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

NASA Astrophysics Data System (ADS)

Davis, A. D.

2015-12-01

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

Improving the Accuracy of Planet Occurrence Rates from Kepler Using Approximate Bayesian Computation

NASA Astrophysics Data System (ADS)

Hsu, Danley C.; Ford, Eric B.; Ragozzine, Darin; Morehead, Robert C.

2018-05-01

We present a new framework to characterize the occurrence rates of planet candidates identified by Kepler based on hierarchical Bayesian modeling, approximate Bayesian computing (ABC), and sequential importance sampling. For this study, we adopt a simple 2D grid in planet radius and orbital period as our model and apply our algorithm to estimate occurrence rates for Q1–Q16 planet candidates orbiting solar-type stars. We arrive at significantly increased planet occurrence rates for small planet candidates (R p < 1.25 R ⊕) at larger orbital periods (P > 80 day) compared to the rates estimated by the more common inverse detection efficiency method (IDEM). Our improved methodology estimates that the occurrence rate density of small planet candidates in the habitable zone of solar-type stars is {1.6}-0.5+1.2 per factor of 2 in planet radius and orbital period. Additionally, we observe a local minimum in the occurrence rate for strong planet candidates marginalized over orbital period between 1.5 and 2 R ⊕ that is consistent with previous studies. For future improvements, the forward modeling approach of ABC is ideally suited to incorporating multiple populations, such as planets, astrophysical false positives, and pipeline false alarms, to provide accurate planet occurrence rates and uncertainties. Furthermore, ABC provides a practical statistical framework for answering complex questions (e.g., frequency of different planetary architectures) and providing sound uncertainties, even in the face of complex selection effects, observational biases, and follow-up strategies. In summary, ABC offers a powerful tool for accurately characterizing a wide variety of astrophysical populations.

Simulation-based estimation of mean and standard deviation for meta-analysis via Approximate Bayesian Computation (ABC).

PubMed

Kwon, Deukwoo; Reis, Isildinha M

2015-08-12

When conducting a meta-analysis of a continuous outcome, estimated means and standard deviations from the selected studies are required in order to obtain an overall estimate of the mean effect and its confidence interval. If these quantities are not directly reported in the publications, they must be estimated from other reported summary statistics, such as the median, the minimum, the maximum, and quartiles. We propose a simulation-based estimation approach using the Approximate Bayesian Computation (ABC) technique for estimating mean and standard deviation based on various sets of summary statistics found in published studies. We conduct a simulation study to compare the proposed ABC method with the existing methods of Hozo et al. (2005), Bland (2015), and Wan et al. (2014). In the estimation of the standard deviation, our ABC method performs better than the other methods when data are generated from skewed or heavy-tailed distributions. The corresponding average relative error (ARE) approaches zero as sample size increases. In data generated from the normal distribution, our ABC performs well. However, the Wan et al. method is best for estimating standard deviation under normal distribution. In the estimation of the mean, our ABC method is best regardless of assumed distribution. ABC is a flexible method for estimating the study-specific mean and standard deviation for meta-analysis, especially with underlying skewed or heavy-tailed distributions. The ABC method can be applied using other reported summary statistics such as the posterior mean and 95 % credible interval when Bayesian analysis has been employed.

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.

Efficient Mean Field Variational Algorithm for Data Assimilation (Invited)

NASA Astrophysics Data System (ADS)

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

2013-12-01

Data assimilation algorithms combine available observations of physical systems with the assumed model dynamics in a systematic manner, to produce better estimates of initial conditions for prediction. Broadly they can be categorized in three main approaches: (a) sequential algorithms, (b) sampling methods and (c) variational algorithms which transform the density estimation problem to an optimization problem. However, given finite computational resources, only a handful of ensemble Kalman filters and 4DVar algorithms have been applied operationally to very high dimensional geophysical applications, such as weather forecasting. In this paper we present a recent extension to our variational Bayesian algorithm which seeks the ';optimal' posterior distribution over the continuous time states, within a family of non-stationary Gaussian processes. Our initial work on variational Bayesian approaches to data assimilation, unlike the well-known 4DVar method which seeks only the most probable solution, computes the best time varying Gaussian process approximation to the posterior smoothing distribution for dynamical systems that can be represented by stochastic differential equations. This approach was based on minimising the Kullback-Leibler divergence, over paths, between the true posterior and our Gaussian process approximation. Whilst the observations were informative enough to keep the posterior smoothing density close to Gaussian the algorithm proved very effective on low dimensional systems (e.g. O(10)D). However for higher dimensional systems, the high computational demands make the algorithm prohibitively expensive. To overcome the difficulties presented in the original framework and make our approach more efficient in higher dimensional systems we have been developing a new mean field version of the algorithm which treats the state variables at any given time as being independent in the posterior approximation, while still accounting for their relationships in the mean solution arising from the original system dynamics. Here we present this new mean field approach, illustrating its performance on a range of benchmark data assimilation problems whose dimensionality varies from O(10) to O(10^3)D. We emphasise that the variational Bayesian approach we adopt, unlike other variational approaches, provides a natural bound on the marginal likelihood of the observations given the model parameters which also allows for inference of (hyper-) parameters such as observational errors, parameters in the dynamical model and model error representation. We also stress that since our approach is intrinsically parallel it can be implemented very efficiently to address very long data assimilation time windows. Moreover, like most traditional variational approaches our Bayesian variational method has the benefit of being posed as an optimisation problem therefore its complexity can be tuned to the available computational resources. We finish with a sketch of possible future directions.

Approximate Bayesian evaluations of measurement uncertainty

NASA Astrophysics Data System (ADS)

Possolo, Antonio; Bodnar, Olha

2018-04-01

The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

Exact posterior computation in non-conjugate Gaussian location-scale parameters models

NASA Astrophysics Data System (ADS)

Andrade, J. A. A.; Rathie, P. N.

2017-12-01

In Bayesian analysis the class of conjugate models allows to obtain exact posterior distributions, however this class quite restrictive in the sense that it involves only a few distributions. In fact, most of the practical applications involves non-conjugate models, thus approximate methods, such as the MCMC algorithms, are required. Although these methods can deal with quite complex structures, some practical problems can make their applications quite time demanding, for example, when we use heavy-tailed distributions, convergence may be difficult, also the Metropolis-Hastings algorithm can become very slow, in addition to the extra work inevitably required on choosing efficient candidate generator distributions. In this work, we draw attention to the special functions as a tools for Bayesian computation, we propose an alternative method for obtaining the posterior distribution in Gaussian non-conjugate models in an exact form. We use complex integration methods based on the H-function in order to obtain the posterior distribution and some of its posterior quantities in an explicit computable form. Two examples are provided in order to illustrate the theory.

Reuse, Recycle, Reweigh: Combating Influenza through Efficient Sequential Bayesian Computation for Massive Data.

PubMed

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

Massive datasets in the gigabyte and terabyte range combined with the availability of increasingly sophisticated statistical tools yield analyses at the boundary of what is computationally feasible. Compromising in the face of this computational burden by partitioning the dataset into more tractable sizes results in stratified analyses, removed from the context that justified the initial data collection. In a Bayesian framework, these stratified analyses generate intermediate realizations, often compared using point estimates that fail to account for the variability within and correlation between the distributions these realizations approximate. However, although the initial concession to stratify generally precludes the more sensible analysis using a single joint hierarchical model, we can circumvent this outcome and capitalize on the intermediate realizations by extending the dynamic iterative reweighting MCMC algorithm. In doing so, we reuse the available realizations by reweighting them with importance weights, recycling them into a now tractable joint hierarchical model. We apply this technique to intermediate realizations generated from stratified analyses of 687 influenza A genomes spanning 13 years allowing us to revisit hypotheses regarding the evolutionary history of influenza within a hierarchical statistical framework.

Reuse, Recycle, Reweigh: Combating Influenza through Efficient Sequential Bayesian Computation for Massive Data

PubMed Central

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

2015-01-01

Massive datasets in the gigabyte and terabyte range combined with the availability of increasingly sophisticated statistical tools yield analyses at the boundary of what is computationally feasible. Compromising in the face of this computational burden by partitioning the dataset into more tractable sizes results in stratified analyses, removed from the context that justified the initial data collection. In a Bayesian framework, these stratified analyses generate intermediate realizations, often compared using point estimates that fail to account for the variability within and correlation between the distributions these realizations approximate. However, although the initial concession to stratify generally precludes the more sensible analysis using a single joint hierarchical model, we can circumvent this outcome and capitalize on the intermediate realizations by extending the dynamic iterative reweighting MCMC algorithm. In doing so, we reuse the available realizations by reweighting them with importance weights, recycling them into a now tractable joint hierarchical model. We apply this technique to intermediate realizations generated from stratified analyses of 687 influenza A genomes spanning 13 years allowing us to revisit hypotheses regarding the evolutionary history of influenza within a hierarchical statistical framework. PMID:26681992

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.

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 Latent Class Analysis Tutorial.

PubMed

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

2018-01-01

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

Model weights and the foundations of multimodel inference

USGS Publications Warehouse

Link, W.A.; Barker, R.J.

2006-01-01

Statistical thinking in wildlife biology and ecology has been profoundly influenced by the introduction of AIC (Akaike?s information criterion) as a tool for model selection and as a basis for model averaging. In this paper, we advocate the Bayesian paradigm as a broader framework for multimodel inference, one in which model averaging and model selection are naturally linked, and in which the performance of AIC-based tools is naturally evaluated. Prior model weights implicitly associated with the use of AIC are seen to highly favor complex models: in some cases, all but the most highly parameterized models in the model set are virtually ignored a priori. We suggest the usefulness of the weighted BIC (Bayesian information criterion) as a computationally simple alternative to AIC, based on explicit selection of prior model probabilities rather than acceptance of default priors associated with AIC. We note, however, that both procedures are only approximate to the use of exact Bayes factors. We discuss and illustrate technical difficulties associated with Bayes factors, and suggest approaches to avoiding these difficulties in the context of model selection for a logistic regression. Our example highlights the predisposition of AIC weighting to favor complex models and suggests a need for caution in using the BIC for computing approximate posterior model weights.

Accelerating Approximate Bayesian Computation with Quantile Regression: application to cosmological redshift distributions

NASA Astrophysics Data System (ADS)

Kacprzak, T.; Herbel, J.; Amara, A.; Réfrégier, A.

2018-02-01

Approximate Bayesian Computation (ABC) is a method to obtain a posterior distribution without a likelihood function, using simulations and a set of distance metrics. For that reason, it has recently been gaining popularity as an analysis tool in cosmology and astrophysics. Its drawback, however, is a slow convergence rate. We propose a novel method, which we call qABC, to accelerate ABC with Quantile Regression. In this method, we create a model of quantiles of distance measure as a function of input parameters. This model is trained on a small number of simulations and estimates which regions of the prior space are likely to be accepted into the posterior. Other regions are then immediately rejected. This procedure is then repeated as more simulations are available. We apply it to the practical problem of estimation of redshift distribution of cosmological samples, using forward modelling developed in previous work. The qABC method converges to nearly same posterior as the basic ABC. It uses, however, only 20% of the number of simulations compared to basic ABC, achieving a fivefold gain in execution time for our problem. For other problems the acceleration rate may vary; it depends on how close the prior is to the final posterior. We discuss possible improvements and extensions to this method.

Fitting models of continuous trait evolution to incompletely sampled comparative data using approximate Bayesian computation.

PubMed

Slater, Graham J; Harmon, Luke J; Wegmann, Daniel; Joyce, Paul; Revell, Liam J; Alfaro, Michael E

2012-03-01

In recent years, a suite of methods has been developed to fit multiple rate models to phylogenetic comparative data. However, most methods have limited utility at broad phylogenetic scales because they typically require complete sampling of both the tree and the associated phenotypic data. Here, we develop and implement a new, tree-based method called MECCA (Modeling Evolution of Continuous Characters using ABC) that uses a hybrid likelihood/approximate Bayesian computation (ABC)-Markov-Chain Monte Carlo approach to simultaneously infer rates of diversification and trait evolution from incompletely sampled phylogenies and trait data. We demonstrate via simulation that MECCA has considerable power to choose among single versus multiple evolutionary rate models, and thus can be used to test hypotheses about changes in the rate of trait evolution across an incomplete tree of life. We finally apply MECCA to an empirical example of body size evolution in carnivores, and show that there is no evidence for an elevated rate of body size evolution in the pinnipeds relative to terrestrial carnivores. ABC approaches can provide a useful alternative set of tools for future macroevolutionary studies where likelihood-dependent approaches are lacking. © 2011 The Author(s). Evolution© 2011 The Society for the Study of Evolution.

Inferring Population Size History from Large Samples of Genome-Wide Molecular Data - An Approximate Bayesian Computation Approach

PubMed Central

Boitard, Simon; Rodríguez, Willy; Jay, Flora; Mona, Stefano; Austerlitz, Frédéric

2016-01-01

Inferring the ancestral dynamics of effective population size is a long-standing question in population genetics, which can now be tackled much more accurately thanks to the massive genomic data available in many species. Several promising methods that take advantage of whole-genome sequences have been recently developed in this context. However, they can only be applied to rather small samples, which limits their ability to estimate recent population size history. Besides, they can be very sensitive to sequencing or phasing errors. Here we introduce a new approximate Bayesian computation approach named PopSizeABC that allows estimating the evolution of the effective population size through time, using a large sample of complete genomes. This sample is summarized using the folded allele frequency spectrum and the average zygotic linkage disequilibrium at different bins of physical distance, two classes of statistics that are widely used in population genetics and can be easily computed from unphased and unpolarized SNP data. Our approach provides accurate estimations of past population sizes, from the very first generations before present back to the expected time to the most recent common ancestor of the sample, as shown by simulations under a wide range of demographic scenarios. When applied to samples of 15 or 25 complete genomes in four cattle breeds (Angus, Fleckvieh, Holstein and Jersey), PopSizeABC revealed a series of population declines, related to historical events such as domestication or modern breed creation. We further highlight that our approach is robust to sequencing errors, provided summary statistics are computed from SNPs with common alleles. PMID:26943927

Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction

NASA Astrophysics Data System (ADS)

Cui, Tiangang; Marzouk, Youssef; Willcox, Karen

2016-06-01

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or noisy data, the state variation and parameter dependence of the forward model, and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting-both in the parameter space of the inverse problem and in the state space of the forward model. To this end, we show how to jointly construct low-dimensional subspaces of the parameter space and the state space in order to accelerate the Bayesian solution of the inverse problem. As a byproduct of state dimension reduction, we also show how to identify low-dimensional subspaces of the data in problems with high-dimensional observations. These subspaces enable approximation of the posterior as a product of two factors: (i) a projection of the posterior onto a low-dimensional parameter subspace, wherein the original likelihood is replaced by an approximation involving a reduced model; and (ii) the marginal prior distribution on the high-dimensional complement of the parameter subspace. We present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations. The resulting posterior approximations can rapidly be characterized using standard sampling techniques, e.g., Markov chain Monte Carlo. Two numerical examples demonstrate the accuracy and efficiency of our approach: inversion of an integral equation in atmospheric remote sensing, where the data dimension is very high; and the inference of a heterogeneous transmissivity field in a groundwater system, which involves a partial differential equation forward model with high dimensional state and parameters.

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Irving, J.; Koepke, C.; Elsheikh, A. H.

2017-12-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward process model linking subsurface parameters to measured data, which is typically assumed to be known perfectly in the inversion procedure. However, in order to make the stochastic solution of the inverse problem computationally tractable using, for example, Markov-chain-Monte-Carlo (MCMC) methods, fast approximations of the forward model are commonly employed. This introduces model error into the problem, which has the potential to significantly bias posterior statistics and hamper data integration efforts if not properly accounted for. Here, we present a new methodology for addressing the issue of model error in Bayesian solutions to hydrogeophysical inverse problems that is geared towards the common case where these errors cannot be effectively characterized globally through some parametric statistical distribution or locally based on interpolation between a small number of computed realizations. Rather than focusing on the construction of a global or local error model, we instead work towards identification of the model-error component of the residual through a projection-based approach. In this regard, pairs of approximate and detailed model runs are stored in a dictionary that grows at a specified rate during the MCMC inversion procedure. At each iteration, a local model-error basis is constructed for the current test set of model parameters using the K-nearest neighbour entries in the dictionary, which is then used to separate the model error from the other error sources before computing the likelihood of the proposed set of model parameters. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar traveltime data for three different subsurface parameterizations of varying complexity. The synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed in the inversion procedure. In each case, the developed model-error approach enables to remove posterior bias and obtain a more realistic characterization of uncertainty.

A High Performance Computing Study of a Scalable FISST-Based Approach to Multi-Target, Multi-Sensor Tracking

NASA Astrophysics Data System (ADS)

Hussein, I.; Wilkins, M.; Roscoe, C.; Faber, W.; Chakravorty, S.; Schumacher, P.

2016-09-01

Finite Set Statistics (FISST) is a rigorous Bayesian multi-hypothesis management tool for the joint detection, classification and tracking of multi-sensor, multi-object systems. Implicit within the approach are solutions to the data association and target label-tracking problems. The full FISST filtering equations, however, are intractable. While FISST-based methods such as the PHD and CPHD filters are tractable, they require heavy moment approximations to the full FISST equations that result in a significant loss of information contained in the collected data. In this paper, we review Smart Sampling Markov Chain Monte Carlo (SSMCMC) that enables FISST to be tractable while avoiding moment approximations. We study the effect of tuning key SSMCMC parameters on tracking quality and computation time. The study is performed on a representative space object catalog with varying numbers of RSOs. The solution is implemented in the Scala computing language at the Maui High Performance Computing Center (MHPCC) facility.

Learning of state-space models with highly informative observations: A tempered sequential Monte Carlo solution

NASA Astrophysics Data System (ADS)

Svensson, Andreas; Schön, Thomas B.; Lindsten, Fredrik

2018-05-01

Probabilistic (or Bayesian) modeling and learning offers interesting possibilities for systematic representation of uncertainty using probability theory. However, probabilistic learning often leads to computationally challenging problems. Some problems of this type that were previously intractable can now be solved on standard personal computers thanks to recent advances in Monte Carlo methods. In particular, for learning of unknown parameters in nonlinear state-space models, methods based on the particle filter (a Monte Carlo method) have proven very useful. A notoriously challenging problem, however, still occurs when the observations in the state-space model are highly informative, i.e. when there is very little or no measurement noise present, relative to the amount of process noise. The particle filter will then struggle in estimating one of the basic components for probabilistic learning, namely the likelihood p (data | parameters). To this end we suggest an algorithm which initially assumes that there is substantial amount of artificial measurement noise present. The variance of this noise is sequentially decreased in an adaptive fashion such that we, in the end, recover the original problem or possibly a very close approximation of it. The main component in our algorithm is a sequential Monte Carlo (SMC) sampler, which gives our proposed method a clear resemblance to the SMC2 method. Another natural link is also made to the ideas underlying the approximate Bayesian computation (ABC). We illustrate it with numerical examples, and in particular show promising results for a challenging Wiener-Hammerstein benchmark problem.

Linking big models to big data: efficient ecosystem model calibration through Bayesian model emulation

NASA Astrophysics Data System (ADS)

Fer, I.; Kelly, R.; Andrews, T.; Dietze, M.; Richardson, A. D.

2016-12-01

Our ability to forecast ecosystems is limited by how well we parameterize ecosystem models. Direct measurements for all model parameters are not always possible and inverse estimation of these parameters through Bayesian methods is computationally costly. A solution to computational challenges of Bayesian calibration is to approximate the posterior probability surface using a Gaussian Process that emulates the complex process-based model. Here we report the integration of this method within an ecoinformatics toolbox, Predictive Ecosystem Analyzer (PEcAn), and its application with two ecosystem models: SIPNET and ED2.1. SIPNET is a simple model, allowing application of MCMC methods both to the model itself and to its emulator. We used both approaches to assimilate flux (CO2 and latent heat), soil respiration, and soil carbon data from Bartlett Experimental Forest. This comparison showed that emulator is reliable in terms of convergence to the posterior distribution. A 10000-iteration MCMC analysis with SIPNET itself required more than two orders of magnitude greater computation time than an MCMC run of same length with its emulator. This difference would be greater for a more computationally demanding model. Validation of the emulator-calibrated SIPNET against both the assimilated data and out-of-sample data showed improved fit and reduced uncertainty around model predictions. We next applied the validated emulator method to the ED2, whose complexity precludes standard Bayesian data assimilation. We used the ED2 emulator to assimilate demographic data from a network of inventory plots. For validation of the calibrated ED2, we compared the model to results from Empirical Succession Mapping (ESM), a novel synthesis of successional patterns in Forest Inventory and Analysis data. Our results revealed that while the pre-assimilation ED2 formulation cannot capture the emergent demographic patterns from ESM analysis, constrained model parameters controlling demographic processes increased their agreement considerably.

Bayesian peak picking for NMR spectra.

PubMed

Cheng, Yichen; Gao, Xin; Liang, Faming

2014-02-01

Protein structure determination is a very important topic in structural genomics, which helps people to understand varieties of biological functions such as protein-protein interactions, protein-DNA interactions and so on. Nowadays, nuclear magnetic resonance (NMR) has often been used to determine the three-dimensional structures of protein in vivo. This study aims to automate the peak picking step, the most important and tricky step in NMR structure determination. We propose to model the NMR spectrum by a mixture of bivariate Gaussian densities and use the stochastic approximation Monte Carlo algorithm as the computational tool to solve the problem. Under the Bayesian framework, the peak picking problem is casted as a variable selection problem. The proposed method can automatically distinguish true peaks from false ones without preprocessing the data. To the best of our knowledge, this is the first effort in the literature that tackles the peak picking problem for NMR spectrum data using Bayesian method. Copyright © 2013. Production and hosting by Elsevier Ltd.

Genetic structure of pike (Esox lucius) reveals a complex and previously unrecognized colonization history of Ireland

PubMed Central

Pedreschi, Debbi; Kelly-Quinn, Mary; Caffrey, Joe; O’Grady, Martin; Mariani, Stefano; Phillimore, Albert

2014-01-01

Aim We investigated genetic variation of Irish pike populations and their relationship with European outgroups, in order to elucidate the origin of this species to the island, which is largely assumed to have occurred as a human-mediated introduction over the past few hundred years. We aimed thereby to provide new insights into population structure to improve fisheries and biodiversity management in Irish freshwaters. Location Ireland, Britain and continental Europe. Methods A total of 752 pike (Esox lucius) were sampled from 15 locations around Ireland, and 9 continental European sites, and genotyped at six polymorphic microsatellite loci. Patterns and mechanisms of population genetic structure were assessed through a diverse array of methods, including Bayesian clustering, hierarchical analysis of molecular variance, and approximate Bayesian computation. Results Varying levels of genetic diversity and a high degree of population genetic differentiation were detected. Clear substructure within Ireland was identified, with two main groups being evident. One of the Irish populations showed high similarity with British populations. The other, more widespread, Irish strain did not group with any European population examined. Approximate Bayesian computation suggested that this widespread Irish strain is older, and may have colonized Ireland independently of humans. Main conclusions Population genetic substructure in Irish pike is high and comparable to the levels observed elsewhere in Europe. A comparison of evolutionary scenarios upholds the possibility that pike may have colonized Ireland in two ‘waves’, the first of which, being independent of human colonization, would represent the first evidence for natural colonization of a non-anadromous freshwater fish to the island of Ireland. Although further investigations using comprehensive genomic techniques will be necessary to confirm this, the present results warrant a reappraisal of current management strategies for this species. PMID:25435649

Genetic structure of pike (Esox lucius) reveals a complex and previously unrecognized colonization history of Ireland.

PubMed

Pedreschi, Debbi; Kelly-Quinn, Mary; Caffrey, Joe; O'Grady, Martin; Mariani, Stefano; Phillimore, Albert

2014-03-01

We investigated genetic variation of Irish pike populations and their relationship with European outgroups, in order to elucidate the origin of this species to the island, which is largely assumed to have occurred as a human-mediated introduction over the past few hundred years. We aimed thereby to provide new insights into population structure to improve fisheries and biodiversity management in Irish freshwaters. Ireland, Britain and continental Europe. A total of 752 pike ( Esox lucius ) were sampled from 15 locations around Ireland, and 9 continental European sites, and genotyped at six polymorphic microsatellite loci. Patterns and mechanisms of population genetic structure were assessed through a diverse array of methods, including Bayesian clustering, hierarchical analysis of molecular variance, and approximate Bayesian computation. Varying levels of genetic diversity and a high degree of population genetic differentiation were detected. Clear substructure within Ireland was identified, with two main groups being evident. One of the Irish populations showed high similarity with British populations. The other, more widespread, Irish strain did not group with any European population examined. Approximate Bayesian computation suggested that this widespread Irish strain is older, and may have colonized Ireland independently of humans. Population genetic substructure in Irish pike is high and comparable to the levels observed elsewhere in Europe. A comparison of evolutionary scenarios upholds the possibility that pike may have colonized Ireland in two 'waves', the first of which, being independent of human colonization, would represent the first evidence for natural colonization of a non-anadromous freshwater fish to the island of Ireland. Although further investigations using comprehensive genomic techniques will be necessary to confirm this, the present results warrant a reappraisal of current management strategies for this species.

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Köpke, Corinna; Irving, James; Elsheikh, Ahmed H.

2018-06-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward model linking subsurface physical properties to measured data, which is typically assumed to be perfectly known in the inversion procedure. However, to make the stochastic solution of the inverse problem computationally tractable using methods such as Markov-chain-Monte-Carlo (MCMC), fast approximations of the forward model are commonly employed. This gives rise to model error, which has the potential to significantly bias posterior statistics if not properly accounted for. Here, we present a new methodology for dealing with the model error arising from the use of approximate forward solvers in Bayesian solutions to hydrogeophysical inverse problems. Our approach is geared towards the common case where this error cannot be (i) effectively characterized through some parametric statistical distribution; or (ii) estimated by interpolating between a small number of computed model-error realizations. To this end, we focus on identification and removal of the model-error component of the residual during MCMC using a projection-based approach, whereby the orthogonal basis employed for the projection is derived in each iteration from the K-nearest-neighboring entries in a model-error dictionary. The latter is constructed during the inversion and grows at a specified rate as the iterations proceed. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar travel-time data considering three different subsurface parameterizations of varying complexity. Synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed for their inversion. In each case, our developed approach enables us to remove posterior bias and obtain a more realistic characterization of uncertainty.

Bayesian inference supports a location and neighbour-dependent model of DNA methylation propagation at the MGMT gene promoter in lung tumours.

PubMed

Bonello, Nicolas; Sampson, James; Burn, John; Wilson, Ian J; McGrown, Gail; Margison, Geoff P; Thorncroft, Mary; Crossbie, Philip; Povey, Andrew C; Santibanez-Koref, Mauro; Walters, Kevin

2013-11-07

We exploit model-based Bayesian inference methodologies to analyse lung tumour-derived methylation data from a CpG island in the O6-methylguanine-DNA methyltransferase (MGMT) promoter. Interest is in modelling the changes in methylation patterns in a CpG island in the first exon of the promoter during lung tumour development. We propose four competils of methylation state propagation based on two mechanisms. The first is the location-dependence mechanism in which the probability of a gain or loss of methylation at a CpG within the promoter depends upon its location in the CpG sequence. The second mechanism is that of neighbour-dependence in which gain or loss of methylation at a CpG depends upon the methylation status of the immediately preceding CpG. Our data comprises the methylation status at 12 CpGs near the 5' end of the CpG island in two lung tumour samples for both alleles of a nearby polymorphism. We use approximate Bayesian computation, a computationally intensive rejection-sampling algorithm to infer model parameters and compare models without the need to evaluate the likelihood function. We compare the four proposed models using two criteria: the approximate Bayes factors and the distribution of the Euclidean distance between the summary statistics of the observed and simulated datasets. Our model-based analysis demonstrates compelling evidence for both location and neighbour dependence in the process of aberrant DNA methylation of this MGMT promoter CpG island in lung tumours. We find equivocal evidence to support the hypothesis that the methylation patterns of the two alleles evolve independently. © 2013 Published by Elsevier Ltd. All rights reserved.

Rational approximations to rational models: alternative algorithms for category learning.

PubMed

Sanborn, Adam N; Griffiths, Thomas L; Navarro, Daniel J

2010-10-01

Rational models of cognition typically consider the abstract computational problems posed by the environment, assuming that people are capable of optimally solving those problems. This differs from more traditional formal models of cognition, which focus on the psychological processes responsible for behavior. A basic challenge for rational models is thus explaining how optimal solutions can be approximated by psychological processes. We outline a general strategy for answering this question, namely to explore the psychological plausibility of approximation algorithms developed in computer science and statistics. In particular, we argue that Monte Carlo methods provide a source of rational process models that connect optimal solutions to psychological processes. We support this argument through a detailed example, applying this approach to Anderson's (1990, 1991) rational model of categorization (RMC), which involves a particularly challenging computational problem. Drawing on a connection between the RMC and ideas from nonparametric Bayesian statistics, we propose 2 alternative algorithms for approximate inference in this model. The algorithms we consider include Gibbs sampling, a procedure appropriate when all stimuli are presented simultaneously, and particle filters, which sequentially approximate the posterior distribution with a small number of samples that are updated as new data become available. Applying these algorithms to several existing datasets shows that a particle filter with a single particle provides a good description of human inferences.

An efficient Bayesian data-worth analysis using a multilevel Monte Carlo method

NASA Astrophysics Data System (ADS)

Lu, Dan; Ricciuto, Daniel; Evans, Katherine

2018-03-01

Improving the understanding of subsurface systems and thus reducing prediction uncertainty requires collection of data. As the collection of subsurface data is costly, it is important that the data collection scheme is cost-effective. Design of a cost-effective data collection scheme, i.e., data-worth analysis, requires quantifying model parameter, prediction, and both current and potential data uncertainties. Assessment of these uncertainties in large-scale stochastic subsurface hydrological model simulations using standard Monte Carlo (MC) sampling or surrogate modeling is extremely computationally intensive, sometimes even infeasible. In this work, we propose an efficient Bayesian data-worth analysis using a multilevel Monte Carlo (MLMC) method. Compared to the standard MC that requires a significantly large number of high-fidelity model executions to achieve a prescribed accuracy in estimating expectations, the MLMC can substantially reduce computational costs using multifidelity approximations. Since the Bayesian data-worth analysis involves a great deal of expectation estimation, the cost saving of the MLMC in the assessment can be outstanding. While the proposed MLMC-based data-worth analysis is broadly applicable, we use it for a highly heterogeneous two-phase subsurface flow simulation to select an optimal candidate data set that gives the largest uncertainty reduction in predicting mass flow rates at four production wells. The choices made by the MLMC estimation are validated by the actual measurements of the potential data, and consistent with the standard MC estimation. But compared to the standard MC, the MLMC greatly reduces the computational costs.

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.

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.

Is probabilistic bias analysis approximately Bayesian?

PubMed Central

MacLehose, Richard F.; Gustafson, Paul

2011-01-01

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

Bayesian models: A statistical primer for ecologists

USGS Publications Warehouse

Hobbs, N. Thompson; Hooten, Mevin B.

2015-01-01

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

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.

Learning the ideal observer for SKE detection tasks by use of convolutional neural networks (Cum Laude Poster Award)

NASA Astrophysics Data System (ADS)

Zhou, Weimin; Anastasio, Mark A.

2018-03-01

It has been advocated that task-based measures of image quality (IQ) should be employed to evaluate and optimize imaging systems. Task-based measures of IQ quantify the performance of an observer on a medically relevant task. The Bayesian Ideal Observer (IO), which employs complete statistical information of the object and noise, achieves the upper limit of the performance for a binary signal classification task. However, computing the IO performance is generally analytically intractable and can be computationally burdensome when Markov-chain Monte Carlo (MCMC) techniques are employed. In this paper, supervised learning with convolutional neural networks (CNNs) is employed to approximate the IO test statistics for a signal-known-exactly and background-known-exactly (SKE/BKE) binary detection task. The receiver operating characteristic (ROC) curve and the area under the ROC curve (AUC) are compared to those produced by the analytically computed IO. The advantages of the proposed supervised learning approach for approximating the IO are demonstrated.

Modeling the Swift BAT Trigger Algorithm with Machine Learning

NASA Technical Reports Server (NTRS)

Graff, Philip B.; Lien, Amy Y.; Baker, John G.; Sakamoto, Takanori

2015-01-01

To draw inferences about gamma-ray burst (GRB) source populations based on Swift observations, it is essential to understand the detection efficiency of the Swift burst alert telescope (BAT). This study considers the problem of modeling the Swift BAT triggering algorithm for long GRBs, a computationally expensive procedure, and models it using machine learning algorithms. A large sample of simulated GRBs from Lien et al. (2014) is used to train various models: random forests, boosted decision trees (with AdaBoost), support vector machines, and artificial neural networks. The best models have accuracies of approximately greater than 97% (approximately less than 3% error), which is a significant improvement on a cut in GRB flux which has an accuracy of 89:6% (10:4% error). These models are then used to measure the detection efficiency of Swift as a function of redshift z, which is used to perform Bayesian parameter estimation on the GRB rate distribution. We find a local GRB rate density of eta(sub 0) approximately 0.48(+0.41/-0.23) Gpc(exp -3) yr(exp -1) with power-law indices of eta(sub 1) approximately 1.7(+0.6/-0.5) and eta(sub 2) approximately -5.9(+5.7/-0.1) for GRBs above and below a break point of z(sub 1) approximately 6.8(+2.8/-3.2). This methodology is able to improve upon earlier studies by more accurately modeling Swift detection and using this for fully Bayesian model fitting. The code used in this is analysis is publicly available online.

Case studies in Bayesian microbial risk assessments.

PubMed

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

2009-12-21

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

CMOL/CMOS hardware architectures and performance/price for Bayesian memory - The building block of intelligent systems

NASA Astrophysics Data System (ADS)

Zaveri, Mazad Shaheriar

The semiconductor/computer industry has been following Moore's law for several decades and has reaped the benefits in speed and density of the resultant scaling. Transistor density has reached almost one billion per chip, and transistor delays are in picoseconds. However, scaling has slowed down, and the semiconductor industry is now facing several challenges. Hybrid CMOS/nano technologies, such as CMOL, are considered as an interim solution to some of the challenges. Another potential architectural solution includes specialized architectures for applications/models in the intelligent computing domain, one aspect of which includes abstract computational models inspired from the neuro/cognitive sciences. Consequently in this dissertation, we focus on the hardware implementations of Bayesian Memory (BM), which is a (Bayesian) Biologically Inspired Computational Model (BICM). This model is a simplified version of George and Hawkins' model of the visual cortex, which includes an inference framework based on Judea Pearl's belief propagation. We then present a "hardware design space exploration" methodology for implementing and analyzing the (digital and mixed-signal) hardware for the BM. This particular methodology involves: analyzing the computational/operational cost and the related micro-architecture, exploring candidate hardware components, proposing various custom hardware architectures using both traditional CMOS and hybrid nanotechnology - CMOL, and investigating the baseline performance/price of these architectures. The results suggest that CMOL is a promising candidate for implementing a BM. Such implementations can utilize the very high density storage/computation benefits of these new nano-scale technologies much more efficiently; for example, the throughput per 858 mm2 (TPM) obtained for CMOL based architectures is 32 to 40 times better than the TPM for a CMOS based multiprocessor/multi-FPGA system, and almost 2000 times better than the TPM for a PC implementation. We later use this methodology to investigate the hardware implementations of cortex-scale spiking neural system, which is an approximate neural equivalent of BICM based cortex-scale system. The results of this investigation also suggest that CMOL is a promising candidate to implement such large-scale neuromorphic systems. In general, the assessment of such hypothetical baseline hardware architectures provides the prospects for building large-scale (mammalian cortex-scale) implementations of neuromorphic/Bayesian/intelligent systems using state-of-the-art and beyond state-of-the-art silicon structures.

Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics.

PubMed

Wu, Xiao-Lin; Sun, Chuanyu; Beissinger, Timothy M; Rosa, Guilherme Jm; Weigel, Kent A; Gatti, Natalia de Leon; Gianola, Daniel

2012-09-25

Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics. Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes. Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs.

Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics

PubMed Central

2012-01-01

Background Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics. Results Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes. Conclusions Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs. PMID:23009363

Bayesian isotonic density regression

PubMed Central

Wang, Lianming; Dunson, David B.

2011-01-01

Density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space. Such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions, and are well supported in many applications. A rich variety of Bayesian methods have been proposed for density regression, but it is not clear whether such priors have full support so that any true data-generating model can be accurately approximated. This article develops a new class of density regression models that incorporate stochastic-ordering constraints which are natural when a response tends to increase or decrease monotonely with a predictor. Theory is developed showing large support. Methods are developed for hypothesis testing, with posterior computation relying on a simple Gibbs sampler. Frequentist properties are illustrated in a simulation study, and an epidemiology application is considered. PMID:22822259

Efficient Bayesian experimental design for contaminant source identification

NASA Astrophysics Data System (ADS)

Zhang, Jiangjiang; Zeng, Lingzao; Chen, Cheng; Chen, Dingjiang; Wu, Laosheng

2015-01-01

In this study, an efficient full Bayesian approach is developed for the optimal sampling well location design and source parameters identification of groundwater contaminants. An information measure, i.e., the relative entropy, is employed to quantify the information gain from concentration measurements in identifying unknown parameters. In this approach, the sampling locations that give the maximum expected relative entropy are selected as the optimal design. After the sampling locations are determined, a Bayesian approach based on Markov Chain Monte Carlo (MCMC) is used to estimate unknown parameters. In both the design and estimation, the contaminant transport equation is required to be solved many times to evaluate the likelihood. To reduce the computational burden, an interpolation method based on the adaptive sparse grid is utilized to construct a surrogate for the contaminant transport equation. The approximated likelihood can be evaluated directly from the surrogate, which greatly accelerates the design and estimation process. The accuracy and efficiency of our approach are demonstrated through numerical case studies. It is shown that the methods can be used to assist in both single sampling location and monitoring network design for contaminant source identifications in groundwater.

Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models

NASA Astrophysics Data System (ADS)

Boudineau, Mégane; Carfantan, Hervé; Bourguignon, Sébastien; Bazot, Michael

2016-06-01

We address the sparse approximation problem in the case where the data are approximated by the linear combination of a small number of elementary signals, each of these signals depending non-linearly on additional parameters. Sparsity is explicitly expressed through a Bernoulli-Gaussian hierarchical model in a Bayesian framework. Posterior mean estimates are computed using Markov Chain Monte-Carlo algorithms. We generalize the partially marginalized Gibbs sampler proposed in the linear case in [1], and build an hybrid Hastings-within-Gibbs algorithm in order to account for the nonlinear parameters. All model parameters are then estimated in an unsupervised procedure. The resulting method is evaluated on a sparse spectral analysis problem. It is shown to converge more efficiently than the classical joint estimation procedure, with only a slight increase of the computational cost per iteration, consequently reducing the global cost of the estimation procedure.

Bayesian prediction of future ice sheet volume using local approximation Markov chain Monte Carlo methods

NASA Astrophysics Data System (ADS)

Davis, A. D.; Heimbach, P.; Marzouk, Y.

2017-12-01

We develop a Bayesian inverse modeling framework for predicting future ice sheet volume with associated formal uncertainty estimates. Marine ice sheets are drained by fast-flowing ice streams, which we simulate using a flowline model. Flowline models depend on geometric parameters (e.g., basal topography), parameterized physical processes (e.g., calving laws and basal sliding), and climate parameters (e.g., surface mass balance), most of which are unknown or uncertain. Given observations of ice surface velocity and thickness, we define a Bayesian posterior distribution over static parameters, such as basal topography. We also define a parameterized distribution over variable parameters, such as future surface mass balance, which we assume are not informed by the data. Hyperparameters are used to represent climate change scenarios, and sampling their distributions mimics internal variation. For example, a warming climate corresponds to increasing mean surface mass balance but an individual sample may have periods of increasing or decreasing surface mass balance. We characterize the predictive distribution of ice volume by evaluating the flowline model given samples from the posterior distribution and the distribution over variable parameters. Finally, we determine the effect of climate change on future ice sheet volume by investigating how changing the hyperparameters affects the predictive distribution. We use state-of-the-art Bayesian computation to address computational feasibility. Characterizing the posterior distribution (using Markov chain Monte Carlo), sampling the full range of variable parameters and evaluating the predictive model is prohibitively expensive. Furthermore, the required resolution of the inferred basal topography may be very high, which is often challenging for sampling methods. Instead, we leverage regularity in the predictive distribution to build a computationally cheaper surrogate over the low dimensional quantity of interest (future ice sheet volume). Continual surrogate refinement guarantees asymptotic sampling from the predictive distribution. Directly characterizing the predictive distribution in this way allows us to assess the ice sheet's sensitivity to climate variability and change.

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 ionospheric multi-instrument 3D tomography

NASA Astrophysics Data System (ADS)

Norberg, Johannes; Vierinen, Juha; Roininen, Lassi

2017-04-01

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

Almost but not quite 2D, Non-linear Bayesian Inversion of CSEM Data

NASA Astrophysics Data System (ADS)

Ray, A.; Key, K.; Bodin, T.

2013-12-01

The geophysical inverse problem can be elegantly stated in a Bayesian framework where a probability distribution can be viewed as a statement of information regarding a random variable. After all, the goal of geophysical inversion is to provide information on the random variables of interest - physical properties of the earth's subsurface. However, though it may be simple to postulate, a practical difficulty of fully non-linear Bayesian inversion is the computer time required to adequately sample the model space and extract the information we seek. As a consequence, in geophysical problems where evaluation of a full 2D/3D forward model is computationally expensive, such as marine controlled source electromagnetic (CSEM) mapping of the resistivity of seafloor oil and gas reservoirs, Bayesian studies have largely been conducted with 1D forward models. While the 1D approximation is indeed appropriate for exploration targets with planar geometry and geological stratification, it only provides a limited, site-specific idea of uncertainty in resistivity with depth. In this work, we extend our fully non-linear 1D Bayesian inversion to a 2D model framework, without requiring the usual regularization of model resistivities in the horizontal or vertical directions used to stabilize quasi-2D inversions. In our approach, we use the reversible jump Markov-chain Monte-Carlo (RJ-MCMC) or trans-dimensional method and parameterize the subsurface in a 2D plane with Voronoi cells. The method is trans-dimensional in that the number of cells required to parameterize the subsurface is variable, and the cells dynamically move around and multiply or combine as demanded by the data being inverted. This approach allows us to expand our uncertainty analysis of resistivity at depth to more than a single site location, allowing for interactions between model resistivities at different horizontal locations along a traverse over an exploration target. While the model is parameterized in 2D, we efficiently evaluate the forward response using 1D profiles extracted from the model at the common-midpoints of the EM source-receiver pairs. Since the 1D approximation is locally valid at different midpoint locations, the computation time is far lower than is required by a full 2D or 3D simulation. We have applied this method to both synthetic and real CSEM survey data from the Scarborough gas field on the Northwest shelf of Australia, resulting in a spatially variable quantification of resistivity and its uncertainty in 2D. This Bayesian approach results in a large database of 2D models that comprise a posterior probability distribution, which we can subset to test various hypotheses about the range of model structures compatible with the data. For example, we can subset the model distributions to examine the hypothesis that a resistive reservoir extends overs a certain spatial extent. Depending on how this conditions other parts of the model space, light can be shed on the geological viability of the hypothesis. Since tackling spatially variable uncertainty and trade-offs in 2D and 3D is a challenging research problem, the insights gained from this work may prove valuable for subsequent full 2D and 3D Bayesian inversions.

Melanoma Cell Colony Expansion Parameters Revealed by Approximate Bayesian Computation

PubMed Central

Vo, Brenda N.; Drovandi, Christopher C.; Pettitt, Anthony N.; Pettet, Graeme J.

2015-01-01

In vitro studies and mathematical models are now being widely used to study the underlying mechanisms driving the expansion of cell colonies. This can improve our understanding of cancer formation and progression. Although much progress has been made in terms of developing and analysing mathematical models, far less progress has been made in terms of understanding how to estimate model parameters using experimental in vitro image-based data. To address this issue, a new approximate Bayesian computation (ABC) algorithm is proposed to estimate key parameters governing the expansion of melanoma cell (MM127) colonies, including cell diffusivity, D, cell proliferation rate, λ, and cell-to-cell adhesion, q, in two experimental scenarios, namely with and without a chemical treatment to suppress cell proliferation. Even when little prior biological knowledge about the parameters is assumed, all parameters are precisely inferred with a small posterior coefficient of variation, approximately 2–12%. The ABC analyses reveal that the posterior distributions of D and q depend on the experimental elapsed time, whereas the posterior distribution of λ does not. The posterior mean values of D and q are in the ranges 226–268 µm2h−1, 311–351 µm2h−1 and 0.23–0.39, 0.32–0.61 for the experimental periods of 0–24 h and 24–48 h, respectively. Furthermore, we found that the posterior distribution of q also depends on the initial cell density, whereas the posterior distributions of D and λ do not. The ABC approach also enables information from the two experiments to be combined, resulting in greater precision for all estimates of D and λ. PMID:26642072

A program for the Bayesian Neural Network in the ROOT framework

NASA Astrophysics Data System (ADS)

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

2011-12-01

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

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…

Children Can Solve Bayesian Problems: The Role of Representation in Mental Computation

ERIC Educational Resources Information Center

Zhu, Liqi; Gigerenzer, Gerd

2006-01-01

Can children reason the Bayesian way? We argue that the answer to this question depends on how numbers are represented, because a representation can do part of the computation. We test, for the first time, whether Bayesian reasoning can be elicited in children by means of natural frequencies. We show that when information was presented to fourth,…

Remembrance of inferences past: Amortization in human hypothesis generation.

PubMed

Dasgupta, Ishita; Schulz, Eric; Goodman, Noah D; Gershman, Samuel J

2018-05-21

Bayesian models of cognition assume that people compute probability distributions over hypotheses. However, the required computations are frequently intractable or prohibitively expensive. Since people often encounter many closely related distributions, selective reuse of computations (amortized inference) is a computationally efficient use of the brain's limited resources. We present three experiments that provide evidence for amortization in human probabilistic reasoning. When sequentially answering two related queries about natural scenes, participants' responses to the second query systematically depend on the structure of the first query. This influence is sensitive to the content of the queries, only appearing when the queries are related. Using a cognitive load manipulation, we find evidence that people amortize summary statistics of previous inferences, rather than storing the entire distribution. These findings support the view that the brain trades off accuracy and computational cost, to make efficient use of its limited cognitive resources to approximate probabilistic inference. Copyright © 2018 Elsevier B.V. All rights reserved.

An extended Kalman filter approach to non-stationary Bayesian estimation of reduced-order vocal fold model parameters.

PubMed

Hadwin, Paul J; Peterson, Sean D

2017-04-01

The Bayesian framework for parameter inference provides a basis from which subject-specific reduced-order vocal fold models can be generated. Previously, it has been shown that a particle filter technique is capable of producing estimates and associated credibility intervals of time-varying reduced-order vocal fold model parameters. However, the particle filter approach is difficult to implement and has a high computational cost, which can be barriers to clinical adoption. This work presents an alternative estimation strategy based upon Kalman filtering aimed at reducing the computational cost of subject-specific model development. The robustness of this approach to Gaussian and non-Gaussian noise is discussed. The extended Kalman filter (EKF) approach is found to perform very well in comparison with the particle filter technique at dramatically lower computational cost. Based upon the test cases explored, the EKF is comparable in terms of accuracy to the particle filter technique when greater than 6000 particles are employed; if less particles are employed, the EKF actually performs better. For comparable levels of accuracy, the solution time is reduced by 2 orders of magnitude when employing the EKF. By virtue of the approximations used in the EKF, however, the credibility intervals tend to be slightly underpredicted.

A novel Bayesian framework for discriminative feature extraction in Brain-Computer Interfaces.

PubMed

Suk, Heung-Il; Lee, Seong-Whan

2013-02-01

As there has been a paradigm shift in the learning load from a human subject to a computer, machine learning has been considered as a useful tool for Brain-Computer Interfaces (BCIs). In this paper, we propose a novel Bayesian framework for discriminative feature extraction for motor imagery classification in an EEG-based BCI in which the class-discriminative frequency bands and the corresponding spatial filters are optimized by means of the probabilistic and information-theoretic approaches. In our framework, the problem of simultaneous spatiospectral filter optimization is formulated as the estimation of an unknown posterior probability density function (pdf) that represents the probability that a single-trial EEG of predefined mental tasks can be discriminated in a state. In order to estimate the posterior pdf, we propose a particle-based approximation method by extending a factored-sampling technique with a diffusion process. An information-theoretic observation model is also devised to measure discriminative power of features between classes. From the viewpoint of classifier design, the proposed method naturally allows us to construct a spectrally weighted label decision rule by linearly combining the outputs from multiple classifiers. We demonstrate the feasibility and effectiveness of the proposed method by analyzing the results and its success on three public databases.

Approximate Bayesian Computation Reveals the Crucial Role of Oceanic Islands for the Assembly of Continental Biodiversity.

PubMed

Patiño, Jairo; Carine, Mark; Mardulyn, Patrick; Devos, Nicolas; Mateo, Rubén G; González-Mancebo, Juana M; Shaw, A Jonathan; Vanderpoorten, Alain

2015-07-01

The perceived low levels of genetic diversity, poor interspecific competitive and defensive ability, and loss of dispersal capacities of insular lineages have driven the view that oceanic islands are evolutionary dead ends. Focusing on the Atlantic bryophyte flora distributed across the archipelagos of the Azores, Madeira, the Canary Islands, Western Europe, and northwestern Africa, we used an integrative approach with species distribution modeling and population genetic analyses based on approximate Bayesian computation to determine whether this view applies to organisms with inherent high dispersal capacities. Genetic diversity was found to be higher in island than in continental populations, contributing to mounting evidence that, contrary to theoretical expectations, island populations are not necessarily genetically depauperate. Patterns of genetic variation among island and continental populations consistently fitted those simulated under a scenario of de novo foundation of continental populations from insular ancestors better than those expected if islands would represent a sink or a refugium of continental biodiversity. We, suggest that the northeastern Atlantic archipelagos have played a key role as a stepping stone for transoceanic migrants. Our results challenge the traditional notion that oceanic islands are the end of the colonization road and illustrate the significant role of oceanic islands as reservoirs of novel biodiversity for the assembly of continental floras. © The Author(s) 2015. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Origin and Dispersal History of Two Colonial Ascidian Clades in the Botryllus schlosseri Species Complex.

PubMed

Nydam, Marie L; Giesbrecht, Kirsten B; Stephenson, Emily E

2017-01-01

Human-induced global warming and species introductions are rapidly altering the composition and functioning of Earth's marine ecosystems. Ascidians (Phylum Chordata, Subphylum Tunicata, Class Ascidiacea) are likely to play an increasingly greater role in marine communities. The colonial ascidian B. schlosseri is a cryptic species complex comprising five genetically divergent clades (A-E). Clade A is a global species, and Clade E has so far been identified in European waters only. Using the largest mitochondrial cytochrome oxidase I datasets yet assembled, we determine the origin and dispersal history of these species. Nucleotide diversity and Approximate Bayesian Computation analyses support a Pacific origin for Clade A, with two likely dispersal scenarios that both show the northwestern Atlantic populations establishing early in the history of the species. Both Discrete Phylogeographic Analysis and Approximate Bayesian Computation support an origin of Clade E on the French side of the English Channel. An unsampled lineage evolved from the French lineage, which reflects the conclusion from the median joining network that not all Clade E lineages have been sampled. This unsampled lineage gave rise to the haplotypes on the English side of the English Channel, which were the ancestors to the Mediterranean and Bay of Biscay populations. Clade E has a wider geographic range than previously thought, and shows evidence of recent range expansion. Both Clade A and Clade E should be considered widespread species: Clade A globally and Clade E within Europe.

Integrating Crop Growth Models with Whole Genome Prediction through Approximate Bayesian Computation.

PubMed

Technow, Frank; Messina, Carlos D; Totir, L Radu; Cooper, Mark

2015-01-01

Genomic selection, enabled by whole genome prediction (WGP) methods, is revolutionizing plant breeding. Existing WGP methods have been shown to deliver accurate predictions in the most common settings, such as prediction of across environment performance for traits with additive gene effects. However, prediction of traits with non-additive gene effects and prediction of genotype by environment interaction (G×E), continues to be challenging. Previous attempts to increase prediction accuracy for these particularly difficult tasks employed prediction methods that are purely statistical in nature. Augmenting the statistical methods with biological knowledge has been largely overlooked thus far. Crop growth models (CGMs) attempt to represent the impact of functional relationships between plant physiology and the environment in the formation of yield and similar output traits of interest. Thus, they can explain the impact of G×E and certain types of non-additive gene effects on the expressed phenotype. Approximate Bayesian computation (ABC), a novel and powerful computational procedure, allows the incorporation of CGMs directly into the estimation of whole genome marker effects in WGP. Here we provide a proof of concept study for this novel approach and demonstrate its use with synthetic data sets. We show that this novel approach can be considerably more accurate than the benchmark WGP method GBLUP in predicting performance in environments represented in the estimation set as well as in previously unobserved environments for traits determined by non-additive gene effects. We conclude that this proof of concept demonstrates that using ABC for incorporating biological knowledge in the form of CGMs into WGP is a very promising and novel approach to improving prediction accuracy for some of the most challenging scenarios in plant breeding and applied genetics.

Integrating Crop Growth Models with Whole Genome Prediction through Approximate Bayesian Computation

PubMed Central

Technow, Frank; Messina, Carlos D.; Totir, L. Radu; Cooper, Mark

2015-01-01

Genomic selection, enabled by whole genome prediction (WGP) methods, is revolutionizing plant breeding. Existing WGP methods have been shown to deliver accurate predictions in the most common settings, such as prediction of across environment performance for traits with additive gene effects. However, prediction of traits with non-additive gene effects and prediction of genotype by environment interaction (G×E), continues to be challenging. Previous attempts to increase prediction accuracy for these particularly difficult tasks employed prediction methods that are purely statistical in nature. Augmenting the statistical methods with biological knowledge has been largely overlooked thus far. Crop growth models (CGMs) attempt to represent the impact of functional relationships between plant physiology and the environment in the formation of yield and similar output traits of interest. Thus, they can explain the impact of G×E and certain types of non-additive gene effects on the expressed phenotype. Approximate Bayesian computation (ABC), a novel and powerful computational procedure, allows the incorporation of CGMs directly into the estimation of whole genome marker effects in WGP. Here we provide a proof of concept study for this novel approach and demonstrate its use with synthetic data sets. We show that this novel approach can be considerably more accurate than the benchmark WGP method GBLUP in predicting performance in environments represented in the estimation set as well as in previously unobserved environments for traits determined by non-additive gene effects. We conclude that this proof of concept demonstrates that using ABC for incorporating biological knowledge in the form of CGMs into WGP is a very promising and novel approach to improving prediction accuracy for some of the most challenging scenarios in plant breeding and applied genetics. PMID:26121133

Donor-Recipient Identification in Para- and Poly-phyletic Trees Under Alternative HIV-1 Transmission Hypotheses Using Approximate Bayesian Computation

PubMed Central

Romero-Severson, Ethan O.; Bulla, Ingo; Hengartner, Nick; Bártolo, Inês; Abecasis, Ana; Azevedo-Pereira, José M.; Taveira, Nuno; Leitner, Thomas

2017-01-01

Diversity of the founding population of Human Immunodeficiency Virus Type 1 (HIV-1) transmissions raises many important biological, clinical, and epidemiological issues. In up to 40% of sexual infections, there is clear evidence for multiple founding variants, which can influence the efficacy of putative prevention methods, and the reconstruction of epidemiologic histories. To infer who-infected-whom, and to compute the probability of alternative transmission scenarios while explicitly taking phylogenetic uncertainty into account, we created an approximate Bayesian computation (ABC) method based on a set of statistics measuring phylogenetic topology, branch lengths, and genetic diversity. We applied our method to a suspected heterosexual transmission case involving three individuals, showing a complex monophyletic-paraphyletic-polyphyletic phylogenetic topology. We detected that seven phylogenetic lineages had been transmitted between two of the individuals based on the available samples, implying that many more unsampled lineages had also been transmitted. Testing whether the lineages had been transmitted at one time or over some length of time suggested that an ongoing superinfection process over several years was most likely. While one individual was found unlinked to the other two, surprisingly, when evaluating two competing epidemiological priors, the donor of the two that did infect each other was not identified by the host root-label, and was also not the primary suspect in that transmission. This highlights that it is important to take epidemiological information into account when analyzing support for one transmission hypothesis over another, as results may be nonintuitive and sensitive to details about sampling dates relative to possible infection dates. Our study provides a formal inference framework to include information on infection and sampling times, and to investigate ancestral node-label states, transmission direction, transmitted genetic diversity, and frequency of transmission. PMID:28912340

Implementing a Bayes Filter in a Neural Circuit: The Case of Unknown Stimulus Dynamics.

PubMed

Sokoloski, Sacha

2017-09-01

In order to interact intelligently with objects in the world, animals must first transform neural population responses into estimates of the dynamic, unknown stimuli that caused them. The Bayesian solution to this problem is known as a Bayes filter, which applies Bayes' rule to combine population responses with the predictions of an internal model. The internal model of the Bayes filter is based on the true stimulus dynamics, and in this note, we present a method for training a theoretical neural circuit to approximately implement a Bayes filter when the stimulus dynamics are unknown. To do this we use the inferential properties of linear probabilistic population codes to compute Bayes' rule and train a neural network to compute approximate predictions by the method of maximum likelihood. In particular, we perform stochastic gradient descent on the negative log-likelihood of the neural network parameters with a novel approximation of the gradient. We demonstrate our methods on a finite-state, a linear, and a nonlinear filtering problem and show how the hidden layer of the neural network develops tuning curves consistent with findings in experimental neuroscience.

With or without you: predictive coding and Bayesian inference in the brain

PubMed Central

Aitchison, Laurence; Lengyel, Máté

2018-01-01

Two theoretical ideas have emerged recently with the ambition to provide a unifying functional explanation of neural population coding and dynamics: predictive coding and Bayesian inference. Here, we describe the two theories and their combination into a single framework: Bayesian predictive coding. We clarify how the two theories can be distinguished, despite sharing core computational concepts and addressing an overlapping set of empirical phenomena. We argue that predictive coding is an algorithmic / representational motif that can serve several different computational goals of which Bayesian inference is but one. Conversely, while Bayesian inference can utilize predictive coding, it can also be realized by a variety of other representations. We critically evaluate the experimental evidence supporting Bayesian predictive coding and discuss how to test it more directly. PMID:28942084

Arlequin suite ver 3.5: a new series of programs to perform population genetics analyses under Linux and Windows.

PubMed

Excoffier, Laurent; Lischer, Heidi E L

2010-05-01

We present here a new version of the Arlequin program available under three different forms: a Windows graphical version (Winarl35), a console version of Arlequin (arlecore), and a specific console version to compute summary statistics (arlsumstat). The command-line versions run under both Linux and Windows. The main innovations of the new version include enhanced outputs in XML format, the possibility to embed graphics displaying computation results directly into output files, and the implementation of a new method to detect loci under selection from genome scans. Command-line versions are designed to handle large series of files, and arlsumstat can be used to generate summary statistics from simulated data sets within an Approximate Bayesian Computation framework. © 2010 Blackwell Publishing Ltd.

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.

Sampling-free Bayesian inversion with adaptive hierarchical tensor representations

NASA Astrophysics Data System (ADS)

Eigel, Martin; Marschall, Manuel; Schneider, Reinhold

2018-03-01

A sampling-free approach to Bayesian inversion with an explicit polynomial representation of the parameter densities is developed, based on an affine-parametric representation of a linear forward model. This becomes feasible due to the complete treatment in function spaces, which requires an efficient model reduction technique for numerical computations. The advocated perspective yields the crucial benefit that error bounds can be derived for all occuring approximations, leading to provable convergence subject to the discretization parameters. Moreover, it enables a fully adaptive a posteriori control with automatic problem-dependent adjustments of the employed discretizations. The method is discussed in the context of modern hierarchical tensor representations, which are used for the evaluation of a random PDE (the forward model) and the subsequent high-dimensional quadrature of the log-likelihood, alleviating the ‘curse of dimensionality’. Numerical experiments demonstrate the performance and confirm the theoretical results.

Inference of missing data and chemical model parameters using experimental statistics

NASA Astrophysics Data System (ADS)

Casey, Tiernan; Najm, Habib

2017-11-01

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

Bayesian bivariate meta-analysis of diagnostic test studies with interpretable priors.

PubMed

Guo, Jingyi; Riebler, Andrea; Rue, Håvard

2017-08-30

In a bivariate meta-analysis, the number of diagnostic studies involved is often very low so that frequentist methods may result in problems. Using Bayesian inference is particularly attractive as informative priors that add a small amount of information can stabilise the analysis without overwhelming the data. However, Bayesian analysis is often computationally demanding and the selection of the prior for the covariance matrix of the bivariate structure is crucial with little data. The integrated nested Laplace approximations method provides an efficient solution to the computational issues by avoiding any sampling, but the important question of priors remain. We explore the penalised complexity (PC) prior framework for specifying informative priors for the variance parameters and the correlation parameter. PC priors facilitate model interpretation and hyperparameter specification as expert knowledge can be incorporated intuitively. We conduct a simulation study to compare the properties and behaviour of differently defined PC priors to currently used priors in the field. The simulation study shows that the PC prior seems beneficial for the variance parameters. The use of PC priors for the correlation parameter results in more precise estimates when specified in a sensible neighbourhood around the truth. To investigate the usage of PC priors in practice, we reanalyse a meta-analysis using the telomerase marker for the diagnosis of bladder cancer and compare the results with those obtained by other commonly used modelling approaches. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

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

Contrast enhancement in EIT imaging of the brain.

PubMed

Nissinen, A; Kaipio, J P; Vauhkonen, M; Kolehmainen, V

2016-01-01

We consider electrical impedance tomography (EIT) imaging of the brain. The brain is surrounded by the poorly conducting skull which has low conductivity compared to the brain. The skull layer causes a partial shielding effect which leads to weak sensitivity for the imaging of the brain tissue. In this paper we propose an approach based on the Bayesian approximation error approach, to enhance the contrast in brain imaging. With this approach, both the (uninteresting) geometry and the conductivity of the skull are embedded in the approximation error statistics, which leads to a computationally efficient algorithm that is able to detect features such as internal haemorrhage with significantly increased sensitivity and specificity. We evaluate the approach with simulations and phantom data.

Digest: Demographic inferences accounting for selection at linked sites†.

PubMed

Simon, Alexis; Duranton, Maud

2018-05-16

Complex demography and selection at linked sites can generate spurious signatures of divergent selection. Unfortunately, many attempts at demographic inference consider overly simple models and neglect the effect of selection at linked sites. In this issue, Rougemont and Bernatchez (2018) applied an approximate Bayesian computation (ABC) framework that accounts for indirect selection to reveal a complex history of secondary contacts in Atlantic salmon (Salmo salar) that might explain a high rate of latitudinal clines in this species. © 2018 The Author(s). Evolution © 2018 The Society for the Study of Evolution.

Approximate Bayesian Computation Using Markov Chain Monte Carlo Simulation: Theory, Concepts, and Applications

NASA Astrophysics Data System (ADS)

Sadegh, M.; Vrugt, J. A.

2013-12-01

The ever increasing pace of computational power, along with continued advances in measurement technologies and improvements in process understanding has stimulated the development of increasingly complex hydrologic models that simulate soil moisture flow, groundwater recharge, surface runoff, root water uptake, and river discharge at increasingly finer spatial and temporal scales. Reconciling these system models with field and remote sensing data is a difficult task, particularly because average measures of model/data similarity inherently lack the power to provide a meaningful comparative evaluation of the consistency in model form and function. The very construction of the likelihood function - as a summary variable of the (usually averaged) properties of the error residuals - dilutes and mixes the available information into an index having little remaining correspondence to specific behaviors of the system (Gupta et al., 2008). The quest for a more powerful method for model evaluation has inspired Vrugt and Sadegh [2013] to introduce "likelihood-free" inference as vehicle for diagnostic model evaluation. This class of methods is also referred to as Approximate Bayesian Computation (ABC) and relaxes the need for an explicit likelihood function in favor of one or multiple different summary statistics rooted in hydrologic theory that together have a much stronger and compelling diagnostic power than some aggregated measure of the size of the error residuals. Here, we will introduce an efficient ABC sampling method that is orders of magnitude faster in exploring the posterior parameter distribution than commonly used rejection and Population Monte Carlo (PMC) samplers. Our methodology uses Markov Chain Monte Carlo simulation with DREAM, and takes advantage of a simple computational trick to resolve discontinuity problems with the application of set-theoretic summary statistics. We will also demonstrate a set of summary statistics that are rather insensitive to errors in the forcing data. This enhances prospects of detecting model structural deficiencies.

Cross-Cultural Invariance of the Mental Toughness Inventory Among Australian, Chinese, and Malaysian Athletes: A Bayesian Estimation Approach.

PubMed

Gucciardi, Daniel F; Zhang, Chun-Qing; Ponnusamy, Vellapandian; Si, Gangyan; Stenling, Andreas

2016-04-01

The aims of this study were to assess the cross-cultural invariance of athletes' self-reports of mental toughness and to introduce and illustrate the application of approximate measurement invariance using Bayesian estimation for sport and exercise psychology scholars. Athletes from Australia (n = 353, Mage = 19.13, SD = 3.27, men = 161), China (n = 254, Mage = 17.82, SD = 2.28, men = 138), and Malaysia (n = 341, Mage = 19.13, SD = 3.27, men = 200) provided a cross-sectional snapshot of their mental toughness. The cross-cultural invariance of the mental toughness inventory in terms of (a) the factor structure (configural invariance), (b) factor loadings (metric invariance), and (c) item intercepts (scalar invariance) was tested using an approximate measurement framework with Bayesian estimation. Results indicated that approximate metric and scalar invariance was established. From a methodological standpoint, this study demonstrated the usefulness and flexibility of Bayesian estimation for single-sample and multigroup analyses of measurement instruments. Substantively, the current findings suggest that the measurement of mental toughness requires cultural adjustments to better capture the contextually salient (emic) aspects of this concept.

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 cost minimisation and Bayesian inference model predicts startle reflex modulation across species.

PubMed

Bach, Dominik R

2015-04-07

In many species, rapid defensive reflexes are paramount to escaping acute danger. These reflexes are modulated by the state of the environment. This is exemplified in fear-potentiated startle, a more vigorous startle response during conditioned anticipation of an unrelated threatening event. Extant explanations of this phenomenon build on descriptive models of underlying psychological states, or neural processes. Yet, they fail to predict invigorated startle during reward anticipation and instructed attention, and do not explain why startle reflex modulation evolved. Here, we fill this lacuna by developing a normative cost minimisation model based on Bayesian optimality principles. This model predicts the observed pattern of startle modification by rewards, punishments, instructed attention, and several other states. Moreover, the mathematical formalism furnishes predictions that can be tested experimentally. Comparing the model with existing data suggests a specific neural implementation of the underlying computations which yields close approximations to the optimal solution under most circumstances. This analysis puts startle modification into the framework of Bayesian decision theory and predictive coding, and illustrates the importance of an adaptive perspective to interpret defensive behaviour across species. Copyright © 2015 The Author. Published by Elsevier Ltd.. All rights reserved.

Utility-based designs for randomized comparative trials with categorical outcomes

PubMed Central

Murray, Thomas A.; Thall, Peter F.; Yuan, Ying

2016-01-01

A general utility-based testing methodology for design and conduct of randomized comparative clinical trials with categorical outcomes is presented. Numerical utilities of all elementary events are elicited to quantify their desirabilities. These numerical values are used to map the categorical outcome probability vector of each treatment to a mean utility, which is used as a one-dimensional criterion for constructing comparative tests. Bayesian tests are presented, including fixed sample and group sequential procedures, assuming Dirichlet-multinomial models for the priors and likelihoods. Guidelines are provided for establishing priors, eliciting utilities, and specifying hypotheses. Efficient posterior computation is discussed, and algorithms are provided for jointly calibrating test cutoffs and sample size to control overall type I error and achieve specified power. Asymptotic approximations for the power curve are used to initialize the algorithms. The methodology is applied to re-design a completed trial that compared two chemotherapy regimens for chronic lymphocytic leukemia, in which an ordinal efficacy outcome was dichotomized and toxicity was ignored to construct the trial’s design. The Bayesian tests also are illustrated by several types of categorical outcomes arising in common clinical settings. Freely available computer software for implementation is provided. PMID:27189672

Bayesian statistical ionospheric tomography improved by incorporating ionosonde measurements

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

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.

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

PubMed

Wang, Jiali; Zhang, Qingnian; Ji, Wenfeng

2014-01-01

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

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

PubMed Central

Wang, Jiali; Zhang, Qingnian; Ji, Wenfeng

2014-01-01

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

Learning topic models by belief propagation.

PubMed

Zeng, Jia; Cheung, William K; Liu, Jiming

2013-05-01

Latent Dirichlet allocation (LDA) is an important hierarchical Bayesian model for probabilistic topic modeling, which attracts worldwide interest and touches on many important applications in text mining, computer vision and computational biology. This paper represents the collapsed LDA as a factor graph, which enables the classic loopy belief propagation (BP) algorithm for approximate inference and parameter estimation. Although two commonly used approximate inference methods, such as variational Bayes (VB) and collapsed Gibbs sampling (GS), have gained great success in learning LDA, the proposed BP is competitive in both speed and accuracy, as validated by encouraging experimental results on four large-scale document datasets. Furthermore, the BP algorithm has the potential to become a generic scheme for learning variants of LDA-based topic models in the collapsed space. To this end, we show how to learn two typical variants of LDA-based topic models, such as author-topic models (ATM) and relational topic models (RTM), using BP based on the factor graph representations.

Birth/birth-death processes and their computable transition probabilities with biological applications.

PubMed

Ho, Lam Si Tung; Xu, Jason; Crawford, Forrest W; Minin, Vladimir N; Suchard, Marc A

2018-03-01

Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computationally expensive methods such as matrix exponentiation or Monte Carlo approximation, restricting likelihood-based inference to small systems, or indirect methods such as approximate Bayesian computation. In this paper, we introduce the birth/birth-death process, a tractable bivariate extension of the birth-death process, where rates are allowed to be nonlinear. We develop an efficient algorithm to calculate its transition probabilities using a continued fraction representation of their Laplace transforms. Next, we identify several exemplary models arising in molecular epidemiology, macro-parasite evolution, and infectious disease modeling that fall within this class, and demonstrate advantages of our proposed method over existing approaches to inference in these models. Notably, the ubiquitous stochastic susceptible-infectious-removed (SIR) model falls within this class, and we emphasize that computable transition probabilities newly enable direct inference of parameters in the SIR model. We also propose a very fast method for approximating the transition probabilities under the SIR model via a novel branching process simplification, and compare it to the continued fraction representation method with application to the 17th century plague in Eyam. Although the two methods produce similar maximum a posteriori estimates, the branching process approximation fails to capture the correlation structure in the joint posterior distribution.

MapReduce Based Parallel Bayesian Network for Manufacturing Quality Control

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Survival Bayesian Estimation of Exponential-Gamma Under Linex Loss Function

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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

PubMed

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

2012-11-01

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

Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods

DOE PAGES

Liu, Peigui; Elshall, Ahmed S.; Ye, Ming; ...

2016-02-05

Evaluating marginal likelihood is the most critical and computationally expensive task, when conducting Bayesian model averaging to quantify parametric and model uncertainties. The evaluation is commonly done by using Laplace approximations to evaluate semianalytical expressions of the marginal likelihood or by using Monte Carlo (MC) methods to evaluate arithmetic or harmonic mean of a joint likelihood function. This study introduces a new MC method, i.e., thermodynamic integration, which has not been attempted in environmental modeling. Instead of using samples only from prior parameter space (as in arithmetic mean evaluation) or posterior parameter space (as in harmonic mean evaluation), the thermodynamicmore » integration method uses samples generated gradually from the prior to posterior parameter space. This is done through a path sampling that conducts Markov chain Monte Carlo simulation with different power coefficient values applied to the joint likelihood function. The thermodynamic integration method is evaluated using three analytical functions by comparing the method with two variants of the Laplace approximation method and three MC methods, including the nested sampling method that is recently introduced into environmental modeling. The thermodynamic integration method outperforms the other methods in terms of their accuracy, convergence, and consistency. The thermodynamic integration method is also applied to a synthetic case of groundwater modeling with four alternative models. The application shows that model probabilities obtained using the thermodynamic integration method improves predictive performance of Bayesian model averaging. As a result, the thermodynamic integration method is mathematically rigorous, and its MC implementation is computationally general for a wide range of environmental problems.« less

Climate change and the spread of vector-borne diseases: using approximate Bayesian computation to compare invasion scenarios for the bluetongue virus vector Culicoides imicola in Italy.

PubMed

Mardulyn, Patrick; Goffredo, Maria; Conte, Annamaria; Hendrickx, Guy; Meiswinkel, Rudolf; Balenghien, Thomas; Sghaier, Soufien; Lohr, Youssef; Gilbert, Marius

2013-05-01

Bluetongue (BT) is a commonly cited example of a disease with a distribution believed to have recently expanded in response to global warming. The BT virus is transmitted to ruminants by biting midges of the genus Culicoides, and it has been hypothesized that the emergence of BT in Mediterranean Europe during the last two decades is a consequence of the recent colonization of the region by Culicoides imicola and linked to climate change. To better understand the mechanism responsible for the northward spread of BT, we tested the hypothesis of a recent colonization of Italy by C. imicola, by obtaining samples from more than 60 localities across Italy, Corsica, Southern France, and Northern Africa (the hypothesized source point for the recent invasion of C. imicola), and by genotyping them with 10 newly identified microsatellite loci. The patterns of genetic variation within and among the sampled populations were characterized and used in a rigorous approximate Bayesian computation framework to compare three competing historical hypotheses related to the arrival and establishment of C. imicola in Italy. The hypothesis of an ancient presence of the insect vector was strongly favoured by this analysis, with an associated P ≥ 99%, suggesting that causes other than the northward range expansion of C. imicola may have supported the emergence of BT in southern Europe. Overall, this study illustrates the potential of molecular genetic markers for exploring the assumed link between climate change and the spread of diseases. © 2013 Blackwell Publishing Ltd.

A Novel Approach for Choosing Summary Statistics in Approximate Bayesian Computation

PubMed Central

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

2012-01-01

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

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.

Joint Model and Parameter Dimension Reduction for Bayesian Inversion Applied to an Ice Sheet Flow Problem

NASA Astrophysics Data System (ADS)

Ghattas, O.; Petra, N.; Cui, T.; Marzouk, Y.; Benjamin, P.; Willcox, K.

2016-12-01

Model-based projections of the dynamics of the polar ice sheets play a central role in anticipating future sea level rise. However, a number of mathematical and computational challenges place significant barriers on improving predictability of these models. One such challenge is caused by the unknown model parameters (e.g., in the basal boundary conditions) that must be inferred from heterogeneous observational data, leading to an ill-posed inverse problem and the need to quantify uncertainties in its solution. In this talk we discuss the problem of estimating the uncertainty in the solution of (large-scale) ice sheet inverse problems within the framework of Bayesian inference. Computing the general solution of the inverse problem--i.e., the posterior probability density--is intractable with current methods on today's computers, due to the expense of solving the forward model (3D full Stokes flow with nonlinear rheology) and the high dimensionality of the uncertain parameters (which are discretizations of the basal sliding coefficient field). To overcome these twin computational challenges, it is essential to exploit problem structure (e.g., sensitivity of the data to parameters, the smoothing property of the forward model, and correlations in the prior). To this end, we present a data-informed approach that identifies low-dimensional structure in both parameter space and the forward model state space. This approach exploits the fact that the observations inform only a low-dimensional parameter space and allows us to construct a parameter-reduced posterior. Sampling this parameter-reduced posterior still requires multiple evaluations of the forward problem, therefore we also aim to identify a low dimensional state space to reduce the computational cost. To this end, we apply a proper orthogonal decomposition (POD) approach to approximate the state using a low-dimensional manifold constructed using ``snapshots'' from the parameter reduced posterior, and the discrete empirical interpolation method (DEIM) to approximate the nonlinearity in the forward problem. We show that using only a limited number of forward solves, the resulting subspaces lead to an efficient method to explore the high-dimensional posterior.

