Cortical plasticity as a mechanism for storing Bayesian priors in sensory perception.
Köver, Hania; Bao, Shaowen
2010-05-05
Human perception of ambiguous sensory signals is biased by prior experiences. It is not known how such prior information is encoded, retrieved and combined with sensory information by neurons. Previous authors have suggested dynamic encoding mechanisms for prior information, whereby top-down modulation of firing patterns on a trial-by-trial basis creates short-term representations of priors. Although such a mechanism may well account for perceptual bias arising in the short-term, it does not account for the often irreversible and robust changes in perception that result from long-term, developmental experience. Based on the finding that more frequently experienced stimuli gain greater representations in sensory cortices during development, we reasoned that prior information could be stored in the size of cortical sensory representations. For the case of auditory perception, we use a computational model to show that prior information about sound frequency distributions may be stored in the size of primary auditory cortex frequency representations, read-out by elevated baseline activity in all neurons and combined with sensory-evoked activity to generate a perception that conforms to Bayesian integration theory. Our results suggest an alternative neural mechanism for experience-induced long-term perceptual bias in the context of auditory perception. They make the testable prediction that the extent of such perceptual prior bias is modulated by both the degree of cortical reorganization and the magnitude of spontaneous activity in primary auditory cortex. Given that cortical over-representation of frequently experienced stimuli, as well as perceptual bias towards such stimuli is a common phenomenon across sensory modalities, our model may generalize to sensory perception, rather than being specific to auditory perception.
Heuristics as Bayesian inference under extreme priors.
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.
Can natural selection encode Bayesian priors?
Ramírez, Juan Camilo; Marshall, James A R
2017-08-07
The evolutionary success of many organisms depends on their ability to make decisions based on estimates of the state of their environment (e.g., predation risk) from uncertain information. These decision problems have optimal solutions and individuals in nature are expected to evolve the behavioural mechanisms to make decisions as if using the optimal solutions. Bayesian inference is the optimal method to produce estimates from uncertain data, thus natural selection is expected to favour individuals with the behavioural mechanisms to make decisions as if they were computing Bayesian estimates in typically-experienced environments, although this does not necessarily imply that favoured decision-makers do perform Bayesian computations exactly. Each individual should evolve to behave as if updating a prior estimate of the unknown environment variable to a posterior estimate as it collects evidence. The prior estimate represents the decision-maker's default belief regarding the environment variable, i.e., the individual's default 'worldview' of the environment. This default belief has been hypothesised to be shaped by natural selection and represent the environment experienced by the individual's ancestors. We present an evolutionary model to explore how accurately Bayesian prior estimates can be encoded genetically and shaped by natural selection when decision-makers learn from uncertain information. The model simulates the evolution of a population of individuals that are required to estimate the probability of an event. Every individual has a prior estimate of this probability and collects noisy cues from the environment in order to update its prior belief to a Bayesian posterior estimate with the evidence gained. The prior is inherited and passed on to offspring. Fitness increases with the accuracy of the posterior estimates produced. Simulations show that prior estimates become accurate over evolutionary time. In addition to these 'Bayesian' individuals, we also
Bayesian Prior Probability Distributions for Internal Dosimetry
Energy Technology Data Exchange (ETDEWEB)
Miller, G.; Inkret, W.C.; Little, T.T.; Martz, H.F.; Schillaci, M.E
2001-07-01
The problem of choosing a prior distribution for the Bayesian interpretation of measurements (specifically internal dosimetry measurements) is considered using a theoretical analysis and by examining historical tritium and plutonium urine bioassay data from Los Alamos. Two models for the prior probability distribution are proposed: (1) the log-normal distribution, when there is some additional information to determine the scale of the true result, and (2) the 'alpha' distribution (a simplified variant of the gamma distribution) when there is not. These models have been incorporated into version 3 of the Bayesian internal dosimetric code in use at Los Alamos (downloadable from our web site). Plutonium internal dosimetry at Los Alamos is now being done using prior probability distribution parameters determined self-consistently from population averages of Los Alamos data. (author)
Varying prior information in Bayesian inversion
International Nuclear Information System (INIS)
Walker, Matthew; Curtis, Andrew
2014-01-01
Bayes' rule is used to combine likelihood and prior probability distributions. The former represents knowledge derived from new data, the latter represents pre-existing knowledge; the Bayesian combination is the so-called posterior distribution, representing the resultant new state of knowledge. While varying the likelihood due to differing data observations is common, there are also situations where the prior distribution must be changed or replaced repeatedly. For example, in mixture density neural network (MDN) inversion, using current methods the neural network employed for inversion needs to be retrained every time prior information changes. We develop a method of prior replacement to vary the prior without re-training the network. Thus the efficiency of MDN inversions can be increased, typically by orders of magnitude when applied to geophysical problems. We demonstrate this for the inversion of seismic attributes in a synthetic subsurface geological reservoir model. We also present results which suggest that prior replacement can be used to control the statistical properties (such as variance) of the final estimate of the posterior in more general (e.g., Monte Carlo based) inverse problem solutions. (paper)
On the prior probabilities for two-stage Bayesian estimates
International Nuclear Information System (INIS)
Kohut, P.
1992-01-01
The method of Bayesian inference is reexamined for its applicability and for the required underlying assumptions in obtaining and using prior probability estimates. Two different approaches are suggested to determine the first-stage priors in the two-stage Bayesian analysis which avoid certain assumptions required for other techniques. In the first scheme, the prior is obtained through a true frequency based distribution generated at selected intervals utilizing actual sampling of the failure rate distributions. The population variability distribution is generated as the weighed average of the frequency distributions. The second method is based on a non-parametric Bayesian approach using the Maximum Entropy Principle. Specific features such as integral properties or selected parameters of prior distributions may be obtained with minimal assumptions. It is indicated how various quantiles may also be generated with a least square technique
Prior Sensitivity Analysis in Default Bayesian Structural Equation Modeling.
van Erp, Sara; Mulder, Joris; Oberski, Daniel L
2017-11-27
Bayesian structural equation modeling (BSEM) has recently gained popularity because it enables researchers to fit complex models and solve some of the issues often encountered in classical maximum likelihood estimation, such as nonconvergence and inadmissible solutions. An important component of any Bayesian analysis is the prior distribution of the unknown model parameters. Often, researchers rely on default priors, which are constructed in an automatic fashion without requiring substantive prior information. However, the prior can have a serious influence on the estimation of the model parameters, which affects the mean squared error, bias, coverage rates, and quantiles of the estimates. In this article, we investigate the performance of three different default priors: noninformative improper priors, vague proper priors, and empirical Bayes priors-with the latter being novel in the BSEM literature. Based on a simulation study, we find that these three default BSEM methods may perform very differently, especially with small samples. A careful prior sensitivity analysis is therefore needed when performing a default BSEM analysis. For this purpose, we provide a practical step-by-step guide for practitioners to conducting a prior sensitivity analysis in default BSEM. Our recommendations are illustrated using a well-known case study from the structural equation modeling literature, and all code for conducting the prior sensitivity analysis is available in the online supplemental materials. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Bayesian genomic selection: the effect of haplotype lenghts and priors
DEFF Research Database (Denmark)
Villumsen, Trine Michelle; Janss, Luc
2009-01-01
Breeding values for animals with marker data are estimated using a genomic selection approach where data is analyzed using Bayesian multi-marker association models. Fourteen model scenarios with varying haplotype lengths, hyper parameter and prior distributions were compared to find the scenario ...
Bayesian nonparametric system reliability using sets of priors
Walter, G.M.; Aslett, L.J.M.; Coolen, F.P.A.
2016-01-01
An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through bounds on the functioning probability. Given component level test
On Bayesian reliability analysis with informative priors and censoring
International Nuclear Information System (INIS)
Coolen, F.P.A.
1996-01-01
In the statistical literature many methods have been presented to deal with censored observations, both within the Bayesian and non-Bayesian frameworks, and such methods have been successfully applied to, e.g., reliability problems. Also, in reliability theory it is often emphasized that, through shortage of statistical data and possibilities for experiments, one often needs to rely heavily on judgements of engineers, or other experts, for which means Bayesian methods are attractive. It is therefore important that such judgements can be elicited easily to provide informative prior distributions that reflect the knowledge of the engineers well. In this paper we focus on this aspect, especially on the situation that the judgements of the consulted engineers are based on experiences in environments where censoring has also been present previously. We suggest the use of the attractive interpretation of hyperparameters of conjugate prior distributions when these are available for assumed parametric models for lifetimes, and we show how one may go beyond the standard conjugate priors, using similar interpretations of hyper-parameters, to enable easier elicitation when censoring has been present in the past. This may even lead to more flexibility for modelling prior knowledge than when using standard conjugate priors, whereas the disadvantage of more complicated calculations that may be needed to determine posterior distributions play a minor role due to the advanced mathematical and statistical software that is widely available these days
Logarithmic Laplacian Prior Based Bayesian Inverse Synthetic Aperture Radar Imaging.
Zhang, Shuanghui; Liu, Yongxiang; Li, Xiang; Bi, Guoan
2016-04-28
This paper presents a novel Inverse Synthetic Aperture Radar Imaging (ISAR) algorithm based on a new sparse prior, known as the logarithmic Laplacian prior. The newly proposed logarithmic Laplacian prior has a narrower main lobe with higher tail values than the Laplacian prior, which helps to achieve performance improvement on sparse representation. The logarithmic Laplacian prior is used for ISAR imaging within the Bayesian framework to achieve better focused radar image. In the proposed method of ISAR imaging, the phase errors are jointly estimated based on the minimum entropy criterion to accomplish autofocusing. The maximum a posterior (MAP) estimation and the maximum likelihood estimation (MLE) are utilized to estimate the model parameters to avoid manually tuning process. Additionally, the fast Fourier Transform (FFT) and Hadamard product are used to minimize the required computational efficiency. Experimental results based on both simulated and measured data validate that the proposed algorithm outperforms the traditional sparse ISAR imaging algorithms in terms of resolution improvement and noise suppression.
Bayesian Image Segmentations by Potts Prior and Loopy Belief Propagation
Tanaka, Kazuyuki; Kataoka, Shun; Yasuda, Muneki; Waizumi, Yuji; Hsu, Chiou-Ting
2014-12-01
This paper presents a Bayesian image segmentation model based on Potts prior and loopy belief propagation. The proposed Bayesian model involves several terms, including the pairwise interactions of Potts models, and the average vectors and covariant matrices of Gauss distributions in color image modeling. These terms are often referred to as hyperparameters in statistical machine learning theory. In order to determine these hyperparameters, we propose a new scheme for hyperparameter estimation based on conditional maximization of entropy in the Potts prior. The algorithm is given based on loopy belief propagation. In addition, we compare our conditional maximum entropy framework with the conventional maximum likelihood framework, and also clarify how the first order phase transitions in loopy belief propagations for Potts models influence our hyperparameter estimation procedures.
An Adaptively Accelerated Bayesian Deblurring Method with Entropy Prior
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Yong-Hoon Kim
2008-05-01
Full Text Available The development of an efficient adaptively accelerated iterative deblurring algorithm based on Bayesian statistical concept has been reported. Entropy of an image has been used as a Ã¢Â€ÂœpriorÃ¢Â€Â distribution and instead of additive form, used in conventional acceleration methods an exponent form of relaxation constant has been used for acceleration. Thus the proposed method is called hereafter as adaptively accelerated maximum a posteriori with entropy prior (AAMAPE. Based on empirical observations in different experiments, the exponent is computed adaptively using first-order derivatives of the deblurred image from previous two iterations. This exponent improves speed of the AAMAPE method in early stages and ensures stability at later stages of iteration. In AAMAPE method, we also consider the constraint of the nonnegativity and flux conservation. The paper discusses the fundamental idea of the Bayesian image deblurring with the use of entropy as prior, and the analytical analysis of superresolution and the noise amplification characteristics of the proposed method. The experimental results show that the proposed AAMAPE method gives lower RMSE and higher SNR in 44% lesser iterations as compared to nonaccelerated maximum a posteriori with entropy prior (MAPE method. Moreover, AAMAPE followed by wavelet wiener filtering gives better result than the state-of-the-art methods.
Learning priors for Bayesian computations in the nervous system.
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Max Berniker
Full Text Available Our nervous system continuously combines new information from our senses with information it has acquired throughout life. Numerous studies have found that human subjects manage this by integrating their observations with their previous experience (priors in a way that is close to the statistical optimum. However, little is known about the way the nervous system acquires or learns priors. Here we present results from experiments where the underlying distribution of target locations in an estimation task was switched, manipulating the prior subjects should use. Our experimental design allowed us to measure a subject's evolving prior while they learned. We confirm that through extensive practice subjects learn the correct prior for the task. We found that subjects can rapidly learn the mean of a new prior while the variance is learned more slowly and with a variable learning rate. In addition, we found that a Bayesian inference model could predict the time course of the observed learning while offering an intuitive explanation for the findings. The evidence suggests the nervous system continuously updates its priors to enable efficient behavior.
Prior processes and their applications nonparametric Bayesian estimation
Phadia, Eswar G
2016-01-01
This book presents a systematic and comprehensive treatment of various prior processes that have been developed over the past four decades for dealing with Bayesian approach to solving selected nonparametric inference problems. This revised edition has been substantially expanded to reflect the current interest in this area. After an overview of different prior processes, it examines the now pre-eminent Dirichlet process and its variants including hierarchical processes, then addresses new processes such as dependent Dirichlet, local Dirichlet, time-varying and spatial processes, all of which exploit the countable mixture representation of the Dirichlet process. It subsequently discusses various neutral to right type processes, including gamma and extended gamma, beta and beta-Stacy processes, and then describes the Chinese Restaurant, Indian Buffet and infinite gamma-Poisson processes, which prove to be very useful in areas such as machine learning, information retrieval and featural modeling. Tailfree and P...
Logarithmic Laplacian Prior Based Bayesian Inverse Synthetic Aperture Radar Imaging
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Shuanghui Zhang
2016-04-01
Full Text Available This paper presents a novel Inverse Synthetic Aperture Radar Imaging (ISAR algorithm based on a new sparse prior, known as the logarithmic Laplacian prior. The newly proposed logarithmic Laplacian prior has a narrower main lobe with higher tail values than the Laplacian prior, which helps to achieve performance improvement on sparse representation. The logarithmic Laplacian prior is used for ISAR imaging within the Bayesian framework to achieve better focused radar image. In the proposed method of ISAR imaging, the phase errors are jointly estimated based on the minimum entropy criterion to accomplish autofocusing. The maximum a posterior (MAP estimation and the maximum likelihood estimation (MLE are utilized to estimate the model parameters to avoid manually tuning process. Additionally, the fast Fourier Transform (FFT and Hadamard product are used to minimize the required computational efficiency. Experimental results based on both simulated and measured data validate that the proposed algorithm outperforms the traditional sparse ISAR imaging algorithms in terms of resolution improvement and noise suppression.
Bayesian inference from count data using discrete uniform priors.
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Federico Comoglio
Full Text Available We consider a set of sample counts obtained by sampling arbitrary fractions of a finite volume containing an homogeneously dispersed population of identical objects. We report a Bayesian derivation of the posterior probability distribution of the population size using a binomial likelihood and non-conjugate, discrete uniform priors under sampling with or without replacement. Our derivation yields a computationally feasible formula that can prove useful in a variety of statistical problems involving absolute quantification under uncertainty. We implemented our algorithm in the R package dupiR and compared it with a previously proposed Bayesian method based on a Gamma prior. As a showcase, we demonstrate that our inference framework can be used to estimate bacterial survival curves from measurements characterized by extremely low or zero counts and rather high sampling fractions. All in all, we provide a versatile, general purpose algorithm to infer population sizes from count data, which can find application in a broad spectrum of biological and physical problems.
Bayesian Model Comparison With the g-Prior
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Cemgil, Ali Taylan
2014-01-01
’s asymptotic MAP rule was an improvement, and in this paper we extend the work by Djuric in several ways. Speciﬁcally, we consider the elicitation of proper prior distributions, treat the case of real- and complex-valued data simultaneously in a Bayesian framework similar to that considered by Djuric......, and develop new model selection rules for a regression model containing both linear and non-linear parameters. Moreover, we use this framework to give a new interpretation of the popular information criteria and relate their performance to the signal-to-noise ratio of the data. By use of simulations, we also...... demonstrate that our proposed model comparison and selection rules outperform the traditional information criteria both in terms of detecting the true model and in terms of predicting unobserved data. The simulation code is available online....
Comparing nonparametric Bayesian tree priors for clonal reconstruction of tumors.
Deshwar, Amit G; Vembu, Shankar; Morris, Quaid
2015-01-01
Statistical machine learning methods, especially nonparametric Bayesian methods, have become increasingly popular to infer clonal population structure of tumors. Here we describe the treeCRP, an extension of the Chinese restaurant process (CRP), a popular construction used in nonparametric mixture models, to infer the phylogeny and genotype of major subclonal lineages represented in the population of cancer cells. We also propose new split-merge updates tailored to the subclonal reconstruction problem that improve the mixing time of Markov chains. In comparisons with the tree-structured stick breaking prior used in PhyloSub, we demonstrate superior mixing and running time using the treeCRP with our new split-merge procedures. We also show that given the same number of samples, TSSB and treeCRP have similar ability to recover the subclonal structure of a tumor…
Walter, G.M.; Augustin, Th.; Kneib, Thomas; Tutz, Gerhard
2010-01-01
The paper is concerned with Bayesian analysis under prior-data conflict, i.e. the situation when observed data are rather unexpected under the prior (and the sample size is not large enough to eliminate the influence of the prior). Two approaches for Bayesian linear regression modeling based on
Prior approval: the growth of Bayesian methods in psychology.
Andrews, Mark; Baguley, Thom
2013-02-01
Within the last few years, Bayesian methods of data analysis in psychology have proliferated. In this paper, we briefly review the history or the Bayesian approach to statistics, and consider the implications that Bayesian methods have for the theory and practice of data analysis in psychology.
Walter, G.
2015-01-01
In the Bayesian approach to statistical inference, possibly subjective knowledge on model parameters can be expressed by so-called prior distributions. A prior distribution is updated, via Bayes’ Rule, to the so-called posterior distribution, which combines prior information and information from
Bayesian optimal experimental design for priors of compact support
Long, Quan
2016-01-08
In this study, we optimize the experimental setup computationally by optimal experimental design (OED) in a Bayesian framework. We approximate the posterior probability density functions (pdf) using truncated Gaussian distributions in order to account for the bounded domain of the uniform prior pdf of the parameters. The underlying Gaussian distribution is obtained in the spirit of the Laplace method, more precisely, the mode is chosen as the maximum a posteriori (MAP) estimate, and the covariance is chosen as the negative inverse of the Hessian of the misfit function at the MAP estimate. The model related entities are obtained from a polynomial surrogate. The optimality, quantified by the information gain measures, can be estimated efficiently by a rejection sampling algorithm against the underlying Gaussian probability distribution, rather than against the true posterior. This approach offers a significant error reduction when the magnitude of the invariants of the posterior covariance are comparable to the size of the bounded domain of the prior. We demonstrate the accuracy and superior computational efficiency of our method for shock-tube experiments aiming to measure the model parameters of a key reaction which is part of the complex kinetic network describing the hydrocarbon oxidation. In the experiments, the initial temperature and fuel concentration are optimized with respect to the expected information gain in the estimation of the parameters of the target reaction rate. We show that the expected information gain surface can change its shape dramatically according to the level of noise introduced into the synthetic data. The information that can be extracted from the data saturates as a logarithmic function of the number of experiments, and few experiments are needed when they are conducted at the optimal experimental design conditions.
Bušs, Ginters
2009-01-01
Bayesian inference requires an analyst to set priors. Setting the right prior is crucial for precise forecasts. This paper analyzes how optimal prior changes when an economy is hit by a recession. For this task, an autoregressive distributed lag (ADL) model is chosen. The results show that a sharp economic slowdown changes the optimal prior in two directions. First, it changes the structure of the optimal weight prior, setting smaller weight on the lagged dependent variable compared to varia...
Directory of Open Access Journals (Sweden)
Xia Lei
2010-12-01
Full Text Available General multi-objective optimization methods are hard to obtain prior information, how to utilize prior information has been a challenge. This paper analyzes the characteristics of Bayesian decision-making based on maximum entropy principle and prior information, especially in case that how to effectively improve decision-making reliability in deficiency of reference samples. The paper exhibits effectiveness of the proposed method using the real application of multi-frequency offset estimation in distributed multiple-input multiple-output system. The simulation results demonstrate Bayesian decision-making based on prior information has better global searching capability when sampling data is deficient.
Bayesian Image Restoration Using a Large-Scale Total Patch Variation Prior
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Yang Chen
2011-01-01
Full Text Available Edge-preserving Bayesian restorations using nonquadratic priors are often inefficient in restoring continuous variations and tend to produce block artifacts around edges in ill-posed inverse image restorations. To overcome this, we have proposed a spatial adaptive (SA prior with improved performance. However, this SA prior restoration suffers from high computational cost and the unguaranteed convergence problem. Concerning these issues, this paper proposes a Large-scale Total Patch Variation (LS-TPV Prior model for Bayesian image restoration. In this model, the prior for each pixel is defined as a singleton conditional probability, which is in a mixture prior form of one patch similarity prior and one weight entropy prior. A joint MAP estimation is thus built to ensure the iteration monotonicity. The intensive calculation of patch distances is greatly alleviated by the parallelization of Compute Unified Device Architecture(CUDA. Experiments with both simulated and real data validate the good performance of the proposed restoration.
Adaptive nonparametric Bayesian inference using location-scale mixture priors
Jonge, de R.; Zanten, van J.H.
2010-01-01
We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptive procedure can be obtained if the prior is properly constructed. In particular, we show that adaptation is achieved if
Bayesian Inference for Structured Spike and Slab Priors
DEFF Research Database (Denmark)
Andersen, Michael Riis; Winther, Ole; Hansen, Lars Kai
2014-01-01
Sparse signal recovery addresses the problem of solving underdetermined linear inverse problems subject to a sparsity constraint. We propose a novel prior formulation, the structured spike and slab prior, which allows to incorporate a priori knowledge of the sparsity pattern by imposing a spatial...
Bayesian optimal experimental design for priors of compact support
Long, Quan
2016-01-01
to account for the bounded domain of the uniform prior pdf of the parameters. The underlying Gaussian distribution is obtained in the spirit of the Laplace method, more precisely, the mode is chosen as the maximum a posteriori (MAP) estimate
Uncertainty plus prior equals rational bias: an intuitive Bayesian probability weighting function.
Fennell, John; Baddeley, Roland
2012-10-01
Empirical research has shown that when making choices based on probabilistic options, people behave as if they overestimate small probabilities, underestimate large probabilities, and treat positive and negative outcomes differently. These distortions have been modeled using a nonlinear probability weighting function, which is found in several nonexpected utility theories, including rank-dependent models and prospect theory; here, we propose a Bayesian approach to the probability weighting function and, with it, a psychological rationale. In the real world, uncertainty is ubiquitous and, accordingly, the optimal strategy is to combine probability statements with prior information using Bayes' rule. First, we show that any reasonable prior on probabilities leads to 2 of the observed effects; overweighting of low probabilities and underweighting of high probabilities. We then investigate 2 plausible kinds of priors: informative priors based on previous experience and uninformative priors of ignorance. Individually, these priors potentially lead to large problems of bias and inefficiency, respectively; however, when combined using Bayesian model comparison methods, both forms of prior can be applied adaptively, gaining the efficiency of empirical priors and the robustness of ignorance priors. We illustrate this for the simple case of generic good and bad options, using Internet blogs to estimate the relevant priors of inference. Given this combined ignorant/informative prior, the Bayesian probability weighting function is not only robust and efficient but also matches all of the major characteristics of the distortions found in empirical research. PsycINFO Database Record (c) 2012 APA, all rights reserved.
Imprecision and prior-data conflict in generalized Bayesian inference
Walter, Gero; Augustin, T. (Thomas)
2009-01-01
A great advantage of imprecise probability models over models based on precise, traditional probabilities is the potential to reflect the amount of knowledge they stand for. Consequently, imprecise probability models promise to offer a vivid tool for handling situations of prior-data conflict in
Gustafsson, Mats G; Wallman, Mikael; Wickenberg Bolin, Ulrika; Göransson, Hanna; Fryknäs, M; Andersson, Claes R; Isaksson, Anders
2010-06-01
Successful use of classifiers that learn to make decisions from a set of patient examples require robust methods for performance estimation. Recently many promising approaches for determination of an upper bound for the error rate of a single classifier have been reported but the Bayesian credibility interval (CI) obtained from a conventional holdout test still delivers one of the tightest bounds. The conventional Bayesian CI becomes unacceptably large in real world applications where the test set sizes are less than a few hundred. The source of this problem is that fact that the CI is determined exclusively by the result on the test examples. In other words, there is no information at all provided by the uniform prior density distribution employed which reflects complete lack of prior knowledge about the unknown error rate. Therefore, the aim of the study reported here was to study a maximum entropy (ME) based approach to improved prior knowledge and Bayesian CIs, demonstrating its relevance for biomedical research and clinical practice. It is demonstrated how a refined non-uniform prior density distribution can be obtained by means of the ME principle using empirical results from a few designs and tests using non-overlapping sets of examples. Experimental results show that ME based priors improve the CIs when employed to four quite different simulated and two real world data sets. An empirically derived ME prior seems promising for improving the Bayesian CI for the unknown error rate of a designed classifier. Copyright 2010 Elsevier B.V. All rights reserved.
Sparse Estimation Using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models
DEFF Research Database (Denmark)
Pedersen, Niels Lovmand; Manchón, Carles Navarro; Badiu, Mihai Alin
2015-01-01
In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued m......In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex...... error, and robustness in low and medium signal-to-noise ratio regimes....
Fletcher, B. C.
1972-01-01
The critical point of any Bayesian analysis concerns the choice and quantification of the prior information. The effects of prior data on a Bayesian analysis are studied. Comparisons of the maximum likelihood estimator, the Bayesian estimator, and the known failure rate are presented. The results of the many simulated trails are then analyzed to show the region of criticality for prior information being supplied to the Bayesian estimator. In particular, effects of prior mean and variance are determined as a function of the amount of test data available.
Saputro, D. R. S.; Amalia, F.; Widyaningsih, P.; Affan, R. C.
2018-05-01
Bayesian method is a method that can be used to estimate the parameters of multivariate multiple regression model. Bayesian method has two distributions, there are prior and posterior distributions. Posterior distribution is influenced by the selection of prior distribution. Jeffreys’ prior distribution is a kind of Non-informative prior distribution. This prior is used when the information about parameter not available. Non-informative Jeffreys’ prior distribution is combined with the sample information resulting the posterior distribution. Posterior distribution is used to estimate the parameter. The purposes of this research is to estimate the parameters of multivariate regression model using Bayesian method with Non-informative Jeffreys’ prior distribution. Based on the results and discussion, parameter estimation of β and Σ which were obtained from expected value of random variable of marginal posterior distribution function. The marginal posterior distributions for β and Σ are multivariate normal and inverse Wishart. However, in calculation of the expected value involving integral of a function which difficult to determine the value. Therefore, approach is needed by generating of random samples according to the posterior distribution characteristics of each parameter using Markov chain Monte Carlo (MCMC) Gibbs sampling algorithm.
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Tabassum Naz Sindhu
2017-03-01
Full Text Available This study deals with Bayesian analysis of shifted Gompertz mixture model under type-I censored samples assuming both informative and noninformative priors. We have discussed the Bayesian estimation of parameters of shifted Gompertz mixture model under the uniform, and gamma priors assuming three loss functions. Further, some properties of the model with some graphs of the mixture density are discussed. These properties include Bayes estimators, posterior risks and reliability function under simulation scheme. Bayes estimates are obtained considering two cases: (a when the shape parameter is known and (b when all parameters are unknown. We analyzed some simulated sets in order to investigate the effect of prior belief, loss functions, and performance of the proposed set of estimators of the mixture model parameters.
Calibrated birth-death phylogenetic time-tree priors for bayesian inference.
Heled, Joseph; Drummond, Alexei J
2015-05-01
Here we introduce a general class of multiple calibration birth-death tree priors for use in Bayesian phylogenetic inference. All tree priors in this class separate ancestral node heights into a set of "calibrated nodes" and "uncalibrated nodes" such that the marginal distribution of the calibrated nodes is user-specified whereas the density ratio of the birth-death prior is retained for trees with equal values for the calibrated nodes. We describe two formulations, one in which the calibration information informs the prior on ranked tree topologies, through the (conditional) prior, and the other which factorizes the prior on divergence times and ranked topologies, thus allowing uniform, or any arbitrary prior distribution on ranked topologies. Although the first of these formulations has some attractive properties, the algorithm we present for computing its prior density is computationally intensive. However, the second formulation is always faster and computationally efficient for up to six calibrations. We demonstrate the utility of the new class of multiple-calibration tree priors using both small simulations and a real-world analysis and compare the results to existing schemes. The two new calibrated tree priors described in this article offer greater flexibility and control of prior specification in calibrated time-tree inference and divergence time dating, and will remove the need for indirect approaches to the assessment of the combined effect of calibration densities and tree priors in Bayesian phylogenetic inference. © The Author(s) 2014. Published by Oxford University Press, on behalf of the Society of Systematic Biologists.
Prior elicitation and Bayesian analysis of the Steroids for Corneal Ulcers Trial.
See, Craig W; Srinivasan, Muthiah; Saravanan, Somu; Oldenburg, Catherine E; Esterberg, Elizabeth J; Ray, Kathryn J; Glaser, Tanya S; Tu, Elmer Y; Zegans, Michael E; McLeod, Stephen D; Acharya, Nisha R; Lietman, Thomas M
2012-12-01
To elicit expert opinion on the use of adjunctive corticosteroid therapy in bacterial corneal ulcers. To perform a Bayesian analysis of the Steroids for Corneal Ulcers Trial (SCUT), using expert opinion as a prior probability. The SCUT was a placebo-controlled trial assessing visual outcomes in patients receiving topical corticosteroids or placebo as adjunctive therapy for bacterial keratitis. Questionnaires were conducted at scientific meetings in India and North America to gauge expert consensus on the perceived benefit of corticosteroids as adjunct treatment. Bayesian analysis, using the questionnaire data as a prior probability and the primary outcome of SCUT as a likelihood, was performed. For comparison, an additional Bayesian analysis was performed using the results of the SCUT pilot study as a prior distribution. Indian respondents believed there to be a 1.21 Snellen line improvement, and North American respondents believed there to be a 1.24 line improvement with corticosteroid therapy. The SCUT primary outcome found a non-significant 0.09 Snellen line benefit with corticosteroid treatment. The results of the Bayesian analysis estimated a slightly greater benefit than did the SCUT primary analysis (0.19 lines verses 0.09 lines). Indian and North American experts had similar expectations on the effectiveness of corticosteroids in bacterial corneal ulcers; that corticosteroids would markedly improve visual outcomes. Bayesian analysis produced results very similar to those produced by the SCUT primary analysis. The similarity in result is likely due to the large sample size of SCUT and helps validate the results of SCUT.