Multimodal, high-dimensional, model-based, Bayesian inverse problems with applications in biomechanics

NASA Astrophysics Data System (ADS)

Franck, I. M.; Koutsourelakis, P. S.

2017-01-01

This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of unknown (latent) variables is high. This is the setting in many problems in computational physics where forward models with nonlinear PDEs are used and the parameters to be calibrated involve spatio-temporarily varying coefficients, which upon discretization give rise to a high-dimensional vector of unknowns. One of the consequences of the well-documented ill-posedness of inverse problems is the possibility of multiple solutions. While such information is contained in the posterior density in Bayesian formulations, the discovery of a single mode, let alone multiple, poses a formidable computational task. The goal of the present paper is two-fold. On one hand, we propose approximate, adaptive inference strategies using mixture densities to capture multi-modal posteriors. On the other, we extend our work in [1] with regard to effective dimensionality reduction techniques that reveal low-dimensional subspaces where the posterior variance is mostly concentrated. We validate the proposed model by employing Importance Sampling which confirms that the bias introduced is small and can be efficiently corrected if the analyst wishes to do so. We demonstrate the performance of the proposed strategy in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, medical diagnosis. The discovery of multiple modes (solutions) in such problems is critical in achieving the diagnostic objectives.

Bayesian modeling of flexible cognitive control

PubMed Central

Jiang, Jiefeng; Heller, Katherine; Egner, Tobias

2014-01-01

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

A New Approach for Obtaining Cosmological Constraints from Type Ia Supernovae using Approximate Bayesian Computation

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

Jennings, Elise; Wolf, Rachel; Sako, Masao

2016-11-09

Cosmological parameter estimation techniques that robustly account for systematic measurement uncertainties will be crucial for the next generation of cosmological surveys. We present a new analysis method, superABC, for obtaining cosmological constraints from Type Ia supernova (SN Ia) light curves using Approximate Bayesian Computation (ABC) without any likelihood assumptions. The ABC method works by using a forward model simulation of the data where systematic uncertainties can be simulated and marginalized over. A key feature of the method presented here is the use of two distinct metrics, the `Tripp' and `Light Curve' metrics, which allow us to compare the simulated data to the observed data set. The Tripp metric takes as input the parameters of models fit to each light curve with the SALT-II method, whereas the Light Curve metric uses the measured fluxes directly without model fitting. We apply the superABC sampler to a simulated data set ofmore » $$\\sim$$1000 SNe corresponding to the first season of the Dark Energy Survey Supernova Program. Varying $$\\Omega_m, w_0, \\alpha$$ and $$\\beta$$ and a magnitude offset parameter, with no systematics we obtain $$\\Delta(w_0) = w_0^{\\rm true} - w_0^{\\rm best \\, fit} = -0.036\\pm0.109$$ (a $$\\sim11$$% 1$$\\sigma$$ uncertainty) using the Tripp metric and $$\\Delta(w_0) = -0.055\\pm0.068$$ (a $$\\sim7$$% 1$$\\sigma$$ uncertainty) using the Light Curve metric. Including 1% calibration uncertainties in four passbands, adding 4 more parameters, we obtain $$\\Delta(w_0) = -0.062\\pm0.132$$ (a $$\\sim14$$% 1$$\\sigma$$ uncertainty) using the Tripp metric. Overall we find a $17$% increase in the uncertainty on $$w_0$$ with systematics compared to without. We contrast this with a MCMC approach where systematic effects are approximately included. We find that the MCMC method slightly underestimates the impact of calibration uncertainties for this simulated data set.« less

Bayesian Analysis for Exponential Random Graph Models Using the Adaptive Exchange Sampler.

PubMed

Jin, Ick Hoon; Yuan, Ying; Liang, Faming

2013-10-01

Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the intractable normalizing constant and model degeneracy. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the intractable normalizing constant and model degeneracy issues encountered in Markov chain Monte Carlo (MCMC) simulations. The adaptive exchange sampler can be viewed as a MCMC extension of the exchange algorithm, and it generates auxiliary networks via an importance sampling procedure from an auxiliary Markov chain running in parallel. The convergence of this algorithm is established under mild conditions. The adaptive exchange sampler is illustrated using a few social networks, including the Florentine business network, molecule synthetic network, and dolphins network. The results indicate that the adaptive exchange algorithm can produce more accurate estimates than approximate exchange algorithms, while maintaining the same computational efficiency.

Efficient Monte Carlo Estimation of the Expected Value of Sample Information Using Moment Matching.

PubMed

Heath, Anna; Manolopoulou, Ioanna; Baio, Gianluca

2018-02-01

The Expected Value of Sample Information (EVSI) is used to calculate the economic value of a new research strategy. Although this value would be important to both researchers and funders, there are very few practical applications of the EVSI. This is due to computational difficulties associated with calculating the EVSI in practical health economic models using nested simulations. We present an approximation method for the EVSI that is framed in a Bayesian setting and is based on estimating the distribution of the posterior mean of the incremental net benefit across all possible future samples, known as the distribution of the preposterior mean. Specifically, this distribution is estimated using moment matching coupled with simulations that are available for probabilistic sensitivity analysis, which is typically mandatory in health economic evaluations. This novel approximation method is applied to a health economic model that has previously been used to assess the performance of other EVSI estimators and accurately estimates the EVSI. The computational time for this method is competitive with other methods. We have developed a new calculation method for the EVSI which is computationally efficient and accurate. This novel method relies on some additional simulation so can be expensive in models with a large computational cost.

The Utility of Cognitive Plausibility in Language Acquisition Modeling: Evidence From Word Segmentation.

PubMed

Phillips, Lawrence; Pearl, Lisa

2015-11-01

The informativity of a computational model of language acquisition is directly related to how closely it approximates the actual acquisition task, sometimes referred to as the model's cognitive plausibility. We suggest that though every computational model necessarily idealizes the modeled task, an informative language acquisition model can aim to be cognitively plausible in multiple ways. We discuss these cognitive plausibility checkpoints generally and then apply them to a case study in word segmentation, investigating a promising Bayesian segmentation strategy. We incorporate cognitive plausibility by using an age-appropriate unit of perceptual representation, evaluating the model output in terms of its utility, and incorporating cognitive constraints into the inference process. Our more cognitively plausible model shows a beneficial effect of cognitive constraints on segmentation performance. One interpretation of this effect is as a synergy between the naive theories of language structure that infants may have and the cognitive constraints that limit the fidelity of their inference processes, where less accurate inference approximations are better when the underlying assumptions about how words are generated are less accurate. More generally, these results highlight the utility of incorporating cognitive plausibility more fully into computational models of language acquisition. Copyright © 2015 Cognitive Science Society, Inc.

The Bayesian Revolution Approaches Psychological Development

ERIC Educational Resources Information Center

Shultz, Thomas R.

2007-01-01

This commentary reviews five articles that apply Bayesian ideas to psychological development, some with psychology experiments, some with computational modeling, and some with both experiments and modeling. The reviewed work extends the current Bayesian revolution into tasks often studied in children, such as causal learning and word learning, and…

Probabilistic Space Weather Forecasting: a Bayesian Perspective

NASA Astrophysics Data System (ADS)

Camporeale, E.; Chandorkar, M.; Borovsky, J.; Care', A.

2017-12-01

Most of the Space Weather forecasts, both at operational and research level, are not probabilistic in nature. Unfortunately, a prediction that does not provide a confidence level is not very useful in a decision-making scenario. Nowadays, forecast models range from purely data-driven, machine learning algorithms, to physics-based approximation of first-principle equations (and everything that sits in between). Uncertainties pervade all such models, at every level: from the raw data to finite-precision implementation of numerical methods. The most rigorous way of quantifying the propagation of uncertainties is by embracing a Bayesian probabilistic approach. One of the simplest and most robust machine learning technique in the Bayesian framework is Gaussian Process regression and classification. Here, we present the application of Gaussian Processes to the problems of the DST geomagnetic index forecast, the solar wind type classification, and the estimation of diffusion parameters in radiation belt modeling. In each of these very diverse problems, the GP approach rigorously provide forecasts in the form of predictive distributions. In turn, these distributions can be used as input for ensemble simulations in order to quantify the amplification of uncertainties. We show that we have achieved excellent results in all of the standard metrics to evaluate our models, with very modest computational cost.

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

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

Sandhu, Rimple; Poirel, Dominique; Pettit, Chris

2016-07-01

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

Bayesian Analysis of High Dimensional Classification

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Subhadeep; Liang, Faming

2009-12-01

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

Bayesian Travel Time Inversion adopting Gaussian Process Regression

NASA Astrophysics Data System (ADS)

Mauerberger, S.; Holschneider, M.

2017-12-01

A major application in seismology is the determination of seismic velocity models. Travel time measurements are putting an integral constraint on the velocity between source and receiver. We provide insight into travel time inversion from a correlation-based Bayesian point of view. Therefore, the concept of Gaussian process regression is adopted to estimate a velocity model. The non-linear travel time integral is approximated by a 1st order Taylor expansion. A heuristic covariance describes correlations amongst observations and a priori model. That approach enables us to assess a proxy of the Bayesian posterior distribution at ordinary computational costs. No multi dimensional numeric integration nor excessive sampling is necessary. Instead of stacking the data, we suggest to progressively build the posterior distribution. Incorporating only a single evidence at a time accounts for the deficit of linearization. As a result, the most probable model is given by the posterior mean whereas uncertainties are described by the posterior covariance.As a proof of concept, a synthetic purely 1d model is addressed. Therefore a single source accompanied by multiple receivers is considered on top of a model comprising a discontinuity. We consider travel times of both phases - direct and reflected wave - corrupted by noise. Left and right of the interface are assumed independent where the squared exponential kernel serves as covariance.

False Discovery Control in Large-Scale Spatial Multiple Testing

PubMed Central

Sun, Wenguang; Reich, Brian J.; Cai, T. Tony; Guindani, Michele; Schwartzman, Armin

2014-01-01

Summary This article develops a unified theoretical and computational framework for false discovery control in multiple testing of spatial signals. We consider both point-wise and cluster-wise spatial analyses, and derive oracle procedures which optimally control the false discovery rate, false discovery exceedance and false cluster rate, respectively. A data-driven finite approximation strategy is developed to mimic the oracle procedures on a continuous spatial domain. Our multiple testing procedures are asymptotically valid and can be effectively implemented using Bayesian computational algorithms for analysis of large spatial data sets. Numerical results show that the proposed procedures lead to more accurate error control and better power performance than conventional methods. We demonstrate our methods for analyzing the time trends in tropospheric ozone in eastern US. PMID:25642138

An ABC estimate of pedigree error rate: application in dog, sheep and cattle breeds.

PubMed

Leroy, G; Danchin-Burge, C; Palhiere, I; Baumung, R; Fritz, S; Mériaux, J C; Gautier, M

2012-06-01

On the basis of correlations between pairwise individual genealogical kinship coefficients and allele sharing distances computed from genotyping data, we propose an approximate Bayesian computation (ABC) approach to assess pedigree file reliability through gene-dropping simulations. We explore the features of the method using simulated data sets and show precision increases with the number of markers. An application is further made with five dog breeds, four sheep breeds and one cattle breed raised in France and displaying various characteristics and population sizes, using microsatellite or SNP markers. Depending on the breeds, pedigree error estimations range between 1% and 9% in dog breeds, 1% and 10% in sheep breeds and 4% in cattle breeds. © 2011 The Authors, Animal Genetics © 2011 Stichting International Foundation for Animal Genetics.

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.

Density-based empirical likelihood procedures for testing symmetry of data distributions and K-sample comparisons.

PubMed

Vexler, Albert; Tanajian, Hovig; Hutson, Alan D

In practice, parametric likelihood-ratio techniques are powerful statistical tools. In this article, we propose and examine novel and simple distribution-free test statistics that efficiently approximate parametric likelihood ratios to analyze and compare distributions of K groups of observations. Using the density-based empirical likelihood methodology, we develop a Stata package that applies to a test for symmetry of data distributions and compares K -sample distributions. Recognizing that recent statistical software packages do not sufficiently address K -sample nonparametric comparisons of data distributions, we propose a new Stata command, vxdbel, to execute exact density-based empirical likelihood-ratio tests using K samples. To calculate p -values of the proposed tests, we use the following methods: 1) a classical technique based on Monte Carlo p -value evaluations; 2) an interpolation technique based on tabulated critical values; and 3) a new hybrid technique that combines methods 1 and 2. The third, cutting-edge method is shown to be very efficient in the context of exact-test p -value computations. This Bayesian-type method considers tabulated critical values as prior information and Monte Carlo generations of test statistic values as data used to depict the likelihood function. In this case, a nonparametric Bayesian method is proposed to compute critical values of exact tests.

Objectified quantification of uncertainties in Bayesian atmospheric inversions

NASA Astrophysics Data System (ADS)

Berchet, A.; Pison, I.; Chevallier, F.; Bousquet, P.; Bonne, J.-L.; Paris, J.-D.

2015-05-01

Classical Bayesian atmospheric inversions process atmospheric observations and prior emissions, the two being connected by an observation operator picturing mainly the atmospheric transport. These inversions rely on prescribed errors in the observations, the prior emissions and the observation operator. When data pieces are sparse, inversion results are very sensitive to the prescribed error distributions, which are not accurately known. The classical Bayesian framework experiences difficulties in quantifying the impact of mis-specified error distributions on the optimized fluxes. In order to cope with this issue, we rely on recent research results to enhance the classical Bayesian inversion framework through a marginalization on a large set of plausible errors that can be prescribed in the system. The marginalization consists in computing inversions for all possible error distributions weighted by the probability of occurrence of the error distributions. The posterior distribution of the fluxes calculated by the marginalization is not explicitly describable. As a consequence, we carry out a Monte Carlo sampling based on an approximation of the probability of occurrence of the error distributions. This approximation is deduced from the well-tested method of the maximum likelihood estimation. Thus, the marginalized inversion relies on an automatic objectified diagnosis of the error statistics, without any prior knowledge about the matrices. It robustly accounts for the uncertainties on the error distributions, contrary to what is classically done with frozen expert-knowledge error statistics. Some expert knowledge is still used in the method for the choice of an emission aggregation pattern and of a sampling protocol in order to reduce the computation cost. The relevance and the robustness of the method is tested on a case study: the inversion of methane surface fluxes at the mesoscale with virtual observations on a realistic network in Eurasia. Observing system simulation experiments are carried out with different transport patterns, flux distributions and total prior amounts of emitted methane. The method proves to consistently reproduce the known "truth" in most cases, with satisfactory tolerance intervals. Additionally, the method explicitly provides influence scores and posterior correlation matrices. An in-depth interpretation of the inversion results is then possible. The more objective quantification of the influence of the observations on the fluxes proposed here allows us to evaluate the impact of the observation network on the characterization of the surface fluxes. The explicit correlations between emission aggregates reveal the mis-separated regions, hence the typical temporal and spatial scales the inversion can analyse. These scales are consistent with the chosen aggregation patterns.

Detecting concerted demographic response across community assemblages using hierarchical approximate Bayesian computation.

PubMed

Chan, Yvonne L; Schanzenbach, David; Hickerson, Michael J

2014-09-01

Methods that integrate population-level sampling from multiple taxa into a single community-level analysis are an essential addition to the comparative phylogeographic toolkit. Detecting how species within communities have demographically tracked each other in space and time is important for understanding the effects of future climate and landscape changes and the resulting acceleration of extinctions, biological invasions, and potential surges in adaptive evolution. Here, we present a statistical framework for such an analysis based on hierarchical approximate Bayesian computation (hABC) with the goal of detecting concerted demographic histories across an ecological assemblage. Our method combines population genetic data sets from multiple taxa into a single analysis to estimate: 1) the proportion of a community sample that demographically expanded in a temporally clustered pulse and 2) when the pulse occurred. To validate the accuracy and utility of this new approach, we use simulation cross-validation experiments and subsequently analyze an empirical data set of 32 avian populations from Australia that are hypothesized to have expanded from smaller refugia populations in the late Pleistocene. The method can accommodate data set heterogeneity such as variability in effective population size, mutation rates, and sample sizes across species and exploits the statistical strength from the simultaneous analysis of multiple species. This hABC framework used in a multitaxa demographic context can increase our understanding of the impact of historical climate change by determining what proportion of the community responded in concert or independently and can be used with a wide variety of comparative phylogeographic data sets as biota-wide DNA barcoding data sets accumulate. © The Author 2014. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.

Large-Scale Optimization for Bayesian Inference in Complex Systems

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

Willcox, Karen; Marzouk, Youssef

2013-11-12

The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimization) Project focused on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimization and inversion methods. The project was a collaborative effort among MIT, the University of Texas at Austin, Georgia Institute of Technology, and Sandia National Laboratories. The research was directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. The MIT--Sandia component of themore » SAGUARO Project addressed the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas--Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to-observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as ``reduce then sample'' and ``sample then reduce.'' In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.« less

Final Report: Large-Scale Optimization for Bayesian Inference in Complex Systems

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

Ghattas, Omar

2013-10-15

The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimiza- tion) Project focuses on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimiza- tion and inversion methods. Our research is directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. Our efforts are integrated in the context of a challenging testbed problem that considers subsurface reacting flow and transport. The MIT component of the SAGUAROmore » Project addresses the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas-Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to- observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as "reduce then sample" and "sample then reduce." In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.« less

Understanding the recent colonization history of a plant pathogenic fungus using population genetic tools and Approximate Bayesian Computation

PubMed Central

Barrès, B; Carlier, J; Seguin, M; Fenouillet, C; Cilas, C; Ravigné, V

2012-01-01

Understanding the processes by which new diseases are introduced in previously healthy areas is of major interest in elaborating prevention and management policies, as well as in understanding the dynamics of pathogen diversity at large spatial scale. In this study, we aimed to decipher the dispersal processes that have led to the emergence of the plant pathogenic fungus Microcyclus ulei, which is responsible for the South American Leaf Blight (SALB). This fungus has devastated rubber tree plantations across Latin America since the beginning of the twentieth century. As only imprecise historical information is available, the study of population evolutionary history based on population genetics appeared most appropriate. The distribution of genetic diversity in a continental sampling of four countries (Brazil, Ecuador, Guatemala and French Guiana) was studied using a set of 16 microsatellite markers developed specifically for this purpose. A very strong genetic structure was found (Fst=0.70), demonstrating that there has been no regular gene flow between Latin American M. ulei populations. Strong bottlenecks probably occurred at the foundation of each population. The most likely scenario of colonization identified by the Approximate Bayesian Computation (ABC) method implemented in 𝒟ℐ𝒴𝒜ℬ𝒞 suggested two independent sources from the Amazonian endemic area. The Brazilian, Ecuadorian and Guatemalan populations might stem from serial introductions through human-mediated movement of infected plant material from an unsampled source population, whereas the French Guiana population seems to have arisen from an independent colonization event through spore dispersal. PMID:22828899

Bayesian alternative to the ISO-GUM's use of the Welch Satterthwaite formula

NASA Astrophysics Data System (ADS)

Kacker, Raghu N.

2006-02-01

In certain disciplines, uncertainty is traditionally expressed as an interval about an estimate for the value of the measurand. Development of such uncertainty intervals with a stated coverage probability based on the International Organization for Standardization (ISO) Guide to the Expression of Uncertainty in Measurement (GUM) requires a description of the probability distribution for the value of the measurand. The ISO-GUM propagates the estimates and their associated standard uncertainties for various input quantities through a linear approximation of the measurement equation to determine an estimate and its associated standard uncertainty for the value of the measurand. This procedure does not yield a probability distribution for the value of the measurand. The ISO-GUM suggests that under certain conditions motivated by the central limit theorem the distribution for the value of the measurand may be approximated by a scaled-and-shifted t-distribution with effective degrees of freedom obtained from the Welch-Satterthwaite (W-S) formula. The approximate t-distribution may then be used to develop an uncertainty interval with a stated coverage probability for the value of the measurand. We propose an approximate normal distribution based on a Bayesian uncertainty as an alternative to the t-distribution based on the W-S formula. A benefit of the approximate normal distribution based on a Bayesian uncertainty is that it greatly simplifies the expression of uncertainty by eliminating altogether the need for calculating effective degrees of freedom from the W-S formula. In the special case where the measurand is the difference between two means, each evaluated from statistical analyses of independent normally distributed measurements with unknown and possibly unequal variances, the probability distribution for the value of the measurand is known to be a Behrens-Fisher distribution. We compare the performance of the approximate normal distribution based on a Bayesian uncertainty and the approximate t-distribution based on the W-S formula with respect to the Behrens-Fisher distribution. The approximate normal distribution is simpler and better in this case. A thorough investigation of the relative performance of the two approximate distributions would require comparison for a range of measurement equations by numerical methods.

Bayes' theorem application in the measure information diagnostic value assessment

NASA Astrophysics Data System (ADS)

Orzechowski, Piotr D.; Makal, Jaroslaw; Nazarkiewicz, Andrzej

2006-03-01

The paper presents Bayesian method application in the measure information diagnostic value assessment that is used in the computer-aided diagnosis system. The computer system described here has been created basing on the Bayesian Network and is used in Benign Prostatic Hyperplasia (BPH) diagnosis. The graphic diagnostic model enables to juxtapose experts' knowledge with data.

Bayesian analysis of zero inflated spatiotemporal HIV/TB child mortality data through the INLA and SPDE approaches: Applied to data observed between 1992 and 2010 in rural North East South Africa

NASA Astrophysics Data System (ADS)

Musenge, Eustasius; Chirwa, Tobias Freeman; Kahn, Kathleen; Vounatsou, Penelope

2013-06-01

Longitudinal mortality data with few deaths usually have problems of zero-inflation. This paper presents and applies two Bayesian models which cater for zero-inflation, spatial and temporal random effects. To reduce the computational burden experienced when a large number of geo-locations are treated as a Gaussian field (GF) we transformed the field to a Gaussian Markov Random Fields (GMRF) by triangulation. We then modelled the spatial random effects using the Stochastic Partial Differential Equations (SPDEs). Inference was done using a computationally efficient alternative to Markov chain Monte Carlo (MCMC) called Integrated Nested Laplace Approximation (INLA) suited for GMRF. The models were applied to data from 71,057 children aged 0 to under 10 years from rural north-east South Africa living in 15,703 households over the years 1992-2010. We found protective effects on HIV/TB mortality due to greater birth weight, older age and more antenatal clinic visits during pregnancy (adjusted RR (95% CI)): 0.73(0.53;0.99), 0.18(0.14;0.22) and 0.96(0.94;0.97) respectively. Therefore childhood HIV/TB mortality could be reduced if mothers are better catered for during pregnancy as this can reduce mother-to-child transmissions and contribute to improved birth weights. The INLA and SPDE approaches are computationally good alternatives in modelling large multilevel spatiotemporal GMRF data structures.

Bayesian Asymmetric Regression as a Means to Estimate and Evaluate Oral Reading Fluency Slopes

ERIC Educational Resources Information Center

Solomon, Benjamin G.; Forsberg, Ole J.

2017-01-01

Bayesian techniques have become increasingly present in the social sciences, fueled by advances in computer speed and the development of user-friendly software. In this paper, we forward the use of Bayesian Asymmetric Regression (BAR) to monitor intervention responsiveness when using Curriculum-Based Measurement (CBM) to assess oral reading…

Influence of gene flow on divergence dating - implications for the speciation history of Takydromus grass lizards.

PubMed

Tseng, Shu-Ping; Li, Shou-Hsien; Hsieh, Chia-Hung; Wang, Hurng-Yi; Lin, Si-Min

2014-10-01

Dating the time of divergence and understanding speciation processes are central to the study of the evolutionary history of organisms but are notoriously difficult. The difficulty is largely rooted in variations in the ancestral population size or in the genealogy variation across loci. To depict the speciation processes and divergence histories of three monophyletic Takydromus species endemic to Taiwan, we sequenced 20 nuclear loci and combined with one mitochondrial locus published in GenBank. They were analysed by a multispecies coalescent approach within a Bayesian framework. Divergence dating based on the gene tree approach showed high variation among loci, and the divergence was estimated at an earlier date than when derived by the species-tree approach. To test whether variations in the ancestral population size accounted for the majority of this variation, we conducted computer inferences using isolation-with-migration (IM) and approximate Bayesian computation (ABC) frameworks. The results revealed that gene flow during the early stage of speciation was strongly favoured over the isolation model, and the initiation of the speciation process was far earlier than the dates estimated by gene- and species-based divergence dating. Due to their limited dispersal ability, it is suggested that geographical isolation may have played a major role in the divergence of these Takydromus species. Nevertheless, this study reveals a more complex situation and demonstrates that gene flow during the speciation process cannot be overlooked and may have a great impact on divergence dating. By using multilocus data and incorporating Bayesian coalescence approaches, we provide a more biologically realistic framework for delineating the divergence history of Takydromus. © 2014 John Wiley & Sons Ltd.

Approximated adjusted fractional Bayes factors: A general method for testing informative hypotheses.

PubMed

Gu, Xin; Mulder, Joris; Hoijtink, Herbert

2018-05-01

Informative hypotheses are increasingly being used in psychological sciences because they adequately capture researchers' theories and expectations. In the Bayesian framework, the evaluation of informative hypotheses often makes use of default Bayes factors such as the fractional Bayes factor. This paper approximates and adjusts the fractional Bayes factor such that it can be used to evaluate informative hypotheses in general statistical models. In the fractional Bayes factor a fraction parameter must be specified which controls the amount of information in the data used for specifying an implicit prior. The remaining fraction is used for testing the informative hypotheses. We discuss different choices of this parameter and present a scheme for setting it. Furthermore, a software package is described which computes the approximated adjusted fractional Bayes factor. Using this software package, psychological researchers can evaluate informative hypotheses by means of Bayes factors in an easy manner. Two empirical examples are used to illustrate the procedure. © 2017 The British Psychological Society.

A Bayesian Framework for False Belief Reasoning in Children: A Rational Integration of Theory-Theory and Simulation Theory

PubMed Central

Asakura, Nobuhiko; Inui, Toshio

2016-01-01

Two apparently contrasting theories have been proposed to account for the development of children's theory of mind (ToM): theory-theory and simulation theory. We present a Bayesian framework that rationally integrates both theories for false belief reasoning. This framework exploits two internal models for predicting the belief states of others: one of self and one of others. These internal models are responsible for simulation-based and theory-based reasoning, respectively. The framework further takes into account empirical studies of a developmental ToM scale (e.g., Wellman and Liu, 2004): developmental progressions of various mental state understandings leading up to false belief understanding. By representing the internal models and their interactions as a causal Bayesian network, we formalize the model of children's false belief reasoning as probabilistic computations on the Bayesian network. This model probabilistically weighs and combines the two internal models and predicts children's false belief ability as a multiplicative effect of their early-developed abilities to understand the mental concepts of diverse beliefs and knowledge access. Specifically, the model predicts that children's proportion of correct responses on a false belief task can be closely approximated as the product of their proportions correct on the diverse belief and knowledge access tasks. To validate this prediction, we illustrate that our model provides good fits to a variety of ToM scale data for preschool children. We discuss the implications and extensions of our model for a deeper understanding of developmental progressions of children's ToM abilities. PMID:28082941

A Bayesian Framework for False Belief Reasoning in Children: A Rational Integration of Theory-Theory and Simulation Theory.

PubMed

Asakura, Nobuhiko; Inui, Toshio

2016-01-01

Two apparently contrasting theories have been proposed to account for the development of children's theory of mind (ToM): theory-theory and simulation theory. We present a Bayesian framework that rationally integrates both theories for false belief reasoning. This framework exploits two internal models for predicting the belief states of others: one of self and one of others. These internal models are responsible for simulation-based and theory-based reasoning, respectively. The framework further takes into account empirical studies of a developmental ToM scale (e.g., Wellman and Liu, 2004): developmental progressions of various mental state understandings leading up to false belief understanding. By representing the internal models and their interactions as a causal Bayesian network, we formalize the model of children's false belief reasoning as probabilistic computations on the Bayesian network. This model probabilistically weighs and combines the two internal models and predicts children's false belief ability as a multiplicative effect of their early-developed abilities to understand the mental concepts of diverse beliefs and knowledge access. Specifically, the model predicts that children's proportion of correct responses on a false belief task can be closely approximated as the product of their proportions correct on the diverse belief and knowledge access tasks. To validate this prediction, we illustrate that our model provides good fits to a variety of ToM scale data for preschool children. We discuss the implications and extensions of our model for a deeper understanding of developmental progressions of children's ToM abilities.

Demographic expansion of two Tamarix species along the Yellow River caused by geological events and climate change in the Pleistocene.

PubMed

Liang, Hong-Yan; Feng, Zhi-Pei; Pei, Bing; Li, Yong; Yang, Xi-Tian

2018-01-08

The geological events and climatic fluctuations during the Pleistocene played important roles in shaping patterns of species distribution. However, few studies have evaluated the patterns of species distribution that were influenced by the Yellow River. The present work analyzed the demography of two endemic tree species that are widely distributed along the Yellow River, Tamarix austromongolica and Tamarix chinensis, to understand the role of the Yellow River and Pleistocene climate in shaping their distribution patterns. The most common chlorotype, chlorotype 1, was found in all populations, and its divergence time could be dated back to 0.19 million years ago (Ma). This dating coincides well with the formation of the modern Yellow River and the timing of Marine Isotope Stages 5e-6 (MIS 5e-6). Bayesian reconstructions along with models of paleodistribution revealed that these two species experienced a demographic expansion in population size during the Quaternary period. Approximate Bayesian computation analyses supported a scenario of expansion approximately from the upper to lower reaches of the Yellow River. Our results provide support for the roles of the Yellow River and the Pleistocene climate in driving demographic expansion of the populations of T. austromongolica and T. chinensis. These findings are useful for understanding the effects of geological events and past climatic fluctuations on species distribution patterns.

A Bayesian Network Approach to Modeling Learning Progressions and Task Performance. CRESST Report 776

ERIC Educational Resources Information Center

West, Patti; Rutstein, Daisy Wise; Mislevy, Robert J.; Liu, Junhui; Choi, Younyoung; Levy, Roy; Crawford, Aaron; DiCerbo, Kristen E.; Chappel, Kristina; Behrens, John T.

2010-01-01

A major issue in the study of learning progressions (LPs) is linking student performance on assessment tasks to the progressions. This report describes the challenges faced in making this linkage using Bayesian networks to model LPs in the field of computer networking. The ideas are illustrated with exemplar Bayesian networks built on Cisco…

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.

Bayesian Structural Equation Modeling: A More Flexible Representation of Substantive Theory

ERIC Educational Resources Information Center

Muthen, Bengt; Asparouhov, Tihomir

2012-01-01

This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed…

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.

Nonlinear and non-Gaussian Bayesian based handwriting beautification

NASA Astrophysics Data System (ADS)

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

2013-03-01

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

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.

Multilevel sequential Monte Carlo samplers

DOE PAGES

Beskos, Alexandros; Jasra, Ajay; Law, Kody; ...

2016-08-24

Here, we study the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods and leading to a discretisation bias, with the step-size level h L. In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods. In the context of this problem, it is known that the introduction of the multilevel Monte Carlo (MLMC) method can reduce the amount of computational effort to estimate expectations, for a given level of error. This is achieved via a telescoping identity associated to a Monte Carlo approximation of a sequence of probability distributions with discretisation levelsmore » $${\\infty}$$ >h 0>h 1 ...>h L. In many practical problems of interest, one cannot achieve an i.i.d. sampling of the associated sequence of probability distributions. A sequential Monte Carlo (SMC) version of the MLMC method is introduced to deal with this problem. In conclusion, it is shown that under appropriate assumptions, the attractive property of a reduction of the amount of computational effort to estimate expectations, for a given level of error, can be maintained within the SMC context.« less

Predictive uncertainty analysis of plume distribution for geological carbon sequestration using sparse-grid Bayesian method

NASA Astrophysics Data System (ADS)

Shi, X.; Zhang, G.

2013-12-01

Because of the extensive computational burden, parametric uncertainty analyses are rarely conducted for geological carbon sequestration (GCS) process based multi-phase models. The difficulty of predictive uncertainty analysis for the CO2 plume migration in realistic GCS models is not only due to the spatial distribution of the caprock and reservoir (i.e. heterogeneous model parameters), but also because the GCS optimization estimation problem has multiple local minima due to the complex nonlinear multi-phase (gas and aqueous), and multi-component (water, CO2, salt) transport equations. The geological model built by Doughty and Pruess (2004) for the Frio pilot site (Texas) was selected and assumed to represent the 'true' system, which was composed of seven different facies (geological units) distributed among 10 layers. We chose to calibrate the permeabilities of these facies. Pressure and gas saturation values from this true model were then extracted and used as observations for subsequent model calibration. Random noise was added to the observations to approximate realistic field conditions. Each simulation of the model lasts about 2 hours. In this study, we develop a new approach that improves computational efficiency of Bayesian inference by constructing a surrogate system based on an adaptive sparse-grid stochastic collocation method. This surrogate response surface global optimization algorithm is firstly used to calibrate the model parameters, then prediction uncertainty of the CO2 plume position is quantified due to the propagation from parametric uncertainty in the numerical experiments, which is also compared to the actual plume from the 'true' model. Results prove that the approach is computationally efficient for multi-modal optimization and prediction uncertainty quantification for computationally expensive simulation models. Both our inverse methodology and findings can be broadly applicable to GCS in heterogeneous storage formations.

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.

A Bayesian Approach to Genome/Linguistic Relationships in Native South Americans

PubMed Central

Amorim, Carlos Eduardo Guerra; Bisso-Machado, Rafael; Ramallo, Virginia; Bortolini, Maria Cátira; Bonatto, Sandro Luis; Salzano, Francisco Mauro; Hünemeier, Tábita

2013-01-01

The relationship between the evolution of genes and languages has been studied for over three decades. These studies rely on the assumption that languages, as many other cultural traits, evolve in a gene-like manner, accumulating heritable diversity through time and being subjected to evolutionary mechanisms of change. In the present work we used genetic data to evaluate South American linguistic classifications. We compared discordant models of language classifications to the current Native American genome-wide variation using realistic demographic models analyzed under an Approximate Bayesian Computation (ABC) framework. Data on 381 STRs spread along the autosomes were gathered from the literature for populations representing the five main South Amerindian linguistic groups: Andean, Arawakan, Chibchan-Paezan, Macro-Jê, and Tupí. The results indicated a higher posterior probability for the classification proposed by J.H. Greenberg in 1987, although L. Campbell's 1997 classification cannot be ruled out. Based on Greenberg's classification, it was possible to date the time of Tupí-Arawakan divergence (2.8 kya), and the time of emergence of the structure between present day major language groups in South America (3.1 kya). PMID:23696865

A bayesian approach to genome/linguistic relationships in native South Americans.

PubMed

Amorim, Carlos Eduardo Guerra; Bisso-Machado, Rafael; Ramallo, Virginia; Bortolini, Maria Cátira; Bonatto, Sandro Luis; Salzano, Francisco Mauro; Hünemeier, Tábita

2013-01-01

The relationship between the evolution of genes and languages has been studied for over three decades. These studies rely on the assumption that languages, as many other cultural traits, evolve in a gene-like manner, accumulating heritable diversity through time and being subjected to evolutionary mechanisms of change. In the present work we used genetic data to evaluate South American linguistic classifications. We compared discordant models of language classifications to the current Native American genome-wide variation using realistic demographic models analyzed under an Approximate Bayesian Computation (ABC) framework. Data on 381 STRs spread along the autosomes were gathered from the literature for populations representing the five main South Amerindian linguistic groups: Andean, Arawakan, Chibchan-Paezan, Macro-Jê, and Tupí. The results indicated a higher posterior probability for the classification proposed by J.H. Greenberg in 1987, although L. Campbell's 1997 classification cannot be ruled out. Based on Greenberg's classification, it was possible to date the time of Tupí-Arawakan divergence (2.8 kya), and the time of emergence of the structure between present day major language groups in South America (3.1 kya).

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

ERIC Educational Resources Information Center

Marsman, Maarten; Wagenmakers, Eric-Jan

2017-01-01

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

Application of Bayesian Approach in Cancer Clinical Trial

PubMed Central

Bhattacharjee, Atanu

2014-01-01

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

Bayesian Nonlinear Assimilation of Eulerian and Lagrangian Coastal Flow Data

DTIC Science & Technology

2015-09-30

Lagrangian Coastal Flow Data Dr. Pierre F.J. Lermusiaux Department of Mechanical Engineering Center for Ocean Science and Engineering Massachusetts...Develop and apply theory, schemes and computational systems for rigorous Bayesian nonlinear assimilation of Eulerian and Lagrangian coastal flow data...coastal ocean fields, both in Eulerian and Lagrangian forms. - Further develop and implement our GMM-DO schemes for robust Bayesian nonlinear estimation

A Bayesian framework for adaptive selection, calibration, and validation of coarse-grained models of atomistic systems

NASA Astrophysics Data System (ADS)

Farrell, Kathryn; Oden, J. Tinsley; Faghihi, Danial

2015-08-01

A general adaptive modeling algorithm for selection and validation of coarse-grained models of atomistic systems is presented. A Bayesian framework is developed to address uncertainties in parameters, data, and model selection. Algorithms for computing output sensitivities to parameter variances, model evidence and posterior model plausibilities for given data, and for computing what are referred to as Occam Categories in reference to a rough measure of model simplicity, make up components of the overall approach. Computational results are provided for representative applications.

UNIFORMLY MOST POWERFUL BAYESIAN TESTS

PubMed Central

Johnson, Valen E.

2014-01-01

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

Bayesian 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.

Calculation of Crystallographic Texture of BCC Steels During Cold Rolling

NASA Astrophysics Data System (ADS)

Das, Arpan

2017-05-01

BCC alloys commonly tend to develop strong fibre textures and often represent as isointensity diagrams in φ 1 sections or by fibre diagrams. Alpha fibre in bcc steels is generally characterised by <110> crystallographic axis parallel to the rolling direction. The objective of present research is to correlate carbon content, carbide dispersion, rolling reduction, Euler angles (ϕ) (when φ 1 = 0° and φ 2 = 45° along alpha fibre) and the resulting alpha fibre texture orientation intensity. In the present research, Bayesian neural computation has been employed to correlate these and compare with the existing feed-forward neural network model comprehensively. Excellent match to the measured texture data within the bounding box of texture training data set has been already predicted through the feed-forward neural network model by other researchers. Feed-forward neural network prediction outside the bounds of training texture data showed deviations from the expected values. Currently, Bayesian computation has been similarly applied to confirm that the predictions are reasonable in the context of basic metallurgical principles, and matched better outside the bounds of training texture data set than the reported feed-forward neural network. Bayesian computation puts error bars on predicted values and allows significance of each individual parameters to be estimated. Additionally, it is also possible by Bayesian computation to estimate the isolated influence of particular variable such as carbon concentration, which exactly cannot in practice be varied independently. This shows the ability of the Bayesian neural network to examine the new phenomenon in situations where the data cannot be accessed through experiments.

Portfolios in Stochastic Local Search: Efficiently Computing Most Probable Explanations in Bayesian Networks

NASA Technical Reports Server (NTRS)

Mengshoel, Ole J.; Roth, Dan; Wilkins, David C.

2001-01-01

Portfolio methods support the combination of different algorithms and heuristics, including stochastic local search (SLS) heuristics, and have been identified as a promising approach to solve computationally hard problems. While successful in experiments, theoretical foundations and analytical results for portfolio-based SLS heuristics are less developed. This article aims to improve the understanding of the role of portfolios of heuristics in SLS. We emphasize the problem of computing most probable explanations (MPEs) in Bayesian networks (BNs). Algorithmically, we discuss a portfolio-based SLS algorithm for MPE computation, Stochastic Greedy Search (SGS). SGS supports the integration of different initialization operators (or initialization heuristics) and different search operators (greedy and noisy heuristics), thereby enabling new analytical and experimental results. Analytically, we introduce a novel Markov chain model tailored to portfolio-based SLS algorithms including SGS, thereby enabling us to analytically form expected hitting time results that explain empirical run time results. For a specific BN, we show the benefit of using a homogenous initialization portfolio. To further illustrate the portfolio approach, we consider novel additive search heuristics for handling determinism in the form of zero entries in conditional probability tables in BNs. Our additive approach adds rather than multiplies probabilities when computing the utility of an explanation. We motivate the additive measure by studying the dramatic impact of zero entries in conditional probability tables on the number of zero-probability explanations, which again complicates the search process. We consider the relationship between MAXSAT and MPE, and show that additive utility (or gain) is a generalization, to the probabilistic setting, of MAXSAT utility (or gain) used in the celebrated GSAT and WalkSAT algorithms and their descendants. Utilizing our Markov chain framework, we show that expected hitting time is a rational function - i.e. a ratio of two polynomials - of the probability of applying an additive search operator. Experimentally, we report on synthetically generated BNs as well as BNs from applications, and compare SGSs performance to that of Hugin, which performs BN inference by compilation to and propagation in clique trees. On synthetic networks, SGS speeds up computation by approximately two orders of magnitude compared to Hugin. In application networks, our approach is highly competitive in Bayesian networks with a high degree of determinism. In addition to showing that stochastic local search can be competitive with clique tree clustering, our empirical results provide an improved understanding of the circumstances under which portfolio-based SLS outperforms clique tree clustering and vice versa.

Application of bayesian networks to real-time flood risk estimation

NASA Astrophysics Data System (ADS)

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

2003-04-01

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

The natural mathematics of behavior analysis.

PubMed

Li, Don; Hautus, Michael J; Elliffe, Douglas

2018-04-19

Models that generate event records have very general scope regarding the dimensions of the target behavior that we measure. From a set of predicted event records, we can generate predictions for any dependent variable that we could compute from the event records of our subjects. In this sense, models that generate event records permit us a freely multivariate analysis. To explore this proposition, we conducted a multivariate examination of Catania's Operant Reserve on single VI schedules in transition using a Markov Chain Monte Carlo scheme for Approximate Bayesian Computation. Although we found systematic deviations between our implementation of Catania's Operant Reserve and our observed data (e.g., mismatches in the shape of the interresponse time distributions), the general approach that we have demonstrated represents an avenue for modelling behavior that transcends the typical constraints of algebraic models. © 2018 Society for the Experimental Analysis of Behavior.

Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo

PubMed Central

Golightly, Andrew; Wilkinson, Darren J.

2011-01-01

Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters that must be estimated from time course data. In this article, we consider the task of inferring the parameters of a stochastic kinetic model defined as a Markov (jump) process. Inference for the parameters of complex nonlinear multivariate stochastic process models is a challenging problem, but we find here that algorithms based on particle Markov chain Monte Carlo turn out to be a very effective computationally intensive approach to the problem. Approximations to the inferential model based on stochastic differential equations (SDEs) are considered, as well as improvements to the inference scheme that exploit the SDE structure. We apply the methodology to a Lotka–Volterra system and a prokaryotic auto-regulatory network. PMID:23226583

The idiosyncratic nature of confidence

PubMed Central

Navajas, Joaquin; Hindocha, Chandni; Foda, Hebah; Keramati, Mehdi; Latham, Peter E; Bahrami, Bahador

2017-01-01

Confidence is the ‘feeling of knowing’ that accompanies decision making. Bayesian theory proposes that confidence is a function solely of the perceived probability of being correct. Empirical research has suggested, however, that different individuals may perform different computations to estimate confidence from uncertain evidence. To test this hypothesis, we collected confidence reports in a task where subjects made categorical decisions about the mean of a sequence. We found that for most individuals, confidence did indeed reflect the perceived probability of being correct. However, in approximately half of them, confidence also reflected a different probabilistic quantity: the perceived uncertainty in the estimated variable. We found that the contribution of both quantities was stable over weeks. We also observed that the influence of the perceived probability of being correct was stable across two tasks, one perceptual and one cognitive. Overall, our findings provide a computational interpretation of individual differences in human confidence. PMID:29152591

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

PubMed Central

2012-01-01

Background A statistical analysis plan (SAP) is a critical link between how a clinical trial is conducted and the clinical study report. To secure objective study results, regulatory bodies expect that the SAP will meet requirements in pre-specifying inferential analyses and other important statistical techniques. To write a good SAP for model-based sensitivity and ancillary analyses involves non-trivial decisions on and justification of many aspects of the chosen setting. In particular, trials with longitudinal count data as primary endpoints pose challenges for model choice and model validation. In the random effects setting, frequentist strategies for model assessment and model diagnosis are complex and not easily implemented and have several limitations. Therefore, it is of interest to explore Bayesian alternatives which provide the needed decision support to finalize a SAP. Methods We focus on generalized linear mixed models (GLMMs) for the analysis of longitudinal count data. A series of distributions with over- and under-dispersion is considered. Additionally, the structure of the variance components is modified. We perform a simulation study to investigate the discriminatory power of Bayesian tools for model criticism in different scenarios derived from the model setting. We apply the findings to the data from an open clinical trial on vertigo attacks. These data are seen as pilot data for an ongoing phase III trial. To fit GLMMs we use a novel Bayesian computational approach based on integrated nested Laplace approximations (INLAs). The INLA methodology enables the direct computation of leave-one-out predictive distributions. These distributions are crucial for Bayesian model assessment. We evaluate competing GLMMs for longitudinal count data according to the deviance information criterion (DIC) or probability integral transform (PIT), and by using proper scoring rules (e.g. the logarithmic score). Results The instruments under study provide excellent tools for preparing decisions within the SAP in a transparent way when structuring the primary analysis, sensitivity or ancillary analyses, and specific analyses for secondary endpoints. The mean logarithmic score and DIC discriminate well between different model scenarios. It becomes obvious that the naive choice of a conventional random effects Poisson model is often inappropriate for real-life count data. The findings are used to specify an appropriate mixed model employed in the sensitivity analyses of an ongoing phase III trial. Conclusions The proposed Bayesian methods are not only appealing for inference but notably provide a sophisticated insight into different aspects of model performance, such as forecast verification or calibration checks, and can be applied within the model selection process. The mean of the logarithmic score is a robust tool for model ranking and is not sensitive to sample size. Therefore, these Bayesian model selection techniques offer helpful decision support for shaping sensitivity and ancillary analyses in a statistical analysis plan of a clinical trial with longitudinal count data as the primary endpoint. PMID:22962944

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

PubMed

Adrion, Christine; Mansmann, Ulrich

2012-09-10

A statistical analysis plan (SAP) is a critical link between how a clinical trial is conducted and the clinical study report. To secure objective study results, regulatory bodies expect that the SAP will meet requirements in pre-specifying inferential analyses and other important statistical techniques. To write a good SAP for model-based sensitivity and ancillary analyses involves non-trivial decisions on and justification of many aspects of the chosen setting. In particular, trials with longitudinal count data as primary endpoints pose challenges for model choice and model validation. In the random effects setting, frequentist strategies for model assessment and model diagnosis are complex and not easily implemented and have several limitations. Therefore, it is of interest to explore Bayesian alternatives which provide the needed decision support to finalize a SAP. We focus on generalized linear mixed models (GLMMs) for the analysis of longitudinal count data. A series of distributions with over- and under-dispersion is considered. Additionally, the structure of the variance components is modified. We perform a simulation study to investigate the discriminatory power of Bayesian tools for model criticism in different scenarios derived from the model setting. We apply the findings to the data from an open clinical trial on vertigo attacks. These data are seen as pilot data for an ongoing phase III trial. To fit GLMMs we use a novel Bayesian computational approach based on integrated nested Laplace approximations (INLAs). The INLA methodology enables the direct computation of leave-one-out predictive distributions. These distributions are crucial for Bayesian model assessment. We evaluate competing GLMMs for longitudinal count data according to the deviance information criterion (DIC) or probability integral transform (PIT), and by using proper scoring rules (e.g. the logarithmic score). The instruments under study provide excellent tools for preparing decisions within the SAP in a transparent way when structuring the primary analysis, sensitivity or ancillary analyses, and specific analyses for secondary endpoints. The mean logarithmic score and DIC discriminate well between different model scenarios. It becomes obvious that the naive choice of a conventional random effects Poisson model is often inappropriate for real-life count data. The findings are used to specify an appropriate mixed model employed in the sensitivity analyses of an ongoing phase III trial. The proposed Bayesian methods are not only appealing for inference but notably provide a sophisticated insight into different aspects of model performance, such as forecast verification or calibration checks, and can be applied within the model selection process. The mean of the logarithmic score is a robust tool for model ranking and is not sensitive to sample size. Therefore, these Bayesian model selection techniques offer helpful decision support for shaping sensitivity and ancillary analyses in a statistical analysis plan of a clinical trial with longitudinal count data as the primary endpoint.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

PubMed

Shah, A A; Xing, W W; Triantafyllidis, V

2017-04-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models

PubMed Central

Xing, W. W.; Triantafyllidis, V.

2017-01-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach. PMID:28484327

Joint inversion for transponder localization and sound-speed profile temporal variation in high-precision acoustic surveys.

PubMed

Li, Zhao; Dosso, Stan E; Sun, Dajun

2016-07-01

This letter develops a Bayesian inversion for localizing underwater acoustic transponders using a surface ship which compensates for sound-speed profile (SSP) temporal variation during the survey. The method is based on dividing observed acoustic travel-time data into time segments and including depth-independent SSP variations for each segment as additional unknown parameters to approximate the SSP temporal variation. SSP variations are estimated jointly with transponder locations, rather than calculated separately as in existing two-step inversions. Simulation and sea-trial results show this localization/SSP joint inversion performs better than two-step inversion in terms of localization accuracy, agreement with measured SSP variations, and computational efficiency.

Applying a Bayesian Approach to Identification of Orthotropic Elastic Constants from Full Field Displacement Measurements

NASA Astrophysics Data System (ADS)

Gogu, C.; Yin, W.; Haftka, R.; Ifju, P.; Molimard, J.; Le Riche, R.; Vautrin, A.

2010-06-01

A major challenge in the identification of material properties is handling different sources of uncertainty in the experiment and the modelling of the experiment for estimating the resulting uncertainty in the identified properties. Numerous improvements in identification methods have provided increasingly accurate estimates of various material properties. However, characterizing the uncertainty in the identified properties is still relatively crude. Different material properties obtained from a single test are not obtained with the same confidence. Typically the highest uncertainty is associated with respect to properties to which the experiment is the most insensitive. In addition, the uncertainty in different properties can be strongly correlated, so that obtaining only variance estimates may be misleading. A possible approach for handling the different sources of uncertainty and estimating the uncertainty in the identified properties is the Bayesian method. This method was introduced in the late 1970s in the context of identification [1] and has been applied since to different problems, notably identification of elastic constants from plate vibration experiments [2]-[4]. The applications of the method to these classical pointwise tests involved only a small number of measurements (typically ten natural frequencies in the previously cited vibration test) which facilitated the application of the Bayesian approach. For identifying elastic constants, full field strain or displacement measurements provide a high number of measured quantities (one measurement per image pixel) and hence a promise of smaller uncertainties in the properties. However, the high number of measurements represents also a major computational challenge in applying the Bayesian approach to full field measurements. To address this challenge we propose an approach based on the proper orthogonal decomposition (POD) of the full fields in order to drastically reduce their dimensionality. POD is based on projecting the full field images on a modal basis, constructed from sample simulations, and which can account for the variations of the full field as the elastic constants and other parameters of interest are varied. The fidelity of the decomposition depends on the number of basis vectors used. Typically even complex fields can be accurately represented with no more than a few dozen modes and for our problem we showed that only four or five modes are sufficient [5]. To further reduce the computational cost of the Bayesian approach we use response surface approximations of the POD coefficients of the fields. We show that 3rd degree polynomial response surface approximations provide a satisfying accuracy. The combination of POD decomposition and response surface methodology allows to bring down the computational time of the Bayesian identification to a few days. The proposed approach is applied to Moiré interferometry full field displacement measurements from a traction experiment on a plate with a hole. The laminate with a layup of [45,- 45,0]s is made out of a Toray® T800/3631 graphite/epoxy prepreg. The measured displacement maps are provided in Figure 1. The mean values of the identified properties joint probability density function are in agreement with previous identifications carried out on the same material. Furthermore the probability density function also provides the coefficient of variation with which the properties are identified as well as the correlations between the various properties. We find that while the longitudinal Young’s modulus is identified with good accuracy (low standard deviation), the Poisson’s ration is identified with much higher uncertainty. Several of the properties are also found to be correlated. The identified uncertainty structure of the elastic constants (i.e. variance co-variance matrix) has potential benefits to reliability analyses, by allowing a more accurate description of the input uncertainty. An additional advantage of the Bayesian approach is that it provides a natural way (in the form of the prior probability density function) for accounting for prior information that may be available on the material properties thought. This is of great interest for reducing the uncertainty on properties that can only be determined with low confidence from the plate with a hole experiment, such as Poisson’s ratio or transverse Young’s modulus in our case.

Moments and Root-Mean-Square Error of the Bayesian MMSE Estimator of Classification Error in the Gaussian Model.

PubMed

Zollanvari, Amin; Dougherty, Edward R

2014-06-01

The most important aspect of any classifier is its error rate, because this quantifies its predictive capacity. Thus, the accuracy of error estimation is critical. Error estimation is problematic in small-sample classifier design because the error must be estimated using the same data from which the classifier has been designed. Use of prior knowledge, in the form of a prior distribution on an uncertainty class of feature-label distributions to which the true, but unknown, feature-distribution belongs, can facilitate accurate error estimation (in the mean-square sense) in circumstances where accurate completely model-free error estimation is impossible. This paper provides analytic asymptotically exact finite-sample approximations for various performance metrics of the resulting Bayesian Minimum Mean-Square-Error (MMSE) error estimator in the case of linear discriminant analysis (LDA) in the multivariate Gaussian model. These performance metrics include the first, second, and cross moments of the Bayesian MMSE error estimator with the true error of LDA, and therefore, the Root-Mean-Square (RMS) error of the estimator. We lay down the theoretical groundwork for Kolmogorov double-asymptotics in a Bayesian setting, which enables us to derive asymptotic expressions of the desired performance metrics. From these we produce analytic finite-sample approximations and demonstrate their accuracy via numerical examples. Various examples illustrate the behavior of these approximations and their use in determining the necessary sample size to achieve a desired RMS. The Supplementary Material contains derivations for some equations and added figures.

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.

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.

Bayesian statistics in medicine: a 25 year review.

PubMed

Ashby, Deborah

2006-11-15

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

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

DOE PAGES

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

2015-02-05

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

Approximate Bayesian algorithm to estimate the basic reproduction number in an influenza pandemic using arrival times of imported cases.

PubMed

Chong, Ka Chun; Zee, Benny Chung Ying; Wang, Maggie Haitian

2018-04-10

In an influenza pandemic, arrival times of cases are a proxy of the epidemic size and disease transmissibility. Because of intense surveillance of travelers from infected countries, detection is more rapid and complete than on local surveillance. Travel information can provide a more reliable estimation of transmission parameters. We developed an Approximate Bayesian Computation algorithm to estimate the basic reproduction number (R 0 ) in addition to the reporting rate and unobserved epidemic start time, utilizing travel, and routine surveillance data in an influenza pandemic. A simulation was conducted to assess the sampling uncertainty. The estimation approach was further applied to the 2009 influenza A/H1N1 pandemic in Mexico as a case study. In the simulations, we showed that the estimation approach was valid and reliable in different simulation settings. We also found estimates of R 0 and the reporting rate to be 1.37 (95% Credible Interval [CI]: 1.26-1.42) and 4.9% (95% CI: 0.1%-18%), respectively, in the 2009 influenza pandemic in Mexico, which were robust to variations in the fixed parameters. The estimated R 0 was consistent with that in the literature. This method is useful for officials to obtain reliable estimates of disease transmissibility for strategic planning. We suggest that improvements to the flow of reporting for confirmed cases among patients arriving at different countries are required. Copyright © 2018 Elsevier Ltd. All rights reserved.

Reconstructing demographic events from population genetic data: the introduction of bumblebees to New Zealand.

PubMed

Lye, G C; Lepais, O; Goulson, D

2011-07-01

Four British bumblebee species (Bombus terrestris, Bombus hortorum, Bombus ruderatus and Bombus subterraneus) became established in New Zealand following their introduction at the turn of the last century. Of these, two remain common in the United Kingdom (B. terrestris and B. hortorum), whilst two (B. ruderatus and B. subterraneus) have undergone marked declines, the latter being declared extinct in 2000. The presence of these bumblebees in New Zealand provides an unique system in which four related species have been isolated from their source population for over 100 years, providing a rare opportunity to examine the impacts of an initial bottleneck and introduction to a novel environment on their population genetics. We used microsatellite markers to compare modern populations of B. terrestris, B. hortorum and B. ruderatus in the United Kingdom and New Zealand and to compare museum specimens of British B. subterraneus with the current New Zealand population. We used approximate Bayesian computation to estimate demographic parameters of the introduction history, notably to estimate the number of founders involved in the initial introduction. Species-specific patterns derived from genetic analysis were consistent with the predictions based on the presumed history of these populations; demographic events have left a marked genetic signature on all four species. Approximate Bayesian analyses suggest that the New Zealand population of B. subterraneus may have been founded by as few as two individuals, giving rise to low genetic diversity and marked genetic divergence from the (now extinct) UK population. © 2011 Blackwell Publishing Ltd.

Efficient Bayesian parameter estimation with implicit sampling and surrogate modeling for a vadose zone hydrological problem

NASA Astrophysics Data System (ADS)

Liu, Y.; Pau, G. S. H.; Finsterle, S.

2015-12-01

Parameter inversion involves inferring the model parameter values based on sparse observations of some observables. To infer the posterior probability distributions of the parameters, Markov chain Monte Carlo (MCMC) methods are typically used. However, the large number of forward simulations needed and limited computational resources limit the complexity of the hydrological model we can use in these methods. In view of this, we studied the implicit sampling (IS) method, an efficient importance sampling technique that generates samples in the high-probability region of the posterior distribution and thus reduces the number of forward simulations that we need to run. For a pilot-point inversion of a heterogeneous permeability field based on a synthetic ponded infiltration experiment simu­lated with TOUGH2 (a subsurface modeling code), we showed that IS with linear map provides an accurate Bayesian description of the parameterized permeability field at the pilot points with just approximately 500 forward simulations. We further studied the use of surrogate models to improve the computational efficiency of parameter inversion. We implemented two reduced-order models (ROMs) for the TOUGH2 forward model. One is based on polynomial chaos expansion (PCE), of which the coefficients are obtained using the sparse Bayesian learning technique to mitigate the "curse of dimensionality" of the PCE terms. The other model is Gaussian process regression (GPR) for which different covariance, likelihood and inference models are considered. Preliminary results indicate that ROMs constructed based on the prior parameter space perform poorly. It is thus impractical to replace this hydrological model by a ROM directly in a MCMC method. However, the IS method can work with a ROM constructed for parameters in the close vicinity of the maximum a posteriori probability (MAP) estimate. We will discuss the accuracy and computational efficiency of using ROMs in the implicit sampling procedure for the hydrological problem considered. This work was supported, in part, by the U.S. Dept. of Energy under Contract No. DE-AC02-05CH11231

Bayesian reconstruction and use of anatomical a priori information for emission tomography

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

Bowsher, J.E.; Johnson, V.E.; Turkington, T.G.

1996-10-01

A Bayesian method is presented for simultaneously segmenting and reconstructing emission computed tomography (ECT) images and for incorporating high-resolution, anatomical information into those reconstructions. The anatomical information is often available from other imaging modalities such as computed tomography (CT) or magnetic resonance imaging (MRI). The Bayesian procedure models the ECT radiopharmaceutical distribution as consisting of regions, such that radiopharmaceutical activity is similar throughout each region. It estimates the number of regions, the mean activity of each region, and the region classification and mean activity of each voxel. Anatomical information is incorporated by assigning higher prior probabilities to ECT segmentations inmore » which each ECT region stays within a single anatomical region. This approach is effective because anatomical tissue type often strongly influences radiopharmaceutical uptake. The Bayesian procedure is evaluated using physically acquired single-photon emission computed tomography (SPECT) projection data and MRI for the three-dimensional (3-D) Hoffman brain phantom. A clinically realistic count level is used. A cold lesion within the brain phantom is created during the SPECT scan but not during the MRI to demonstrate that the estimation procedure can detect ECT structure that is not present anatomically.« less

Variational learning and bits-back coding: an information-theoretic view to Bayesian learning.

PubMed

Honkela, Antti; Valpola, Harri

2004-07-01

The bits-back coding first introduced by Wallace in 1990 and later by Hinton and van Camp in 1993 provides an interesting link between Bayesian learning and information-theoretic minimum-description-length (MDL) learning approaches. The bits-back coding allows interpreting the cost function used in the variational Bayesian method called ensemble learning as a code length in addition to the Bayesian view of misfit of the posterior approximation and a lower bound of model evidence. Combining these two viewpoints provides interesting insights to the learning process and the functions of different parts of the model. In this paper, the problem of variational Bayesian learning of hierarchical latent variable models is used to demonstrate the benefits of the two views. The code-length interpretation provides new views to many parts of the problem such as model comparison and pruning and helps explain many phenomena occurring in learning.

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.

Reference analysis of the signal + background model in counting experiments II. Approximate reference prior

NASA Astrophysics Data System (ADS)

Casadei, D.

2014-10-01

The objective Bayesian treatment of a model representing two independent Poisson processes, labelled as ``signal'' and ``background'' and both contributing additively to the total number of counted events, is considered. It is shown that the reference prior for the parameter of interest (the signal intensity) can be well approximated by the widely (ab)used flat prior only when the expected background is very high. On the other hand, a very simple approximation (the limiting form of the reference prior for perfect prior background knowledge) can be safely used over a large portion of the background parameters space. The resulting approximate reference posterior is a Gamma density whose parameters are related to the observed counts. This limiting form is simpler than the result obtained with a flat prior, with the additional advantage of representing a much closer approximation to the reference posterior in all cases. Hence such limiting prior should be considered a better default or conventional prior than the uniform prior. On the computing side, it is shown that a 2-parameter fitting function is able to reproduce extremely well the reference prior for any background prior. Thus, it can be useful in applications requiring the evaluation of the reference prior for a very large number of times.

Uncertainty Analysis Based on Sparse Grid Collocation and Quasi-Monte Carlo Sampling with Application in Groundwater Modeling

NASA Astrophysics Data System (ADS)

Zhang, G.; Lu, D.; Ye, M.; Gunzburger, M.

2011-12-01

Markov Chain Monte Carlo (MCMC) methods have been widely used in many fields of uncertainty analysis to estimate the posterior distributions of parameters and credible intervals of predictions in the Bayesian framework. However, in practice, MCMC may be computationally unaffordable due to slow convergence and the excessive number of forward model executions required, especially when the forward model is expensive to compute. Both disadvantages arise from the curse of dimensionality, i.e., the posterior distribution is usually a multivariate function of parameters. Recently, sparse grid method has been demonstrated to be an effective technique for coping with high-dimensional interpolation or integration problems. Thus, in order to accelerate the forward model and avoid the slow convergence of MCMC, we propose a new method for uncertainty analysis based on sparse grid interpolation and quasi-Monte Carlo sampling. First, we construct a polynomial approximation of the forward model in the parameter space by using the sparse grid interpolation. This approximation then defines an accurate surrogate posterior distribution that can be evaluated repeatedly at minimal computational cost. Second, instead of using MCMC, a quasi-Monte Carlo method is applied to draw samples in the parameter space. Then, the desired probability density function of each prediction is approximated by accumulating the posterior density values of all the samples according to the prediction values. Our method has the following advantages: (1) the polynomial approximation of the forward model on the sparse grid provides a very efficient evaluation of the surrogate posterior distribution; (2) the quasi-Monte Carlo method retains the same accuracy in approximating the PDF of predictions but avoids all disadvantages of MCMC. The proposed method is applied to a controlled numerical experiment of groundwater flow modeling. The results show that our method attains the same accuracy much more efficiently than traditional MCMC.

Efficient computation of the phylogenetic likelihood function on multi-gene alignments and multi-core architectures.

PubMed

Stamatakis, Alexandros; Ott, Michael

2008-12-27

The continuous accumulation of sequence data, for example, due to novel wet-laboratory techniques such as pyrosequencing, coupled with the increasing popularity of multi-gene phylogenies and emerging multi-core processor architectures that face problems of cache congestion, poses new challenges with respect to the efficient computation of the phylogenetic maximum-likelihood (ML) function. Here, we propose two approaches that can significantly speed up likelihood computations that typically represent over 95 per cent of the computational effort conducted by current ML or Bayesian inference programs. Initially, we present a method and an appropriate data structure to efficiently compute the likelihood score on 'gappy' multi-gene alignments. By 'gappy' we denote sampling-induced gaps owing to missing sequences in individual genes (partitions), i.e. not real alignment gaps. A first proof-of-concept implementation in RAXML indicates that this approach can accelerate inferences on large and gappy alignments by approximately one order of magnitude. Moreover, we present insights and initial performance results on multi-core architectures obtained during the transition from an OpenMP-based to a Pthreads-based fine-grained parallelization of the ML function.

Approximate string matching algorithms for limited-vocabulary OCR output correction

NASA Astrophysics Data System (ADS)

Lasko, Thomas A.; Hauser, Susan E.

2000-12-01

Five methods for matching words mistranslated by optical character recognition to their most likely match in a reference dictionary were tested on data from the archives of the National Library of Medicine. The methods, including an adaptation of the cross correlation algorithm, the generic edit distance algorithm, the edit distance algorithm with a probabilistic substitution matrix, Bayesian analysis, and Bayesian analysis on an actively thinned reference dictionary were implemented and their accuracy rates compared. Of the five, the Bayesian algorithm produced the most correct matches (87%), and had the advantage of producing scores that have a useful and practical interpretation.

A Fast and Scalable Method for A-Optimal Design of Experiments for Infinite-dimensional Bayesian Nonlinear Inverse Problems with Application to Porous Medium Flow

NASA Astrophysics Data System (ADS)

Petra, N.; Alexanderian, A.; Stadler, G.; Ghattas, O.

2015-12-01

We address the problem of optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs). The inverse problem seeks to infer a parameter field (e.g., the log permeability field in a porous medium flow model problem) from synthetic observations at a set of sensor locations and from the governing PDEs. The goal of the OED problem is to find an optimal placement of sensors so as to minimize the uncertainty in the inferred parameter field. We formulate the OED objective function by generalizing the classical A-optimal experimental design criterion using the expected value of the trace of the posterior covariance. This expected value is computed through sample averaging over the set of likely experimental data. Due to the infinite-dimensional character of the parameter field, we seek an optimization method that solves the OED problem at a cost (measured in the number of forward PDE solves) that is independent of both the parameter and the sensor dimension. To facilitate this goal, we construct a Gaussian approximation to the posterior at the maximum a posteriori probability (MAP) point, and use the resulting covariance operator to define the OED objective function. We use randomized trace estimation to compute the trace of this covariance operator. The resulting OED problem includes as constraints the system of PDEs characterizing the MAP point, and the PDEs describing the action of the covariance (of the Gaussian approximation to the posterior) to vectors. We control the sparsity of the sensor configurations using sparsifying penalty functions, and solve the resulting penalized bilevel optimization problem via an interior-point quasi-Newton method, where gradient information is computed via adjoints. We elaborate our OED method for the problem of determining the optimal sensor configuration to best infer the log permeability field in a porous medium flow problem. Numerical results show that the number of PDE solves required for the evaluation of the OED objective function and its gradient is essentially independent of both the parameter dimension and the sensor dimension (i.e., the number of candidate sensor locations). The number of quasi-Newton iterations for computing an OED also exhibits the same dimension invariance properties.

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.

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.

Bayesian Inference for Functional Dynamics Exploring in fMRI Data.

PubMed

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

2016-01-01

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

Using Approximate Bayesian Computation to infer sex ratios from acoustic data.

PubMed

Lehnen, Lisa; Schorcht, Wigbert; Karst, Inken; Biedermann, Martin; Kerth, Gerald; Puechmaille, Sebastien J

2018-01-01

Population sex ratios are of high ecological relevance, but are challenging to determine in species lacking conspicuous external cues indicating their sex. Acoustic sexing is an option if vocalizations differ between sexes, but is precluded by overlapping distributions of the values of male and female vocalizations in many species. A method allowing the inference of sex ratios despite such an overlap will therefore greatly increase the information extractable from acoustic data. To meet this demand, we developed a novel approach using Approximate Bayesian Computation (ABC) to infer the sex ratio of populations from acoustic data. Additionally, parameters characterizing the male and female distribution of acoustic values (mean and standard deviation) are inferred. This information is then used to probabilistically assign a sex to a single acoustic signal. We furthermore develop a simpler means of sex ratio estimation based on the exclusion of calls from the overlap zone. Applying our methods to simulated data demonstrates that sex ratio and acoustic parameter characteristics of males and females are reliably inferred by the ABC approach. Applying both the ABC and the exclusion method to empirical datasets (echolocation calls recorded in colonies of lesser horseshoe bats, Rhinolophus hipposideros) provides similar sex ratios as molecular sexing. Our methods aim to facilitate evidence-based conservation, and to benefit scientists investigating ecological or conservation questions related to sex- or group specific behaviour across a wide range of organisms emitting acoustic signals. The developed methodology is non-invasive, low-cost and time-efficient, thus allowing the study of many sites and individuals. We provide an R-script for the easy application of the method and discuss potential future extensions and fields of applications. The script can be easily adapted to account for numerous biological systems by adjusting the type and number of groups to be distinguished (e.g. age, social rank, cryptic species) and the acoustic parameters investigated.

astroABC : An Approximate Bayesian Computation Sequential Monte Carlo sampler for cosmological parameter estimation

NASA Astrophysics Data System (ADS)

Jennings, E.; Madigan, M.

2017-04-01

Given the complexity of modern cosmological parameter inference where we are faced with non-Gaussian data and noise, correlated systematics and multi-probe correlated datasets,the Approximate Bayesian Computation (ABC) method is a promising alternative to traditional Markov Chain Monte Carlo approaches in the case where the Likelihood is intractable or unknown. The ABC method is called "Likelihood free" as it avoids explicit evaluation of the Likelihood by using a forward model simulation of the data which can include systematics. We introduce astroABC, an open source ABC Sequential Monte Carlo (SMC) sampler for parameter estimation. A key challenge in astrophysics is the efficient use of large multi-probe datasets to constrain high dimensional, possibly correlated parameter spaces. With this in mind astroABC allows for massive parallelization using MPI, a framework that handles spawning of processes across multiple nodes. A key new feature of astroABC is the ability to create MPI groups with different communicators, one for the sampler and several others for the forward model simulation, which speeds up sampling time considerably. For smaller jobs the Python multiprocessing option is also available. Other key features of this new sampler include: a Sequential Monte Carlo sampler; a method for iteratively adapting tolerance levels; local covariance estimate using scikit-learn's KDTree; modules for specifying optimal covariance matrix for a component-wise or multivariate normal perturbation kernel and a weighted covariance metric; restart files output frequently so an interrupted sampling run can be resumed at any iteration; output and restart files are backed up at every iteration; user defined distance metric and simulation methods; a module for specifying heterogeneous parameter priors including non-standard prior PDFs; a module for specifying a constant, linear, log or exponential tolerance level; well-documented examples and sample scripts. This code is hosted online at https://github.com/EliseJ/astroABC.

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

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

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

2015-02-01

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

Moving beyond qualitative evaluations of Bayesian models of cognition.

PubMed

Hemmer, Pernille; Tauber, Sean; Steyvers, Mark

2015-06-01

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

Bayesian analysis of caustic-crossing microlensing events

NASA Astrophysics Data System (ADS)

Cassan, A.; Horne, K.; Kains, N.; Tsapras, Y.; Browne, P.

2010-06-01

Aims: Caustic-crossing binary-lens microlensing events are important anomalous events because they are capable of detecting an extrasolar planet companion orbiting the lens star. Fast and robust modelling methods are thus of prime interest in helping to decide whether a planet is detected by an event. Cassan introduced a new set of parameters to model binary-lens events, which are closely related to properties of the light curve. In this work, we explain how Bayesian priors can be added to this framework, and investigate on interesting options. Methods: We develop a mathematical formulation that allows us to compute analytically the priors on the new parameters, given some previous knowledge about other physical quantities. We explicitly compute the priors for a number of interesting cases, and show how this can be implemented in a fully Bayesian, Markov chain Monte Carlo algorithm. Results: Using Bayesian priors can accelerate microlens fitting codes by reducing the time spent considering physically implausible models, and helps us to discriminate between alternative models based on the physical plausibility of their parameters.

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

PubMed Central

Gilet, Estelle; Diard, Julien; Bessière, Pierre

2011-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2005-10-01

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

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.

BUMPER: the Bayesian User-friendly Model for Palaeo-Environmental Reconstruction

NASA Astrophysics Data System (ADS)

Holden, Phil; Birks, John; Brooks, Steve; Bush, Mark; Hwang, Grace; Matthews-Bird, Frazer; Valencia, Bryan; van Woesik, Robert

2017-04-01

We describe the Bayesian User-friendly Model for Palaeo-Environmental Reconstruction (BUMPER), a Bayesian transfer function for inferring past climate and other environmental variables from microfossil assemblages. The principal motivation for a Bayesian approach is that the palaeoenvironment is treated probabilistically, and can be updated as additional data become available. Bayesian approaches therefore provide a reconstruction-specific quantification of the uncertainty in the data and in the model parameters. BUMPER is fully self-calibrating, straightforward to apply, and computationally fast, requiring 2 seconds to build a 100-taxon model from a 100-site training-set on a standard personal computer. We apply the model's probabilistic framework to generate thousands of artificial training-sets under ideal assumptions. We then use these to demonstrate both the general applicability of the model and the sensitivity of reconstructions to the characteristics of the training-set, considering assemblage richness, taxon tolerances, and the number of training sites. We demonstrate general applicability to real data, considering three different organism types (chironomids, diatoms, pollen) and different reconstructed variables. In all of these applications an identically configured model is used, the only change being the input files that provide the training-set environment and taxon-count data.

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

NASA Astrophysics Data System (ADS)

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

2005-02-01

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

Model criticism based on likelihood-free inference, with an application to protein network evolution.

PubMed

Ratmann, Oliver; Andrieu, Christophe; Wiuf, Carsten; Richardson, Sylvia

2009-06-30

Mathematical models are an important tool to explain and comprehend complex phenomena, and unparalleled computational advances enable us to easily explore them without any or little understanding of their global properties. In fact, the likelihood of the data under complex stochastic models is often analytically or numerically intractable in many areas of sciences. This makes it even more important to simultaneously investigate the adequacy of these models-in absolute terms, against the data, rather than relative to the performance of other models-but no such procedure has been formally discussed when the likelihood is intractable. We provide a statistical interpretation to current developments in likelihood-free Bayesian inference that explicitly accounts for discrepancies between the model and the data, termed Approximate Bayesian Computation under model uncertainty (ABCmicro). We augment the likelihood of the data with unknown error terms that correspond to freely chosen checking functions, and provide Monte Carlo strategies for sampling from the associated joint posterior distribution without the need of evaluating the likelihood. We discuss the benefit of incorporating model diagnostics within an ABC framework, and demonstrate how this method diagnoses model mismatch and guides model refinement by contrasting three qualitative models of protein network evolution to the protein interaction datasets of Helicobacter pylori and Treponema pallidum. Our results make a number of model deficiencies explicit, and suggest that the T. pallidum network topology is inconsistent with evolution dominated by link turnover or lateral gene transfer alone.