Jiang, Yu; Simon, Steve; Mayo, Matthew S; Gajewski, Byron J
2015-02-20
Slow recruitment in clinical trials leads to increased costs and resource utilization, which includes both the clinic staff and patient volunteers. Careful planning and monitoring of the accrual process can prevent the unnecessary loss of these resources. We propose two hierarchical extensions to the existing Bayesian constant accrual model: the accelerated prior and the hedging prior. The new proposed priors are able to adaptively utilize the researcher's previous experience and current accrual data to produce the estimation of trial completion time. The performance of these models, including prediction precision, coverage probability, and correct decision-making ability, is evaluated using actual studies from our cancer center and simulation. The results showed that a constant accrual model with strongly informative priors is very accurate when accrual is on target or slightly off, producing smaller mean squared error, high percentage of coverage, and a high number of correct decisions as to whether or not continue the trial, but it is strongly biased when off target. Flat or weakly informative priors provide protection against an off target prior but are less efficient when the accrual is on target. The accelerated prior performs similar to a strong prior. The hedging prior performs much like the weak priors when the accrual is extremely off target but closer to the strong priors when the accrual is on target or only slightly off target. We suggest improvements in these models and propose new models for future research. Copyright © 2014 John Wiley & Sons, Ltd.
BAYESIAN ANALYSIS FOR THE PAIRED COMPARISON MODEL WITH ORDER EFFECTS (USING NON-INFORMATIVE PRIORS
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Ghausia Masood Gilani
2008-07-01
Full Text Available Sometimes it may be difficult for a panelist to rank or compare more than two objects or treatments at the same time. For this reason, paired comparison method is used. In this study, the Davidson and Beaver (1977 model for paired comparisons with order effects is analyzed through the Bayesian Approach. For this purpose, the posterior means and the posterior modes are compared using the noninformative priors.
Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics
Abe, Sumiyoshi
2014-11-01
The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach to systems governed by dynamics with largely separated time scales and is based on three key concepts: conjugate pairs of variables, dimensionless integration measures with coarse-graining factors and partial maximization of the joint entropy. The method enables one to calculate a prior purely from a likelihood in a simple way. It is shown, in particular, how it not only yields Jeffreys's rules but also reveals new structures hidden behind them.
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Gao Shouguo
2011-08-01
Full Text Available Abstract Background Bayesian Network (BN is a powerful approach to reconstructing genetic regulatory networks from gene expression data. However, expression data by itself suffers from high noise and lack of power. Incorporating prior biological knowledge can improve the performance. As each type of prior knowledge on its own may be incomplete or limited by quality issues, integrating multiple sources of prior knowledge to utilize their consensus is desirable. Results We introduce a new method to incorporate the quantitative information from multiple sources of prior knowledge. It first uses the Naïve Bayesian classifier to assess the likelihood of functional linkage between gene pairs based on prior knowledge. In this study we included cocitation in PubMed and schematic similarity in Gene Ontology annotation. A candidate network edge reservoir is then created in which the copy number of each edge is proportional to the estimated likelihood of linkage between the two corresponding genes. In network simulation the Markov Chain Monte Carlo sampling algorithm is adopted, and samples from this reservoir at each iteration to generate new candidate networks. We evaluated the new algorithm using both simulated and real gene expression data including that from a yeast cell cycle and a mouse pancreas development/growth study. Incorporating prior knowledge led to a ~2 fold increase in the number of known transcription regulations recovered, without significant change in false positive rate. In contrast, without the prior knowledge BN modeling is not always better than a random selection, demonstrating the necessity in network modeling to supplement the gene expression data with additional information. Conclusion our new development provides a statistical means to utilize the quantitative information in prior biological knowledge in the BN modeling of gene expression data, which significantly improves the performance.
Marcoulides, Katerina M.
2018-01-01
This study examined the use of Bayesian analysis methods for the estimation of item parameters in a two-parameter logistic item response theory model. Using simulated data under various design conditions with both informative and non-informative priors, the parameter recovery of Bayesian analysis methods were examined. Overall results showed that…
Gamma prior distribution selection for Bayesian analysis of failure rate and reliability
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Waler, R.A.; Johnson, M.M.; Waterman, M.S.; Martz, H.F. Jr.
1977-01-01
It is assumed that the phenomenon under study is such that the time-to-failure may be modeled by an exponential distribution with failure-rate parameter, lambda. For Bayesian analyses of the assumed model, the family of gamma distributions provides conjugate prior models for lambda. Thus, an experimenter needs to select a particular gamma model to conduct a Bayesian reliability analysis. The purpose of this paper is to present a methodology which can be used to translate engineering information, experience, and judgment into a choice of a gamma prior distribution. The proposed methodology assumes that the practicing engineer can provide percentile data relating to either the failure rate or the reliability of the phenomenon being investigated. For example, the methodology will select the gamma prior distribution which conveys an engineer's belief that the failure rate, lambda, simultaneously satisfies the probability statements, P(lambda less than 1.0 x 10 -3 ) = 0.50 and P(lambda less than 1.0 x 10 -5 ) = 0.05. That is, two percentiles provided by an engineer are used to determine a gamma prior model which agrees with the specified percentiles. For those engineers who prefer to specify reliability percentiles rather than the failure-rate percentiles illustrated above, one can use the induced negative-log gamma prior distribution which satisfies the probability statements, P(R(t 0 ) less than 0.99) = 0.50 and P(R(t 0 ) less than 0.99999) = 0.95 for some operating time t 0 . Also, the paper includes graphs for selected percentiles which assist an engineer in applying the methodology
Gamma prior distribution selection for Bayesian analysis of failure rate and reliability
International Nuclear Information System (INIS)
Waller, R.A.; Johnson, M.M.; Waterman, M.S.; Martz, H.F. Jr.
1976-07-01
It is assumed that the phenomenon under study is such that the time-to-failure may be modeled by an exponential distribution with failure rate lambda. For Bayesian analyses of the assumed model, the family of gamma distributions provides conjugate prior models for lambda. Thus, an experimenter needs to select a particular gamma model to conduct a Bayesian reliability analysis. The purpose of this report is to present a methodology that can be used to translate engineering information, experience, and judgment into a choice of a gamma prior distribution. The proposed methodology assumes that the practicing engineer can provide percentile data relating to either the failure rate or the reliability of the phenomenon being investigated. For example, the methodology will select the gamma prior distribution which conveys an engineer's belief that the failure rate lambda simultaneously satisfies the probability statements, P(lambda less than 1.0 x 10 -3 ) equals 0.50 and P(lambda less than 1.0 x 10 -5 ) equals 0.05. That is, two percentiles provided by an engineer are used to determine a gamma prior model which agrees with the specified percentiles. For those engineers who prefer to specify reliability percentiles rather than the failure rate percentiles illustrated above, it is possible to use the induced negative-log gamma prior distribution which satisfies the probability statements, P(R(t 0 ) less than 0.99) equals 0.50 and P(R(t 0 ) less than 0.99999) equals 0.95, for some operating time t 0 . The report also includes graphs for selected percentiles which assist an engineer in applying the procedure. 28 figures, 16 tables
Bayesian image reconstruction in SPECT using higher order mechanical models as priors
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Lee, S.J.; Gindi, G.; Rangarajan, A.
1995-01-01
While the ML-EM (maximum-likelihood-expectation maximization) algorithm for reconstruction for emission tomography is unstable due to the ill-posed nature of the problem, Bayesian reconstruction methods overcome this instability by introducing prior information, often in the form of a spatial smoothness regularizer. More elaborate forms of smoothness constraints may be used to extend the role of the prior beyond that of a stabilizer in order to capture actual spatial information about the object. Previously proposed forms of such prior distributions were based on the assumption of a piecewise constant source distribution. Here, the authors propose an extension to a piecewise linear model--the weak plate--which is more expressive than the piecewise constant model. The weak plate prior not only preserves edges but also allows for piecewise ramplike regions in the reconstruction. Indeed, for the application in SPECT, such ramplike regions are observed in ground-truth source distributions in the form of primate autoradiographs of rCBF radionuclides. To incorporate the weak plate prior in a MAP approach, the authors model the prior as a Gibbs distribution and use a GEM formulation for the optimization. They compare quantitative performance of the ML-EM algorithm, a GEM algorithm with a prior favoring piecewise constant regions, and a GEM algorithm with the weak plate prior. Pointwise and regional bias and variance of ensemble image reconstructions are used as indications of image quality. The results show that the weak plate and membrane priors exhibit improved bias and variance relative to ML-EM techniques
Youngs, Noah; Penfold-Brown, Duncan; Drew, Kevin; Shasha, Dennis; Bonneau, Richard
2013-05-01
Computational biologists have demonstrated the utility of using machine learning methods to predict protein function from an integration of multiple genome-wide data types. Yet, even the best performing function prediction algorithms rely on heuristics for important components of the algorithm, such as choosing negative examples (proteins without a given function) or determining key parameters. The improper choice of negative examples, in particular, can hamper the accuracy of protein function prediction. We present a novel approach for choosing negative examples, using a parameterizable Bayesian prior computed from all observed annotation data, which also generates priors used during function prediction. We incorporate this new method into the GeneMANIA function prediction algorithm and demonstrate improved accuracy of our algorithm over current top-performing function prediction methods on the yeast and mouse proteomes across all metrics tested. Code and Data are available at: http://bonneaulab.bio.nyu.edu/funcprop.html
Impact of Bayesian Priors on the Characterization of Binary Black Hole Coalescences.
Vitale, Salvatore; Gerosa, Davide; Haster, Carl-Johan; Chatziioannou, Katerina; Zimmerman, Aaron
2017-12-22
In a regime where data are only mildly informative, prior choices can play a significant role in Bayesian statistical inference, potentially affecting the inferred physics. We show this is indeed the case for some of the parameters inferred from current gravitational-wave measurements of binary black hole coalescences. We reanalyze the first detections performed by the twin LIGO interferometers using alternative (and astrophysically motivated) prior assumptions. We find different prior distributions can introduce deviations in the resulting posteriors that impact the physical interpretation of these systems. For instance, (i) limits on the 90% credible interval on the effective black hole spin χ_{eff} are subject to variations of ∼10% if a prior with black hole spins mostly aligned to the binary's angular momentum is considered instead of the standard choice of isotropic spin directions, and (ii) under priors motivated by the initial stellar mass function, we infer tighter constraints on the black hole masses, and in particular, we find no support for any of the inferred masses within the putative mass gap M≲5 M_{⊙}.
A NOVEL TECHNIQUE TO IMPROVE PHOTOMETRY IN CONFUSED IMAGES USING GRAPHS AND BAYESIAN PRIORS
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Safarzadeh, Mohammadtaher; Ferguson, Henry C.; Lu, Yu; Inami, Hanae; Somerville, Rachel S.
2015-01-01
We present a new technique for overcoming confusion noise in deep far-infrared Herschel space telescope images making use of prior information from shorter λ < 2 μm wavelengths. For the deepest images obtained by Herschel, the flux limit due to source confusion is about a factor of three brighter than the flux limit due to instrumental noise and (smooth) sky background. We have investigated the possibility of de-confusing simulated Herschel PACS 160 μm images by using strong Bayesian priors on the positions and weak priors on the flux of sources. We find the blended sources and group them together and simultaneously fit their fluxes. We derive the posterior probability distribution function of fluxes subject to these priors through Monte Carlo Markov Chain (MCMC) sampling by fitting the image. Assuming we can predict the FIR flux of sources based on the ultraviolet-optical part of their SEDs to within an order of magnitude, the simulations show that we can obtain reliable fluxes and uncertainties at least a factor of three fainter than the confusion noise limit of 3σ c = 2.7 mJy in our simulated PACS-160 image. This technique could in principle be used to mitigate the effects of source confusion in any situation where one has prior information of positions and plausible fluxes of blended sources. For Herschel, application of this technique will improve our ability to constrain the dust content in normal galaxies at high redshift
Using Tranformation Group Priors and Maximum Relative Entropy for Bayesian Glaciological Inversions
Arthern, R. J.; Hindmarsh, R. C. A.; Williams, C. R.
2014-12-01
One of the key advances that has allowed better simulations of the large ice sheets of Greenland and Antarctica has been the use of inverse methods. These have allowed poorly known parameters such as the basal drag coefficient and ice viscosity to be constrained using a wide variety of satellite observations. Inverse methods used by glaciologists have broadly followed one of two related approaches. The first is minimization of a cost function that describes the misfit to the observations, often accompanied by some kind of explicit or implicit regularization that promotes smallness or smoothness in the inverted parameters. The second approach is a probabilistic framework that makes use of Bayes' theorem to update prior assumptions about the probability of parameters, making use of data with known error estimates. Both approaches have much in common and questions of regularization often map onto implicit choices of prior probabilities that are made explicit in the Bayesian framework. In both approaches questions can arise that seem to demand subjective input. What should the functional form of the cost function be if there are alternatives? What kind of regularization should be applied, and how much? How should the prior probability distribution for a parameter such as basal slipperiness be specified when we know so little about the details of the subglacial environment? Here we consider some approaches that have been used to address these questions and discuss ways that probabilistic prior information used for regularizing glaciological inversions might be specified with greater objectivity.
Cucchi, K.; Kawa, N.; Hesse, F.; Rubin, Y.
2017-12-01
In order to reduce uncertainty in the prediction of subsurface flow and transport processes, practitioners should use all data available. However, classic inverse modeling frameworks typically only make use of information contained in in-situ field measurements to provide estimates of hydrogeological parameters. Such hydrogeological information about an aquifer is difficult and costly to acquire. In this data-scarce context, the transfer of ex-situ information coming from previously investigated sites can be critical for improving predictions by better constraining the estimation procedure. Bayesian inverse modeling provides a coherent framework to represent such ex-situ information by virtue of the prior distribution and combine them with in-situ information from the target site. In this study, we present an innovative data-driven approach for defining such informative priors for hydrogeological parameters at the target site. Our approach consists in two steps, both relying on statistical and machine learning methods. The first step is data selection; it consists in selecting sites similar to the target site. We use clustering methods for selecting similar sites based on observable hydrogeological features. The second step is data assimilation; it consists in assimilating data from the selected similar sites into the informative prior. We use a Bayesian hierarchical model to account for inter-site variability and to allow for the assimilation of multiple types of site-specific data. We present the application and validation of the presented methods on an established database of hydrogeological parameters. Data and methods are implemented in the form of an open-source R-package and therefore facilitate easy use by other practitioners.
Combining symbolic cues with sensory input and prior experience in an iterative Bayesian framework
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Frederike Hermi Petzschner
2012-08-01
Full Text Available Perception and action are the result of an integration of various sources of information, such as current sensory input, prior experience, or the context in which a stimulus occurs. Often, the interpretation is not trivial hence needs to be learned from the co-occurrence of stimuli. Yet, how do we combine such diverse information to guide our action?Here we use a distance production-reproduction task to investigate the influence of auxiliary, symbolic cues, sensory input, and prior experience on human performance under three different conditions that vary in the information provided. Our results indicate that subjects can (1 learn the mapping of a verbal, symbolic cue onto the stimulus dimension and (2 integrate symbolic information and prior experience into their estimate of displacements.The behavioral results are explained by to two distinct generative models that represent different structural approaches of how a Bayesian observer would combine prior experience, sensory input, and symbolic cue information into a single estimate of displacement. The first model interprets the symbolic cue in the context of categorization, assuming that it reflects information about a distinct underlying stimulus range (categorical model. The second model applies a multi-modal integration approach and treats the symbolic cue as additional sensory input to the system, which is combined with the current sensory measurement and the subjects’ prior experience (cue-combination model. Notably, both models account equally well for the observed behavior despite their different structural assumptions. The present work thus provides evidence that humans can interpret abstract symbolic information and combine it with other types of information such as sensory input and prior experience. The similar explanatory power of the two models further suggest that issues such as categorization and cue-combination could be explained by alternative probabilistic approaches.
International Nuclear Information System (INIS)
Chan, M.T.; Herman, G.T.; Levitan, E.
1996-01-01
We demonstrate that (i) classical methods of image reconstruction from projections can be improved upon by considering the output of such a method as a distorted version of the original image and applying a Bayesian approach to estimate from it the original image (based on a model of distortion and on a Gibbs distribution as the prior) and (ii) by selecting an open-quotes image-modelingclose quotes prior distribution (i.e., one which is such that it is likely that a random sample from it shares important characteristics of the images of the application area) one can improve over another Gibbs prior formulated using only pairwise interactions. We illustrate our approach using simulated Positron Emission Tomography (PET) data from realistic brain phantoms. Since algorithm performance ultimately depends on the diagnostic task being performed. we examine a number of different medically relevant figures of merit to give a fair comparison. Based on a training-and-testing evaluation strategy, we demonstrate that statistically significant improvements can be obtained using the proposed approach
Gong, Maozhen
Selecting an appropriate prior distribution is a fundamental issue in Bayesian Statistics. In this dissertation, under the framework provided by Berger and Bernardo, I derive the reference priors for several models which include: Analysis of Variance (ANOVA)/Analysis of Covariance (ANCOVA) models with a categorical variable under common ordering constraints, the conditionally autoregressive (CAR) models and the simultaneous autoregressive (SAR) models with a spatial autoregression parameter rho considered. The performances of reference priors for ANOVA/ANCOVA models are evaluated by simulation studies with comparisons to Jeffreys' prior and Least Squares Estimation (LSE). The priors are then illustrated in a Bayesian model of the "Risk of Type 2 Diabetes in New Mexico" data, where the relationship between the type 2 diabetes risk (through Hemoglobin A1c) and different smoking levels is investigated. In both simulation studies and real data set modeling, the reference priors that incorporate internal order information show good performances and can be used as default priors. The reference priors for the CAR and SAR models are also illustrated in the "1999 SAT State Average Verbal Scores" data with a comparison to a Uniform prior distribution. Due to the complexity of the reference priors for both CAR and SAR models, only a portion (12 states in the Midwest) of the original data set is considered. The reference priors can give a different marginal posterior distribution compared to a Uniform prior, which provides an alternative for prior specifications for areal data in Spatial statistics.
Apples and oranges: avoiding different priors in Bayesian DNA sequence analysis
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Posch Stefan
2010-03-01
Full Text Available Abstract Background One of the challenges of bioinformatics remains the recognition of short signal sequences in genomic DNA such as donor or acceptor splice sites, splicing enhancers or silencers, translation initiation sites, transcription start sites, transcription factor binding sites, nucleosome binding sites, miRNA binding sites, or insulator binding sites. During the last decade, a wealth of algorithms for the recognition of such DNA sequences has been developed and compared with the goal of improving their performance and to deepen our understanding of the underlying cellular processes. Most of these algorithms are based on statistical models belonging to the family of Markov random fields such as position weight matrix models, weight array matrix models, Markov models of higher order, or moral Bayesian networks. While in many comparative studies different learning principles or different statistical models have been compared, the influence of choosing different prior distributions for the model parameters when using different learning principles has been overlooked, and possibly lead to questionable conclusions. Results With the goal of allowing direct comparisons of different learning principles for models from the family of Markov random fields based on the same a-priori information, we derive a generalization of the commonly-used product-Dirichlet prior. We find that the derived prior behaves like a Gaussian prior close to the maximum and like a Laplace prior in the far tails. In two case studies, we illustrate the utility of the derived prior for a direct comparison of different learning principles with different models for the recognition of binding sites of the transcription factor Sp1 and human donor splice sites. Conclusions We find that comparisons of different learning principles using the same a-priori information can lead to conclusions different from those of previous studies in which the effect resulting from different
Haddad, Tarek; Himes, Adam; Thompson, Laura; Irony, Telba; Nair, Rajesh
2017-01-01
Evaluation of medical devices via clinical trial is often a necessary step in the process of bringing a new product to market. In recent years, device manufacturers are increasingly using stochastic engineering models during the product development process. These models have the capability to simulate virtual patient outcomes. This article presents a novel method based on the power prior for augmenting a clinical trial using virtual patient data. To properly inform clinical evaluation, the virtual patient model must simulate the clinical outcome of interest, incorporating patient variability, as well as the uncertainty in the engineering model and in its input parameters. The number of virtual patients is controlled by a discount function which uses the similarity between modeled and observed data. This method is illustrated by a case study of cardiac lead fracture. Different discount functions are used to cover a wide range of scenarios in which the type I error rates and power vary for the same number of enrolled patients. Incorporation of engineering models as prior knowledge in a Bayesian clinical trial design can provide benefits of decreased sample size and trial length while still controlling type I error rate and power.
A Bayesian hierarchical model with novel prior specifications for estimating HIV testing rates.
An, Qian; Kang, Jian; Song, Ruiguang; Hall, H Irene
2016-04-30
Human immunodeficiency virus (HIV) infection is a severe infectious disease actively spreading globally, and acquired immunodeficiency syndrome (AIDS) is an advanced stage of HIV infection. The HIV testing rate, that is, the probability that an AIDS-free HIV infected person seeks a test for HIV during a particular time interval, given no previous positive test has been obtained prior to the start of the time, is an important parameter for public health. In this paper, we propose a Bayesian hierarchical model with two levels of hierarchy to estimate the HIV testing rate using annual AIDS and AIDS-free HIV diagnoses data. At level one, we model the latent number of HIV infections for each year using a Poisson distribution with the intensity parameter representing the HIV incidence rate. At level two, the annual numbers of AIDS and AIDS-free HIV diagnosed cases and all undiagnosed cases stratified by the HIV infections at different years are modeled using a multinomial distribution with parameters including the HIV testing rate. We propose a new class of priors for the HIV incidence rate and HIV testing rate taking into account the temporal dependence of these parameters to improve the estimation accuracy. We develop an efficient posterior computation algorithm based on the adaptive rejection metropolis sampling technique. We demonstrate our model using simulation studies and the analysis of the national HIV surveillance data in the USA. Copyright © 2015 John Wiley & Sons, Ltd.
Bayesian road safety analysis: incorporation of past evidence and effect of hyper-prior choice.
Miranda-Moreno, Luis F; Heydari, Shahram; Lord, Dominique; Fu, Liping
2013-09-01
This paper aims to address two related issues when applying hierarchical Bayesian models for road safety analysis, namely: (a) how to incorporate available information from previous studies or past experiences in the (hyper) prior distributions for model parameters and (b) what are the potential benefits of incorporating past evidence on the results of a road safety analysis when working with scarce accident data (i.e., when calibrating models with crash datasets characterized by a very low average number of accidents and a small number of sites). A simulation framework was developed to evaluate the performance of alternative hyper-priors including informative and non-informative Gamma, Pareto, as well as Uniform distributions. Based on this simulation framework, different data scenarios (i.e., number of observations and years of data) were defined and tested using crash data collected at 3-legged rural intersections in California and crash data collected for rural 4-lane highway segments in Texas. This study shows how the accuracy of model parameter estimates (inverse dispersion parameter) is considerably improved when incorporating past evidence, in particular when working with the small number of observations and crash data with low mean. The results also illustrates that when the sample size (more than 100 sites) and the number of years of crash data is relatively large, neither the incorporation of past experience nor the choice of the hyper-prior distribution may affect the final results of a traffic safety analysis. As a potential solution to the problem of low sample mean and small sample size, this paper suggests some practical guidance on how to incorporate past evidence into informative hyper-priors. By combining evidence from past studies and data available, the model parameter estimates can significantly be improved. The effect of prior choice seems to be less important on the hotspot identification. The results show the benefits of incorporating prior
Bayesian image reconstruction for emission tomography based on median root prior
International Nuclear Information System (INIS)
Alenius, S.
1997-01-01
The aim of the present study was to investigate a new type of Bayesian one-step late reconstruction method which utilizes a median root prior (MRP). The method favours images which have locally monotonous radioactivity concentrations. The new reconstruction algorithm was applied to ideal simulated data, phantom data and some patient examinations with PET. The same projection data were reconstructed with filtered back-projection (FBP) and maximum likelihood-expectation maximization (ML-EM) methods for comparison. The MRP method provided good-quality images with a similar resolution to the FBP method with a ramp filter, and at the same time the noise properties were as good as with Hann-filtered FBP images. The typical artefacts seen in FBP reconstructed images outside of the object were completely removed, as was the grainy noise inside the object. Quantitativley, the resulting average regional radioactivity concentrations in a large region of interest in images produced by the MRP method corresponded to the FBP and ML-EM results but at the pixel by pixel level the MRP method proved to be the most accurate of the tested methods. In contrast to other iterative reconstruction methods, e.g. ML-EM, the MRP method was not sensitive to the number of iterations nor to the adjustment of reconstruction parameters. Only the Bayesian parameter β had to be set. The proposed MRP method is much more simple to calculate than the methods described previously, both with regard to the parameter settings and in terms of general use. The new MRP reconstruction method was shown to produce high-quality quantitative emission images with only one parameter setting in addition to the number of iterations. (orig.)
2004-01-01
Following the introduction of Condensators, resistors and potentiometers from the Farnell electronic-catalogue into CERN Stores' catalogue, following products are now available: PRODUCT FAMILY GROUP SCEM Oscillators and quartz crystals 07.94.10 / 07.94.12 Diodes 08.51.14 / 08.51.54 Thyristors 08.51.60 / 08.51.66 Opto-electronics 08.52 Transistors 08.53 Integrated circuits 08.54 / 08.55 These articles can be procured in the same way as any other stores item, by completing a Material Request. N.B. Individual Farnell order codes can be used as keywords to facilitate searches in the CERN Stores Catalogue.
Forecasting Long-Term Crude Oil Prices Using a Bayesian Model with Informative Priors
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Chul-Yong Lee
2017-01-01
Full Text Available In the long-term, crude oil prices may impact the economic stability and sustainability of many countries, especially those depending on oil imports. This study thus suggests an alternative model for accurately forecasting oil prices while reflecting structural changes in the oil market by using a Bayesian approach. The prior information is derived from the recent and expected structure of the oil market, using a subjective approach, and then updated with available market data. The model includes as independent variables factors affecting oil prices, such as world oil demand and supply, the financial situation, upstream costs, and geopolitical events. To test the model’s forecasting performance, it is compared with other models, including a linear ordinary least squares model and a neural network model. The proposed model outperforms on the forecasting performance test even though the neural network model shows the best results on a goodness-of-fit test. The results show that the crude oil price is estimated to increase to $169.3/Bbl by 2040.
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André Chiaradia
Full Text Available Reconstructing the diet of top marine predators is of great significance in several key areas of applied ecology, requiring accurate estimation of their true diet. However, from conventional stomach content analysis to recent stable isotope and DNA analyses, no one method is bias or error free. Here, we evaluated the accuracy of recent methods to estimate the actual proportion of a controlled diet fed to a top-predator seabird, the Little penguin (Eudyptula minor. We combined published DNA data of penguins scats with blood plasma δ(15N and δ(13C values to reconstruct the diet of individual penguins fed experimentally. Mismatch between controlled (true ingested diet and dietary estimates obtained through the separately use of stable isotope and DNA data suggested some degree of differences in prey assimilation (stable isotope and digestion rates (DNA analysis. In contrast, combined posterior isotope mixing model with DNA Bayesian priors provided the closest match to the true diet. We provided the first evidence suggesting that the combined use of these complementary techniques may provide better estimates of the actual diet of top marine predators- a powerful tool in applied ecology in the search for the true consumed diet.
Barba-Montoya, Jose; Dos Reis, Mario; Yang, Ziheng
2017-09-01
Fossil calibrations are the utmost source of information for resolving the distances between molecular sequences into estimates of absolute times and absolute rates in molecular clock dating analysis. The quality of calibrations is thus expected to have a major impact on divergence time estimates even if a huge amount of molecular data is available. In Bayesian molecular clock dating, fossil calibration information is incorporated in the analysis through the prior on divergence times (the time prior). Here, we evaluate three strategies for converting fossil calibrations (in the form of minimum- and maximum-age bounds) into the prior on times, which differ according to whether they borrow information from the maximum age of ancestral nodes and minimum age of descendent nodes to form constraints for any given node on the phylogeny. We study a simple example that is analytically tractable, and analyze two real datasets (one of 10 primate species and another of 48 seed plant species) using three Bayesian dating programs: MCMCTree, MrBayes and BEAST2. We examine how different calibration strategies, the birth-death process, and automatic truncation (to enforce the constraint that ancestral nodes are older than descendent nodes) interact to determine the time prior. In general, truncation has a great impact on calibrations so that the effective priors on the calibration node ages after the truncation can be very different from the user-specified calibration densities. The different strategies for generating the effective prior also had considerable impact, leading to very different marginal effective priors. Arbitrary parameters used to implement minimum-bound calibrations were found to have a strong impact upon the prior and posterior of the divergence times. Our results highlight the importance of inspecting the joint time prior used by the dating program before any Bayesian dating analysis. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Wang, Li; Gac, Nicolas; Mohammad-Djafari, Ali
2015-01-01
In order to improve quality of 3D X-ray tomography reconstruction for Non Destructive Testing (NDT), we investigate in this paper hierarchical Bayesian methods. In NDT, useful prior information on the volume like the limited number of materials or the presence of homogeneous area can be included in the iterative reconstruction algorithms. In hierarchical Bayesian methods, not only the volume is estimated thanks to the prior model of the volume but also the hyper parameters of this prior. This additional complexity in the reconstruction methods when applied to large volumes (from 512 3 to 8192 3 voxels) results in an increasing computational cost. To reduce it, the hierarchical Bayesian methods investigated in this paper lead to an algorithm acceleration by Variational Bayesian Approximation (VBA) [1] and hardware acceleration thanks to projection and back-projection operators paralleled on many core processors like GPU [2]. In this paper, we will consider a Student-t prior on the gradient of the image implemented in a hierarchical way [3, 4, 1]. Operators H (forward or projection) and H t (adjoint or back-projection) implanted in multi-GPU [2] have been used in this study. Different methods will be evalued on synthetic volume 'Shepp and Logan' in terms of quality and time of reconstruction. We used several simple regularizations of order 1 and order 2. Other prior models also exists [5]. Sometimes for a discrete image, we can do the segmentation and reconstruction at the same time, then the reconstruction can be done with less projections
Kittisuwan, Pichid
2015-03-01
The application of image processing in industry has shown remarkable success over the last decade, for example, in security and telecommunication systems. The denoising of natural image corrupted by Gaussian noise is a classical problem in image processing. So, image denoising is an indispensable step during image processing. This paper is concerned with dual-tree complex wavelet-based image denoising using Bayesian techniques. One of the cruxes of the Bayesian image denoising algorithms is to estimate the statistical parameter of the image. Here, we employ maximum a posteriori (MAP) estimation to calculate local observed variance with generalized Gamma density prior for local observed variance and Laplacian or Gaussian distribution for noisy wavelet coefficients. Evidently, our selection of prior distribution is motivated by efficient and flexible properties of generalized Gamma density. The experimental results show that the proposed method yields good denoising results.