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

On the predictive information criteria for model determination in seismic hazard analysis

NASA Astrophysics Data System (ADS)

Varini, Elisa; Rotondi, Renata

2016-04-01

Many statistical tools have been developed for evaluating, understanding, and comparing models, from both frequentist and Bayesian perspectives. In particular, the problem of model selection can be addressed according to whether the primary goal is explanation or, alternatively, prediction. In the former case, the criteria for model selection are defined over the parameter space whose physical interpretation can be difficult; in the latter case, they are defined over the space of the observations, which has a more direct physical meaning. In the frequentist approaches, model selection is generally based on an asymptotic approximation which may be poor for small data sets (e.g. the F-test, the Kolmogorov-Smirnov test, etc.); moreover, these methods often apply under specific assumptions on models (e.g. models have to be nested in the likelihood ratio test). In the Bayesian context, among the criteria for explanation, the ratio of the observed marginal densities for two competing models, named Bayes Factor (BF), is commonly used for both model choice and model averaging (Kass and Raftery, J. Am. Stat. Ass., 1995). But BF does not apply to improper priors and, even when the prior is proper, it is not robust to the specification of the prior. These limitations can be extended to two famous penalized likelihood methods as the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), since they are proved to be approximations of -2log BF . In the perspective that a model is as good as its predictions, the predictive information criteria aim at evaluating the predictive accuracy of Bayesian models or, in other words, at estimating expected out-of-sample prediction error using a bias-correction adjustment of within-sample error (Gelman et al., Stat. Comput., 2014). In particular, the Watanabe criterion is fully Bayesian because it averages the predictive distribution over the posterior distribution of parameters rather than conditioning on a point estimate, but it is hardly applicable to data which are not independent given parameters (Watanabe, J. Mach. Learn. Res., 2010). A solution is given by Ando and Tsay criterion where the joint density may be decomposed into the product of the conditional densities (Ando and Tsay, Int. J. Forecast., 2010). The above mentioned criteria are global summary measures of model performance, but more detailed analysis could be required to discover the reasons for poor global performance. In this latter case, a retrospective predictive analysis is performed on each individual observation. In this study we performed the Bayesian analysis of Italian data sets by four versions of a long-term hazard model known as the stress release model (Vere-Jones, J. Physics Earth, 1978; Bebbington and Harte, Geophys. J. Int., 2003; Varini and Rotondi, Environ. Ecol. Stat., 2015). Then we illustrate the results on their performance evaluated by Bayes Factor, predictive information criteria and retrospective predictive analysis.

A FAST BAYESIAN METHOD FOR UPDATING AND FORECASTING HOURLY OZONE LEVELS

EPA Science Inventory

A Bayesian hierarchical space-time model is proposed by combining information from real-time ambient AIRNow air monitoring data, and output from a computer simulation model known as the Community Multi-scale Air Quality (Eta-CMAQ) forecast model. A model validation analysis shows...

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

DTIC Science & Technology

2014-10-02

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

Emulation: A fast stochastic Bayesian method to eliminate model space

NASA Astrophysics Data System (ADS)

Roberts, Alan; Hobbs, Richard; Goldstein, Michael

2010-05-01

Joint inversion of large 3D datasets has been the goal of geophysicists ever since the datasets first started to be produced. There are two broad approaches to this kind of problem, traditional deterministic inversion schemes and more recently developed Bayesian search methods, such as MCMC (Markov Chain Monte Carlo). However, using both these kinds of schemes has proved prohibitively expensive, both in computing power and time cost, due to the normally very large model space which needs to be searched using forward model simulators which take considerable time to run. At the heart of strategies aimed at accomplishing this kind of inversion is the question of how to reliably and practicably reduce the size of the model space in which the inversion is to be carried out. Here we present a practical Bayesian method, known as emulation, which can address this issue. Emulation is a Bayesian technique used with considerable success in a number of technical fields, such as in astronomy, where the evolution of the universe has been modelled using this technique, and in the petroleum industry where history matching is carried out of hydrocarbon reservoirs. The method of emulation involves building a fast-to-compute uncertainty-calibrated approximation to a forward model simulator. We do this by modelling the output data from a number of forward simulator runs by a computationally cheap function, and then fitting the coefficients defining this function to the model parameters. By calibrating the error of the emulator output with respect to the full simulator output, we can use this to screen out large areas of model space which contain only implausible models. For example, starting with what may be considered a geologically reasonable prior model space of 10000 models, using the emulator we can quickly show that only models which lie within 10% of that model space actually produce output data which is plausibly similar in character to an observed dataset. We can thus much more tightly constrain the input model space for a deterministic inversion or MCMC method. By using this technique jointly on several datasets (specifically seismic, gravity, and magnetotelluric (MT) describing the same region), we can include in our modelling uncertainties in the data measurements, the relationships between the various physical parameters involved, as well as the model representation uncertainty, and at the same time further reduce the range of plausible models to several percent of the original model space. Being stochastic in nature, the output posterior parameter distributions also allow our understanding of/beliefs about a geological region can be objectively updated, with full assessment of uncertainties, and so the emulator is also an inversion-type tool in it's own right, with the advantage (as with any Bayesian method) that our uncertainties from all sources (both data and model) can be fully evaluated.

A fast Bayesian approach to discrete object detection in astronomical data sets - PowellSnakes I

NASA Astrophysics Data System (ADS)

Carvalho, Pedro; Rocha, Graça; Hobson, M. P.

2009-03-01

A new fast Bayesian approach is introduced for the detection of discrete objects immersed in a diffuse background. This new method, called PowellSnakes, speeds up traditional Bayesian techniques by (i) replacing the standard form of the likelihood for the parameters characterizing the discrete objects by an alternative exact form that is much quicker to evaluate; (ii) using a simultaneous multiple minimization code based on Powell's direction set algorithm to locate rapidly the local maxima in the posterior and (iii) deciding whether each located posterior peak corresponds to a real object by performing a Bayesian model selection using an approximate evidence value based on a local Gaussian approximation to the peak. The construction of this Gaussian approximation also provides the covariance matrix of the uncertainties in the derived parameter values for the object in question. This new approach provides a speed up in performance by a factor of `100' as compared to existing Bayesian source extraction methods that use Monte Carlo Markov chain to explore the parameter space, such as that presented by Hobson & McLachlan. The method can be implemented in either real or Fourier space. In the case of objects embedded in a homogeneous random field, working in Fourier space provides a further speed up that takes advantage of the fact that the correlation matrix of the background is circulant. We illustrate the capabilities of the method by applying to some simplified toy models. Furthermore, PowellSnakes has the advantage of consistently defining the threshold for acceptance/rejection based on priors which cannot be said of the frequentist methods. We present here the first implementation of this technique (version I). Further improvements to this implementation are currently under investigation and will be published shortly. The application of the method to realistic simulated Planck observations will be presented in a forthcoming publication.

Eddington's demon: inferring galaxy mass functions and other distributions from uncertain data

NASA Astrophysics Data System (ADS)

Obreschkow, D.; Murray, S. G.; Robotham, A. S. G.; Westmeier, T.

2018-03-01

We present a general modified maximum likelihood (MML) method for inferring generative distribution functions from uncertain and biased data. The MML estimator is identical to, but easier and many orders of magnitude faster to compute than the solution of the exact Bayesian hierarchical modelling of all measurement errors. As a key application, this method can accurately recover the mass function (MF) of galaxies, while simultaneously dealing with observational uncertainties (Eddington bias), complex selection functions and unknown cosmic large-scale structure. The MML method is free of binning and natively accounts for small number statistics and non-detections. Its fast implementation in the R-package dftools is equally applicable to other objects, such as haloes, groups, and clusters, as well as observables other than mass. The formalism readily extends to multidimensional distribution functions, e.g. a Choloniewski function for the galaxy mass-angular momentum distribution, also handled by dftools. The code provides uncertainties and covariances for the fitted model parameters and approximate Bayesian evidences. We use numerous mock surveys to illustrate and test the MML method, as well as to emphasize the necessity of accounting for observational uncertainties in MFs of modern galaxy surveys.

Bayesian inference on EMRI signals using low frequency approximations

NASA Astrophysics Data System (ADS)

Ali, Asad; Christensen, Nelson; Meyer, Renate; Röver, Christian

2012-07-01

Extreme mass ratio inspirals (EMRIs) are thought to be one of the most exciting gravitational wave sources to be detected with LISA. Due to their complicated nature and weak amplitudes the detection and parameter estimation of such sources is a challenging task. In this paper we present a statistical methodology based on Bayesian inference in which the estimation of parameters is carried out by advanced Markov chain Monte Carlo (MCMC) algorithms such as parallel tempering MCMC. We analysed high and medium mass EMRI systems that fall well inside the low frequency range of LISA. In the context of the Mock LISA Data Challenges, our investigation and results are also the first instance in which a fully Markovian algorithm is applied for EMRI searches. Results show that our algorithm worked well in recovering EMRI signals from different (simulated) LISA data sets having single and multiple EMRI sources and holds great promise for posterior computation under more realistic conditions. The search and estimation methods presented in this paper are general in their nature, and can be applied in any other scenario such as AdLIGO, AdVIRGO and Einstein Telescope with their respective response functions.

Pre-Whaling Genetic Diversity and Population Ecology in Eastern Pacific Gray Whales: Insights from Ancient DNA and Stable Isotopes

PubMed Central

Alter, S. Elizabeth; Newsome, Seth D.; Palumbi, Stephen R.

2012-01-01

Commercial whaling decimated many whale populations, including the eastern Pacific gray whale, but little is known about how population dynamics or ecology differed prior to these removals. Of particular interest is the possibility of a large population decline prior to whaling, as such a decline could explain the ∼5-fold difference between genetic estimates of prior abundance and estimates based on historical records. We analyzed genetic (mitochondrial control region) and isotopic information from modern and prehistoric gray whales using serial coalescent simulations and Bayesian skyline analyses to test for a pre-whaling decline and to examine prehistoric genetic diversity, population dynamics and ecology. Simulations demonstrate that significant genetic differences observed between ancient and modern samples could be caused by a large, recent population bottleneck, roughly concurrent with commercial whaling. Stable isotopes show minimal differences between modern and ancient gray whale foraging ecology. Using rejection-based Approximate Bayesian Computation, we estimate the size of the population bottleneck at its minimum abundance and the pre-bottleneck abundance. Our results agree with previous genetic studies suggesting the historical size of the eastern gray whale population was roughly three to five times its current size. PMID:22590499

An empirical Bayes approach to network recovery using external knowledge.

PubMed

Kpogbezan, Gino B; van der Vaart, Aad W; van Wieringen, Wessel N; Leday, Gwenaël G R; van de Wiel, Mark A

2017-09-01

Reconstruction of a high-dimensional network may benefit substantially from the inclusion of prior knowledge on the network topology. In the case of gene interaction networks such knowledge may come for instance from pathway repositories like KEGG, or be inferred from data of a pilot study. The Bayesian framework provides a natural means of including such prior knowledge. Based on a Bayesian Simultaneous Equation Model, we develop an appealing Empirical Bayes (EB) procedure that automatically assesses the agreement of the used prior knowledge with the data at hand. We use variational Bayes method for posterior densities approximation and compare its accuracy with that of Gibbs sampling strategy. Our method is computationally fast, and can outperform known competitors. In a simulation study, we show that accurate prior data can greatly improve the reconstruction of the network, but need not harm the reconstruction if wrong. We demonstrate the benefits of the method in an analysis of gene expression data from GEO. In particular, the edges of the recovered network have superior reproducibility (compared to that of competitors) over resampled versions of the data. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

NASA Astrophysics Data System (ADS)

Gopalan, Giri; Hrafnkelsson, Birgir; Aðalgeirsdóttir, Guðfinna; Jarosch, Alexander H.; Pálsson, Finnur

2018-03-01

Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier.

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.

Validation of the thermal challenge problem using Bayesian Belief Networks.

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

McFarland, John; Swiler, Laura Painton

The thermal challenge problem has been developed at Sandia National Laboratories as a testbed for demonstrating various types of validation approaches and prediction methods. This report discusses one particular methodology to assess the validity of a computational model given experimental data. This methodology is based on Bayesian Belief Networks (BBNs) and can incorporate uncertainty in experimental measurements, in physical quantities, and model uncertainties. The approach uses the prior and posterior distributions of model output to compute a validation metric based on Bayesian hypothesis testing (a Bayes' factor). This report discusses various aspects of the BBN, specifically in the context ofmore » the thermal challenge problem. A BBN is developed for a given set of experimental data in a particular experimental configuration. The development of the BBN and the method for ''solving'' the BBN to develop the posterior distribution of model output through Monte Carlo Markov Chain sampling is discussed in detail. The use of the BBN to compute a Bayes' factor is demonstrated.« less

Demographic history and gene flow during silkworm domestication

PubMed Central

2014-01-01

Background Gene flow plays an important role in domestication history of domesticated species. However, little is known about the demographic history of domesticated silkworm involving gene flow with its wild relative. Results In this study, four model-based evolutionary scenarios to describe the demographic history of B. mori were hypothesized. Using Approximate Bayesian Computation method and DNA sequence data from 29 nuclear loci, we found that the gene flow at bottleneck model is the most likely scenario for silkworm domestication. The starting time of silkworm domestication was estimated to be approximate 7,500 years ago; the time of domestication termination was 3,984 years ago. Using coalescent simulation analysis, we also found that bi-directional gene flow occurred during silkworm domestication. Conclusions Estimates of silkworm domestication time are nearly consistent with the archeological evidence and our previous results. Importantly, we found that the bi-directional gene flow might occur during silkworm domestication. Our findings add a dimension to highlight the important role of gene flow in domestication of crops and animals. PMID:25123546

Can the Site-Frequency Spectrum Distinguish Exponential Population Growth from Multiple-Merger Coalescents?

PubMed Central

Eldon, Bjarki; Birkner, Matthias; Blath, Jochen; Freund, Fabian

2015-01-01

The ability of the site-frequency spectrum (SFS) to reflect the particularities of gene genealogies exhibiting multiple mergers of ancestral lines as opposed to those obtained in the presence of population growth is our focus. An excess of singletons is a well-known characteristic of both population growth and multiple mergers. Other aspects of the SFS, in particular, the weight of the right tail, are, however, affected in specific ways by the two model classes. Using an approximate likelihood method and minimum-distance statistics, our estimates of statistical power indicate that exponential and algebraic growth can indeed be distinguished from multiple-merger coalescents, even for moderate sample sizes, if the number of segregating sites is high enough. A normalized version of the SFS (nSFS) is also used as a summary statistic in an approximate Bayesian computation (ABC) approach. The results give further positive evidence as to the general eligibility of the SFS to distinguish between the different histories. PMID:25575536

Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations

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

Verde, Licia; Jimenez, Raul; Alvarez-Gaume, Luis

2013-06-01

We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non-Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to more than 7σ for f{sub NL} values (both true and sampled) not ruledmore » out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.« less

Probabilistic Cross-identification of Cosmic Events

NASA Astrophysics Data System (ADS)

Budavári, Tamás

2011-08-01

I discuss a novel approach to identifying cosmic events in separate and independent observations. The focus is on the true events, such as supernova explosions, that happen once and, hence, whose measurements are not repeatable. Their classification and analysis must make the best use of all available data. Bayesian hypothesis testing is used to associate streams of events in space and time. Probabilities are assigned to the matches by studying their rates of occurrence. A case study of Type Ia supernovae illustrates how to use light curves in the cross-identification process. Constraints from realistic light curves happen to be well approximated by Gaussians in time, which makes the matching process very efficient. Model-dependent associations are computationally more demanding but can further boost one's confidence.

MUMPS Based Integration of Disparate Computer-Assisted Medical Diagnosis Modules

DTIC Science & Technology

1989-12-12

modules use a Bayesian approach, while the Opthalmology module uses a Rule Based approach. In the current effort, MUMPS is used to develop an...Abdominal and Chest Pain modules use a Bayesian approach, while the Opthalmology module uses a Rule Based approach. In the current effort, MUMPS is used

Hierarchical Bayesian Models of Subtask Learning

ERIC Educational Resources Information Center

Anglim, Jeromy; Wynton, Sarah K. A.

2015-01-01

The current study used Bayesian hierarchical methods to challenge and extend previous work on subtask learning consistency. A general model of individual-level subtask learning was proposed focusing on power and exponential functions with constraints to test for inconsistency. To study subtask learning, we developed a novel computer-based booking…

Nonparametric Bayesian Modeling for Automated Database Schema Matching

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

Ferragut, Erik M; Laska, Jason A

2015-01-01

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

Species trees from consensus single nucleotide polymorphism (SNP) data: Testing phylogenetic approaches with simulated and empirical data.

PubMed

Schmidt-Lebuhn, Alexander N; Aitken, Nicola C; Chuah, Aaron

2017-11-01

Datasets of hundreds or thousands of SNPs (Single Nucleotide Polymorphisms) from multiple individuals per species are increasingly used to study population structure, species delimitation and shallow phylogenetics. The principal software tool to infer species or population trees from SNP data is currently the BEAST template SNAPP which uses a Bayesian coalescent analysis. However, it is computationally extremely demanding and tolerates only small amounts of missing data. We used simulated and empirical SNPs from plants (Australian Craspedia, Asteraceae, and Pelargonium, Geraniaceae) to compare species trees produced (1) by SNAPP, (2) using SVD quartets, and (3) using Bayesian and parsimony analysis with several different approaches to summarising data from multiple samples into one set of traits per species. Our aims were to explore the impact of tree topology and missing data on the results, and to test which data summarising and analyses approaches would best approximate the results obtained from SNAPP for empirical data. SVD quartets retrieved the correct topology from simulated data, as did SNAPP except in the case of a very unbalanced phylogeny. Both methods failed to retrieve the correct topology when large amounts of data were missing. Bayesian analysis of species level summary data scoring the two alleles of each SNP as independent characters and parsimony analysis of data scoring each SNP as one character produced trees with branch length distributions closest to the true trees on which SNPs were simulated. For empirical data, Bayesian inference and Dollo parsimony analysis of data scored allele-wise produced phylogenies most congruent with the results of SNAPP. In the case of study groups divergent enough for missing data to be phylogenetically informative (because of additional mutations preventing amplification of genomic fragments or bioinformatic establishment of homology), scoring of SNP data as a presence/absence matrix irrespective of allele content might be an additional option. As this depends on sampling across species being reasonably even and a random distribution of non-informative instances of missing data, however, further exploration of this approach is needed. Properly chosen data summary approaches to inferring species trees from SNP data may represent a potential alternative to currently available individual-level coalescent analyses especially for quick data exploration and when dealing with computationally demanding or patchy datasets. Crown Copyright © 2017. Published by Elsevier Inc. All rights reserved.

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.

Reparametrization-based estimation of genetic parameters in multi-trait animal model using Integrated Nested Laplace Approximation.

PubMed

Mathew, Boby; Holand, Anna Marie; Koistinen, Petri; Léon, Jens; Sillanpää, Mikko J

2016-02-01

A novel reparametrization-based INLA approach as a fast alternative to MCMC for the Bayesian estimation of genetic parameters in multivariate animal model is presented. Multi-trait genetic parameter estimation is a relevant topic in animal and plant breeding programs because multi-trait analysis can take into account the genetic correlation between different traits and that significantly improves the accuracy of the genetic parameter estimates. Generally, multi-trait analysis is computationally demanding and requires initial estimates of genetic and residual correlations among the traits, while those are difficult to obtain. In this study, we illustrate how to reparametrize covariance matrices of a multivariate animal model/animal models using modified Cholesky decompositions. This reparametrization-based approach is used in the Integrated Nested Laplace Approximation (INLA) methodology to estimate genetic parameters of multivariate animal model. Immediate benefits are: (1) to avoid difficulties of finding good starting values for analysis which can be a problem, for example in Restricted Maximum Likelihood (REML); (2) Bayesian estimation of (co)variance components using INLA is faster to execute than using Markov Chain Monte Carlo (MCMC) especially when realized relationship matrices are dense. The slight drawback is that priors for covariance matrices are assigned for elements of the Cholesky factor but not directly to the covariance matrix elements as in MCMC. Additionally, we illustrate the concordance of the INLA results with the traditional methods like MCMC and REML approaches. We also present results obtained from simulated data sets with replicates and field data in rice.

Reconstructing the history of a fragmented and heavily exploited red deer population using ancient and contemporary DNA.

PubMed

Rosvold, Jørgen; Røed, Knut H; Hufthammer, Anne Karin; Andersen, Reidar; Stenøien, Hans K

2012-09-26

Red deer (Cervus elaphus) have been an important human resource for millennia, experiencing intensive human influence through habitat alterations, hunting and translocation of animals. In this study we investigate a time series of ancient and contemporary DNA from Norwegian red deer spanning about 7,000 years. Our main aim was to investigate how increasing agricultural land use, hunting pressure and possibly human mediated translocation of animals have affected the genetic diversity on a long-term scale. We obtained mtDNA (D-loop) sequences from 73 ancient specimens. These show higher genetic diversity in ancient compared to extant samples, with the highest diversity preceding the onset of agricultural intensification in the Early Iron Age. Using standard diversity indices, Bayesian skyline plot and approximate Bayesian computation, we detected a population reduction which was more prolonged than, but not as severe as, historic documents indicate. There are signs of substantial changes in haplotype frequencies primarily due to loss of haplotypes through genetic drift. There is no indication of human mediated translocations into the Norwegian population. All the Norwegian sequences show a western European origin, from which the Norwegian lineage diverged approximately 15,000 years ago. Our results provide direct insight into the effects of increasing habitat fragmentation and human hunting pressure on genetic diversity and structure of red deer populations. They also shed light on the northward post-glacial colonisation process of red deer in Europe and suggest increased precision in inferring past demographic events when including both ancient and contemporary DNA.

Near Real-Time Probabilistic Damage Diagnosis Using Surrogate Modeling and High Performance Computing

NASA Technical Reports Server (NTRS)

Warner, James E.; Zubair, Mohammad; Ranjan, Desh

2017-01-01

This work investigates novel approaches to probabilistic damage diagnosis that utilize surrogate modeling and high performance computing (HPC) to achieve substantial computational speedup. Motivated by Digital Twin, a structural health management (SHM) paradigm that integrates vehicle-specific characteristics with continual in-situ damage diagnosis and prognosis, the methods studied herein yield near real-time damage assessments that could enable monitoring of a vehicle's health while it is operating (i.e. online SHM). High-fidelity modeling and uncertainty quantification (UQ), both critical to Digital Twin, are incorporated using finite element method simulations and Bayesian inference, respectively. The crux of the proposed Bayesian diagnosis methods, however, is the reformulation of the numerical sampling algorithms (e.g. Markov chain Monte Carlo) used to generate the resulting probabilistic damage estimates. To this end, three distinct methods are demonstrated for rapid sampling that utilize surrogate modeling and exploit various degrees of parallelism for leveraging HPC. The accuracy and computational efficiency of the methods are compared on the problem of strain-based crack identification in thin plates. While each approach has inherent problem-specific strengths and weaknesses, all approaches are shown to provide accurate probabilistic damage diagnoses and several orders of magnitude computational speedup relative to a baseline Bayesian diagnosis implementation.

Radiation dose reduction in computed tomography perfusion using spatial-temporal Bayesian methods

NASA Astrophysics Data System (ADS)

Fang, Ruogu; Raj, Ashish; Chen, Tsuhan; Sanelli, Pina C.

2012-03-01

In current computed tomography (CT) examinations, the associated X-ray radiation dose is of significant concern to patients and operators, especially CT perfusion (CTP) imaging that has higher radiation dose due to its cine scanning technique. A simple and cost-effective means to perform the examinations is to lower the milliampere-seconds (mAs) parameter as low as reasonably achievable in data acquisition. However, lowering the mAs parameter will unavoidably increase data noise and degrade CT perfusion maps greatly if no adequate noise control is applied during image reconstruction. To capture the essential dynamics of CT perfusion, a simple spatial-temporal Bayesian method that uses a piecewise parametric model of the residual function is used, and then the model parameters are estimated from a Bayesian formulation of prior smoothness constraints on perfusion parameters. From the fitted residual function, reliable CTP parameter maps are obtained from low dose CT data. The merit of this scheme exists in the combination of analytical piecewise residual function with Bayesian framework using a simpler prior spatial constrain for CT perfusion application. On a dataset of 22 patients, this dynamic spatial-temporal Bayesian model yielded an increase in signal-tonoise-ratio (SNR) of 78% and a decrease in mean-square-error (MSE) of 40% at low dose radiation of 43mA.

Uncertainty quantification in capacitive RF MEMS switches

NASA Astrophysics Data System (ADS)

Pax, Benjamin J.

Development of radio frequency micro electrical-mechanical systems (RF MEMS) has led to novel approaches to implement electrical circuitry. The introduction of capacitive MEMS switches, in particular, has shown promise in low-loss, low-power devices. However, the promise of MEMS switches has not yet been completely realized. RF-MEMS switches are known to fail after only a few months of operation, and nominally similar designs show wide variability in lifetime. Modeling switch operation using nominal or as-designed parameters cannot predict the statistical spread in the number of cycles to failure, and probabilistic methods are necessary. A Bayesian framework for calibration, validation and prediction offers an integrated approach to quantifying the uncertainty in predictions of MEMS switch performance. The objective of this thesis is to use the Bayesian framework to predict the creep-related deflection of the PRISM RF-MEMS switch over several thousand hours of operation. The PRISM switch used in this thesis is the focus of research at Purdue's PRISM center, and is a capacitive contacting RF-MEMS switch. It employs a fixed-fixed nickel membrane which is electrostatically actuated by applying voltage between the membrane and a pull-down electrode. Creep plays a central role in the reliability of this switch. The focus of this thesis is on the creep model, which is calibrated against experimental data measured for a frog-leg varactor fabricated and characterized at Purdue University. Creep plasticity is modeled using plate element theory with electrostatic forces being generated using either parallel plate approximations where appropriate, or solving for the full 3D potential field. For the latter, structure-electrostatics interaction is determined through immersed boundary method. A probabilistic framework using generalized polynomial chaos (gPC) is used to create surrogate models to mitigate the costly full physics simulations, and Bayesian calibration and forward propagation of uncertainty are performed using this surrogate model. The first step in the analysis is Bayesian calibration of the creep related parameters. A computational model of the frog-leg varactor is created, and the computed creep deflection of the device over 800 hours is used to generate a surrogate model using a polynomial chaos expansion in Hermite polynomials. Parameters related to the creep phenomenon are calibrated using Bayesian calibration with experimental deflection data from the frog-leg device. The calibrated input distributions are subsequently propagated through a surrogate gPC model for the PRISM MEMS switch to produce probability density functions of the maximum membrane deflection of the membrane over several thousand hours. The assumptions related to the Bayesian calibration and forward propagation are analyzed to determine the sensitivity to these assumptions of the calibrated input distributions and propagated output distributions of the PRISM device. The work is an early step in understanding the role of geometric variability, model uncertainty, numerical errors and experimental uncertainties in the long-term performance of RF-MEMS.

Integrating probabilistic models of perception and interactive neural networks: a historical and tutorial review

PubMed Central

McClelland, James L.

2013-01-01

This article seeks to establish a rapprochement between explicitly Bayesian models of contextual effects in perception and neural network models of such effects, particularly the connectionist interactive activation (IA) model of perception. The article is in part an historical review and in part a tutorial, reviewing the probabilistic Bayesian approach to understanding perception and how it may be shaped by context, and also reviewing ideas about how such probabilistic computations may be carried out in neural networks, focusing on the role of context in interactive neural networks, in which both bottom-up and top-down signals affect the interpretation of sensory inputs. It is pointed out that connectionist units that use the logistic or softmax activation functions can exactly compute Bayesian posterior probabilities when the bias terms and connection weights affecting such units are set to the logarithms of appropriate probabilistic quantities. Bayesian concepts such the prior, likelihood, (joint and marginal) posterior, probability matching and maximizing, and calculating vs. sampling from the posterior are all reviewed and linked to neural network computations. Probabilistic and neural network models are explicitly linked to the concept of a probabilistic generative model that describes the relationship between the underlying target of perception (e.g., the word intended by a speaker or other source of sensory stimuli) and the sensory input that reaches the perceiver for use in inferring the underlying target. It is shown how a new version of the IA model called the multinomial interactive activation (MIA) model can sample correctly from the joint posterior of a proposed generative model for perception of letters in words, indicating that interactive processing is fully consistent with principled probabilistic computation. Ways in which these computations might be realized in real neural systems are also considered. PMID:23970868

Integrating probabilistic models of perception and interactive neural networks: a historical and tutorial review.

PubMed

McClelland, James L

2013-01-01

This article seeks to establish a rapprochement between explicitly Bayesian models of contextual effects in perception and neural network models of such effects, particularly the connectionist interactive activation (IA) model of perception. The article is in part an historical review and in part a tutorial, reviewing the probabilistic Bayesian approach to understanding perception and how it may be shaped by context, and also reviewing ideas about how such probabilistic computations may be carried out in neural networks, focusing on the role of context in interactive neural networks, in which both bottom-up and top-down signals affect the interpretation of sensory inputs. It is pointed out that connectionist units that use the logistic or softmax activation functions can exactly compute Bayesian posterior probabilities when the bias terms and connection weights affecting such units are set to the logarithms of appropriate probabilistic quantities. Bayesian concepts such the prior, likelihood, (joint and marginal) posterior, probability matching and maximizing, and calculating vs. sampling from the posterior are all reviewed and linked to neural network computations. Probabilistic and neural network models are explicitly linked to the concept of a probabilistic generative model that describes the relationship between the underlying target of perception (e.g., the word intended by a speaker or other source of sensory stimuli) and the sensory input that reaches the perceiver for use in inferring the underlying target. It is shown how a new version of the IA model called the multinomial interactive activation (MIA) model can sample correctly from the joint posterior of a proposed generative model for perception of letters in words, indicating that interactive processing is fully consistent with principled probabilistic computation. Ways in which these computations might be realized in real neural systems are also considered.

Bayesian design of decision rules for failure detection

NASA Technical Reports Server (NTRS)

Chow, E. Y.; Willsky, A. S.

1984-01-01

The formulation of the decision making process of a failure detection algorithm as a Bayes sequential decision problem provides a simple conceptualization of the decision rule design problem. As the optimal Bayes rule is not computable, a methodology that is based on the Bayesian approach and aimed at a reduced computational requirement is developed for designing suboptimal rules. A numerical algorithm is constructed to facilitate the design and performance evaluation of these suboptimal rules. The result of applying this design methodology to an example shows that this approach is potentially a useful one.

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

PubMed

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

2014-01-01

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

Reconstructing Constructivism: Causal Models, Bayesian Learning Mechanisms, and the Theory Theory

ERIC Educational Resources Information Center

Gopnik, Alison; Wellman, Henry M.

2012-01-01

We propose a new version of the "theory theory" grounded in the computational framework of probabilistic causal models and Bayesian learning. Probabilistic models allow a constructivist but rigorous and detailed approach to cognitive development. They also explain the learning of both more specific causal hypotheses and more abstract framework…

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

NASA Astrophysics Data System (ADS)

Daum, Fred; Huang, Jim

2015-05-01

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

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

PubMed

Merlé, Y; Mentré, F

1995-02-01

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

Calibrating Bayesian Network Representations of Social-Behavioral Models

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

Whitney, Paul D.; Walsh, Stephen J.

2010-04-08

While human behavior has long been studied, recent and ongoing advances in computational modeling present opportunities for recasting research outcomes in human behavior. In this paper we describe how Bayesian networks can represent outcomes of human behavior research. We demonstrate a Bayesian network that represents political radicalization research – and show a corresponding visual representation of aspects of this research outcome. Since Bayesian networks can be quantitatively compared with external observations, the representation can also be used for empirical assessments of the research which the network summarizes. For a political radicalization model based on published research, we show this empiricalmore » comparison with data taken from the Minorities at Risk Organizational Behaviors database.« less

New insights into faster computation of uncertainties

NASA Astrophysics Data System (ADS)

Bhattacharya, Atreyee

2012-11-01

Heavy computation power, lengthy simulations, and an exhaustive number of model runs—often these seem like the only statistical tools that scientists have at their disposal when computing uncertainties associated with predictions, particularly in cases of environmental processes such as groundwater movement. However, calculation of uncertainties need not be as lengthy, a new study shows. Comparing two approaches—the classical Bayesian “credible interval” and a less commonly used regression-based “confidence interval” method—Lu et al. show that for many practical purposes both methods provide similar estimates of uncertainties. The advantage of the regression method is that it demands 10-1000 model runs, whereas the classical Bayesian approach requires 10,000 to millions of model runs.

Multilocus approach to clarify species status and the divergence history of the Bemisia tabaci (Hemiptera: Aleyrodidae) species complex.

PubMed

Hsieh, Chia-Hung; Ko, Chiun-Cheng; Chung, Cheng-Han; Wang, Hurng-Yi

2014-07-01

The sweet potato whitefly, Bemisia tabaci, is a highly differentiated species complex. Despite consisting of several morphologically indistinguishable entities and frequent invasions on all continents with important associated economic losses, the phylogenetic relationships, species status, and evolutionary history of this species complex is still debated. We sequenced and analyzed one mitochondrial and three single-copy nuclear genes from 9 of the 12 genetic groups of B. tabaci and 5 closely related species. Bayesian species delimitation was applied to investigate the speciation events of B. tabaci. The species statuses of the different genetic groups were strongly supported under different prior settings and phylogenetic scenarios. Divergence histories were estimated by a multispecies coalescence approach implemented in (*)BEAST. Based on mitochondrial locus, B. tabaci was originated 6.47 million years ago (MYA). Nevertheless, the time was 1.25MYA based on nuclear loci. According to the method of approximate Bayesian computation, this difference is probably due to different degrees of migration among loci; i.e., although the mitochondrial locus had differentiated, gene flow at nuclear loci was still possible, a scenario similar to parapatric mode of speciation. This is the first study in whiteflies using multilocus data and incorporating Bayesian coalescence approaches, both of which provide a more biologically realistic framework for delimiting species status and delineating the divergence history of B. tabaci. Our study illustrates that gene flow during species divergence should not be overlooked and has a great impact on divergence time estimation. Copyright © 2014 Elsevier Inc. All rights reserved.

Bayesian Hierarchical Modeling for Big Data Fusion in Soil Hydrology

NASA Astrophysics Data System (ADS)

Mohanty, B.; Kathuria, D.; Katzfuss, M.

2016-12-01

Soil moisture datasets from remote sensing (RS) platforms (such as SMOS and SMAP) and reanalysis products from land surface models are typically available on a coarse spatial granularity of several square km. Ground based sensors on the other hand provide observations on a finer spatial scale (meter scale or less) but are sparsely available. Soil moisture is affected by high variability due to complex interactions between geologic, topographic, vegetation and atmospheric variables. Hydrologic processes usually occur at a scale of 1 km or less and therefore spatially ubiquitous and temporally periodic soil moisture products at this scale are required to aid local decision makers in agriculture, weather prediction and reservoir operations. Past literature has largely focused on downscaling RS soil moisture for a small extent of a field or a watershed and hence the applicability of such products has been limited. The present study employs a spatial Bayesian Hierarchical Model (BHM) to derive soil moisture products at a spatial scale of 1 km for the state of Oklahoma by fusing point scale Mesonet data and coarse scale RS data for soil moisture and its auxiliary covariates such as precipitation, topography, soil texture and vegetation. It is seen that the BHM model handles change of support problems easily while performing accurate uncertainty quantification arising from measurement errors and imperfect retrieval algorithms. The computational challenge arising due to the large number of measurements is tackled by utilizing basis function approaches and likelihood approximations. The BHM model can be considered as a complex Bayesian extension of traditional geostatistical prediction methods (such as Kriging) for large datasets in the presence of uncertainties.

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

PubMed

Karabatsos, George

2018-06-01

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

Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs

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

Karagiannis, Georgios, E-mail: georgios.karagiannis@pnnl.gov; Lin, Guang, E-mail: guang.lin@pnnl.gov

2014-02-15

Generalized polynomial chaos (gPC) expansions allow us to represent the solution of a stochastic system using a series of polynomial chaos basis functions. The number of gPC terms increases dramatically as the dimension of the random input variables increases. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs when the corresponding deterministic solver is computationally expensive, evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solutions, in both spatial and random domains, bymore » coupling Bayesian model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spatial points, via (1) the Bayesian model average (BMA) or (2) the median probability model, and their construction as spatial functions on the spatial domain via spline interpolation. The former accounts for the model uncertainty and provides Bayes-optimal predictions; while the latter provides a sparse representation of the stochastic solutions by evaluating the expansion on a subset of dominating gPC bases. Moreover, the proposed methods quantify the importance of the gPC bases in the probabilistic sense through inclusion probabilities. We design a Markov chain Monte Carlo (MCMC) sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed methods are suitable for, but not restricted to, problems whose stochastic solutions are sparse in the stochastic space with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the accuracy and performance of the proposed methods and make comparisons with other approaches on solving elliptic SPDEs with 1-, 14- and 40-random dimensions.« less

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

USGS Publications Warehouse

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

2006-01-01

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

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

PubMed

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

2013-01-01

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

Bayesian 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 linkage and segregation analysis: factoring the problem.

PubMed

Matthysse, S

2000-01-01

Complex segregation analysis and linkage methods are mathematical techniques for the genetic dissection of complex diseases. They are used to delineate complex modes of familial transmission and to localize putative disease susceptibility loci to specific chromosomal locations. The computational problem of Bayesian linkage and segregation analysis is one of integration in high-dimensional spaces. In this paper, three available techniques for Bayesian linkage and segregation analysis are discussed: Markov Chain Monte Carlo (MCMC), importance sampling, and exact calculation. The contribution of each to the overall integration will be explicitly discussed.

Learning classification trees

NASA Technical Reports Server (NTRS)

Buntine, Wray

1991-01-01

Algorithms for learning classification trees have had successes in artificial intelligence and statistics over many years. How a tree learning algorithm can be derived from Bayesian decision theory is outlined. This introduces Bayesian techniques for splitting, smoothing, and tree averaging. The splitting rule turns out to be similar to Quinlan's information gain splitting rule, while smoothing and averaging replace pruning. Comparative experiments with reimplementations of a minimum encoding approach, Quinlan's C4 and Breiman et al. Cart show the full Bayesian algorithm is consistently as good, or more accurate than these other approaches though at a computational price.

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

PubMed Central

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

2015-01-01

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

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

USGS Publications Warehouse

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

2011-01-01

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

Asteroid orbital error analysis: Theory and application

NASA Technical Reports Server (NTRS)

Muinonen, K.; Bowell, Edward

1992-01-01

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

A local approach for focussed Bayesian fusion

NASA Astrophysics Data System (ADS)

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

2009-04-01

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

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.

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

PubMed Central

Puig, X; Ginebra, J; Graffelman, J

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

Takiyama, Ken

2016-05-01

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

Uses and misuses of Bayes' rule and Bayesian classifiers in cybersecurity

NASA Astrophysics Data System (ADS)

Bard, Gregory V.

2017-12-01

This paper will discuss the applications of Bayes' Rule and Bayesian Classifiers in Cybersecurity. While the most elementary form of Bayes' rule occurs in undergraduate coursework, there are more complicated forms as well. As an extended example, Bayesian spam filtering is explored, and is in many ways the most triumphant accomplishment of Bayesian reasoning in computer science, as nearly everyone with an email address has a spam folder. Bayesian Classifiers have also been responsible significant cybersecurity research results; yet, because they are not part of the standard curriculum, few in the mathematics or information-technology communities have seen the exact definitions, requirements, and proofs that comprise the subject. Moreover, numerous errors have been made by researchers (described in this paper), due to some mathematical misunderstandings dealing with conditional independence, or other badly chosen assumptions. Finally, to provide instructors and researchers with real-world examples, 25 published cybersecurity papers that use Bayesian reasoning are given, with 2-4 sentence summaries of the focus and contributions of each paper.