Directory of Open Access Journals (Sweden)
Chris Bambey Guure
2012-01-01
Full Text Available The Weibull distribution has been observed as one of the most useful distribution, for modelling and analysing lifetime data in engineering, biology, and others. Studies have been done vigorously in the literature to determine the best method in estimating its parameters. Recently, much attention has been given to the Bayesian estimation approach for parameters estimation which is in contention with other estimation methods. In this paper, we examine the performance of maximum likelihood estimator and Bayesian estimator using extension of Jeffreys prior information with three loss functions, namely, the linear exponential loss, general entropy loss, and the square error loss function for estimating the two-parameter Weibull failure time distribution. These methods are compared using mean square error through simulation study with varying sample sizes. The results show that Bayesian estimator using extension of Jeffreys' prior under linear exponential loss function in most cases gives the smallest mean square error and absolute bias for both the scale parameter α and the shape parameter β for the given values of extension of Jeffreys' prior.
Directory of Open Access Journals (Sweden)
Tabassum Naz Sindhu
2014-05-01
Full Text Available The paper is concerned with the preference of prior for the Bayesian analysis of the shape parameter of the mixture of Burr type X distribution using the censored data. We modeled the heterogeneous population using two components mixture of the Burr type X distribution. A comprehensive simulation scheme, through probabilistic mixing, has been followed to highlight the properties and behavior of the estimates in terms of sample size, corresponding risks and the proportion of the component of the mixture. The Bayes estimators of the parameters have been evaluated under the assumption of informative and non-informative priors using symmetric and asymmetric loss functions. The model selection criterion for the preference of the prior has been introduced. The hazard rate function of the mixture distribution has been discussed. The Bayes estimates under exponential prior and precautionary loss function exhibit the minimum posterior risks with some exceptions.
Sraj, Ihab
2015-10-22
This paper addresses model dimensionality reduction for Bayesian inference based on prior Gaussian fields with uncertainty in the covariance function hyper-parameters. The dimensionality reduction is traditionally achieved using the Karhunen-Loève expansion of a prior Gaussian process assuming covariance function with fixed hyper-parameters, despite the fact that these are uncertain in nature. The posterior distribution of the Karhunen-Loève coordinates is then inferred using available observations. The resulting inferred field is therefore dependent on the assumed hyper-parameters. Here, we seek to efficiently estimate both the field and covariance hyper-parameters using Bayesian inference. To this end, a generalized Karhunen-Loève expansion is derived using a coordinate transformation to account for the dependence with respect to the covariance hyper-parameters. Polynomial Chaos expansions are employed for the acceleration of the Bayesian inference using similar coordinate transformations, enabling us to avoid expanding explicitly the solution dependence on the uncertain hyper-parameters. We demonstrate the feasibility of the proposed method on a transient diffusion equation by inferring spatially-varying log-diffusivity fields from noisy data. The inferred profiles were found closer to the true profiles when including the hyper-parameters’ uncertainty in the inference formulation.
Le Maitre, Olivier
2015-01-07
We address model dimensionality reduction in the Bayesian inference of Gaussian fields, considering prior covariance function with unknown hyper-parameters. The Karhunen-Loeve (KL) expansion of a prior Gaussian process is traditionally derived assuming fixed covariance function with pre-assigned hyperparameter values. Thus, the modes strengths of the Karhunen-Loeve expansion inferred using available observations, as well as the resulting inferred process, dependent on the pre-assigned values for the covariance hyper-parameters. Here, we seek to infer the process and its the covariance hyper-parameters in a single Bayesian inference. To this end, the uncertainty in the hyper-parameters is treated by means of a coordinate transformation, leading to a KL-type expansion on a fixed reference basis of spatial modes, but with random coordinates conditioned on the hyper-parameters. A Polynomial Chaos (PC) expansion of the model prediction is also introduced to accelerate the Bayesian inference and the sampling of the posterior distribution with MCMC method. The PC expansion of the model prediction also rely on a coordinates transformation, enabling us to avoid expanding the dependence of the prediction with respect to the covariance hyper-parameters. We demonstrate the efficiency of the proposed method on a transient diffusion equation by inferring spatially-varying log-diffusivity fields from noisy data.
Energy Technology Data Exchange (ETDEWEB)
Passos de Figueiredo, Leandro, E-mail: leandrop.fgr@gmail.com [Physics Department, Federal University of Santa Catarina, Florianópolis (Brazil); Grana, Dario [Department of Geology and Geophysics, University of Wyoming, Laramie (United States); Santos, Marcio; Figueiredo, Wagner [Physics Department, Federal University of Santa Catarina, Florianópolis (Brazil); Roisenberg, Mauro [Informatic and Statistics Department, Federal University of Santa Catarina, Florianópolis (Brazil); Schwedersky Neto, Guenther [Petrobras Research Center, Rio de Janeiro (Brazil)
2017-05-01
We propose a Bayesian approach for seismic inversion to estimate acoustic impedance, porosity and lithofacies within the reservoir conditioned to post-stack seismic and well data. The link between elastic and petrophysical properties is given by a joint prior distribution for the logarithm of impedance and porosity, based on a rock-physics model. The well conditioning is performed through a background model obtained by well log interpolation. Two different approaches are presented: in the first approach, the prior is defined by a single Gaussian distribution, whereas in the second approach it is defined by a Gaussian mixture to represent the well data multimodal distribution and link the Gaussian components to different geological lithofacies. The forward model is based on a linearized convolutional model. For the single Gaussian case, we obtain an analytical expression for the posterior distribution, resulting in a fast algorithm to compute the solution of the inverse problem, i.e. the posterior distribution of acoustic impedance and porosity as well as the facies probability given the observed data. For the Gaussian mixture prior, it is not possible to obtain the distributions analytically, hence we propose a Gibbs algorithm to perform the posterior sampling and obtain several reservoir model realizations, allowing an uncertainty analysis of the estimated properties and lithofacies. Both methodologies are applied to a real seismic dataset with three wells to obtain 3D models of acoustic impedance, porosity and lithofacies. The methodologies are validated through a blind well test and compared to a standard Bayesian inversion approach. Using the probability of the reservoir lithofacies, we also compute a 3D isosurface probability model of the main oil reservoir in the studied field.
Directory of Open Access Journals (Sweden)
Charles eGreen
2012-10-01
Full Text Available Background: Marijuana use is prevalent among patients with cocaine dependence and often non-exclusionary in clinical trials of potential cocaine medications. The dual-focus of this study was to (1 examine the moderating effect of baseline marijuana use on response to treatment with levodopa/carbidopa for cocaine dependence; and (2 apply an informative-priors, Bayesian approach for estimating the probability of a subgroup-by-treatment interaction effect.Method: A secondary data analysis of two previously published, double-blind, randomized controlled trials provided samples for the historical dataset (Study 1: N = 64 complete observations and current dataset (Study 2: N = 113 complete observations. Negative binomial regression evaluated Treatment Effectiveness Scores (TES as a function of medication condition (levodopa/carbidopa, placebo, baseline marijuana use (days in past 30, and their interaction. Results: Bayesian analysis indicated that there was a 96% chance that baseline marijuana use predicts differential response to treatment with levodopa/carbidopa. Simple effects indicated that among participants receiving levodopa/carbidopa the probability that baseline marijuana confers harm in terms of reducing TES was 0.981; whereas the probability that marijuana confers harm within the placebo condition was 0.163. For every additional day of marijuana use reported at baseline, participants in the levodopa/carbidopa condition demonstrated a 5.4% decrease in TES; while participants in the placebo condition demonstrated a 4.9% increase in TES.Conclusion: The potential moderating effect of marijuana on cocaine treatment response should be considered in future trial designs. Applying Bayesian subgroup analysis proved informative in characterizing this patient-treatment interaction effect.
Bayesian assessment of moving group membership: importance of models and prior knowledge
Lee, Jinhee; Song, Inseok
2018-04-01
Young nearby moving groups are important and useful in many fields of astronomy such as studying exoplanets, low-mass stars, and the stellar evolution of the early planetary systems over tens of millions of years, which has led to intensive searches for their members. Identification of members depends on the used models sensitively; therefore, careful examination of the models is required. In this study, we investigate the effects of the models used in moving group membership calculations based on a Bayesian framework (e.g. BANYAN II) focusing on the beta-Pictoris moving group (BPMG). Three improvements for building models are suggested: (1) updating a list of accepted members by re-assessing memberships in terms of position, motion, and age, (2) investigating member distribution functions in XYZ, and (3) exploring field star distribution functions in XYZ and UVW. The effect of each change is investigated, and we suggest using all of these improvements simultaneously in future membership probability calculations. Using this improved MG membership calculation and the careful examination of the age, 57 bona fide members of BPMG are confirmed including 12 new members. We additionally suggest 17 highly probable members.
Energy Technology Data Exchange (ETDEWEB)
Greco, Johnny P. [Department of Astrophysical Sciences, Princeton University, Princeton, NJ (United States); Brandt, Timothy D. [Institute for Advanced Study, Princeton, NJ (United States)
2016-12-20
The recovery of an exoplanet’s atmospheric parameters from its spectrum requires accurate knowledge of the spectral errors and covariances. Unfortunately, the complex image processing used in high-contrast integral-field spectrograph (IFS) observations generally produces spectral covariances that are poorly understood and often ignored. In this work, we show how to measure the spectral errors and covariances and include them self-consistently in parameter retrievals. By combining model exoplanet spectra with a realistic noise model generated from the Gemini Planet Imager (GPI) early science data, we show that ignoring spectral covariance in high-contrast IFS data can both bias inferred parameters and lead to unreliable confidence regions on those parameters. This problem is made worse by the common practice of scaling the χ {sup 2} per degree of freedom to unity; the input parameters then fall outside the 95% confidence regions in as many as ∼80% of noise realizations. The biases we observe can approach the typical levels of precision achieved in high-contrast spectroscopy. Accounting for realistic priors in fully Bayesian retrievals can also have a significant impact on the inferred parameters. Plausible priors on effective temperature and surface gravity can vary by an order of magnitude across the confidence regions appropriate for objects with weak age constraints; priors for objects with good age constraints are dominated by modeling uncertainties. Our methods are directly applicable to existing high-contrast IFSs including GPI and SPHERE, as well as upcoming instruments like CHARIS and, ultimately, WFIRST-AFTA.
Tang, Niansheng; Chow, Sy-Miin; Ibrahim, Joseph G; Zhu, Hongtu
2017-12-01
Many psychological concepts are unobserved and usually represented as latent factors apprehended through multiple observed indicators. When multiple-subject multivariate time series data are available, dynamic factor analysis models with random effects offer one way of modeling patterns of within- and between-person variations by combining factor analysis and time series analysis at the factor level. Using the Dirichlet process (DP) as a nonparametric prior for individual-specific time series parameters further allows the distributional forms of these parameters to deviate from commonly imposed (e.g., normal or other symmetric) functional forms, arising as a result of these parameters' restricted ranges. Given the complexity of such models, a thorough sensitivity analysis is critical but computationally prohibitive. We propose a Bayesian local influence method that allows for simultaneous sensitivity analysis of multiple modeling components within a single fitting of the model of choice. Five illustrations and an empirical example are provided to demonstrate the utility of the proposed approach in facilitating the detection of outlying cases and common sources of misspecification in dynamic factor analysis models, as well as identification of modeling components that are sensitive to changes in the DP prior specification.
How about a Bayesian M/EEG imaging method correcting for incomplete spatio-temporal priors
DEFF Research Database (Denmark)
Stahlhut, Carsten; Attias, Hagai T.; Sekihara, Kensuke
2013-01-01
previous spatio-temporal inverse M/EEG models, the proposed model benefits of consisting of two source terms, namely, a spatio-temporal pattern term limiting the source configuration to a spatio-temporal subspace and a source correcting term to pick up source activity not covered by the spatio......-temporal prior belief. We have tested the model on both artificial data and real EEG data in order to demonstrate the efficacy of the model. The model was tested at different SNRs (-10.0,-5.2, -3.0, -1.0, 0, 0.8, 3.0 dB) using white noise. At all SNRs the sAquavit performs best in AUC measure, e.g. at SNR=0d...
Gaskins, J T; Daniels, M J
2016-01-02
The estimation of the covariance matrix is a key concern in the analysis of longitudinal data. When data consists of multiple groups, it is often assumed the covariance matrices are either equal across groups or are completely distinct. We seek methodology to allow borrowing of strength across potentially similar groups to improve estimation. To that end, we introduce a covariance partition prior which proposes a partition of the groups at each measurement time. Groups in the same set of the partition share dependence parameters for the distribution of the current measurement given the preceding ones, and the sequence of partitions is modeled as a Markov chain to encourage similar structure at nearby measurement times. This approach additionally encourages a lower-dimensional structure of the covariance matrices by shrinking the parameters of the Cholesky decomposition toward zero. We demonstrate the performance of our model through two simulation studies and the analysis of data from a depression study. This article includes Supplementary Material available online.
International Nuclear Information System (INIS)
Lucka, Felix
2012-01-01
Sparsity has become a key concept for solving of high-dimensional inverse problems using variational regularization techniques. Recently, using similar sparsity-constraints in the Bayesian framework for inverse problems by encoding them in the prior distribution has attracted attention. Important questions about the relation between regularization theory and Bayesian inference still need to be addressed when using sparsity promoting inversion. A practical obstacle for these examinations is the lack of fast posterior sampling algorithms for sparse, high-dimensional Bayesian inversion. Accessing the full range of Bayesian inference methods requires being able to draw samples from the posterior probability distribution in a fast and efficient way. This is usually done using Markov chain Monte Carlo (MCMC) sampling algorithms. In this paper, we develop and examine a new implementation of a single component Gibbs MCMC sampler for sparse priors relying on L1-norms. We demonstrate that the efficiency of our Gibbs sampler increases when the level of sparsity or the dimension of the unknowns is increased. This property is contrary to the properties of the most commonly applied Metropolis–Hastings (MH) sampling schemes. We demonstrate that the efficiency of MH schemes for L1-type priors dramatically decreases when the level of sparsity or the dimension of the unknowns is increased. Practically, Bayesian inversion for L1-type priors using MH samplers is not feasible at all. As this is commonly believed to be an intrinsic feature of MCMC sampling, the performance of our Gibbs sampler also challenges common beliefs about the applicability of sample based Bayesian inference. (paper)
Harper, Aaron; Lu, Chuanyong; Sun, Yi; Garcia, Rafael; Rets, Anton; Alexis, Herol; Saad, Heba; Eid, Ikram; Harris, Loretta; Marshall, Barbara; Tafani, Edlira; Pincus, Matthew R
2016-05-01
The goal of this work was to determine if immediate versus postponed centrifugation of samples affects the levels of serum potassium. Twenty participants donated normal venous blood that was collected in four serum separator tubes per donor, each of which was analyzed at 0, 1, 2, or 4 hr on the Siemens Advia 1800 autoanalyzer. Coefficients of variation (CVs) for potassium levels ranged from 0% to 7.6% with a mean of 3 ± 2%. ANOVA testing of the means for all 20 samples showed a P-value of 0.72 (>0.05) indicating that there was no statistically significant difference between the means of the samples at the four time points. Sixteen samples were found to have CVs that were ≤5%. Two samples showed increases of potassium from the reference range to levels higher than the upper reference limit, one of which had a 4-hr value that was within the reference or normal range (3.5-5 mEq/l). Overall, most samples were found to have reproducible levels of serum potassium. Serum potassium levels from stored whole blood collected in serum separator tubes are, for the most part, stable at room temperature for at least 4 hr prior to analysis. However, some samples can exhibit significant fluctuations of values. © 2015 Wiley Periodicals, Inc.