A Bayesian approach to modeling 2D gravity data using polygon states

NASA Astrophysics Data System (ADS)

Titus, W. J.; Titus, S.; Davis, J. R.

2015-12-01

We present a Bayesian Markov chain Monte Carlo (MCMC) method for the 2D gravity inversion of a localized subsurface object with constant density contrast. Our models have four parameters: the density contrast, the number of vertices in a polygonal approximation of the object, an upper bound on the ratio of the perimeter squared to the area, and the vertices of a polygon container that bounds the object. Reasonable parameter values can be estimated prior to inversion using a forward model and geologic information. In addition, we assume that the field data have a common random uncertainty that lies between two bounds but that it has no systematic uncertainty. Finally, we assume that there is no uncertainty in the spatial locations of the measurement stations. For any set of model parameters, we use MCMC methods to generate an approximate probability distribution of polygons for the object. We then compute various probability distributions for the object, including the variance between the observed and predicted fields (an important quantity in the MCMC method), the area, the center of area, and the occupancy probability (the probability that a spatial point lies within the object). In addition, we compare probabilities of different models using parallel tempering, a technique which also mitigates trapping in local optima that can occur in certain model geometries. We apply our method to several synthetic data sets generated from objects of varying shape and location. We also analyze a natural data set collected across the Rio Grande Gorge Bridge in New Mexico, where the object (i.e. the air below the bridge) is known and the canyon is approximately 2D. Although there are many ways to view results, the occupancy probability proves quite powerful. We also find that the choice of the container is important. In particular, large containers should be avoided, because the more closely a container confines the object, the better the predictions match properties of object.

Laminar fMRI and computational theories of brain function.

PubMed

Stephan, K E; Petzschner, F H; Kasper, L; Bayer, J; Wellstein, K V; Stefanics, G; Pruessmann, K P; Heinzle, J

2017-11-02

Recently developed methods for functional MRI at the resolution of cortical layers (laminar fMRI) offer a novel window into neurophysiological mechanisms of cortical activity. Beyond physiology, laminar fMRI also offers an unprecedented opportunity to test influential theories of brain function. Specifically, hierarchical Bayesian theories of brain function, such as predictive coding, assign specific computational roles to different cortical layers. Combined with computational models, laminar fMRI offers a unique opportunity to test these proposals noninvasively in humans. This review provides a brief overview of predictive coding and related hierarchical Bayesian theories, summarises their predictions with regard to layered cortical computations, examines how these predictions could be tested by laminar fMRI, and considers methodological challenges. We conclude by discussing the potential of laminar fMRI for clinically useful computational assays of layer-specific information processing. Copyright © 2017 Elsevier Inc. All rights reserved.

Computational modelling of cellular level metabolism

NASA Astrophysics Data System (ADS)

Calvetti, D.; Heino, J.; Somersalo, E.

2008-07-01

The steady and stationary state inverse problems consist of estimating the reaction and transport fluxes, blood concentrations and possibly the rates of change of some of the concentrations based on data which are often scarce noisy and sampled over a population. The Bayesian framework provides a natural setting for the solution of this inverse problem, because a priori knowledge about the system itself and the unknown reaction fluxes and transport rates can compensate for the insufficiency of measured data, provided that the computational costs do not become prohibitive. This article identifies the computational challenges which have to be met when analyzing the steady and stationary states of multicompartment model for cellular metabolism and suggest stable and efficient ways to handle the computations. The outline of a computational tool based on the Bayesian paradigm for the simulation and analysis of complex cellular metabolic systems is also presented.

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

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

Bayesian Factor Analysis When Only a Sample Covariance Matrix Is Available

ERIC Educational Resources Information Center

Hayashi, Kentaro; Arav, Marina

2006-01-01

In traditional factor analysis, the variance-covariance matrix or the correlation matrix has often been a form of inputting data. In contrast, in Bayesian factor analysis, the entire data set is typically required to compute the posterior estimates, such as Bayes factor loadings and Bayes unique variances. We propose a simple method for computing…

QUEST - A Bayesian adaptive psychometric method

NASA Technical Reports Server (NTRS)

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

1983-01-01

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

Designing a Mobile Training System in Rural Areas with Bayesian Factor Models

ERIC Educational Resources Information Center

Omidi Najafabadi, Maryam; Mirdamadi, Seyed Mehdi; Payandeh Najafabadi, Amir Teimour

2014-01-01

The facts that the wireless technologies (1) are more convenient; and (2) need less skill than desktop computers, play a crucial role to decrease digital gap in rural areas. This study employed the Bayesian Confirmatory Factor Analysis (CFA) to design a mobile training system in rural areas of Iran. It categorized challenges, potential, and…

A combined Fuzzy and Naive Bayesian strategy can be used to assign event codes to injury narratives.

PubMed

Marucci-Wellman, H; Lehto, M; Corns, H

2011-12-01

Bayesian methods show promise for classifying injury narratives from large administrative datasets into cause groups. This study examined a combined approach where two Bayesian models (Fuzzy and Naïve) were used to either classify a narrative or select it for manual review. Injury narratives were extracted from claims filed with a worker's compensation insurance provider between January 2002 and December 2004. Narratives were separated into a training set (n=11,000) and prediction set (n=3,000). Expert coders assigned two-digit Bureau of Labor Statistics Occupational Injury and Illness Classification event codes to each narrative. Fuzzy and Naïve Bayesian models were developed using manually classified cases in the training set. Two semi-automatic machine coding strategies were evaluated. The first strategy assigned cases for manual review if the Fuzzy and Naïve models disagreed on the classification. The second strategy selected additional cases for manual review from the Agree dataset using prediction strength to reach a level of 50% computer coding and 50% manual coding. When agreement alone was used as the filtering strategy, the majority were coded by the computer (n=1,928, 64%) leaving 36% for manual review. The overall combined (human plus computer) sensitivity was 0.90 and positive predictive value (PPV) was >0.90 for 11 of 18 2-digit event categories. Implementing the 2nd strategy improved results with an overall sensitivity of 0.95 and PPV >0.90 for 17 of 18 categories. A combined Naïve-Fuzzy Bayesian approach can classify some narratives with high accuracy and identify others most beneficial for manual review, reducing the burden on human coders.

Genomic signature of successful colonization of Eurasia by the allopolyploid shepherd's purse (Capsella bursa-pastoris).

PubMed

Cornille, A; Salcedo, A; Kryvokhyzha, D; Glémin, S; Holm, K; Wright, S I; Lascoux, M

2016-01-01

Polyploidization is a dominant feature of flowering plant evolution. However, detailed genomic analyses of the interpopulation diversification of polyploids following genome duplication are still in their infancy, mainly because of methodological limits, both in terms of sequencing and computational analyses. The shepherd's purse (Capsella bursa-pastoris) is one of the most common weed species in the world. It is highly self-fertilizing, and recent genomic data indicate that it is an allopolyploid, resulting from hybridization between the ancestors of the diploid species Capsella grandiflora and Capsella orientalis. Here, we investigated the genomic diversity of C. bursa-pastoris, its population structure and demographic history, following allopolyploidization in Eurasia. To that end, we genotyped 261 C. bursa-pastoris accessions spread across Europe, the Middle East and Asia, using genotyping-by-sequencing, leading to a total of 4274 SNPs after quality control. Bayesian clustering analyses revealed three distinct genetic clusters in Eurasia: one cluster grouping samples from Western Europe and Southeastern Siberia, the second one centred on Eastern Asia and the third one in the Middle East. Approximate Bayesian computation (ABC) supported the hypothesis that C. bursa-pastoris underwent a typical colonization history involving low gene flow among colonizing populations, likely starting from the Middle East towards Europe and followed by successive human-mediated expansions into Eastern Asia. Altogether, these findings bring new insights into the recent multistage colonization history of the allotetraploid C. bursa-pastoris and highlight ABC and genotyping-by-sequencing data as promising but still challenging tools to infer demographic histories of selfing allopolyploids. © 2015 John Wiley & Sons Ltd.

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.

A Revised Velocity for the Globular Cluster GC-98 in the Ultra Diffuse Galaxy NGC 1052-DF2

NASA Astrophysics Data System (ADS)

van Dokkum, Pieter; Cohen, Yotam; Danieli, Shany; Romanowsky, Aaron; Abraham, Roberto; Brodie, Jean; Conroy, Charlie; Kruijssen, J. M. Diederik; Lokhorst, Deborah; Merritt, Allison; Mowla, Lamiya; Zhang, Jielai

2018-06-01

We recently published velocity measurements of luminous globular clusters in the galaxy NGC1052-DF2, concluding that it lies far off the canonical stellar mass - halo mass relation. Here we present a revised velocity for one of the globular clusters, GC-98, and a revised velocity dispersion measurement for the galaxy. We find that the intrinsic dispersion $\\sigma=5.6^{+5.2}_{-3.8}$ km/s using Approximate Bayesian Computation, or $\\sigma=7.8^{+5.2}_{-2.2}$ km/s using the likelihood. The expected dispersion from the stars alone is ~7 km/s. Responding to a request from the Editors of ApJ Letters and RNAAS, we also briefly comment on the recent analysis of our measurements by Martin et al. (2018).

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

PubMed Central

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

2016-01-01

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

Practical Bayesian tomography

NASA Astrophysics Data System (ADS)

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

2016-03-01

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

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

Markov Chain Monte Carlo Methods for Bayesian Data Analysis in Astronomy

NASA Astrophysics Data System (ADS)

Sharma, Sanjib

2017-08-01

Markov Chain Monte Carlo based Bayesian data analysis has now become the method of choice for analyzing and interpreting data in almost all disciplines of science. In astronomy, over the last decade, we have also seen a steady increase in the number of papers that employ Monte Carlo based Bayesian analysis. New, efficient Monte Carlo based methods are continuously being developed and explored. In this review, we first explain the basics of Bayesian theory and discuss how to set up data analysis problems within this framework. Next, we provide an overview of various Monte Carlo based methods for performing Bayesian data analysis. Finally, we discuss advanced ideas that enable us to tackle complex problems and thus hold great promise for the future. We also distribute downloadable computer software (available at https://github.com/sanjibs/bmcmc/ ) that implements some of the algorithms and examples discussed here.

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

PubMed

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

2017-12-01

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

Bayesian analysis of rare events

NASA Astrophysics Data System (ADS)

Straub, Daniel; Papaioannou, Iason; Betz, Wolfgang

2016-06-01

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

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.

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

NASA Astrophysics Data System (ADS)

Wang, Dong; Tsui, Kwok-Leung

2017-05-01

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

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.

Bayesian statistics in radionuclide metrology: measurement of a decaying source

NASA Astrophysics Data System (ADS)

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

2007-08-01

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

Can Bayesian Theories of Autism Spectrum Disorder Help Improve Clinical Practice?

PubMed

Haker, Helene; Schneebeli, Maya; Stephan, Klaas Enno

2016-01-01

Diagnosis and individualized treatment of autism spectrum disorder (ASD) represent major problems for contemporary psychiatry. Tackling these problems requires guidance by a pathophysiological theory. In this paper, we consider recent theories that re-conceptualize ASD from a "Bayesian brain" perspective, which posit that the core abnormality of ASD resides in perceptual aberrations due to a disbalance in the precision of prediction errors (sensory noise) relative to the precision of predictions (prior beliefs). This results in percepts that are dominated by sensory inputs and less guided by top-down regularization and shifts the perceptual focus to detailed aspects of the environment with difficulties in extracting meaning. While these Bayesian theories have inspired ongoing empirical studies, their clinical implications have not yet been carved out. Here, we consider how this Bayesian perspective on disease mechanisms in ASD might contribute to improving clinical care for affected individuals. Specifically, we describe a computational strategy, based on generative (e.g., hierarchical Bayesian) models of behavioral and functional neuroimaging data, for establishing diagnostic tests. These tests could provide estimates of specific cognitive processes underlying ASD and delineate pathophysiological mechanisms with concrete treatment targets. Written with a clinical audience in mind, this article outlines how the development of computational diagnostics applicable to behavioral and functional neuroimaging data in routine clinical practice could not only fundamentally alter our concept of ASD but eventually also transform the clinical management of this disorder.

Can Bayesian Theories of Autism Spectrum Disorder Help Improve Clinical Practice?

PubMed Central

Haker, Helene; Schneebeli, Maya; Stephan, Klaas Enno

2016-01-01

Diagnosis and individualized treatment of autism spectrum disorder (ASD) represent major problems for contemporary psychiatry. Tackling these problems requires guidance by a pathophysiological theory. In this paper, we consider recent theories that re-conceptualize ASD from a “Bayesian brain” perspective, which posit that the core abnormality of ASD resides in perceptual aberrations due to a disbalance in the precision of prediction errors (sensory noise) relative to the precision of predictions (prior beliefs). This results in percepts that are dominated by sensory inputs and less guided by top-down regularization and shifts the perceptual focus to detailed aspects of the environment with difficulties in extracting meaning. While these Bayesian theories have inspired ongoing empirical studies, their clinical implications have not yet been carved out. Here, we consider how this Bayesian perspective on disease mechanisms in ASD might contribute to improving clinical care for affected individuals. Specifically, we describe a computational strategy, based on generative (e.g., hierarchical Bayesian) models of behavioral and functional neuroimaging data, for establishing diagnostic tests. These tests could provide estimates of specific cognitive processes underlying ASD and delineate pathophysiological mechanisms with concrete treatment targets. Written with a clinical audience in mind, this article outlines how the development of computational diagnostics applicable to behavioral and functional neuroimaging data in routine clinical practice could not only fundamentally alter our concept of ASD but eventually also transform the clinical management of this disorder. PMID:27378955

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.

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

PubMed

Romanescu, Razvan; Deardon, Rob

2016-04-01

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

Secondary Contact and Admixture between Independently Invading Populations of the Western Corn Rootworm, Diabrotica virgifera virgifera in Europe

PubMed Central

Bermond, Gérald; Ciosi, Marc; Lombaert, Eric; Blin, Aurélie; Boriani, Marco; Furlan, Lorenzo; Toepfer, Stefan; Guillemaud, Thomas

2012-01-01

The western corn rootworm, Diabrotica virgifera virgifera (Coleoptera: Chrysomelidae), is one of the most destructive pests of corn in North America and is currently invading Europe. The two major invasive outbreaks of rootworm in Europe have occurred, in North-West Italy and in Central and South-Eastern Europe. These two outbreaks originated from independent introductions from North America. Secondary contact probably occurred in North Italy between these two outbreaks, in 2008. We used 13 microsatellite markers to conduct a population genetics study, to demonstrate that this geographic contact resulted in a zone of admixture in the Italian region of Veneto. We show that i) genetic variation is greater in the contact zone than in the parental outbreaks; ii) several signs of admixture were detected in some Venetian samples, in a Bayesian analysis of the population structure and in an approximate Bayesian computation analysis of historical scenarios and, finally, iii) allelic frequency clines were observed at microsatellite loci. The contact between the invasive outbreaks in North-West Italy and Central and South-Eastern Europe resulted in a zone of admixture, with particular characteristics. The evolutionary implications of the existence of a zone of admixture in Northern Italy and their possible impact on the invasion success of the western corn rootworm are discussed. PMID:23189184

Bayesian block-diagonal variable selection and model averaging

PubMed Central

Papaspiliopoulos, O.; Rossell, D.

2018-01-01

Summary We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general designs. In block-diagonal designs our approach returns the most probable model of any given size without resorting to numerical integration. The algorithm also provides a novel and efficient solution to the frequentist best subset selection problem for block-diagonal designs. Posterior probabilities for any number of models are obtained by evaluating a single one-dimensional integral, and other quantities of interest such as variable inclusion probabilities and model-averaged regression estimates are obtained by an adaptive, deterministic one-dimensional numerical integration. The overall computational cost scales linearly with the number of blocks, which can be processed in parallel, and exponentially with the block size, rendering it most adequate in situations where predictors are organized in many moderately-sized blocks. For general designs, we approximate the Gram matrix by a block-diagonal matrix using spectral clustering and propose an iterative algorithm that capitalizes on the block-diagonal algorithms to explore efficiently the model space. All methods proposed in this paper are implemented in the R library mombf. PMID:29861501

We introduce an algorithm for the simultaneous reconstruction of faults and slip fields. We prove that the minimum of a related regularized functional converges to the unique solution of the fault inverse problem. We consider a Bayesian approach. We use a parallel multi-core platform and we discuss techniques to save on computational time.

NASA Astrophysics Data System (ADS)

Volkov, D.

2017-12-01

We introduce an algorithm for the simultaneous reconstruction of faults and slip fields on those faults. We define a regularized functional to be minimized for the reconstruction. We prove that the minimum of that functional converges to the unique solution of the related fault inverse problem. Due to inherent uncertainties in measurements, rather than seeking a deterministic solution to the fault inverse problem, we consider a Bayesian approach. The advantage of such an approach is that we obtain a way of quantifying uncertainties as part of our final answer. On the downside, this Bayesian approach leads to a very large computation. To contend with the size of this computation we developed an algorithm for the numerical solution to the stochastic minimization problem which can be easily implemented on a parallel multi-core platform and we discuss techniques to save on computational time. After showing how this algorithm performs on simulated data and assessing the effect of noise, we apply it to measured data. The data was recorded during a slow slip event in Guerrero, Mexico.

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

PubMed

Shen, Y; Cooper, G F

2010-01-01

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

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

ERIC Educational Resources Information Center

Tsutakawa, Robert K.; Lin, Hsin Ying

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

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 methods for outliers detection in GNSS time series

NASA Astrophysics Data System (ADS)

Qianqian, Zhang; Qingming, Gui

2013-07-01

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

A simulation study on Bayesian Ridge regression models for several collinearity levels

NASA Astrophysics Data System (ADS)

Efendi, Achmad; Effrihan

2017-12-01

When analyzing data with multiple regression model if there are collinearities, then one or several predictor variables are usually omitted from the model. However, there sometimes some reasons, for instance medical or economic reasons, the predictors are all important and should be included in the model. Ridge regression model is not uncommon in some researches to use to cope with collinearity. Through this modeling, weights for predictor variables are used for estimating parameters. The next estimation process could follow the concept of likelihood. Furthermore, for the estimation nowadays the Bayesian version could be an alternative. This estimation method does not match likelihood one in terms of popularity due to some difficulties; computation and so forth. Nevertheless, with the growing improvement of computational methodology recently, this caveat should not at the moment become a problem. This paper discusses about simulation process for evaluating the characteristic of Bayesian Ridge regression parameter estimates. There are several simulation settings based on variety of collinearity levels and sample sizes. The results show that Bayesian method gives better performance for relatively small sample sizes, and for other settings the method does perform relatively similar to the likelihood method.

Embedding the results of focussed Bayesian fusion into a global context

NASA Astrophysics Data System (ADS)

Sander, Jennifer; Heizmann, Michael

2014-05-01

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

A New Computational Framework for Atmospheric and Surface Remote Sensing

NASA Technical Reports Server (NTRS)

Timucin, Dogan A.

2004-01-01

A Bayesian data-analysis framework is described for atmospheric and surface retrievals from remotely-sensed hyper-spectral data. Some computational techniques are high- lighted for improved accuracy in the forward physics model.

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

DOE PAGES

Williams, Brian P.; Lougovski, Pavel

2017-04-06

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

Uncertainty aggregation and reduction in structure-material performance prediction

NASA Astrophysics Data System (ADS)

Hu, Zhen; Mahadevan, Sankaran; Ao, Dan

2018-02-01

An uncertainty aggregation and reduction framework is presented for structure-material performance prediction. Different types of uncertainty sources, structural analysis model, and material performance prediction model are connected through a Bayesian network for systematic uncertainty aggregation analysis. To reduce the uncertainty in the computational structure-material performance prediction model, Bayesian updating using experimental observation data is investigated based on the Bayesian network. It is observed that the Bayesian updating results will have large error if the model cannot accurately represent the actual physics, and that this error will be propagated to the predicted performance distribution. To address this issue, this paper proposes a novel uncertainty reduction method by integrating Bayesian calibration with model validation adaptively. The observation domain of the quantity of interest is first discretized into multiple segments. An adaptive algorithm is then developed to perform model validation and Bayesian updating over these observation segments sequentially. Only information from observation segments where the model prediction is highly reliable is used for Bayesian updating; this is found to increase the effectiveness and efficiency of uncertainty reduction. A composite rotorcraft hub component fatigue life prediction model, which combines a finite element structural analysis model and a material damage model, is used to demonstrate the proposed method.

The image recognition based on neural network and Bayesian decision

NASA Astrophysics Data System (ADS)

Wang, Chugege

2018-04-01

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

Computational studies of novel chymase inhibitors against cardiovascular and allergic diseases: mechanism and inhibition.

PubMed

Arooj, Mahreen; Thangapandian, Sundarapandian; John, Shalini; Hwang, Swan; Park, Jong K; Lee, Keun W

2012-12-01

To provide a new idea for drug design, a computational investigation is performed on chymase and its novel 1,4-diazepane-2,5-diones inhibitors that explores the crucial molecular features contributing to binding specificity. Molecular docking studies of inhibitors within the active site of chymase were carried out to rationalize the inhibitory properties of these compounds and understand their inhibition mechanism. The density functional theory method was used to optimize molecular structures with the subsequent analysis of highest occupied molecular orbital, lowest unoccupied molecular orbital, and molecular electrostatic potential maps, which revealed that negative potentials near 1,4-diazepane-2,5-diones ring are essential for effective binding of inhibitors at active site of enzyme. The Bayesian model with receiver operating curve statistic of 0.82 also identified arylsulfonyl and aminocarbonyl as the molecular features favoring and not favoring inhibition of chymase, respectively. Moreover, genetic function approximation was applied to construct 3D quantitative structure-activity relationships models. Two models (genetic function approximation model 1 r(2) = 0.812 and genetic function approximation model 2 r(2) = 0.783) performed better in terms of correlation coefficients and cross-validation analysis. In general, this study is used as example to illustrate how combinational use of 2D/3D quantitative structure-activity relationships modeling techniques, molecular docking, frontier molecular orbital density fields (highest occupied molecular orbital and lowest unoccupied molecular orbital), and molecular electrostatic potential analysis may be useful to gain an insight into the binding mechanism between enzyme and its inhibitors. © 2012 John Wiley & Sons A/S.

Strategies for improving approximate Bayesian computation tests for synchronous diversification.

PubMed

Overcast, Isaac; Bagley, Justin C; Hickerson, Michael J

2017-08-24

Estimating the variability in isolation times across co-distributed taxon pairs that may have experienced the same allopatric isolating mechanism is a core goal of comparative phylogeography. The use of hierarchical Approximate Bayesian Computation (ABC) and coalescent models to infer temporal dynamics of lineage co-diversification has been a contentious topic in recent years. Key issues that remain unresolved include the choice of an appropriate prior on the number of co-divergence events (Ψ), as well as the optimal strategies for data summarization. Through simulation-based cross validation we explore the impact of the strategy for sorting summary statistics and the choice of prior on Ψ on the estimation of co-divergence variability. We also introduce a new setting (β) that can potentially improve estimation of Ψ by enforcing a minimal temporal difference between pulses of co-divergence. We apply this new method to three empirical datasets: one dataset each of co-distributed taxon pairs of Panamanian frogs and freshwater fishes, and a large set of Neotropical butterfly sister-taxon pairs. We demonstrate that the choice of prior on Ψ has little impact on inference, but that sorting summary statistics yields substantially more reliable estimates of co-divergence variability despite violations of assumptions about exchangeability. We find the implementation of β improves estimation of Ψ, with improvement being most dramatic given larger numbers of taxon pairs. We find equivocal support for synchronous co-divergence for both of the Panamanian groups, but we find considerable support for asynchronous divergence among the Neotropical butterflies. Our simulation experiments demonstrate that using sorted summary statistics results in improved estimates of the variability in divergence times, whereas the choice of hyperprior on Ψ has negligible effect. Additionally, we demonstrate that estimating the number of pulses of co-divergence across co-distributed taxon-pairs is improved by applying a flexible buffering regime over divergence times. This improves the correlation between Ψ and the true variability in isolation times and allows for more meaningful interpretation of this hyperparameter. This will allow for more accurate identification of the number of temporally distinct pulses of co-divergence that generated the diversification pattern of a given regional assemblage of sister-taxon-pairs.

Model selection for the North American Breeding Bird Survey: A comparison of methods

USGS Publications Warehouse

Link, William; Sauer, John; Niven, Daniel

2017-01-01

The North American Breeding Bird Survey (BBS) provides data for >420 bird species at multiple geographic scales over 5 decades. Modern computational methods have facilitated the fitting of complex hierarchical models to these data. It is easy to propose and fit new models, but little attention has been given to model selection. Here, we discuss and illustrate model selection using leave-one-out cross validation, and the Bayesian Predictive Information Criterion (BPIC). Cross-validation is enormously computationally intensive; we thus evaluate the performance of the Watanabe-Akaike Information Criterion (WAIC) as a computationally efficient approximation to the BPIC. Our evaluation is based on analyses of 4 models as applied to 20 species covered by the BBS. Model selection based on BPIC provided no strong evidence of one model being consistently superior to the others; for 14/20 species, none of the models emerged as superior. For the remaining 6 species, a first-difference model of population trajectory was always among the best fitting. Our results show that WAIC is not reliable as a surrogate for BPIC. Development of appropriate model sets and their evaluation using BPIC is an important innovation for the analysis of BBS data.

Target-type probability combining algorithms for multisensor tracking

NASA Astrophysics Data System (ADS)

Wigren, Torbjorn

2001-08-01

Algorithms for the handing of target type information in an operational multi-sensor tracking system are presented. The paper discusses recursive target type estimation, computation of crosses from passive data (strobe track triangulation), as well as the computation of the quality of the crosses for deghosting purposes. The focus is on Bayesian algorithms that operate in the discrete target type probability space, and on the approximations introduced for computational complexity reduction. The centralized algorithms are able to fuse discrete data from a variety of sensors and information sources, including IFF equipment, ESM's, IRST's as well as flight envelopes estimated from track data. All algorithms are asynchronous and can be tuned to handle clutter, erroneous associations as well as missed and erroneous detections. A key to obtain this ability is the inclusion of data forgetting by a procedure for propagation of target type probability states between measurement time instances. Other important properties of the algorithms are their abilities to handle ambiguous data and scenarios. The above aspects are illustrated in a simulations study. The simulation setup includes 46 air targets of 6 different types that are tracked by 5 airborne sensor platforms using ESM's and IRST's as data sources.

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

PubMed

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

2015-07-01

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

Bayes and the Law

PubMed Central

Fenton, Norman; Neil, Martin; Berger, Daniel

2016-01-01

Although the last forty years has seen considerable growth in the use of statistics in legal proceedings, it is primarily classical statistical methods rather than Bayesian methods that have been used. Yet the Bayesian approach avoids many of the problems of classical statistics and is also well suited to a broader range of problems. This paper reviews the potential and actual use of Bayes in the law and explains the main reasons for its lack of impact on legal practice. These include misconceptions by the legal community about Bayes’ theorem, over-reliance on the use of the likelihood ratio and the lack of adoption of modern computational methods. We argue that Bayesian Networks (BNs), which automatically produce the necessary Bayesian calculations, provide an opportunity to address most concerns about using Bayes in the law. PMID:27398389

Bayes and the Law.

PubMed

Fenton, Norman; Neil, Martin; Berger, Daniel

2016-06-01

Although the last forty years has seen considerable growth in the use of statistics in legal proceedings, it is primarily classical statistical methods rather than Bayesian methods that have been used. Yet the Bayesian approach avoids many of the problems of classical statistics and is also well suited to a broader range of problems. This paper reviews the potential and actual use of Bayes in the law and explains the main reasons for its lack of impact on legal practice. These include misconceptions by the legal community about Bayes' theorem, over-reliance on the use of the likelihood ratio and the lack of adoption of modern computational methods. We argue that Bayesian Networks (BNs), which automatically produce the necessary Bayesian calculations, provide an opportunity to address most concerns about using Bayes in the law.

An Approximate Markov Model for the Wright-Fisher Diffusion and Its Application to Time Series Data.

PubMed

Ferrer-Admetlla, Anna; Leuenberger, Christoph; Jensen, Jeffrey D; Wegmann, Daniel

2016-06-01

The joint and accurate inference of selection and demography from genetic data is considered a particularly challenging question in population genetics, since both process may lead to very similar patterns of genetic diversity. However, additional information for disentangling these effects may be obtained by observing changes in allele frequencies over multiple time points. Such data are common in experimental evolution studies, as well as in the comparison of ancient and contemporary samples. Leveraging this information, however, has been computationally challenging, particularly when considering multilocus data sets. To overcome these issues, we introduce a novel, discrete approximation for diffusion processes, termed mean transition time approximation, which preserves the long-term behavior of the underlying continuous diffusion process. We then derive this approximation for the particular case of inferring selection and demography from time series data under the classic Wright-Fisher model and demonstrate that our approximation is well suited to describe allele trajectories through time, even when only a few states are used. We then develop a Bayesian inference approach to jointly infer the population size and locus-specific selection coefficients with high accuracy and further extend this model to also infer the rates of sequencing errors and mutations. We finally apply our approach to recent experimental data on the evolution of drug resistance in influenza virus, identifying likely targets of selection and finding evidence for much larger viral population sizes than previously reported. Copyright © 2016 by the Genetics Society of America.

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

Efficient Bayesian experimental design for contaminant source identification

NASA Astrophysics Data System (ADS)

Zhang, J.; Zeng, L.

2013-12-01

In this study, an efficient full Bayesian approach is developed for the optimal sampling well location design and source parameter identification of groundwater contaminants. An information measure, i.e., the relative entropy, is employed to quantify the information gain from indirect concentration measurements in identifying unknown source parameters such as the release time, strength and location. In this approach, the sampling location that gives the maximum relative entropy is selected as the optimal one. Once the sampling location is determined, a Bayesian approach based on Markov Chain Monte Carlo (MCMC) is used to estimate unknown source parameters. In both the design and estimation, the contaminant transport equation is required to be solved many times to evaluate the likelihood. To reduce the computational burden, an interpolation method based on the adaptive sparse grid is utilized to construct a surrogate for the contaminant transport. The approximated likelihood can be evaluated directly from the surrogate, which greatly accelerates the design and estimation process. The accuracy and efficiency of our approach are demonstrated through numerical case studies. Compared with the traditional optimal design, which is based on the Gaussian linear assumption, the method developed in this study can cope with arbitrary nonlinearity. It can be used to assist in groundwater monitor network design and identification of unknown contaminant sources. Contours of the expected information gain. The optimal observing location corresponds to the maximum value. Posterior marginal probability densities of unknown parameters, the thick solid black lines are for the designed location. For comparison, other 7 lines are for randomly chosen locations. The true values are denoted by vertical lines. It is obvious that the unknown parameters are estimated better with the desinged location.

Speech Enhancement Using Gaussian Scale Mixture Models

PubMed Central

Hao, Jiucang; Lee, Te-Won; Sejnowski, Terrence J.

2011-01-01

This paper presents a novel probabilistic approach to speech enhancement. Instead of a deterministic logarithmic relationship, we assume a probabilistic relationship between the frequency coefficients and the log-spectra. The speech model in the log-spectral domain is a Gaussian mixture model (GMM). The frequency coefficients obey a zero-mean Gaussian whose covariance equals to the exponential of the log-spectra. This results in a Gaussian scale mixture model (GSMM) for the speech signal in the frequency domain, since the log-spectra can be regarded as scaling factors. The probabilistic relation between frequency coefficients and log-spectra allows these to be treated as two random variables, both to be estimated from the noisy signals. Expectation-maximization (EM) was used to train the GSMM and Bayesian inference was used to compute the posterior signal distribution. Because exact inference of this full probabilistic model is computationally intractable, we developed two approaches to enhance the efficiency: the Laplace method and a variational approximation. The proposed methods were applied to enhance speech corrupted by Gaussian noise and speech-shaped noise (SSN). For both approximations, signals reconstructed from the estimated frequency coefficients provided higher signal-to-noise ratio (SNR) and those reconstructed from the estimated log-spectra produced lower word recognition error rate because the log-spectra fit the inputs to the recognizer better. Our algorithms effectively reduced the SSN, which algorithms based on spectral analysis were not able to suppress. PMID:21359139

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

PubMed

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

2016-05-01

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

Bayesian analysis of rare events

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

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

2016-06-01

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

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

Bayesian Research at the NASA Ames Research Center,Computational Sciences Division

NASA Technical Reports Server (NTRS)

Morris, Robin D.

2003-01-01

NASA Ames Research Center is one of NASA s oldest centers, having started out as part of the National Advisory Committee on Aeronautics, (NACA). The site, about 40 miles south of San Francisco, still houses many wind tunnels and other aviation related departments. In recent years, with the growing realization that space exploration is heavily dependent on computing and data analysis, its focus has turned more towards Information Technology. The Computational Sciences Division has expanded rapidly as a result. In this article, I will give a brief overview of some of the past and present projects with a Bayesian content. Much more than is described here goes on with the Division. The web pages at http://ic.arc. nasa.gov give more information on these, and the other Division projects.

Efficient implementation of the Metropolis-Hastings algorithm, with application to the Cormack?Jolly?Seber model

USGS Publications Warehouse

Link, W.A.; Barker, R.J.

2008-01-01

Judicious choice of candidate generating distributions improves efficiency of the Metropolis-Hastings algorithm. In Bayesian applications, it is sometimes possible to identify an approximation to the target posterior distribution; this approximate posterior distribution is a good choice for candidate generation. These observations are applied to analysis of the Cormack?Jolly?Seber model and its extensions.

As-built design specification for proportion estimate software subsystem

NASA Technical Reports Server (NTRS)

Obrien, S. (Principal Investigator)

1980-01-01

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

A Massively Parallel Bayesian Approach to Planetary Protection Trajectory Analysis and Design

NASA Technical Reports Server (NTRS)

Wallace, Mark S.

2015-01-01

The NASA Planetary Protection Office has levied a requirement that the upper stage of future planetary launches have a less than 10(exp -4) chance of impacting Mars within 50 years after launch. A brute-force approach requires a decade of computer time to demonstrate compliance. By using a Bayesian approach and taking advantage of the demonstrated reliability of the upper stage, the required number of fifty-year propagations can be massively reduced. By spreading the remaining embarrassingly parallel Monte Carlo simulations across multiple computers, compliance can be demonstrated in a reasonable time frame. The method used is described here.

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

PubMed

Gajewski, Byron J; Mayo, Matthew S

2006-08-15

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

Valence-Dependent Belief Updating: Computational Validation

PubMed Central

Kuzmanovic, Bojana; Rigoux, Lionel

2017-01-01

People tend to update beliefs about their future outcomes in a valence-dependent way: they are likely to incorporate good news and to neglect bad news. However, belief formation is a complex process which depends not only on motivational factors such as the desire for favorable conclusions, but also on multiple cognitive variables such as prior beliefs, knowledge about personal vulnerabilities and resources, and the size of the probabilities and estimation errors. Thus, we applied computational modeling in order to test for valence-induced biases in updating while formally controlling for relevant cognitive factors. We compared biased and unbiased Bayesian models of belief updating, and specified alternative models based on reinforcement learning. The experiment consisted of 80 trials with 80 different adverse future life events. In each trial, participants estimated the base rate of one of these events and estimated their own risk of experiencing the event before and after being confronted with the actual base rate. Belief updates corresponded to the difference between the two self-risk estimates. Valence-dependent updating was assessed by comparing trials with good news (better-than-expected base rates) with trials with bad news (worse-than-expected base rates). After receiving bad relative to good news, participants' updates were smaller and deviated more strongly from rational Bayesian predictions, indicating a valence-induced bias. Model comparison revealed that the biased (i.e., optimistic) Bayesian model of belief updating better accounted for data than the unbiased (i.e., rational) Bayesian model, confirming that the valence of the new information influenced the amount of updating. Moreover, alternative computational modeling based on reinforcement learning demonstrated higher learning rates for good than for bad news, as well as a moderating role of personal knowledge. Finally, in this specific experimental context, the approach based on reinforcement learning was superior to the Bayesian approach. The computational validation of valence-dependent belief updating represents a novel support for a genuine optimism bias in human belief formation. Moreover, the precise control of relevant cognitive variables justifies the conclusion that the motivation to adopt the most favorable self-referential conclusions biases human judgments. PMID:28706499

Valence-Dependent Belief Updating: Computational Validation.

PubMed

Kuzmanovic, Bojana; Rigoux, Lionel

2017-01-01

People tend to update beliefs about their future outcomes in a valence-dependent way: they are likely to incorporate good news and to neglect bad news. However, belief formation is a complex process which depends not only on motivational factors such as the desire for favorable conclusions, but also on multiple cognitive variables such as prior beliefs, knowledge about personal vulnerabilities and resources, and the size of the probabilities and estimation errors. Thus, we applied computational modeling in order to test for valence-induced biases in updating while formally controlling for relevant cognitive factors. We compared biased and unbiased Bayesian models of belief updating, and specified alternative models based on reinforcement learning. The experiment consisted of 80 trials with 80 different adverse future life events. In each trial, participants estimated the base rate of one of these events and estimated their own risk of experiencing the event before and after being confronted with the actual base rate. Belief updates corresponded to the difference between the two self-risk estimates. Valence-dependent updating was assessed by comparing trials with good news (better-than-expected base rates) with trials with bad news (worse-than-expected base rates). After receiving bad relative to good news, participants' updates were smaller and deviated more strongly from rational Bayesian predictions, indicating a valence-induced bias. Model comparison revealed that the biased (i.e., optimistic) Bayesian model of belief updating better accounted for data than the unbiased (i.e., rational) Bayesian model, confirming that the valence of the new information influenced the amount of updating. Moreover, alternative computational modeling based on reinforcement learning demonstrated higher learning rates for good than for bad news, as well as a moderating role of personal knowledge. Finally, in this specific experimental context, the approach based on reinforcement learning was superior to the Bayesian approach. The computational validation of valence-dependent belief updating represents a novel support for a genuine optimism bias in human belief formation. Moreover, the precise control of relevant cognitive variables justifies the conclusion that the motivation to adopt the most favorable self-referential conclusions biases human judgments.