Bisetti, Fabrizio
2016-01-12
The analysis of reactive systems in combustion science and technology relies on detailed models comprising many chemical reactions that describe the conversion of fuel and oxidizer into products and the formation of pollutants. Shock-tube experiments are a convenient setting for measuring the rate parameters of individual reactions. The temperature, pressure, and concentration of reactants are chosen to maximize the sensitivity of the measured quantities to the rate parameter of the target reaction. In this study, we optimize the experimental setup computationally by optimal experimental design (OED) in a Bayesian framework. We approximate the posterior probability density functions (pdf) using truncated Gaussian distributions in order to account for the bounded domain of the uniform prior pdf of the parameters. The underlying Gaussian distribution is obtained in the spirit of the Laplace method, more precisely, the mode is chosen as the maximum a posteriori (MAP) estimate, and the covariance is chosen as the negative inverse of the Hessian of the misfit function at the MAP estimate. The model related entities are obtained from a polynomial surrogate. The optimality, quantified by the information gain measures, can be estimated efficiently by a rejection sampling algorithm against the underlying Gaussian probability distribution, rather than against the true posterior. This approach offers a significant error reduction when the magnitude of the invariants of the posterior covariance are comparable to the size of the bounded domain of the prior. We demonstrate the accuracy and superior computational efficiency of our method for shock-tube experiments aiming to measure the model parameters of a key reaction which is part of the complex kinetic network describing the hydrocarbon oxidation. In the experiments, the initial temperature and fuel concentration are optimized with respect to the expected information gain in the estimation of the parameters of the target
Sraj, Ihab; Le Maî tre, Olivier P.; Knio, Omar; Hoteit, Ibrahim
2015-01-01
using a coordinate transformation to account for the dependence with respect to the covariance hyper-parameters. Polynomial Chaos expansions are employed for the acceleration of the Bayesian inference using similar coordinate transformations, enabling us
Baur, Brittany; Bozdag, Serdar
2015-04-01
One of the challenging and important computational problems in systems biology is to infer gene regulatory networks (GRNs) of biological systems. Several methods that exploit gene expression data have been developed to tackle this problem. In this study, we propose the use of copy number and DNA methylation data to infer GRNs. We developed an algorithm that scores regulatory interactions between genes based on canonical correlation analysis. In this algorithm, copy number or DNA methylation variables are treated as potential regulator variables, and expression variables are treated as potential target variables. We first validated that the canonical correlation analysis method is able to infer true interactions in high accuracy. We showed that the use of DNA methylation or copy number datasets leads to improved inference over steady-state expression. Our results also showed that epigenetic and structural information could be used to infer directionality of regulatory interactions. Additional improvements in GRN inference can be gleaned from incorporating the result in an informative prior in a dynamic Bayesian algorithm. This is the first study that incorporates copy number and DNA methylation into an informative prior in dynamic Bayesian framework. By closely examining top-scoring interactions with different sources of epigenetic or structural information, we also identified potential novel regulatory interactions.
Bisetti, Fabrizio; Kim, Daesang; Knio, Omar; Long, Quan; Tempone, Raul
2016-01-01
to account for the bounded domain of the uniform prior pdf of the parameters. The underlying Gaussian distribution is obtained in the spirit of the Laplace method, more precisely, the mode is chosen as the maximum a posteriori (MAP) estimate
Goossens, Bart; Aelterman, Jan; Luong, Hiep; Pizurica, Aleksandra; Philips, Wilfried
2013-02-01
In digital cameras and mobile phones, there is an ongoing trend to increase the image resolution, decrease the sensor size and to use lower exposure times. Because smaller sensors inherently lead to more noise and a worse spatial resolution, digital post-processing techniques are required to resolve many of the artifacts. Color filter arrays (CFAs), which use alternating patterns of color filters, are very popular because of price and power consumption reasons. However, color filter arrays require the use of a post-processing technique such as demosaicing to recover full resolution RGB images. Recently, there has been some interest in techniques that jointly perform the demosaicing and denoising. This has the advantage that the demosaicing and denoising can be performed optimally (e.g. in the MSE sense) for the considered noise model, while avoiding artifacts introduced when using demosaicing and denoising sequentially. In this paper, we will continue the research line of the wavelet-based demosaicing techniques. These approaches are computationally simple and very suited for combination with denoising. Therefore, we will derive Bayesian Minimum Squared Error (MMSE) joint demosaicing and denoising rules in the complex wavelet packet domain, taking local adaptivity into account. As an image model, we will use Gaussian Scale Mixtures, thereby taking advantage of the directionality of the complex wavelets. Our results show that this technique is well capable of reconstructing fine details in the image, while removing all of the noise, at a relatively low computational cost. In particular, the complete reconstruction (including color correction, white balancing etc) of a 12 megapixel RAW image takes 3.5 sec on a recent mid-range GPU.
Yuan, Ying; MacKinnon, David P.
2009-01-01
This article proposes Bayesian analysis of mediation effects. Compared to conventional frequentist mediation analysis, the Bayesian approach has several advantages. First, it allows researchers to incorporate prior information into the mediation analysis, thus potentially improving the efficiency of estimates. Second, under the Bayesian mediation analysis, inference is straightforward and exact, which makes it appealing for studies with small samples. Third, the Bayesian approach is conceptua...
Directory of Open Access Journals (Sweden)
Jonathan J Derbridge
Full Text Available Stable isotope analysis of diet has become a common tool in conservation research. However, the multiple sources of uncertainty inherent in this analysis framework involve consequences that have not been thoroughly addressed. Uncertainty arises from the choice of trophic discrimination factors, and for Bayesian stable isotope mixing models (SIMMs, the specification of prior information; the combined effect of these aspects has not been explicitly tested. We used a captive feeding study of gray wolves (Canis lupus to determine the first experimentally-derived trophic discrimination factors of C and N for this large carnivore of broad conservation interest. Using the estimated diet in our controlled system and data from a published study on wild wolves and their prey in Montana, USA, we then investigated the simultaneous effect of discrimination factors and prior information on diet reconstruction with Bayesian SIMMs. Discrimination factors for gray wolves and their prey were 1.97‰ for δ13C and 3.04‰ for δ15N. Specifying wolf discrimination factors, as opposed to the commonly used red fox (Vulpes vulpes factors, made little practical difference to estimates of wolf diet, but prior information had a strong effect on bias, precision, and accuracy of posterior estimates. Without specifying prior information in our Bayesian SIMM, it was not possible to produce SIMM posteriors statistically similar to the estimated diet in our controlled study or the diet of wild wolves. Our study demonstrates the critical effect of prior information on estimates of animal diets using Bayesian SIMMs, and suggests species-specific trophic discrimination factors are of secondary importance. When using stable isotope analysis to inform conservation decisions researchers should understand the limits of their data. It may be difficult to obtain useful information from SIMMs if informative priors are omitted and species-specific discrimination factors are unavailable.
Bayesian methods for data analysis
Carlin, Bradley P.
2009-01-01
Approaches for statistical inference Introduction Motivating Vignettes Defining the Approaches The Bayes-Frequentist Controversy Some Basic Bayesian Models The Bayes approach Introduction Prior Distributions Bayesian Inference Hierarchical Modeling Model Assessment Nonparametric Methods Bayesian computation Introduction Asymptotic Methods Noniterative Monte Carlo Methods Markov Chain Monte Carlo Methods Model criticism and selection Bayesian Modeling Bayesian Robustness Model Assessment Bayes Factors via Marginal Density Estimation Bayes Factors
Lagasse, Lisa P; Love, David C; Smith, Katherine Clegg
2014-01-01
The country-of-origin labeling (COOL) law requires United States grocers to indicate the origin and procurement method (farm-raised or wild-caught) for seafood. This study explored the presentation of COOL on fresh, frozen, packaged, and unpackaged seafood in Baltimore City grocery stores. Eight stores were visited bi-monthly to photograph seafood labels, and circulars were collected weekly from fourteen stores over three months. Ninety-six percent of products were labeled correctly. Forty-eight percent of advertisements included COOL. While in-store labels did not highlight COOL, advertising featured references to domestic and wild-caught seafood, signaling to customers that these are high-value product qualities.
Bayesian data analysis for newcomers.
Kruschke, John K; Liddell, Torrin M
2018-02-01
This article explains the foundational concepts of Bayesian data analysis using virtually no mathematical notation. Bayesian ideas already match your intuitions from everyday reasoning and from traditional data analysis. Simple examples of Bayesian data analysis are presented that illustrate how the information delivered by a Bayesian analysis can be directly interpreted. Bayesian approaches to null-value assessment are discussed. The article clarifies misconceptions about Bayesian methods that newcomers might have acquired elsewhere. We discuss prior distributions and explain how they are not a liability but an important asset. We discuss the relation of Bayesian data analysis to Bayesian models of mind, and we briefly discuss what methodological problems Bayesian data analysis is not meant to solve. After you have read this article, you should have a clear sense of how Bayesian data analysis works and the sort of information it delivers, and why that information is so intuitive and useful for drawing conclusions from data.
Yuan, Ying; MacKinnon, David P.
2009-01-01
In this article, we propose Bayesian analysis of mediation effects. Compared with conventional frequentist mediation analysis, the Bayesian approach has several advantages. First, it allows researchers to incorporate prior information into the mediation analysis, thus potentially improving the efficiency of estimates. Second, under the Bayesian…
Bayesian statistics an introduction
Lee, Peter M
2012-01-01
Bayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee’s book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques. This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as wel
Sets of priors reflecting prior-data conflict and agreement
Walter, G.M.; Coolen, F.P.A.; Carvalho, J.P.; Lesot, M.-J.; Kaymak, U.; Vieira, S.; Bouchon-Meunier, B.; Yager, R.R.
2016-01-01
Bayesian inference enables combination of observations with prior knowledge in the reasoning process. The choice of a particular prior distribution to represent the available prior knowledge is, however, often debatable, especially when prior knowledge is limited or data are scarce, as then
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.
Bayesian Data Analysis (lecture 2)
CERN. Geneva
2018-01-01
framework but we will also go into more detail and discuss for example the role of the prior. The second part of the lecture will cover further examples and applications that heavily rely on the bayesian approach, as well as some computational tools needed to perform a bayesian analysis.
Bayesian Data Analysis (lecture 1)
CERN. Geneva
2018-01-01
framework but we will also go into more detail and discuss for example the role of the prior. The second part of the lecture will cover further examples and applications that heavily rely on the bayesian approach, as well as some computational tools needed to perform a bayesian analysis.
DEFF Research Database (Denmark)
Hartelius, Karsten; Carstensen, Jens Michael
2003-01-01
A method for locating distorted grid structures in images is presented. The method is based on the theories of template matching and Bayesian image restoration. The grid is modeled as a deformable template. Prior knowledge of the grid is described through a Markov random field (MRF) model which r...
Bayesian Independent Component Analysis
DEFF Research Database (Denmark)
Winther, Ole; Petersen, Kaare Brandt
2007-01-01
In this paper we present an empirical Bayesian framework for independent component analysis. The framework provides estimates of the sources, the mixing matrix and the noise parameters, and is flexible with respect to choice of source prior and the number of sources and sensors. Inside the engine...
Bayesian methods in reliability
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.
Sampling, feasibility, and priors in Bayesian estimation
Chorin, Alexandre J.; Lu, Fei; Miller, Robert N.; Morzfeld, Matthias; Tu, Xuemin
2015-01-01
Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it possible to use the data to find high-probability samples at relatively low cost, making the assimilation more efficient. A new analysis of the feasibility of data assimilation is presented, showing in detail why feasibility depends on the Frobenius norm of the covariance matrix of the noise and not on the number of va...
Sparse reconstruction using distribution agnostic bayesian matching pursuit
Masood, Mudassir; Al-Naffouri, Tareq Y.
2013-01-01
A fast matching pursuit method using a Bayesian approach is introduced for sparse signal recovery. This method performs Bayesian estimates of sparse signals even when the signal prior is non-Gaussian or unknown. It is agnostic on signal statistics
Lesaffre, Emmanuel
2012-01-01
The growth of biostatistics has been phenomenal in recent years and has been marked by considerable technical innovation in both methodology and computational practicality. One area that has experienced significant growth is Bayesian methods. The growing use of Bayesian methodology has taken place partly due to an increasing number of practitioners valuing the Bayesian paradigm as matching that of scientific discovery. In addition, computational advances have allowed for more complex models to be fitted routinely to realistic data sets. Through examples, exercises and a combination of introd
Bayesian image restoration, using configurations
Thorarinsdottir, Thordis
2006-01-01
In this paper, we develop a Bayesian procedure for removing noise from images that can be viewed as noisy realisations of random sets in the plane. The procedure utilises recent advances in configuration theory for noise free random sets, where the probabilities of observing the different boundary configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the re...
ZHOU, Lin
1996-01-01
In this paper I consider social choices under uncertainty. I prove that any social choice rule that satisfies independence of irrelevant alternatives, translation invariance, and weak anonymity is consistent with ex post Bayesian utilitarianism
DEFF Research Database (Denmark)
Antoniou, Constantinos; Harrison, Glenn W.; Lau, Morten I.
2015-01-01
A large literature suggests that many individuals do not apply Bayes’ Rule when making decisions that depend on them correctly pooling prior information and sample data. We replicate and extend a classic experimental study of Bayesian updating from psychology, employing the methods of experimenta...... economics, with careful controls for the confounding effects of risk aversion. Our results show that risk aversion significantly alters inferences on deviations from Bayes’ Rule....
Accommodating Uncertainty in Prior Distributions
Energy Technology Data Exchange (ETDEWEB)
Picard, Richard Roy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Vander Wiel, Scott Alan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-01-19
A fundamental premise of Bayesian methodology is that a priori information is accurately summarized by a single, precisely de ned prior distribution. In many cases, especially involving informative priors, this premise is false, and the (mis)application of Bayes methods produces posterior quantities whose apparent precisions are highly misleading. We examine the implications of uncertainty in prior distributions, and present graphical methods for dealing with them.
A Bayesian model for binary Markov chains
Directory of Open Access Journals (Sweden)
Belkheir Essebbar
2004-02-01
Full Text Available This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on the Jeffreys' prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC techniques. The performance of the Bayesian estimates is illustrated by analyzing a small simulated data set.
3D Bayesian contextual classifiers
DEFF Research Database (Denmark)
Larsen, Rasmus
2000-01-01
We extend a series of multivariate Bayesian 2-D contextual classifiers to 3-D by specifying a simultaneous Gaussian distribution for the feature vectors as well as a prior distribution of the class variables of a pixel and its 6 nearest 3-D neighbours.......We extend a series of multivariate Bayesian 2-D contextual classifiers to 3-D by specifying a simultaneous Gaussian distribution for the feature vectors as well as a prior distribution of the class variables of a pixel and its 6 nearest 3-D neighbours....
A default Bayesian hypothesis test for ANOVA designs
Wetzels, R.; Grasman, R.P.P.P.; Wagenmakers, E.J.
2012-01-01
This article presents a Bayesian hypothesis test for analysis of variance (ANOVA) designs. The test is an application of standard Bayesian methods for variable selection in regression models. We illustrate the effect of various g-priors on the ANOVA hypothesis test. The Bayesian test for ANOVA
Bayesian adaptive methods for clinical trials
National Research Council Canada - National Science Library
Berry, Scott M
2011-01-01
.... One is that Bayesian approaches implemented with the majority of their informative content coming from the current data, and not any external prior informa- tion, typically have good frequentist properties (e.g...
International Nuclear Information System (INIS)
Rajabalinejad, M.
2010-01-01
To reduce cost of Monte Carlo (MC) simulations for time-consuming processes, Bayesian Monte Carlo (BMC) is introduced in this paper. The BMC method reduces number of realizations in MC according to the desired accuracy level. BMC also provides a possibility of considering more priors. In other words, different priors can be integrated into one model by using BMC to further reduce cost of simulations. This study suggests speeding up the simulation process by considering the logical dependence of neighboring points as prior information. This information is used in the BMC method to produce a predictive tool through the simulation process. The general methodology and algorithm of BMC method are presented in this paper. The BMC method is applied to the simplified break water model as well as the finite element model of 17th Street Canal in New Orleans, and the results are compared with the MC and Dynamic Bounds methods.
Bayesian probability theory and inverse problems
International Nuclear Information System (INIS)
Kopec, S.
1994-01-01
Bayesian probability theory is applied to approximate solving of the inverse problems. In order to solve the moment problem with the noisy data, the entropic prior is used. The expressions for the solution and its error bounds are presented. When the noise level tends to zero, the Bayesian solution tends to the classic maximum entropy solution in the L 2 norm. The way of using spline prior is also shown. (author)
Bayesian image restoration, using configurations
DEFF Research Database (Denmark)
Thorarinsdottir, Thordis
configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for salt and pepper noise. The inference in the model is discussed...
Bayesian image restoration, using configurations
DEFF Research Database (Denmark)
Thorarinsdottir, Thordis Linda
2006-01-01
configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for the salt and pepper noise. The inference in the model is discussed...
Differentiated Bayesian Conjoint Choice Designs
Z. Sándor (Zsolt); M. Wedel (Michel)
2003-01-01
textabstractPrevious conjoint choice design construction procedures have produced a single design that is administered to all subjects. This paper proposes to construct a limited set of different designs. The designs are constructed in a Bayesian fashion, taking into account prior uncertainty about
Systematic search of Bayesian statistics in the field of psychotraumatology
van de Schoot, Rens; Schalken, Naomi; Olff, Miranda
2017-01-01
In many different disciplines there is a recent increase in interest of Bayesian analysis. Bayesian methods implement Bayes' theorem, which states that prior beliefs are updated with data, and this process produces updated beliefs about model parameters. The prior is based on how much information we
Bessiere, Pierre; Ahuactzin, Juan Manuel; Mekhnacha, Kamel
2013-01-01
Probability as an Alternative to Boolean LogicWhile logic is the mathematical foundation of rational reasoning and the fundamental principle of computing, it is restricted to problems where information is both complete and certain. However, many real-world problems, from financial investments to email filtering, are incomplete or uncertain in nature. Probability theory and Bayesian computing together provide an alternative framework to deal with incomplete and uncertain data. Decision-Making Tools and Methods for Incomplete and Uncertain DataEmphasizing probability as an alternative to Boolean
The Bayesian Covariance Lasso.
Khondker, Zakaria S; Zhu, Hongtu; Chu, Haitao; Lin, Weili; Ibrahim, Joseph G
2013-04-01
Estimation of sparse covariance matrices and their inverse subject to positive definiteness constraints has drawn a lot of attention in recent years. The abundance of high-dimensional data, where the sample size ( n ) is less than the dimension ( d ), requires shrinkage estimation methods since the maximum likelihood estimator is not positive definite in this case. Furthermore, when n is larger than d but not sufficiently larger, shrinkage estimation is more stable than maximum likelihood as it reduces the condition number of the precision matrix. Frequentist methods have utilized penalized likelihood methods, whereas Bayesian approaches rely on matrix decompositions or Wishart priors for shrinkage. In this paper we propose a new method, called the Bayesian Covariance Lasso (BCLASSO), for the shrinkage estimation of a precision (covariance) matrix. We consider a class of priors for the precision matrix that leads to the popular frequentist penalties as special cases, develop a Bayes estimator for the precision matrix, and propose an efficient sampling scheme that does not precalculate boundaries for positive definiteness. The proposed method is permutation invariant and performs shrinkage and estimation simultaneously for non-full rank data. Simulations show that the proposed BCLASSO performs similarly as frequentist methods for non-full rank data.
The Importance of Prior Knowledge.
Cleary, Linda Miller
1989-01-01
Recounts a college English teacher's experience of reading and rereading Noam Chomsky, building up a greater store of prior knowledge. Argues that Frank Smith provides a theory for the importance of prior knowledge and Chomsky's work provided a personal example with which to interpret and integrate that theory. (RS)
Reproducing kernel Hilbert spaces of Gaussian priors
Vaart, van der A.W.; Zanten, van J.H.; Clarke, B.; Ghosal, S.
2008-01-01
We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using Gaussian priors. The rate of contraction of posterior distributions based on Gaussian priors can be described
Bayesian natural language semantics and pragmatics
Zeevat, Henk
2015-01-01
The contributions in this volume focus on the Bayesian interpretation of natural languages, which is widely used in areas of artificial intelligence, cognitive science, and computational linguistics. This is the first volume to take up topics in Bayesian Natural Language Interpretation and make proposals based on information theory, probability theory, and related fields. The methodologies offered here extend to the target semantic and pragmatic analyses of computational natural language interpretation. Bayesian approaches to natural language semantics and pragmatics are based on methods from signal processing and the causal Bayesian models pioneered by especially Pearl. In signal processing, the Bayesian method finds the most probable interpretation by finding the one that maximizes the product of the prior probability and the likelihood of the interpretation. It thus stresses the importance of a production model for interpretation as in Grice's contributions to pragmatics or in interpretation by abduction.
Uncertainties in ozone concentrations predicted with a Lagrangian photochemical air quality model have been estimated using Bayesian Monte Carlo (BMC) analysis. Bayesian Monte Carlo analysis provides a means of combining subjective "prior" uncertainty estimates developed ...
Implementing the Bayesian paradigm in risk analysis
International Nuclear Information System (INIS)
Aven, T.; Kvaloey, J.T.
2002-01-01
The Bayesian paradigm comprises a unified and consistent framework for analyzing and expressing risk. Yet, we see rather few examples of applications where the full Bayesian setting has been adopted with specifications of priors of unknown parameters. In this paper, we discuss some of the practical challenges of implementing Bayesian thinking and methods in risk analysis, emphasizing the introduction of probability models and parameters and associated uncertainty assessments. We conclude that there is a need for a pragmatic view in order to 'successfully' apply the Bayesian approach, such that we can do the assignments of some of the probabilities without adopting the somewhat sophisticated procedure of specifying prior distributions of parameters. A simple risk analysis example is presented to illustrate ideas
DEFF Research Database (Denmark)
Jensen, Finn Verner; Nielsen, Thomas Dyhre
2016-01-01
Mathematically, a Bayesian graphical model is a compact representation of the joint probability distribution for a set of variables. The most frequently used type of Bayesian graphical models are Bayesian networks. The structural part of a Bayesian graphical model is a graph consisting of nodes...
A Bayesian Justification for Random Sampling in Sample Survey
Directory of Open Access Journals (Sweden)
Glen Meeden
2012-07-01
Full Text Available In the usual Bayesian approach to survey sampling the sampling design, plays a minimal role, at best. Although a close relationship between exchangeable prior distributions and simple random sampling has been noted; how to formally integrate simple random sampling into the Bayesian paradigm is not clear. Recently it has been argued that the sampling design can be thought of as part of a Bayesian's prior distribution. We will show here that under this scenario simple random sample can be given a Bayesian justification in survey sampling.
Bayesian nonparametric hierarchical modeling.
Dunson, David B
2009-04-01
In biomedical research, hierarchical models are very widely used to accommodate dependence in multivariate and longitudinal data and for borrowing of information across data from different sources. A primary concern in hierarchical modeling is sensitivity to parametric assumptions, such as linearity and normality of the random effects. Parametric assumptions on latent variable distributions can be challenging to check and are typically unwarranted, given available prior knowledge. This article reviews some recent developments in Bayesian nonparametric methods motivated by complex, multivariate and functional data collected in biomedical studies. The author provides a brief review of flexible parametric approaches relying on finite mixtures and latent class modeling. Dirichlet process mixture models are motivated by the need to generalize these approaches to avoid assuming a fixed finite number of classes. Focusing on an epidemiology application, the author illustrates the practical utility and potential of nonparametric Bayes methods.
Introduction to Bayesian statistics
Bolstad, William M
2017-01-01
There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this Third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian staistics. The author continues to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inferenfe cfor discrete random variables, bionomial proprotion, Poisson, normal mean, and simple linear regression. In addition, newly-developing topics in the field are presented in four new chapters: Bayesian inference with unknown mean and variance; Bayesian inference for Multivariate Normal mean vector; Bayesian inference for Multiple Linear RegressionModel; and Computati...
Bayesian artificial intelligence
Korb, Kevin B
2010-01-01
Updated and expanded, Bayesian Artificial Intelligence, Second Edition provides a practical and accessible introduction to the main concepts, foundation, and applications of Bayesian networks. It focuses on both the causal discovery of networks and Bayesian inference procedures. Adopting a causal interpretation of Bayesian networks, the authors discuss the use of Bayesian networks for causal modeling. They also draw on their own applied research to illustrate various applications of the technology.New to the Second EditionNew chapter on Bayesian network classifiersNew section on object-oriente
Bayesian artificial intelligence
Korb, Kevin B
2003-01-01
As the power of Bayesian techniques has become more fully realized, the field of artificial intelligence has embraced Bayesian methodology and integrated it to the point where an introduction to Bayesian techniques is now a core course in many computer science programs. Unlike other books on the subject, Bayesian Artificial Intelligence keeps mathematical detail to a minimum and covers a broad range of topics. The authors integrate all of Bayesian net technology and learning Bayesian net technology and apply them both to knowledge engineering. They emphasize understanding and intuition but also provide the algorithms and technical background needed for applications. Software, exercises, and solutions are available on the authors' website.
Towards Bayesian Inference of the Fast-Ion Distribution Function
DEFF Research Database (Denmark)
Stagner, L.; Heidbrink, W.W.; Salewski, Mirko
2012-01-01
sensitivity of the measurements are incorporated into Bayesian likelihood probabilities, while prior probabilities enforce physical constraints. As an initial step, this poster uses Bayesian statistics to infer the DIII-D electron density profile from multiple diagnostic measurements. Likelihood functions....... However, when theory and experiment disagree (for one or more diagnostics), it is unclear how to proceed. Bayesian statistics provides a framework to infer the DF, quantify errors, and reconcile discrepant diagnostic measurements. Diagnostic errors and ``weight functions" that describe the phase space...
Bayesian estimates of linkage disequilibrium
Directory of Open Access Journals (Sweden)
Abad-Grau María M
2007-06-01
Full Text Available Abstract Background The maximum likelihood estimator of D' – a standard measure of linkage disequilibrium – is biased toward disequilibrium, and the bias is particularly evident in small samples and rare haplotypes. Results This paper proposes a Bayesian estimation of D' to address this problem. The reduction of the bias is achieved by using a prior distribution on the pair-wise associations between single nucleotide polymorphisms (SNPs that increases the likelihood of equilibrium with increasing physical distances between pairs of SNPs. We show how to compute the Bayesian estimate using a stochastic estimation based on MCMC methods, and also propose a numerical approximation to the Bayesian estimates that can be used to estimate patterns of LD in large datasets of SNPs. Conclusion Our Bayesian estimator of D' corrects the bias toward disequilibrium that affects the maximum likelihood estimator. A consequence of this feature is a more objective view about the extent of linkage disequilibrium in the human genome, and a more realistic number of tagging SNPs to fully exploit the power of genome wide association studies.
Bayesian Estimation of Wave Spectra – Proper Formulation of ABIC
DEFF Research Database (Denmark)
Nielsen, Ulrik Dam
2007-01-01
It is possible to estimate on-site wave spectra using measured ship responses applied to Bayesian Modelling based on two prior information: the wave spectrum must be smooth both directional-wise and frequency-wise. This paper introduces two hyperparameters into Bayesian Modelling and, hence, a pr...
On Bayesian Inference under Sampling from Scale Mixtures of Normals
Fernández, C.; Steel, M.F.J.
1996-01-01
This paper considers a Bayesian analysis of the linear regression model under independent sampling from general scale mixtures of Normals.Using a common reference prior, we investigate the validity of Bayesian inference and the existence of posterior moments of the regression and precision
The Prior Can Often Only Be Understood in the Context of the Likelihood
Directory of Open Access Journals (Sweden)
Andrew Gelman
2017-10-01
Full Text Available A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys’ priors, reference priors, maximum entropy priors, and weakly informative priors. These methods, however, often manifest a key conceptual tension in prior modeling: a model encoding true prior information should be chosen without reference to the model of the measurement process, but almost all common prior modeling techniques are implicitly motivated by a reference likelihood. In this paper we resolve this apparent paradox by placing the choice of prior into the context of the entire Bayesian analysis, from inference to prediction to model evaluation.
Correct Bayesian and frequentist intervals are similar
International Nuclear Information System (INIS)
Atwood, C.L.
1986-01-01
This paper argues that Bayesians and frequentists will normally reach numerically similar conclusions, when dealing with vague data or sparse data. It is shown that both statistical methodologies can deal reasonably with vague data. With sparse data, in many important practical cases Bayesian interval estimates and frequentist confidence intervals are approximately equal, although with discrete data the frequentist intervals are somewhat longer. This is not to say that the two methodologies are equally easy to use: The construction of a frequentist confidence interval may require new theoretical development. Bayesians methods typically require numerical integration, perhaps over many variables. Also, Bayesian can easily fall into the trap of over-optimism about their amount of prior knowledge. But in cases where both intervals are found correctly, the two intervals are usually not very different. (orig.)
SPL Division
2001-01-01
Stores users are informed that the Stores (Central, Emergency window, Raw materials, Chemical products and Prévessin Self service stores) will be closed on Friday, 7 December owing to migration of the Stores computers to Windows 2000. Thank you for your understanding.
Marsman, M.; Wagenmakers, E.-J.
2017-01-01
We illustrate the Bayesian approach to data analysis using the newly developed statistical software program JASP. With JASP, researchers are able to take advantage of the benefits that the Bayesian framework has to offer in terms of parameter estimation and hypothesis testing. The Bayesian
BAYESIAN IMAGE RESTORATION, USING CONFIGURATIONS
Directory of Open Access Journals (Sweden)
Thordis Linda Thorarinsdottir
2011-05-01
Full Text Available In this paper, we develop a Bayesian procedure for removing noise from images that can be viewed as noisy realisations of random sets in the plane. The procedure utilises recent advances in configuration theory for noise free random sets, where the probabilities of observing the different boundary configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for salt and pepper noise. The inference in the model is discussed in detail for 3 X 3 and 5 X 5 configurations and examples of the performance of the procedure are given.
Bayesian inference of chemical kinetic models from proposed reactions
Galagali, Nikhil; Marzouk, Youssef M.