Bayesian just-so stories in psychology and neuroscience.

PubMed

Bowers, Jeffrey S; Davis, Colin J

2012-05-01

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

Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo

NASA Astrophysics Data System (ADS)

Bui-Thanh, T.; Girolami, M.

2014-11-01

We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The Bayesian framework is employed to cast the inverse problem into the task of statistical inference whose solution is the posterior distribution in infinite dimensional parameter space conditional upon observation data and Gaussian prior measure. We discretize both the likelihood and the prior using the H1-conforming finite element method together with a matrix transfer technique. The power of the RMHMC method is that it exploits the geometric structure induced by the PDE constraints of the underlying inverse problem. Consequently, each RMHMC posterior sample is almost uncorrelated/independent from the others providing statistically efficient Markov chain simulation. However this statistical efficiency comes at a computational cost. This motivates us to consider computationally more efficient strategies for RMHMC. At the heart of our construction is the fact that for Gaussian error structures the Fisher information matrix coincides with the Gauss-Newton Hessian. We exploit this fact in considering a computationally simplified RMHMC method combining state-of-the-art adjoint techniques and the superiority of the RMHMC method. Specifically, we first form the Gauss-Newton Hessian at the maximum a posteriori point and then use it as a fixed constant metric tensor throughout RMHMC simulation. This eliminates the need for the computationally costly differential geometric Christoffel symbols, which in turn greatly reduces computational effort at a corresponding loss of sampling efficiency. We further reduce the cost of forming the Fisher information matrix by using a low rank approximation via a randomized singular value decomposition technique. This is efficient since a small number of Hessian-vector products are required. The Hessian-vector product in turn requires only two extra PDE solves using the adjoint technique. Various numerical results up to 1025 parameters are presented to demonstrate the ability of the RMHMC method in exploring the geometric structure of the problem to propose (almost) uncorrelated/independent samples that are far away from each other, and yet the acceptance rate is almost unity. The results also suggest that for the PDE models considered the proposed fixed metric RMHMC can attain almost as high a quality performance as the original RMHMC, i.e. generating (almost) uncorrelated/independent samples, while being two orders of magnitude less computationally expensive.

Quantifying the uncertainty in heritability.

PubMed

Furlotte, Nicholas A; Heckerman, David; Lippert, Christoph

2014-05-01

The use of mixed models to determine narrow-sense heritability and related quantities such as SNP heritability has received much recent attention. Less attention has been paid to the inherent variability in these estimates. One approach for quantifying variability in estimates of heritability is a frequentist approach, in which heritability is estimated using maximum likelihood and its variance is quantified through an asymptotic normal approximation. An alternative approach is to quantify the uncertainty in heritability through its Bayesian posterior distribution. In this paper, we develop the latter approach, make it computationally efficient and compare it to the frequentist approach. We show theoretically that, for a sufficiently large sample size and intermediate values of heritability, the two approaches provide similar results. Using the Atherosclerosis Risk in Communities cohort, we show empirically that the two approaches can give different results and that the variance/uncertainty can remain large.

Multiple independent introductions of Plasmodium falciparum in South America

PubMed Central

Yalcindag, Erhan; Elguero, Eric; Arnathau, Céline; Durand, Patrick; Akiana, Jean; Anderson, Timothy J.; Aubouy, Agnes; Balloux, François; Besnard, Patrick; Bogreau, Hervé; Carnevale, Pierre; D'Alessandro, Umberto; Fontenille, Didier; Gamboa, Dionicia; Jombart, Thibaut; Le Mire, Jacques; Leroy, Eric; Maestre, Amanda; Mayxay, Mayfong; Ménard, Didier; Musset, Lise; Newton, Paul N.; Nkoghé, Dieudonné; Noya, Oscar; Ollomo, Benjamin; Rogier, Christophe; Veron, Vincent; Wide, Albina; Zakeri, Sedigheh; Carme, Bernard; Legrand, Eric; Chevillon, Christine; Ayala, Francisco J.; Renaud, François; Prugnolle, Franck

2012-01-01

The origin of Plasmodium falciparum in South America is controversial. Some studies suggest a recent introduction during the European colonizations and the transatlantic slave trade. Other evidence—archeological and genetic—suggests a much older origin. We collected and analyzed P. falciparum isolates from different regions of the world, encompassing the distribution range of the parasite, including populations from sub-Saharan Africa, the Middle East, Southeast Asia, and South America. Analyses of microsatellite and SNP polymorphisms show that the populations of P. falciparum in South America are subdivided in two main genetic clusters (northern and southern). Phylogenetic analyses, as well as Approximate Bayesian Computation methods suggest independent introductions of the two clusters from African sources. Our estimates of divergence time between the South American populations and their likely sources favor a likely introduction from Africa during the transatlantic slave trade. PMID:22203975

Methods used to calculate doses resulting from inhalation of Capstone depleted uranium aerosols.

PubMed

Miller, Guthrie; Cheng, Yung Sung; Traub, Richard J; Little, Tom T; Guilmette, Raymond A

2009-03-01

The methods used to calculate radiological and toxicological doses to hypothetical persons inside either a U.S. Army Abrams tank or Bradley Fighting Vehicle that has been perforated by depleted uranium munitions are described. Data from time- and particle-size-resolved measurements of depleted uranium aerosol as well as particle-size-resolved measurements of aerosol solubility in lung fluids for aerosol produced in the breathing zones of the hypothetical occupants were used. The aerosol was approximated as a mixture of nine monodisperse (single particle size) components corresponding to particle size increments measured by the eight stages plus the backup filter of the cascade impactors used. A Markov Chain Monte Carlo Bayesian analysis technique was employed, which straightforwardly calculates the uncertainties in doses. Extensive quality control checking of the various computer codes used is described.

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

PubMed Central

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

2014-01-01

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

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 networks in neuroscience: a survey.

PubMed

Bielza, Concha; Larrañaga, Pedro

2014-01-01

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

Bayesian networks in neuroscience: a survey

PubMed Central

Bielza, Concha; Larrañaga, Pedro

2014-01-01

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

BELM: Bayesian extreme learning machine.

PubMed

Soria-Olivas, Emilio; Gómez-Sanchis, Juan; Martín, José D; Vila-Francés, Joan; Martínez, Marcelino; Magdalena, José R; Serrano, Antonio J

2011-03-01

The theory of extreme learning machine (ELM) has become very popular on the last few years. ELM is a new approach for learning the parameters of the hidden layers of a multilayer neural network (as the multilayer perceptron or the radial basis function neural network). Its main advantage is the lower computational cost, which is especially relevant when dealing with many patterns defined in a high-dimensional space. This brief proposes a bayesian approach to ELM, which presents some advantages over other approaches: it allows the introduction of a priori knowledge; obtains the confidence intervals (CIs) without the need of applying methods that are computationally intensive, e.g., bootstrap; and presents high generalization capabilities. Bayesian ELM is benchmarked against classical ELM in several artificial and real datasets that are widely used for the evaluation of machine learning algorithms. Achieved results show that the proposed approach produces a competitive accuracy with some additional advantages, namely, automatic production of CIs, reduction of probability of model overfitting, and use of a priori knowledge.

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

PubMed

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

2016-01-01

Classical statistical methods for analyzing exposure data with values below the detection limits are well described in the occupational hygiene literature, but an evaluation of a Bayesian approach for handling such data is currently lacking. Here, we first describe a Bayesian framework for analyzing censored data. We then present the results of a simulation study conducted to compare the β-substitution method with a Bayesian method for exposure datasets drawn from lognormal distributions and mixed lognormal distributions with varying sample sizes, geometric standard deviations (GSDs), and censoring for single and multiple limits of detection. For each set of factors, estimates for the arithmetic mean (AM), geometric mean, GSD, and the 95th percentile (X0.95) of the exposure distribution were obtained. We evaluated the performance of each method using relative bias, the root mean squared error (rMSE), and coverage (the proportion of the computed 95% uncertainty intervals containing the true value). The Bayesian method using non-informative priors and the β-substitution method were generally comparable in bias and rMSE when estimating the AM and GM. For the GSD and the 95th percentile, the Bayesian method with non-informative priors was more biased and had a higher rMSE than the β-substitution method, but use of more informative priors generally improved the Bayesian method's performance, making both the bias and the rMSE more comparable to the β-substitution method. An advantage of the Bayesian method is that it provided estimates of uncertainty for these parameters of interest and good coverage, whereas the β-substitution method only provided estimates of uncertainty for the AM, and coverage was not as consistent. Selection of one or the other method depends on the needs of the practitioner, the availability of prior information, and the distribution characteristics of the measurement data. We suggest the use of Bayesian methods if the practitioner has the computational resources and prior information, as the method would generally provide accurate estimates and also provides the distributions of all of the parameters, which could be useful for making decisions in some applications. © The Author 2015. Published by Oxford University Press on behalf of the British Occupational Hygiene Society.

Exact Bayesian Inference for Phylogenetic Birth-Death Models.

PubMed

Parag, K V; Pybus, O G

2018-04-26

Inferring the rates of change of a population from a reconstructed phylogeny of genetic sequences is a central problem in macro-evolutionary biology, epidemiology, and many other disciplines. A popular solution involves estimating the parameters of a birth-death process (BDP), which links the shape of the phylogeny to its birth and death rates. Modern BDP estimators rely on random Markov chain Monte Carlo (MCMC) sampling to infer these rates. Such methods, while powerful and scalable, cannot be guaranteed to converge, leading to results that may be hard to replicate or difficult to validate. We present a conceptually and computationally different parametric BDP inference approach using flexible and easy to implement Snyder filter (SF) algorithms. This method is deterministic so its results are provable, guaranteed, and reproducible. We validate the SF on constant rate BDPs and find that it solves BDP likelihoods known to produce robust estimates. We then examine more complex BDPs with time-varying rates. Our estimates compare well with a recently developed parametric MCMC inference method. Lastly, we performmodel selection on an empirical Agamid species phylogeny, obtaining results consistent with the literature. The SF makes no approximations, beyond those required for parameter quantisation and numerical integration, and directly computes the posterior distribution of model parameters. It is a promising alternative inference algorithm that may serve either as a standalone Bayesian estimator or as a useful diagnostic reference for validating more involved MCMC strategies. The Snyder filter is implemented in Matlab and the time-varying BDP models are simulated in R. The source code and data are freely available at https://github.com/kpzoo/snyder-birth-death-code. kris.parag@zoo.ox.ac.uk. Supplementary material is available at Bioinformatics online.

Sparse Polynomial Chaos Surrogate for ACME Land Model via Iterative Bayesian Compressive Sensing

NASA Astrophysics Data System (ADS)

Sargsyan, K.; Ricciuto, D. M.; Safta, C.; Debusschere, B.; Najm, H. N.; Thornton, P. E.

2015-12-01

For computationally expensive climate models, Monte-Carlo approaches of exploring the input parameter space are often prohibitive due to slow convergence with respect to ensemble size. To alleviate this, we build inexpensive surrogates using uncertainty quantification (UQ) methods employing Polynomial Chaos (PC) expansions that approximate the input-output relationships using as few model evaluations as possible. However, when many uncertain input parameters are present, such UQ studies suffer from the curse of dimensionality. In particular, for 50-100 input parameters non-adaptive PC representations have infeasible numbers of basis terms. To this end, we develop and employ Weighted Iterative Bayesian Compressive Sensing to learn the most important input parameter relationships for efficient, sparse PC surrogate construction with posterior uncertainty quantified due to insufficient data. Besides drastic dimensionality reduction, the uncertain surrogate can efficiently replace the model in computationally intensive studies such as forward uncertainty propagation and variance-based sensitivity analysis, as well as design optimization and parameter estimation using observational data. We applied the surrogate construction and variance-based uncertainty decomposition to Accelerated Climate Model for Energy (ACME) Land Model for several output QoIs at nearly 100 FLUXNET sites covering multiple plant functional types and climates, varying 65 input parameters over broad ranges of possible values. This work is supported by the U.S. Department of Energy, Office of Science, Biological and Environmental Research, Accelerated Climate Modeling for Energy (ACME) project. Sandia National Laboratories is a multi-program 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.

A novel latent gaussian copula framework for modeling spatial correlation in quantized SAR imagery with applications to ATR

NASA Astrophysics Data System (ADS)

Thelen, Brian T.; Xique, Ismael J.; Burns, Joseph W.; Goley, G. Steven; Nolan, Adam R.; Benson, Jonathan W.

2017-04-01

With all of the new remote sensing modalities available, and with ever increasing capabilities and frequency of collection, there is a desire to fundamentally understand/quantify the information content in the collected image data relative to various exploitation goals, such as detection/classification. A fundamental approach for this is the framework of Bayesian decision theory, but a daunting challenge is to have significantly flexible and accurate multivariate models for the features and/or pixels that capture a wide assortment of distributions and dependen- cies. In addition, data can come in the form of both continuous and discrete representations, where the latter is often generated based on considerations of robustness to imaging conditions and occlusions/degradations. In this paper we propose a novel suite of "latent" models fundamentally based on multivariate Gaussian copula models that can be used for quantized data from SAR imagery. For this Latent Gaussian Copula (LGC) model, we derive an approximate, maximum-likelihood estimation algorithm and demonstrate very reasonable estimation performance even for the larger images with many pixels. However applying these LGC models to large dimen- sions/images within a Bayesian decision/classification theory is infeasible due to the computational/numerical issues in evaluating the true full likelihood, and we propose an alternative class of novel pseudo-likelihoood detection statistics that are computationally feasible. We show in a few simple examples that these statistics have the potential to provide very good and robust detection/classification performance. All of this framework is demonstrated on a simulated SLICY data set, and the results show the importance of modeling the dependencies, and of utilizing the pseudo-likelihood methods.

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

PubMed

Molitor, John

2012-03-01

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

Progress in computational toxicology.

PubMed

Ekins, Sean

2014-01-01

Computational methods have been widely applied to toxicology across pharmaceutical, consumer product and environmental fields over the past decade. Progress in computational toxicology is now reviewed. A literature review was performed on computational models for hepatotoxicity (e.g. for drug-induced liver injury (DILI)), cardiotoxicity, renal toxicity and genotoxicity. In addition various publications have been highlighted that use machine learning methods. Several computational toxicology model datasets from past publications were used to compare Bayesian and Support Vector Machine (SVM) learning methods. The increasing amounts of data for defined toxicology endpoints have enabled machine learning models that have been increasingly used for predictions. It is shown that across many different models Bayesian and SVM perform similarly based on cross validation data. Considerable progress has been made in computational toxicology in a decade in both model development and availability of larger scale or 'big data' models. The future efforts in toxicology data generation will likely provide us with hundreds of thousands of compounds that are readily accessible for machine learning models. These models will cover relevant chemistry space for pharmaceutical, consumer product and environmental applications. Copyright © 2013 Elsevier Inc. All rights reserved.

Data Assimilation and Propagation of Uncertainty in Multiscale Cardiovascular Simulation

NASA Astrophysics Data System (ADS)

Schiavazzi, Daniele; Marsden, Alison

2015-11-01

Cardiovascular modeling is the application of computational tools to predict hemodynamics. State-of-the-art techniques couple a 3D incompressible Navier-Stokes solver with a boundary circulation model and can predict local and peripheral hemodynamics, analyze the post-operative performance of surgical designs and complement clinical data collection minimizing invasive and risky measurement practices. The ability of these tools to make useful predictions is directly related to their accuracy in representing measured physiologies. Tuning of model parameters is therefore a topic of paramount importance and should include clinical data uncertainty, revealing how this uncertainty will affect the predictions. We propose a fully Bayesian, multi-level approach to data assimilation of uncertain clinical data in multiscale circulation models. To reduce the computational cost, we use a stable, condensed approximation of the 3D model build by linear sparse regression of the pressure/flow rate relationship at the outlets. Finally, we consider the problem of non-invasively propagating the uncertainty in model parameters to the resulting hemodynamics and compare Monte Carlo simulation with Stochastic Collocation approaches based on Polynomial or Multi-resolution Chaos expansions.

In defence of model-based inference in phylogeography

PubMed Central

Beaumont, Mark A.; Nielsen, Rasmus; Robert, Christian; Hey, Jody; Gaggiotti, Oscar; Knowles, Lacey; Estoup, Arnaud; Panchal, Mahesh; Corander, Jukka; Hickerson, Mike; Sisson, Scott A.; Fagundes, Nelson; Chikhi, Lounès; Beerli, Peter; Vitalis, Renaud; Cornuet, Jean-Marie; Huelsenbeck, John; Foll, Matthieu; Yang, Ziheng; Rousset, Francois; Balding, David; Excoffier, Laurent

2017-01-01

Recent papers have promoted the view that model-based methods in general, and those based on Approximate Bayesian Computation (ABC) in particular, are flawed in a number of ways, and are therefore inappropriate for the analysis of phylogeographic data. These papers further argue that Nested Clade Phylogeographic Analysis (NCPA) offers the best approach in statistical phylogeography. In order to remove the confusion and misconceptions introduced by these papers, we justify and explain the reasoning behind model-based inference. We argue that ABC is a statistically valid approach, alongside other computational statistical techniques that have been successfully used to infer parameters and compare models in population genetics. We also examine the NCPA method and highlight numerous deficiencies, either when used with single or multiple loci. We further show that the ages of clades are carelessly used to infer ages of demographic events, that these ages are estimated under a simple model of panmixia and population stationarity but are then used under different and unspecified models to test hypotheses, a usage the invalidates these testing procedures. We conclude by encouraging researchers to study and use model-based inference in population genetics. PMID:29284924

Error regions in quantum state tomography: computational complexity caused by geometry of quantum states

NASA Astrophysics Data System (ADS)

Suess, Daniel; Rudnicki, Łukasz; maciel, Thiago O.; Gross, David

2017-09-01

The outcomes of quantum mechanical measurements are inherently random. It is therefore necessary to develop stringent methods for quantifying the degree of statistical uncertainty about the results of quantum experiments. For the particularly relevant task of quantum state tomography, it has been shown that a significant reduction in uncertainty can be achieved by taking the positivity of quantum states into account. However—the large number of partial results and heuristics notwithstanding—no efficient general algorithm is known that produces an optimal uncertainty region from experimental data, while making use of the prior constraint of positivity. Here, we provide a precise formulation of this problem and show that the general case is NP-hard. Our result leaves room for the existence of efficient approximate solutions, and therefore does not in itself imply that the practical task of quantum uncertainty quantification is intractable. However, it does show that there exists a non-trivial trade-off between optimality and computational efficiency for error regions. We prove two versions of the result: one for frequentist and one for Bayesian statistics.

About approximation of integer factorization problem by the combination fixed-point iteration method and Bayesian rounding for quantum cryptography

NASA Astrophysics Data System (ADS)

Ogorodnikov, Yuri; Khachay, Michael; Pljonkin, Anton

2018-04-01

We describe the possibility of employing the special case of the 3-SAT problem stemming from the well known integer factorization problem for the quantum cryptography. It is known, that for every instance of our 3-SAT setting the given 3-CNF is satisfiable by a unique truth assignment, and the goal is to find this assignment. Since the complexity status of the factorization problem is still undefined, development of approximation algorithms and heuristics adopts interest of numerous researchers. One of promising approaches to construction of approximation techniques is based on real-valued relaxation of the given 3-CNF followed by minimizing of the appropriate differentiable loss function, and subsequent rounding of the fractional minimizer obtained. Actually, algorithms developed this way differ by the rounding scheme applied on their final stage. We propose a new rounding scheme based on Bayesian learning. The article shows that the proposed method can be used to determine the security in quantum key distribution systems. In the quantum distribution the Shannon rules is applied and the factorization problem is paramount when decrypting secret keys.

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

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.

Classifying emotion in Twitter using Bayesian network

NASA Astrophysics Data System (ADS)

Surya Asriadie, Muhammad; Syahrul Mubarok, Mohamad; Adiwijaya

2018-03-01

Language is used to express not only facts, but also emotions. Emotions are noticeable from behavior up to the social media statuses written by a person. Analysis of emotions in a text is done in a variety of media such as Twitter. This paper studies classification of emotions on twitter using Bayesian network because of its ability to model uncertainty and relationships between features. The result is two models based on Bayesian network which are Full Bayesian Network (FBN) and Bayesian Network with Mood Indicator (BNM). FBN is a massive Bayesian network where each word is treated as a node. The study shows the method used to train FBN is not very effective to create the best model and performs worse compared to Naive Bayes. F1-score for FBN is 53.71%, while for Naive Bayes is 54.07%. BNM is proposed as an alternative method which is based on the improvement of Multinomial Naive Bayes and has much lower computational complexity compared to FBN. Even though it’s not better compared to FBN, the resulting model successfully improves the performance of Multinomial Naive Bayes. F1-Score for Multinomial Naive Bayes model is 51.49%, while for BNM is 52.14%.

A bayesian approach to classification criteria for spectacled eiders

USGS Publications Warehouse

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

1996-01-01

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

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

PubMed

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

2014-08-01

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

Bayesian flood forecasting methods: A review

NASA Astrophysics Data System (ADS)

Han, Shasha; Coulibaly, Paulin

2017-08-01

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

MDTS: automatic complex materials design using Monte Carlo tree search.

PubMed

M Dieb, Thaer; Ju, Shenghong; Yoshizoe, Kazuki; Hou, Zhufeng; Shiomi, Junichiro; Tsuda, Koji

2017-01-01

Complex materials design is often represented as a black-box combinatorial optimization problem. In this paper, we present a novel python library called MDTS (Materials Design using Tree Search). Our algorithm employs a Monte Carlo tree search approach, which has shown exceptional performance in computer Go game. Unlike evolutionary algorithms that require user intervention to set parameters appropriately, MDTS has no tuning parameters and works autonomously in various problems. In comparison to a Bayesian optimization package, our algorithm showed competitive search efficiency and superior scalability. We succeeded in designing large Silicon-Germanium (Si-Ge) alloy structures that Bayesian optimization could not deal with due to excessive computational cost. MDTS is available at https://github.com/tsudalab/MDTS.

MDTS: automatic complex materials design using Monte Carlo tree search

NASA Astrophysics Data System (ADS)

Dieb, Thaer M.; Ju, Shenghong; Yoshizoe, Kazuki; Hou, Zhufeng; Shiomi, Junichiro; Tsuda, Koji

2017-12-01

Complex materials design is often represented as a black-box combinatorial optimization problem. In this paper, we present a novel python library called MDTS (Materials Design using Tree Search). Our algorithm employs a Monte Carlo tree search approach, which has shown exceptional performance in computer Go game. Unlike evolutionary algorithms that require user intervention to set parameters appropriately, MDTS has no tuning parameters and works autonomously in various problems. In comparison to a Bayesian optimization package, our algorithm showed competitive search efficiency and superior scalability. We succeeded in designing large Silicon-Germanium (Si-Ge) alloy structures that Bayesian optimization could not deal with due to excessive computational cost. MDTS is available at https://github.com/tsudalab/MDTS.

Bayesian Modeling for Identification and Estimation of the Learning Effects of Pointing Tasks

NASA Astrophysics Data System (ADS)

Kyo, Koki

Recently, in the field of human-computer interaction, a model containing the systematic factor and human factor has been proposed to evaluate the performance of the input devices of a computer. This is called the SH-model. In this paper, in order to extend the range of application of the SH-model, we propose some new models based on the Box-Cox transformation and apply a Bayesian modeling method for identification and estimation of the learning effects of pointing tasks. We consider the parameters describing the learning effect as random variables and introduce smoothness priors for them. Illustrative results show that the newly-proposed models work well.

Bayesian X-ray computed tomography using a three-level hierarchical prior model

NASA Astrophysics Data System (ADS)

Wang, Li; Mohammad-Djafari, Ali; Gac, Nicolas

2017-06-01

In recent decades X-ray Computed Tomography (CT) image reconstruction has been largely developed in both medical and industrial domain. In this paper, we propose using the Bayesian inference approach with a new hierarchical prior model. In the proposed model, a generalised Student-t distribution is used to enforce the Haar transformation of images to be sparse. Comparisons with some state of the art methods are presented. It is shown that by using the proposed model, the sparsity of sparse representation of images is enforced, so that edges of images are preserved. Simulation results are also provided to demonstrate the effectiveness of the new hierarchical model for reconstruction with fewer projections.

Combining historical eyewitness accounts on tsunami-induced waves and numerical simulations for getting insights in uncertainty of source parameters

NASA Astrophysics Data System (ADS)

Rohmer, Jeremy; Rousseau, Marie; Lemoine, Anne; Pedreros, Rodrigo; Lambert, Jerome; benki, Aalae

2017-04-01

Recent tsunami events including the 2004 Indian Ocean tsunami and the 2011 Tohoku tsunami have caused many casualties and damages to structures. Advances in numerical simulation of tsunami-induced wave processes have tremendously improved forecast, hazard and risk assessment and design of early warning for tsunamis. Among the major challenges, several studies have underlined uncertainties in earthquake slip distributions and rupture processes as major contributor on tsunami wave height and inundation extent. Constraining these uncertainties can be performed by taking advantage of observations either on tsunami waves (using network of water level gauge) or on inundation characteristics (using field evidence and eyewitness accounts). Despite these successful applications, combining tsunami observations and simulations still faces several limitations when the problem is addressed for past tsunamis events like 1755 Lisbon. 1) While recent inversion studies can benefit from current modern networks (e.g., tide gauges, sea bottom pressure gauges, GPS-mounted buoys), the number of tide gauges can be very scarce and testimonies on tsunami observations can be limited, incomplete and imprecise for past tsunamis events. These observations often restrict to eyewitness accounts on wave heights (e.g., maximum reached wave height at the coast) instead of the full observed waveforms; 2) Tsunami phenomena involve a large span of spatial scales (from ocean basin scales to local coastal wave interactions), which can make the modelling very demanding: the computation time cost of tsunami simulation can be very prohibitive; often reaching several hours. This often limits the number of allowable long-running simulations for performing the inversion, especially when the problem is addressed from a Bayesian inference perspective. The objective of the present study is to overcome both afore-described difficulties in the view to combine historical observations on past tsunami-induced waves and numerical simulations. In order to learn the uncertainty information on source parameters, we treat the problem within the Bayesian setting, which enables to incorporate in a flexible manner the different uncertainty sources. We propose to rely on an emerging technique called Approximate Bayesian Computation ABC, which has been developed to estimate the posterior distribution in modelling scenarios where the likelihood function is either unknown or cannot be explicitly defined. To overcome the computational issue, we combine ABC with statistical emulators (aka meta-model). We apply the proposed approach on the case study of Ligurian (North West of Italy) tsunami (1887) and discuss the results with a special attention paid to the impact of the observational error.

Fast Low-Rank Bayesian Matrix Completion With Hierarchical Gaussian Prior Models

NASA Astrophysics Data System (ADS)

Yang, Linxiao; Fang, Jun; Duan, Huiping; Li, Hongbin; Zeng, Bing

2018-06-01

The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a Wishart distribution is specified as a hyperprior over the precision matrix. We show that such a hierarchical Gaussian prior has the potential to encourage a low-rank solution. Based on the proposed hierarchical prior model, a variational Bayesian method is developed for matrix completion, where the generalized approximate massage passing (GAMP) technique is embedded into the variational Bayesian inference in order to circumvent cumbersome matrix inverse operations. Simulation results show that our proposed method demonstrates superiority over existing state-of-the-art matrix completion methods.

Improving timing sensitivity in the microhertz frequency regime: limits from PSR J1713+0747 on gravitational waves produced by supermassive black hole binaries

NASA Astrophysics Data System (ADS)

Perera, B. B. P.; Stappers, B. W.; Babak, S.; Keith, M. J.; Antoniadis, J.; Bassa, C. G.; Caballero, R. N.; Champion, D. J.; Cognard, I.; Desvignes, G.; Graikou, E.; Guillemot, L.; Janssen, G. H.; Karuppusamy, R.; Kramer, M.; Lazarus, P.; Lentati, L.; Liu, K.; Lyne, A. G.; McKee, J. W.; Osłowski, S.; Perrodin, D.; Sanidas, S. A.; Sesana, A.; Shaifullah, G.; Theureau, G.; Verbiest, J. P. W.; Taylor, S. R.

2018-07-01

We search for continuous gravitational waves (CGWs) produced by individual supermassive black hole binaries in circular orbits using high-cadence timing observations of PSR J1713+0747. We observe this millisecond pulsar using the telescopes in the European Pulsar Timing Array with an average cadence of approximately 1.6 d over the period between 2011 April and 2015 July, including an approximately daily average between 2013 February and 2014 April. The high-cadence observations are used to improve the pulsar timing sensitivity across the gravitational wave frequency range of 0.008-5μHz. We use two algorithms in the analysis, including a spectral fitting method and a Bayesian approach. For an independent comparison, we also use a previously published Bayesian algorithm. We find that the Bayesian approaches provide optimal results and the timing observations of the pulsar place a 95 per cent upper limit on the sky-averaged strain amplitude of CGWs to be ≲3.5 × 10-13 at a reference frequency of 1 μHz. We also find a 95 per cent upper limit on the sky-averaged strain amplitude of low-frequency CGWs to be ≲1.4 × 10-14 at a reference frequency of 20 nHz.

Improving timing sensitivity in the microhertz frequency regime: limits from PSR J1713+0747 on gravitational waves produced by super-massive black-hole binaries

NASA Astrophysics Data System (ADS)

Perera, B. B. P.; Stappers, B. W.; Babak, S.; Keith, M. J.; Antoniadis, J.; Bassa, C. G.; Caballero, R. N.; Champion, D. J.; Cognard, I.; Desvignes, G.; Graikou, E.; Guillemot, L.; Janssen, G. H.; Karuppusamy, R.; Kramer, M.; Lazarus, P.; Lentati, L.; Liu, K.; Lyne, A. G.; McKee, J. W.; Osłowski, S.; Perrodin, D.; Sanidas, S. A.; Sesana, A.; Shaifullah, G.; Theureau, G.; Verbiest, J. P. W.; Taylor, S. R.

2018-05-01

We search for continuous gravitational waves (CGWs) produced by individual super-massive black-hole binaries (SMBHBs) in circular orbits using high-cadence timing observations of PSR J1713+0747. We observe this millisecond pulsar using the telescopes in the European Pulsar Timing Array (EPTA) with an average cadence of approximately 1.6 days over the period between April 2011 and July 2015, including an approximately daily average between February 2013 and April 2014. The high-cadence observations are used to improve the pulsar timing sensitivity across the GW frequency range of 0.008 - 5 μHz. We use two algorithms in the analysis, including a spectral fitting method and a Bayesian approach. For an independent comparison, we also use a previously published Bayesian algorithm. We find that the Bayesian approaches provide optimal results and the timing observations of the pulsar place a 95 per cent upper limit on the sky-averaged strain amplitude of CGWs to be ≲ 3.5 × 10-13 at a reference frequency of 1 μHz. We also find a 95 per cent upper limit on the sky-averaged strain amplitude of low-frequency CGWs to be ≲ 1.4 × 10-14 at a reference frequency of 20 nHz.

Sequential structural damage diagnosis algorithm using a change point detection method

NASA Astrophysics Data System (ADS)

Noh, H.; Rajagopal, R.; Kiremidjian, A. S.

2013-11-01

This paper introduces a damage diagnosis algorithm for civil structures that uses a sequential change point detection method. The general change point detection method uses the known pre- and post-damage feature distributions to perform a sequential hypothesis test. In practice, however, the post-damage distribution is unlikely to be known a priori, unless we are looking for a known specific type of damage. Therefore, we introduce an additional algorithm that estimates and updates this distribution as data are collected using the maximum likelihood and the Bayesian methods. We also applied an approximate method to reduce the computation load and memory requirement associated with the estimation. The algorithm is validated using a set of experimental data collected from a four-story steel special moment-resisting frame and multiple sets of simulated data. Various features of different dimensions have been explored, and the algorithm was able to identify damage, particularly when it uses multidimensional damage sensitive features and lower false alarm rates, with a known post-damage feature distribution. For unknown feature distribution cases, the post-damage distribution was consistently estimated and the detection delays were only a few time steps longer than the delays from the general method that assumes we know the post-damage feature distribution. We confirmed that the Bayesian method is particularly efficient in declaring damage with minimal memory requirement, but the maximum likelihood method provides an insightful heuristic approach.

Damage diagnosis algorithm using a sequential change point detection method with an unknown distribution for damage

NASA Astrophysics Data System (ADS)

Noh, Hae Young; Rajagopal, Ram; Kiremidjian, Anne S.

2012-04-01

This paper introduces a damage diagnosis algorithm for civil structures that uses a sequential change point detection method for the cases where the post-damage feature distribution is unknown a priori. This algorithm extracts features from structural vibration data using time-series analysis and then declares damage using the change point detection method. The change point detection method asymptotically minimizes detection delay for a given false alarm rate. The conventional method uses the known pre- and post-damage feature distributions to perform a sequential hypothesis test. In practice, however, the post-damage distribution is unlikely to be known a priori. Therefore, our algorithm estimates and updates this distribution as data are collected using the maximum likelihood and the Bayesian methods. We also applied an approximate method to reduce the computation load and memory requirement associated with the estimation. The algorithm is validated using multiple sets of simulated data and a set of experimental data collected from a four-story steel special moment-resisting frame. Our algorithm was able to estimate the post-damage distribution consistently and resulted in detection delays only a few seconds longer than the delays from the conventional method that assumes we know the post-damage feature distribution. We confirmed that the Bayesian method is particularly efficient in declaring damage with minimal memory requirement, but the maximum likelihood method provides an insightful heuristic approach.

Cuckoo Search with Lévy Flights for Weighted Bayesian Energy Functional Optimization in Global-Support Curve Data Fitting

PubMed Central

Gálvez, Akemi; Iglesias, Andrés; Cabellos, Luis

2014-01-01

The problem of data fitting is very important in many theoretical and applied fields. In this paper, we consider the problem of optimizing a weighted Bayesian energy functional for data fitting by using global-support approximating curves. By global-support curves we mean curves expressed as a linear combination of basis functions whose support is the whole domain of the problem, as opposed to other common approaches in CAD/CAM and computer graphics driven by piecewise functions (such as B-splines and NURBS) that provide local control of the shape of the curve. Our method applies a powerful nature-inspired metaheuristic algorithm called cuckoo search, introduced recently to solve optimization problems. A major advantage of this method is its simplicity: cuckoo search requires only two parameters, many fewer than other metaheuristic approaches, so the parameter tuning becomes a very simple task. The paper shows that this new approach can be successfully used to solve our optimization problem. To check the performance of our approach, it has been applied to five illustrative examples of different types, including open and closed 2D and 3D curves that exhibit challenging features, such as cusps and self-intersections. Our results show that the method performs pretty well, being able to solve our minimization problem in an astonishingly straightforward way. PMID:24977175

Cuckoo search with Lévy flights for weighted Bayesian energy functional optimization in global-support curve data fitting.

PubMed

Gálvez, Akemi; Iglesias, Andrés; Cabellos, Luis

2014-01-01

The problem of data fitting is very important in many theoretical and applied fields. In this paper, we consider the problem of optimizing a weighted Bayesian energy functional for data fitting by using global-support approximating curves. By global-support curves we mean curves expressed as a linear combination of basis functions whose support is the whole domain of the problem, as opposed to other common approaches in CAD/CAM and computer graphics driven by piecewise functions (such as B-splines and NURBS) that provide local control of the shape of the curve. Our method applies a powerful nature-inspired metaheuristic algorithm called cuckoo search, introduced recently to solve optimization problems. A major advantage of this method is its simplicity: cuckoo search requires only two parameters, many fewer than other metaheuristic approaches, so the parameter tuning becomes a very simple task. The paper shows that this new approach can be successfully used to solve our optimization problem. To check the performance of our approach, it has been applied to five illustrative examples of different types, including open and closed 2D and 3D curves that exhibit challenging features, such as cusps and self-intersections. Our results show that the method performs pretty well, being able to solve our minimization problem in an astonishingly straightforward way.

The narrow endemic Norwegian peat moss Sphagnum troendelagicum originated before the last glacial maximum

PubMed Central

Stenøien, H K; Shaw, A J; Stengrundet, K; Flatberg, K I

2011-01-01

It is commonly found that individual hybrid, polyploid species originate recurrently and that many polyploid species originated relatively recently. It has been previously hypothesized that the extremely rare allopolyploid peat moss Sphagnum troendelagicum has originated multiple times, possibly after the last glacial maximum in Scandinavia. This conclusion was based on low linkage disequilibrium in anonymous genetic markers within natural populations, in which sexual reproduction has never been observed. Here we employ microsatellite markers and chloroplast DNA (cpDNA)-encoded trnG sequence data to test hypotheses concerning the origin and evolution of this species. We find that S. tenellum is the maternal progenitor and S. balticum is the paternal progenitor of S. troendelagicum. Using various Bayesian approaches, we estimate that S. troendelagicum originated before the Holocene but not before c. 80 000 years ago (median expected time since speciation 40 000 years before present). The observed lack of complete linkage disequilibrium in the genome of this species suggests cryptic sexual reproduction and recombination. Several lines of evidence suggest multiple origins for S. troendelagicum, but a single origin is supported by approximate Bayesian computation analyses. We hypothesize that S. troendelagicum originated in a peat-dominated refugium before last glacial maximum, and subsequently immigrated to central Norway by means of spore flow during the last thousands of years. PMID:20717162

Gene network reconstruction from transcriptional dynamics under kinetic model uncertainty: a case for the second derivative

PubMed Central

Bickel, David R.; Montazeri, Zahra; Hsieh, Pei-Chun; Beatty, Mary; Lawit, Shai J.; Bate, Nicholas J.

2009-01-01

Motivation: Measurements of gene expression over time enable the reconstruction of transcriptional networks. However, Bayesian networks and many other current reconstruction methods rely on assumptions that conflict with the differential equations that describe transcriptional kinetics. Practical approximations of kinetic models would enable inferring causal relationships between genes from expression data of microarray, tag-based and conventional platforms, but conclusions are sensitive to the assumptions made. Results: The representation of a sufficiently large portion of genome enables computation of an upper bound on how much confidence one may place in influences between genes on the basis of expression data. Information about which genes encode transcription factors is not necessary but may be incorporated if available. The methodology is generalized to cover cases in which expression measurements are missing for many of the genes that might control the transcription of the genes of interest. The assumption that the gene expression level is roughly proportional to the rate of translation led to better empirical performance than did either the assumption that the gene expression level is roughly proportional to the protein level or the Bayesian model average of both assumptions. Availability: http://www.oisb.ca points to R code implementing the methods (R Development Core Team 2004). Contact: dbickel@uottawa.ca Supplementary information: http://www.davidbickel.com PMID:19218351

Climate change underlies global demographic, genetic, and cultural transitions in pre-Columbian southern Peru.

PubMed

Fehren-Schmitz, Lars; Haak, Wolfgang; Mächtle, Bertil; Masch, Florian; Llamas, Bastien; Cagigao, Elsa Tomasto; Sossna, Volker; Schittek, Karsten; Isla Cuadrado, Johny; Eitel, Bernhard; Reindel, Markus

2014-07-01

Several archaeological studies in the Central Andes have pointed at the temporal coincidence of climatic fluctuations (both long- and short-term) and episodes of cultural transition and changes of socioeconomic structures throughout the pre-Columbian period. Although most scholars explain the connection between environmental and cultural changes by the impact of climatic alterations on the capacities of the ecosystems inhabited by pre-Columbian cultures, direct evidence for assumed demographic consequences is missing so far. In this study, we address directly the impact of climatic changes on the spatial population dynamics of the Central Andes. We use a large dataset of pre-Columbian mitochondrial DNA sequences from the northern Rio Grande de Nasca drainage (RGND) in southern Peru, dating from ∼840 BC to 1450 AD. Alternative demographic scenarios are tested using Bayesian serial coalescent simulations in an approximate Bayesian computational framework. Our results indicate migrations from the lower coastal valleys of southern Peru into the Andean highlands coincident with increasing climate variability at the end of the Nasca culture at ∼640 AD. We also find support for a back-migration from the highlands to the coast coincident with droughts in the southeastern Andean highlands and improvement of climatic conditions on the coast after the decline of the Wari and Tiwanaku empires (∼1200 AD), leading to a genetic homogenization in the RGND and probably southern Peru as a whole.

Spatiotemporal modeling of ecological and sociological ...

EPA Pesticide Factsheets

Suffolk County, New York, is a locus for West Nile virus (WNV) infection in the American northeast that includes the majority of Long Island to the east of New York City. The county has a system of light and gravid traps used for mosquito collection and disease monitoring. In order to identify predictors of WNV incidence in mosquitoes and predict future occurrence of WNV, we have developed a spatiotemporal Bayesian model, beginning with over 40 ecological, meteorological, and built-environment covariates. A mixed-effects model including spatially and temporally correlated errors was fit to WNV surveillance data from 2008 to 2014 using the R package “R-INLA,” which allows for Bayesian modeling using the stochastic partial differential equation (SPDE) approach. The integrated nested Laplace approximation (INLA) SPDE allows for simultaneous fitting of a temporal parameter and a spatial covariance, while incorporating a variety of likelihood functions and running in R statistical software on a home computer. We found that land cover classified as open water and woody wetlands had a negative association with WNV incidence in mosquitoes, and the count of septic systems was associated with an increase in WNV. Mean temperature at two-week lag was associated with a strong positive impact, while mean precipitation at no lag and one-week lag was associated with positive and negative impacts on WNV, respectively. Incorporation of spatiotemporal factors resulted in a mar

Climate change underlies global demographic, genetic, and cultural transitions in pre-Columbian southern Peru

PubMed Central

Fehren-Schmitz, Lars; Haak, Wolfgang; Mächtle, Bertil; Masch, Florian; Llamas, Bastien; Tomasto Cagigao, Elsa; Sossna, Volker; Schittek, Karsten; Isla Cuadrado, Johny; Eitel, Bernhard; Reindel, Markus

2014-01-01

Several archaeological studies in the Central Andes have pointed at the temporal coincidence of climatic fluctuations (both long- and short-term) and episodes of cultural transition and changes of socioeconomic structures throughout the pre-Columbian period. Although most scholars explain the connection between environmental and cultural changes by the impact of climatic alterations on the capacities of the ecosystems inhabited by pre-Columbian cultures, direct evidence for assumed demographic consequences is missing so far. In this study, we address directly the impact of climatic changes on the spatial population dynamics of the Central Andes. We use a large dataset of pre-Columbian mitochondrial DNA sequences from the northern Rio Grande de Nasca drainage (RGND) in southern Peru, dating from ∼840 BC to 1450 AD. Alternative demographic scenarios are tested using Bayesian serial coalescent simulations in an approximate Bayesian computational framework. Our results indicate migrations from the lower coastal valleys of southern Peru into the Andean highlands coincident with increasing climate variability at the end of the Nasca culture at ∼640 AD. We also find support for a back-migration from the highlands to the coast coincident with droughts in the southeastern Andean highlands and improvement of climatic conditions on the coast after the decline of the Wari and Tiwanaku empires (∼1200 AD), leading to a genetic homogenization in the RGND and probably southern Peru as a whole. PMID:24979787

Cryptic genetic diversity, population structure, and gene flow in the Mojave rattlesnake (Crotalus scutulatus).

PubMed

Schield, Drew R; Adams, Richard H; Card, Daren C; Corbin, Andrew B; Jezkova, Tereza; Hales, Nicole R; Meik, Jesse M; Perry, Blair W; Spencer, Carol L; Smith, Lydia L; García, Gustavo Campillo; Bouzid, Nassima M; Strickland, Jason L; Parkinson, Christopher L; Borja, Miguel; Castañeda-Gaytán, Gamaliel; Bryson, Robert W; Flores-Villela, Oscar A; Mackessy, Stephen P; Castoe, Todd A

2018-06-15

The Mojave rattlesnake (Crotalus scutulatus) inhabits deserts and arid grasslands of the western United States and Mexico. Despite considerable interest in its highly toxic venom and the recognition of two subspecies, no molecular studies have characterized range-wide genetic diversity and population structure or tested species limits within C. scutulatus. We used mitochondrial DNA and thousands of nuclear loci from double-digest restriction site associated DNA sequencing to infer population genetic structure throughout the range of C. scutulatus, and to evaluate divergence times and gene flow between populations. We find strong support for several divergent mitochondrial and nuclear clades of C. scutulatus, including splits coincident with two major phylogeographic barriers: the Continental Divide and the elevational increase associated with the Central Mexican Plateau. We apply Bayesian clustering, phylogenetic inference, and coalescent-based species delimitation to our nuclear genetic data to test hypotheses of population structure. We also performed demographic analyses to test hypotheses relating to population divergence and gene flow. Collectively, our results support the existence of four distinct lineages within C. scutulatus, and genetically defined populations do not correspond with currently recognized subspecies ranges. Finally, we use approximate Bayesian computation to test hypotheses of divergence among multiple rattlesnake species groups distributed across the Continental Divide, and find evidence for co-divergence at this boundary during the mid-Pleistocene. Copyright © 2018 Elsevier Inc. All rights reserved.

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.

Algorithm for ion beam figuring of low-gradient mirrors.

PubMed

Jiao, Changjun; Li, Shengyi; Xie, Xuhui

2009-07-20

Ion beam figuring technology for low-gradient mirrors is discussed. Ion beam figuring is a noncontact machining technique in which a beam of high-energy ions is directed toward a target workpiece to remove material in a predetermined and controlled fashion. Owing to this noncontact mode of material removal, problems associated with tool wear and edge effects, which are common in conventional contact polishing processes, are avoided. Based on the Bayesian principle, an iterative dwell time algorithm for planar mirrors is deduced from the computer-controlled optical surfacing (CCOS) principle. With the properties of the removal function, the shaping process of low-gradient mirrors can be approximated by the linear model for planar mirrors. With these discussions, the error surface figuring technology for low-gradient mirrors with a linear path is set up. With the near-Gaussian property of the removal function, the figuring process with a spiral path can be described by the conventional linear CCOS principle, and a Bayesian-based iterative algorithm can be used to deconvolute the dwell time. Moreover, the selection criterion of the spiral parameter is given. Ion beam figuring technology with a spiral scan path based on these methods can be used to figure mirrors with non-axis-symmetrical errors. Experiments on SiC chemical vapor deposition planar and Zerodur paraboloid samples are made, and the final surface errors are all below 1/100 lambda.

Nonparametric Bayesian models through probit stick-breaking processes

PubMed Central

Rodríguez, Abel; Dunson, David B.

2013-01-01

We describe a novel class of Bayesian nonparametric priors based on stick-breaking constructions where the weights of the process are constructed as probit transformations of normal random variables. We show that these priors are extremely flexible, allowing us to generate a great variety of models while preserving computational simplicity. Particular emphasis is placed on the construction of rich temporal and spatial processes, which are applied to two problems in finance and ecology. PMID:24358072

Nonparametric Bayesian models through probit stick-breaking processes.

PubMed

Rodríguez, Abel; Dunson, David B

2011-03-01

We describe a novel class of Bayesian nonparametric priors based on stick-breaking constructions where the weights of the process are constructed as probit transformations of normal random variables. We show that these priors are extremely flexible, allowing us to generate a great variety of models while preserving computational simplicity. Particular emphasis is placed on the construction of rich temporal and spatial processes, which are applied to two problems in finance and ecology.

Bayesian Hypothesis Testing

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

Andrews, Stephen A.; Sigeti, David E.

These are a set of slides about Bayesian hypothesis testing, where many hypotheses are tested. The conclusions are the following: The value of the Bayes factor obtained when using the median of the posterior marginal is almost the minimum value of the Bayes factor. The value of τ 2 which minimizes the Bayes factor is a reasonable choice for this parameter. This allows a likelihood ratio to be computed with is the least favorable to H 0.

Bayesian randomized clinical trials: From fixed to adaptive design.

PubMed

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

2017-08-01

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

Using Bayesian Networks for Candidate Generation in Consistency-based Diagnosis

NASA Technical Reports Server (NTRS)

Narasimhan, Sriram; Mengshoel, Ole

2008-01-01

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

Bayesian least squares deconvolution

NASA Astrophysics Data System (ADS)

Asensio Ramos, A.; Petit, P.

2015-11-01

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

Robust Learning of High-dimensional Biological Networks with Bayesian Networks

NASA Astrophysics Data System (ADS)

Nägele, Andreas; Dejori, Mathäus; Stetter, Martin

Structure learning of Bayesian networks applied to gene expression data has become a potentially useful method to estimate interactions between genes. However, the NP-hardness of Bayesian network structure learning renders the reconstruction of the full genetic network with thousands of genes unfeasible. Consequently, the maximal network size is usually restricted dramatically to a small set of genes (corresponding with variables in the Bayesian network). Although this feature reduction step makes structure learning computationally tractable, on the downside, the learned structure might be adversely affected due to the introduction of missing genes. Additionally, gene expression data are usually very sparse with respect to the number of samples, i.e., the number of genes is much greater than the number of different observations. Given these problems, learning robust network features from microarray data is a challenging task. This chapter presents several approaches tackling the robustness issue in order to obtain a more reliable estimation of learned network features.

Bayesian Group Bridge for Bi-level Variable Selection.

PubMed

Mallick, Himel; Yi, Nengjun

2017-06-01

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

Hidden Markov induced Dynamic Bayesian Network for recovering time evolving gene regulatory networks

NASA Astrophysics Data System (ADS)

Zhu, Shijia; Wang, Yadong

2015-12-01

Dynamic Bayesian Networks (DBN) have been widely used to recover gene regulatory relationships from time-series data in computational systems biology. Its standard assumption is ‘stationarity’, and therefore, several research efforts have been recently proposed to relax this restriction. However, those methods suffer from three challenges: long running time, low accuracy and reliance on parameter settings. To address these problems, we propose a novel non-stationary DBN model by extending each hidden node of Hidden Markov Model into a DBN (called HMDBN), which properly handles the underlying time-evolving networks. Correspondingly, an improved structural EM algorithm is proposed to learn the HMDBN. It dramatically reduces searching space, thereby substantially improving computational efficiency. Additionally, we derived a novel generalized Bayesian Information Criterion under the non-stationary assumption (called BWBIC), which can help significantly improve the reconstruction accuracy and largely reduce over-fitting. Moreover, the re-estimation formulas for all parameters of our model are derived, enabling us to avoid reliance on parameter settings. Compared to the state-of-the-art methods, the experimental evaluation of our proposed method on both synthetic and real biological data demonstrates more stably high prediction accuracy and significantly improved computation efficiency, even with no prior knowledge and parameter settings.

Optimal Sequential Rules for Computer-Based Instruction.

ERIC Educational Resources Information Center

Vos, Hans J.

1998-01-01

Formulates sequential rules for adapting the appropriate amount of instruction to learning needs in the context of computer-based instruction. Topics include Bayesian decision theory, threshold and linear-utility structure, psychometric model, optimal sequential number of test questions, and an empirical example of sequential instructional…

A Bayesian Method for Evaluating and Discovering Disease Loci Associations

PubMed Central

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

2011-01-01

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

Understanding and predicting changing use of groundwater with climate and other uncertainties: a Bayesian approach

NASA Astrophysics Data System (ADS)

Costa, F. A. F.; Keir, G.; McIntyre, N.; Bulovic, N.

2015-12-01

Most groundwater supply bores in Australia do not have flow metering equipment and so regional groundwater abstraction rates are not well known. Past estimates of unmetered abstraction for regional numerical groundwater modelling typically have not attempted to quantify the uncertainty inherent in the estimation process in detail. In particular, the spatial properties of errors in the estimates are almost always neglected. Here, we apply Bayesian spatial models to estimate these abstractions at a regional scale, using the state-of-the-art computationally inexpensive approaches of integrated nested Laplace approximation (INLA) and stochastic partial differential equations (SPDE). We examine a case study in the Condamine Alluvium aquifer in southern Queensland, Australia; even in this comparatively data-rich area with extensive groundwater abstraction for agricultural irrigation, approximately 80% of bores do not have reliable metered flow records. Additionally, the metering data in this area are characterised by complicated statistical features, such as zero-valued observations, non-normality, and non-stationarity. While this precludes the use of many classical spatial estimation techniques, such as kriging, our model (using the R-INLA package) is able to accommodate these features. We use a joint model to predict both probability and magnitude of abstraction from bores in space and time, and examine the effect of a range of high-resolution gridded meteorological covariates upon the predictive ability of the model. Deviance Information Criterion (DIC) scores are used to assess a range of potential models, which reward good model fit while penalising excessive model complexity. We conclude that maximum air temperature (as a reasonably effective surrogate for evapotranspiration) is the most significant single predictor of abstraction rate; and that a significant spatial effect exists (represented by the SPDE approximation of a Gaussian random field with a Matérn covariance function). Our final model adopts air temperature, solar exposure, and normalized difference vegetation index (NDVI) as covariates, shows good agreement with previous estimates at a regional scale, and additionally offers rigorous quantification of uncertainty in the estimate.

Dealing with missing standard deviation and mean values in meta-analysis of continuous outcomes: a systematic review.

PubMed

Weir, Christopher J; Butcher, Isabella; Assi, Valentina; Lewis, Stephanie C; Murray, Gordon D; Langhorne, Peter; Brady, Marian C

2018-03-07

Rigorous, informative meta-analyses rely on availability of appropriate summary statistics or individual participant data. For continuous outcomes, especially those with naturally skewed distributions, summary information on the mean or variability often goes unreported. While full reporting of original trial data is the ideal, we sought to identify methods for handling unreported mean or variability summary statistics in meta-analysis. We undertook two systematic literature reviews to identify methodological approaches used to deal with missing mean or variability summary statistics. Five electronic databases were searched, in addition to the Cochrane Colloquium abstract books and the Cochrane Statistics Methods Group mailing list archive. We also conducted cited reference searching and emailed topic experts to identify recent methodological developments. Details recorded included the description of the method, the information required to implement the method, any underlying assumptions and whether the method could be readily applied in standard statistical software. We provided a summary description of the methods identified, illustrating selected methods in example meta-analysis scenarios. For missing standard deviations (SDs), following screening of 503 articles, fifteen methods were identified in addition to those reported in a previous review. These included Bayesian hierarchical modelling at the meta-analysis level; summary statistic level imputation based on observed SD values from other trials in the meta-analysis; a practical approximation based on the range; and algebraic estimation of the SD based on other summary statistics. Following screening of 1124 articles for methods estimating the mean, one approximate Bayesian computation approach and three papers based on alternative summary statistics were identified. Illustrative meta-analyses showed that when replacing a missing SD the approximation using the range minimised loss of precision and generally performed better than omitting trials. When estimating missing means, a formula using the median, lower quartile and upper quartile performed best in preserving the precision of the meta-analysis findings, although in some scenarios, omitting trials gave superior results. Methods based on summary statistics (minimum, maximum, lower quartile, upper quartile, median) reported in the literature facilitate more comprehensive inclusion of randomised controlled trials with missing mean or variability summary statistics within meta-analyses.

NIMROD: a program for inference via a normal approximation of the posterior in models with random effects based on ordinary differential equations.

PubMed

Prague, Mélanie; Commenges, Daniel; Guedj, Jérémie; Drylewicz, Julia; Thiébaut, Rodolphe

2013-08-01

Models based on ordinary differential equations (ODE) are widespread tools for describing dynamical systems. In biomedical sciences, data from each subject can be sparse making difficult to precisely estimate individual parameters by standard non-linear regression but information can often be gained from between-subjects variability. This makes natural the use of mixed-effects models to estimate population parameters. Although the maximum likelihood approach is a valuable option, identifiability issues favour Bayesian approaches which can incorporate prior knowledge in a flexible way. However, the combination of difficulties coming from the ODE system and from the presence of random effects raises a major numerical challenge. Computations can be simplified by making a normal approximation of the posterior to find the maximum of the posterior distribution (MAP). Here we present the NIMROD program (normal approximation inference in models with random effects based on ordinary differential equations) devoted to the MAP estimation in ODE models. We describe the specific implemented features such as convergence criteria and an approximation of the leave-one-out cross-validation to assess the model quality of fit. In pharmacokinetics models, first, we evaluate the properties of this algorithm and compare it with FOCE and MCMC algorithms in simulations. Then, we illustrate NIMROD use on Amprenavir pharmacokinetics data from the PUZZLE clinical trial in HIV infected patients. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Bayesian Integration of Information in Hippocampal Place Cells

PubMed Central

Madl, Tamas; Franklin, Stan; Chen, Ke; Montaldi, Daniela; Trappl, Robert

2014-01-01

Accurate spatial localization requires a mechanism that corrects for errors, which might arise from inaccurate sensory information or neuronal noise. In this paper, we propose that Hippocampal place cells might implement such an error correction mechanism by integrating different sources of information in an approximately Bayes-optimal fashion. We compare the predictions of our model with physiological data from rats. Our results suggest that useful predictions regarding the firing fields of place cells can be made based on a single underlying principle, Bayesian cue integration, and that such predictions are possible using a remarkably small number of model parameters. PMID:24603429

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.

Bayesian analysis of the flutter margin method in aeroelasticity

DOE PAGES

Khalil, Mohammad; Poirel, Dominique; Sarkar, Abhijit

2016-08-27

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

Delamination detection using methods of computational intelligence

NASA Astrophysics Data System (ADS)

Ihesiulor, Obinna K.; Shankar, Krishna; Zhang, Zhifang; Ray, Tapabrata

2012-11-01

Abstract Reliable delamination prediction scheme is indispensable in order to prevent potential risks of catastrophic failures in composite structures. The existence of delaminations changes the vibration characteristics of composite laminates and hence such indicators can be used to quantify the health characteristics of laminates. An approach for online health monitoring of in-service composite laminates is presented in this paper that relies on methods based on computational intelligence. Typical changes in the observed vibration characteristics (i.e. change in natural frequencies) are considered as inputs to identify the existence, location and magnitude of delaminations. The performance of the proposed approach is demonstrated using numerical models of composite laminates. Since this identification problem essentially involves the solution of an optimization problem, the use of finite element (FE) methods as the underlying tool for analysis turns out to be computationally expensive. A surrogate assisted optimization approach is hence introduced to contain the computational time within affordable limits. An artificial neural network (ANN) model with Bayesian regularization is used as the underlying approximation scheme while an improved rate of convergence is achieved using a memetic algorithm. However, building of ANN surrogate models usually requires large training datasets. K-means clustering is effectively employed to reduce the size of datasets. ANN is also used via inverse modeling to determine the position, size and location of delaminations using changes in measured natural frequencies. The results clearly highlight the efficiency and the robustness of the approach.

Distributed multisensory integration in a recurrent network model through supervised learning

NASA Astrophysics Data System (ADS)

Wang, He; Wong, K. Y. Michael

Sensory integration between different modalities has been extensively studied. It is suggested that the brain integrates signals from different modalities in a Bayesian optimal way. However, how the Bayesian rule is implemented in a neural network remains under debate. In this work we propose a biologically plausible recurrent network model, which can perform Bayesian multisensory integration after trained by supervised learning. Our model is composed of two modules, each for one modality. We assume that each module is a recurrent network, whose activity represents the posterior distribution of each stimulus. The feedforward input on each module is the likelihood of each modality. Two modules are integrated through cross-links, which are feedforward connections from the other modality, and reciprocal connections, which are recurrent connections between different modules. By stochastic gradient descent, we successfully trained the feedforward and recurrent coupling matrices simultaneously, both of which resembles the Mexican-hat. We also find that there are more than one set of coupling matrices that can approximate the Bayesian theorem well. Specifically, reciprocal connections and cross-links will compensate each other if one of them is removed. Even though trained with two inputs, the network's performance with only one input is in good accordance with what is predicted by the Bayesian theorem.

Bayesian approach for counting experiment statistics applied to a neutrino point source analysis

NASA Astrophysics Data System (ADS)

Bose, D.; Brayeur, L.; Casier, M.; de Vries, K. D.; Golup, G.; van Eijndhoven, N.

2013-12-01

In this paper we present a model independent analysis method following Bayesian statistics to analyse data from a generic counting experiment and apply it to the search for neutrinos from point sources. We discuss a test statistic defined following a Bayesian framework that will be used in the search for a signal. In case no signal is found, we derive an upper limit without the introduction of approximations. The Bayesian approach allows us to obtain the full probability density function for both the background and the signal rate. As such, we have direct access to any signal upper limit. The upper limit derivation directly compares with a frequentist approach and is robust in the case of low-counting observations. Furthermore, it allows also to account for previous upper limits obtained by other analyses via the concept of prior information without the need of the ad hoc application of trial factors. To investigate the validity of the presented Bayesian approach, we have applied this method to the public IceCube 40-string configuration data for 10 nearby blazars and we have obtained a flux upper limit, which is in agreement with the upper limits determined via a frequentist approach. Furthermore, the upper limit obtained compares well with the previously published result of IceCube, using the same data set.

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.

Demographic History of European Populations of Arabidopsis thaliana

PubMed Central

François, Olivier; Blum, Michael G. B.; Jakobsson, Mattias; Rosenberg, Noah A.

2008-01-01

The model plant species Arabidopsis thaliana is successful at colonizing land that has recently undergone human-mediated disturbance. To investigate the prehistoric spread of A. thaliana, we applied approximate Bayesian computation and explicit spatial modeling to 76 European accessions sequenced at 876 nuclear loci. We find evidence that a major migration wave occurred from east to west, affecting most of the sampled individuals. The longitudinal gradient appears to result from the plant having spread in Europe from the east ∼10,000 years ago, with a rate of westward spread of ∼0.9 km/year. This wave-of-advance model is consistent with a natural colonization from an eastern glacial refugium that overwhelmed ancient western lineages. However, the speed and time frame of the model also suggest that the migration of A. thaliana into Europe may have accompanied the spread of agriculture during the Neolithic transition. PMID:18483550

Statistical analysis of loopy belief propagation in random fields

NASA Astrophysics Data System (ADS)

Yasuda, Muneki; Kataoka, Shun; Tanaka, Kazuyuki

2015-10-01

Loopy belief propagation (LBP), which is equivalent to the Bethe approximation in statistical mechanics, is a message-passing-type inference method that is widely used to analyze systems based on Markov random fields (MRFs). In this paper, we propose a message-passing-type method to analytically evaluate the quenched average of LBP in random fields by using the replica cluster variation method. The proposed analytical method is applicable to general pairwise MRFs with random fields whose distributions differ from each other and can give the quenched averages of the Bethe free energies over random fields, which are consistent with numerical results. The order of its computational cost is equivalent to that of standard LBP. In the latter part of this paper, we describe the application of the proposed method to Bayesian image restoration, in which we observed that our theoretical results are in good agreement with the numerical results for natural images.

Mitochondrial diversity and phylogeography of Acrossocheilus paradoxus (Teleostei: Cyprinidae).

PubMed

Ju, Yu-Min; Hsu, Kui-Ching; Yang, Jin-Quan; Wu, Jui-Hsien; Li, Shan; Wang, Wei-Kuang; Ding, Fang; Li, Jun; Lin, Hung-Du

2018-01-31

Mitochondrial DNA cytochrome b sequences (1141 bp) in 229 specimens of Acrossocheilus paradoxus from 26 populations were identified as four lineages. The pairwise genetic distances among these four lineages ranged from 1.57 to 2.37% (mean= 2.00%). Statistical dispersal-vicariance analysis suggests that the ancestral populations were distributed over mainland China and Northern and Western Taiwan. Approximate Bayesian computation approaches show that the three lineages in Taiwan originated from the lineage in mainland China through three colonization routes during two glaciations. The results indicated that during the glaciation and inter-glacial periods, the Taiwan Strait was exposed and sank, which contributed to the dispersion and differentiation of populations. Furthermore, the populations of A. paradoxus colonized Taiwan through a land bridge to the north of the Formosa Bank, and the Miaoli Plateau in Taiwan was an important barrier that limited gene exchange between populations on both the sides.

Quantifying the uncertainty in heritability

PubMed Central

Furlotte, Nicholas A; Heckerman, David; Lippert, Christoph

2014-01-01

The use of mixed models to determine narrow-sense heritability and related quantities such as SNP heritability has received much recent attention. Less attention has been paid to the inherent variability in these estimates. One approach for quantifying variability in estimates of heritability is a frequentist approach, in which heritability is estimated using maximum likelihood and its variance is quantified through an asymptotic normal approximation. An alternative approach is to quantify the uncertainty in heritability through its Bayesian posterior distribution. In this paper, we develop the latter approach, make it computationally efficient and compare it to the frequentist approach. We show theoretically that, for a sufficiently large sample size and intermediate values of heritability, the two approaches provide similar results. Using the Atherosclerosis Risk in Communities cohort, we show empirically that the two approaches can give different results and that the variance/uncertainty can remain large. PMID:24670270

An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions

DOE PAGES

Li, Weixuan; Lin, Guang

2015-03-21

Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes’ rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle thesemore » challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.« less

An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions

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

Li, Weixuan; Lin, Guang, E-mail: guanglin@purdue.edu

2015-08-01

Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes' rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle thesemore » challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.« less

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

NASA Astrophysics Data System (ADS)

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

2015-06-01

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

Bayesian depth estimation from monocular natural images.

PubMed

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

2017-05-01

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

Adaptive Annealed Importance Sampling for Multimodal Posterior Exploration and Model Selection with Application to Extrasolar Planet Detection

NASA Astrophysics Data System (ADS)

Liu, Bin

2014-07-01

We describe an algorithm that can adaptively provide mixture summaries of multimodal posterior distributions. The parameter space of the involved posteriors ranges in size from a few dimensions to dozens of dimensions. This work was motivated by an astrophysical problem called extrasolar planet (exoplanet) detection, wherein the computation of stochastic integrals that are required for Bayesian model comparison is challenging. The difficulty comes from the highly nonlinear models that lead to multimodal posterior distributions. We resort to importance sampling (IS) to estimate the integrals, and thus translate the problem to be how to find a parametric approximation of the posterior. To capture the multimodal structure in the posterior, we initialize a mixture proposal distribution and then tailor its parameters elaborately to make it resemble the posterior to the greatest extent possible. We use the effective sample size (ESS) calculated based on the IS draws to measure the degree of approximation. The bigger the ESS is, the better the proposal resembles the posterior. A difficulty within this tailoring operation lies in the adjustment of the number of mixing components in the mixture proposal. Brute force methods just preset it as a large constant, which leads to an increase in the required computational resources. We provide an iterative delete/merge/add process, which works in tandem with an expectation-maximization step to tailor such a number online. The efficiency of our proposed method is tested via both simulation studies and real exoplanet data analysis.

Update on Bayesian Blocks: Segmented Models for Sequential Data

NASA Technical Reports Server (NTRS)

Scargle, Jeff

2017-01-01

The Bayesian Block algorithm, in wide use in astronomy and other areas, has been improved in several ways. The model for block shape has been generalized to include other than constant signal rate - e.g., linear, exponential, or other parametric models. In addition the computational efficiency has been improved, so that instead of O(N**2) the basic algorithm is O(N) in most cases. Other improvements in the theory and application of segmented representations will be described.

Artificial Intelligence (AI) Center of Excellence at the University of Pennsylvania

DTIC Science & Technology

1995-07-01

that controls impact forces. Robust Location Estimation for MLR and Non-MLR Distributions (Dissertation Proposal) Gerda L. Kamberova MS-CIS-92-28...Bayesian Approach To Computer Vision Problems Gerda L. Kamberova MS-CIS-92-29 GRASP LAB 310 The object of our study is the Bayesian approach in...Estimation for MLR and Non-MLR Distributions (Dissertation) Gerda L. Kamberova MS-CIS-92-93 GRASP LAB 340 We study the problem of estimating an unknown

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

PubMed Central

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

2017-01-01

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

High-throughput Bayesian Network Learning using Heterogeneous Multicore Computers

PubMed Central

Linderman, Michael D.; Athalye, Vivek; Meng, Teresa H.; Asadi, Narges Bani; Bruggner, Robert; Nolan, Garry P.

2017-01-01

Aberrant intracellular signaling plays an important role in many diseases. The causal structure of signal transduction networks can be modeled as Bayesian Networks (BNs), and computationally learned from experimental data. However, learning the structure of Bayesian Networks (BNs) is an NP-hard problem that, even with fast heuristics, is too time consuming for large, clinically important networks (20–50 nodes). In this paper, we present a novel graphics processing unit (GPU)-accelerated implementation of a Monte Carlo Markov Chain-based algorithm for learning BNs that is up to 7.5-fold faster than current general-purpose processor (GPP)-based implementations. The GPU-based implementation is just one of several implementations within the larger application, each optimized for a different input or machine configuration. We describe the methodology we use to build an extensible application, assembled from these variants, that can target a broad range of heterogeneous systems, e.g., GPUs, multicore GPPs. Specifically we show how we use the Merge programming model to efficiently integrate, test and intelligently select among the different potential implementations. PMID:28819655

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

NASA Astrophysics Data System (ADS)

Sahai, Swupnil

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

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

PubMed

Perdikaris, Paris; Karniadakis, George Em

2016-05-01

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

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

PubMed Central

Perdikaris, Paris; Karniadakis, George Em

2016-01-01

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

A Comparison of FPGA and GPGPU Designs for Bayesian Occupancy Filters.

PubMed

Medina, Luis; Diez-Ochoa, Miguel; Correal, Raul; Cuenca-Asensi, Sergio; Serrano, Alejandro; Godoy, Jorge; Martínez-Álvarez, Antonio; Villagra, Jorge

2017-11-11

Grid-based perception techniques in the automotive sector based on fusing information from different sensors and their robust perceptions of the environment are proliferating in the industry. However, one of the main drawbacks of these techniques is the traditionally prohibitive, high computing performance that is required for embedded automotive systems. In this work, the capabilities of new computing architectures that embed these algorithms are assessed in a real car. The paper compares two ad hoc optimized designs of the Bayesian Occupancy Filter; one for General Purpose Graphics Processing Unit (GPGPU) and the other for Field-Programmable Gate Array (FPGA). The resulting implementations are compared in terms of development effort, accuracy and performance, using datasets from a realistic simulator and from a real automated vehicle.

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.

Diagnosis and Reconfiguration using Bayesian Networks: An Electrical Power System Case Study

NASA Technical Reports Server (NTRS)

Knox, W. Bradley; Mengshoel, Ole

2009-01-01

Automated diagnosis and reconfiguration are important computational techniques that aim to minimize human intervention in autonomous systems. In this paper, we develop novel techniques and models in the context of diagnosis and reconfiguration reasoning using causal Bayesian networks (BNs). We take as starting point a successful diagnostic approach, using a static BN developed for a real-world electrical power system. We discuss in this paper the extension of this diagnostic approach along two dimensions, namely: (i) from a static BN to a dynamic BN; and (ii) from a diagnostic task to a reconfiguration task. More specifically, we discuss the auto-generation of a dynamic Bayesian network from a static Bayesian network. In addition, we discuss subtle, but important, differences between Bayesian networks when used for diagnosis versus reconfiguration. We discuss a novel reconfiguration agent, which models a system causally, including effects of actions through time, using a dynamic Bayesian network. Though the techniques we discuss are general, we demonstrate them in the context of electrical power systems (EPSs) for aircraft and spacecraft. EPSs are vital subsystems on-board aircraft and spacecraft, and many incidents and accidents of these vehicles have been attributed to EPS failures. We discuss a case study that provides initial but promising results for our approach in the setting of electrical power systems.

A Bayesian Approach to the Overlap Analysis of Epidemiologically Linked Traits.

PubMed

Asimit, Jennifer L; Panoutsopoulou, Kalliope; Wheeler, Eleanor; Berndt, Sonja I; Cordell, Heather J; Morris, Andrew P; Zeggini, Eleftheria; Barroso, Inês

2015-12-01

Diseases often cooccur in individuals more often than expected by chance, and may be explained by shared underlying genetic etiology. A common approach to genetic overlap analyses is to use summary genome-wide association study data to identify single-nucleotide polymorphisms (SNPs) that are associated with multiple traits at a selected P-value threshold. However, P-values do not account for differences in power, whereas Bayes' factors (BFs) do, and may be approximated using summary statistics. We use simulation studies to compare the power of frequentist and Bayesian approaches with overlap analyses, and to decide on appropriate thresholds for comparison between the two methods. It is empirically illustrated that BFs have the advantage over P-values of a decreasing type I error rate as study size increases for single-disease associations. Consequently, the overlap analysis of traits from different-sized studies encounters issues in fair P-value threshold selection, whereas BFs are adjusted automatically. Extensive simulations show that Bayesian overlap analyses tend to have higher power than those that assess association strength with P-values, particularly in low-power scenarios. Calibration tables between BFs and P-values are provided for a range of sample sizes, as well as an approximation approach for sample sizes that are not in the calibration table. Although P-values are sometimes thought more intuitive, these tables assist in removing the opaqueness of Bayesian thresholds and may also be used in the selection of a BF threshold to meet a certain type I error rate. An application of our methods is used to identify variants associated with both obesity and osteoarthritis. © 2015 The Authors. *Genetic Epidemiology published by Wiley Periodicals, Inc.

Computational Linguistics in the Netherlands 1996. Papers from the CLIN Meeting (7th, Eindhoven, Netherlands, November 15, 1996).

ERIC Educational Resources Information Center

Landsbergen, Jan, Ed.; Odijk, Jan, Ed.; van Deemter, Kees, Ed.; van Zanten, Gert Veldhuijzen, Ed.

Papers from the meeting on computational linguistics include: "Conversational Games, Belief Revision and Bayesian Networks" (Stephen G. Pulman); "Valence Alternation without Lexical Rules" (Gosse Bouma); "Filtering Left Dislocation Chains in Parsing Categorical Grammar" (Crit Cremers, Maarten Hijzelendoorn);…

Specifying and Refining a Measurement Model for a Computer-Based Interactive Assessment

ERIC Educational Resources Information Center

Levy, Roy; Mislevy, Robert J.

2004-01-01

The challenges of modeling students' performance in computer-based interactive assessments include accounting for multiple aspects of knowledge and skill that arise in different situations and the conditional dependencies among multiple aspects of performance. This article describes a Bayesian approach to modeling and estimating cognitive models…

Bayesian Methods and Confidence Intervals for Automatic Target Recognition of SAR Canonical Shapes

DTIC Science & Technology

2014-03-27

and DirectX [22]. The CUDA platform was developed by the NVIDIA Corporation to allow programmers access to the computational capabilities of the...were used for the intense repetitive computations. Developing CUDA software requires writing code for specialized compilers provided by NVIDIA and

Computer Aided Evaluation of Higher Education Tutors' Performance

ERIC Educational Resources Information Center

Xenos, Michalis; Papadopoulos, Thanos

2007-01-01

This article presents a method for computer-aided tutor evaluation: Bayesian Networks are used for organizing the collected data about tutors and for enabling accurate estimations and predictions about future tutor behavior. The model provides indications about each tutor's strengths and weaknesses, which enables the evaluator to exploit strengths…

Extremely low nucleotide polymorphism in Pinus krempfii Lecomte, a unique flat needle pine endemic to Vietnam

PubMed Central

Wang, Baosheng; Khalili Mahani, Marjan; Ng, Wei Lun; Kusumi, Junko; Phi, Hai Hong; Inomata, Nobuyuki; Wang, Xiao-Ru; Szmidt, Alfred E

2014-01-01

Pinus krempfii Lecomte is a morphologically and ecologically unique pine, endemic to Vietnam. It is regarded as vulnerable species with distribution limited to just two provinces: Khanh Hoa and Lam Dong. Although a few phylogenetic studies have included this species, almost nothing is known about its genetic features. In particular, there are no studies addressing the levels and patterns of genetic variation in natural populations of P. krempfii. In this study, we sampled 57 individuals from six natural populations of P. krempfii and analyzed their sequence variation in ten nuclear gene regions (approximately 9 kb) and 14 mitochondrial (mt) DNA regions (approximately 10 kb). We also analyzed variation at seven chloroplast (cp) microsatellite (SSR) loci. We found very low haplotype and nucleotide diversity at nuclear loci compared with other pine species. Furthermore, all investigated populations were monomorphic across all mitochondrial DNA (mtDNA) regions included in our study, which are polymorphic in other pine species. Population differentiation at nuclear loci was low (5.2%) but significant. However, structure analysis of nuclear loci did not detect genetically differentiated groups of populations. Approximate Bayesian computation (ABC) using nuclear sequence data and mismatch distribution analysis for cpSSR loci suggested recent expansion of the species. The implications of these findings for the management and conservation of P. krempfii genetic resources were discussed. PMID:25360263