2015-01-01
© 2014 Elsevier Ltd. Bayesian inference provides a natural framework for combining experimental data with prior knowledge to develop chemical kinetic models and quantify the associated uncertainties, not only in parameter values but also in model
Bayesian Inference Methods for Sparse Channel Estimation
DEFF Research Database (Denmark)
Pedersen, Niels Lovmand
2013-01-01
This thesis deals with sparse Bayesian learning (SBL) with application to radio channel estimation. As opposed to the classical approach for sparse signal representation, we focus on the problem of inferring complex signals. Our investigations within SBL constitute the basis for the development...... of Bayesian inference algorithms for sparse channel estimation. Sparse inference methods aim at finding the sparse representation of a signal given in some overcomplete dictionary of basis vectors. Within this context, one of our main contributions to the field of SBL is a hierarchical representation...... analysis of the complex prior representation, where we show that the ability to induce sparse estimates of a given prior heavily depends on the inference method used and, interestingly, whether real or complex variables are inferred. We also show that the Bayesian estimators derived from the proposed...
A Robust Bayesian Truth Serum for Non-binary Signals
Radanovic, Goran; Faltings, Boi
2013-01-01
Several mechanisms have been proposed for incentivizing truthful reports of a private signals owned by rational agents, among them the peer prediction method and the Bayesian truth serum. The robust Bayesian truth serum (RBTS) for small populations and binary signals is particularly interesting since it does not require a common prior to be known to the mechanism. We further analyze the problem of the common prior not known to the mechanism and give several results regarding the restrictions ...
Multisnapshot Sparse Bayesian Learning for DOA
DEFF Research Database (Denmark)
Gerstoft, Peter; Mecklenbrauker, Christoph F.; Xenaki, Angeliki
2016-01-01
The directions of arrival (DOA) of plane waves are estimated from multisnapshot sensor array data using sparse Bayesian learning (SBL). The prior for the source amplitudes is assumed independent zero-mean complex Gaussian distributed with hyperparameters, the unknown variances (i.e., the source...
Error probabilities in default Bayesian hypothesis testing
Gu, Xin; Hoijtink, Herbert; Mulder, J,
2016-01-01
This paper investigates the classical type I and type II error probabilities of default Bayes factors for a Bayesian t test. Default Bayes factors quantify the relative evidence between the null hypothesis and the unrestricted alternative hypothesis without needing to specify prior distributions for
Bayesian Averaging is Well-Temperated
DEFF Research Database (Denmark)
Hansen, Lars Kai
2000-01-01
Bayesian predictions are stochastic just like predictions of any other inference scheme that generalize from a finite sample. While a simple variational argument shows that Bayes averaging is generalization optimal given that the prior matches the teacher parameter distribution the situation is l...
Comparison between Fisherian and Bayesian approach to ...
African Journals Online (AJOL)
... of its simplicity and optimality properties is normally used for two group cases. However, Bayesian approach is found to be better than Fisher's approach because of its low misclassification error rate. Keywords: variance-covariance matrices, centroids, prior probability, mahalanobis distance, probability of misclassification ...
A Bayesian Approach to Interactive Retrieval
Tague, Jean M.
1973-01-01
A probabilistic model for interactive retrieval is presented. Bayesian statistical decision theory principles are applied: use of prior and sample information about the relationship of document descriptions to query relevance; maximization of expected value of a utility function, to the problem of optimally restructuring search strategies in an…
An introduction to using Bayesian linear regression with clinical data.
Baldwin, Scott A; Larson, Michael J
2017-11-01
Statistical training psychology focuses on frequentist methods. Bayesian methods are an alternative to standard frequentist methods. This article provides researchers with an introduction to fundamental ideas in Bayesian modeling. We use data from an electroencephalogram (EEG) and anxiety study to illustrate Bayesian models. Specifically, the models examine the relationship between error-related negativity (ERN), a particular event-related potential, and trait anxiety. Methodological topics covered include: how to set up a regression model in a Bayesian framework, specifying priors, examining convergence of the model, visualizing and interpreting posterior distributions, interval estimates, expected and predicted values, and model comparison tools. We also discuss situations where Bayesian methods can outperform frequentist methods as well has how to specify more complicated regression models. Finally, we conclude with recommendations about reporting guidelines for those using Bayesian methods in their own research. We provide data and R code for replicating our analyses. Copyright © 2017 Elsevier Ltd. All rights reserved.
Philosophy and the practice of Bayesian statistics.
Gelman, Andrew; Shalizi, Cosma Rohilla
2013-02-01
A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework. © 2012 The British Psychological Society.
College Store Journal, 1979
1979-01-01
Topics discussed by the NACS Store Planning/Renovation Committees in this updated version of the college store renovation manual include: short- and long-range planning, financial considerations, professional planning assistance, the store's image and business character, location considerations, building requirements, space requirements, fixtures,…
Understanding Computational Bayesian Statistics
Bolstad, William M
2011-01-01
A hands-on introduction to computational statistics from a Bayesian point of view Providing a solid grounding in statistics while uniquely covering the topics from a Bayesian perspective, Understanding Computational Bayesian Statistics successfully guides readers through this new, cutting-edge approach. With its hands-on treatment of the topic, the book shows how samples can be drawn from the posterior distribution when the formula giving its shape is all that is known, and how Bayesian inferences can be based on these samples from the posterior. These ideas are illustrated on common statistic
Space Shuttle RTOS Bayesian Network
Morris, A. Terry; Beling, Peter A.
2001-01-01
With shrinking budgets and the requirements to increase reliability and operational life of the existing orbiter fleet, NASA has proposed various upgrades for the Space Shuttle that are consistent with national space policy. The cockpit avionics upgrade (CAU), a high priority item, has been selected as the next major upgrade. The primary functions of cockpit avionics include flight control, guidance and navigation, communication, and orbiter landing support. Secondary functions include the provision of operational services for non-avionics systems such as data handling for the payloads and caution and warning alerts to the crew. Recently, a process to selection the optimal commercial-off-the-shelf (COTS) real-time operating system (RTOS) for the CAU was conducted by United Space Alliance (USA) Corporation, which is a joint venture between Boeing and Lockheed Martin, the prime contractor for space shuttle operations. In order to independently assess the RTOS selection, NASA has used the Bayesian network-based scoring methodology described in this paper. Our two-stage methodology addresses the issue of RTOS acceptability by incorporating functional, performance and non-functional software measures related to reliability, interoperability, certifiability, efficiency, correctness, business, legal, product history, cost and life cycle. The first stage of the methodology involves obtaining scores for the various measures using a Bayesian network. The Bayesian network incorporates the causal relationships between the various and often competing measures of interest while also assisting the inherently complex decision analysis process with its ability to reason under uncertainty. The structure and selection of prior probabilities for the network is extracted from experts in the field of real-time operating systems. Scores for the various measures are computed using Bayesian probability. In the second stage, multi-criteria trade-off analyses are performed between the scores
Bayesian uncertainty analyses of probabilistic risk models
International Nuclear Information System (INIS)
Pulkkinen, U.
1989-01-01
Applications of Bayesian principles to the uncertainty analyses are discussed in the paper. A short review of the most important uncertainties and their causes is provided. An application of the principle of maximum entropy to the determination of Bayesian prior distributions is described. An approach based on so called probabilistic structures is presented in order to develop a method of quantitative evaluation of modelling uncertainties. The method is applied to a small example case. Ideas for application areas for the proposed method are discussed
Bayesian parameter estimation in probabilistic risk assessment
International Nuclear Information System (INIS)
Siu, Nathan O.; Kelly, Dana L.
1998-01-01
Bayesian statistical methods are widely used in probabilistic risk assessment (PRA) because of their ability to provide useful estimates of model parameters when data are sparse and because the subjective probability framework, from which these methods are derived, is a natural framework to address the decision problems motivating PRA. This paper presents a tutorial on Bayesian parameter estimation especially relevant to PRA. It summarizes the philosophy behind these methods, approaches for constructing likelihood functions and prior distributions, some simple but realistic examples, and a variety of cautions and lessons regarding practical applications. References are also provided for more in-depth coverage of various topics
Bayesian Inference of a Multivariate Regression Model
Directory of Open Access Journals (Sweden)
Marick S. Sinay
2014-01-01
Full Text Available We explore Bayesian inference of a multivariate linear regression model with use of a flexible prior for the covariance structure. The commonly adopted Bayesian setup involves the conjugate prior, multivariate normal distribution for the regression coefficients and inverse Wishart specification for the covariance matrix. Here we depart from this approach and propose a novel Bayesian estimator for the covariance. A multivariate normal prior for the unique elements of the matrix logarithm of the covariance matrix is considered. Such structure allows for a richer class of prior distributions for the covariance, with respect to strength of beliefs in prior location hyperparameters, as well as the added ability, to model potential correlation amongst the covariance structure. The posterior moments of all relevant parameters of interest are calculated based upon numerical results via a Markov chain Monte Carlo procedure. The Metropolis-Hastings-within-Gibbs algorithm is invoked to account for the construction of a proposal density that closely matches the shape of the target posterior distribution. As an application of the proposed technique, we investigate a multiple regression based upon the 1980 High School and Beyond Survey.
Bayesianism and inference to the best explanation
Directory of Open Access Journals (Sweden)
Valeriano IRANZO
2008-01-01
Full Text Available Bayesianism and Inference to the best explanation (IBE are two different models of inference. Recently there has been some debate about the possibility of “bayesianizing” IBE. Firstly I explore several alternatives to include explanatory considerations in Bayes’s Theorem. Then I distinguish two different interpretations of prior probabilities: “IBE-Bayesianism” (IBE-Bay and “frequentist-Bayesianism” (Freq-Bay. After detailing the content of the latter, I propose a rule for assessing the priors. I also argue that Freq-Bay: (i endorses a role for explanatory value in the assessment of scientific hypotheses; (ii avoids a purely subjectivist reading of prior probabilities; and (iii fits better than IBE-Bayesianism with two basic facts about science, i.e., the prominent role played by empirical testing and the existence of many scientific theories in the past that failed to fulfil their promises and were subsequently abandoned.
Prior elicitation: Interactive spreadsheet graphics with sliders can be fun, and informative
Jones, G; Johnson, WO
2014-01-01
There are several approaches to setting priors in Bayesian data analysis. Some attempt to minimize the impact of the prior on the posterior, allowing the data to "speak for themselves," or to provide Bayesian inferences that have good frequentist properties. In contrast, this note focuses on priors where scientific knowledge is used, possibly partially informative. There are many articles on the use of such subjective information. We focus on using standard software for eliciting priors from ...
An introduction to Bayesian statistics in health psychology.
Depaoli, Sarah; Rus, Holly M; Clifton, James P; van de Schoot, Rens; Tiemensma, Jitske
2017-09-01
The aim of the current article is to provide a brief introduction to Bayesian statistics within the field of health psychology. Bayesian methods are increasing in prevalence in applied fields, and they have been shown in simulation research to improve the estimation accuracy of structural equation models, latent growth curve (and mixture) models, and hierarchical linear models. Likewise, Bayesian methods can be used with small sample sizes since they do not rely on large sample theory. In this article, we discuss several important components of Bayesian statistics as they relate to health-based inquiries. We discuss the incorporation and impact of prior knowledge into the estimation process and the different components of the analysis that should be reported in an article. We present an example implementing Bayesian estimation in the context of blood pressure changes after participants experienced an acute stressor. We conclude with final thoughts on the implementation of Bayesian statistics in health psychology, including suggestions for reviewing Bayesian manuscripts and grant proposals. We have also included an extensive amount of online supplementary material to complement the content presented here, including Bayesian examples using many different software programmes and an extensive sensitivity analysis examining the impact of priors.
Kleibergen, F.R.; Kleijn, R.; Paap, R.
2000-01-01
We propose a novel Bayesian test under a (noninformative) Jeffreys'priorspecification. We check whether the fixed scalar value of the so-calledBayesian Score Statistic (BSS) under the null hypothesis is aplausiblerealization from its known and standardized distribution under thealternative. Unlike
Logistics Group
2004-01-01
As the FARNELL Catalogue CAPACITORS, RESISTORS and POTENTIOMETERS have now been integrated into the CERN Stores Catalogue (SCEM Groups 10 and 11) they can now be obtained via an EDH 'Material Request' like any other Stores item. N.B. The Farnell 'Order code' is one of the key-words that make it easier to find items in the Stores Catalogue. Logistics Group FI Department
Distributed energy store railgun
International Nuclear Information System (INIS)
Marshall, R.A.
1991-01-01
This paper reports that when the limiting case of a distributed energy store railgun is analyzed, i.e., the case where the space between adjacent energy stores become indefinitely small, three important results are obtained. First, the shape of the current pulse delivered by each store is sinusoidal and an exponential tail. Second, the rail-to-rail voltage behind the rear-most active store approaches zero. Third, it is not possible to choose parameters in such a way that capacitor crowbars can be eliminated
von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo
2014-06-01
Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.
Fast Bayesian JPEG Decompression and Denoising With Tight Frame Priors
Czech Academy of Sciences Publication Activity Database
Šorel, Michal; Bartoš, Michal
2017-01-01
Roč. 26, č. 1 (2017), s. 490-501 ISSN 1057-7149 R&D Projects: GA ČR(CZ) GA16-13830S Institutional support: RVO:67985556 Keywords : image processing * image restoration * JPEG Subject RIV: JD - Computer Applications, Robotics OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 4.828, year: 2016 http://library.utia.cas.cz/separaty/2017/ZOI/sorel-0471741. pdf
Rate-optimal Bayesian intensity smoothing for inhomogeneous Poisson processes
Belitser, E.; Andrade Serra, De P.J.; Zanten, van J.H.
2013-01-01
We apply nonparametric Bayesian methods to study the problem of estimating the intensity function of an inhomogeneous Poisson process. We exhibit a prior on intensities which both leads to a computationally feasible method and enjoys desirable theoretical optimality properties. The prior we use is
Augmenting Data with Published Results in Bayesian Linear Regression
de Leeuw, Christiaan; Klugkist, Irene
2012-01-01
In most research, linear regression analyses are performed without taking into account published results (i.e., reported summary statistics) of similar previous studies. Although the prior density in Bayesian linear regression could accommodate such prior knowledge, formal models for doing so are absent from the literature. The goal of this…
Nonparametric Bayesian predictive distributions for future order statistics
Richard A. Johnson; James W. Evans; David W. Green
1999-01-01
We derive the predictive distribution for a specified order statistic, determined from a future random sample, under a Dirichlet process prior. Two variants of the approach are treated and some limiting cases studied. A practical application to monitoring the strength of lumber is discussed including choices of prior expectation and comparisons made to a Bayesian...
Predicting Commissary Store Success
2014-12-01
stores or if it is possible to predict that success. Multiple studies of private commercial grocery consumer preferences , habits and demographics have...appropriate number of competitors due to the nature of international cultures and consumer preferences . 2. Missing Data Four of the remaining stores
International Nuclear Information System (INIS)
Townsley, M.
1992-01-01
Scottish Nuclear have applied for permission to build a temporary ground-level dry store for spent fuel at Torness. However, Nirex's failure to find a suitable site for a long-term repository could mean that the Torness store will be less temporary than planned. (author)
Bayesian Correlation Analysis for Sequence Count Data.
Directory of Open Access Journals (Sweden)
Daniel Sánchez-Taltavull
Full Text Available Evaluating the similarity of different measured variables is a fundamental task of statistics, and a key part of many bioinformatics algorithms. Here we propose a Bayesian scheme for estimating the correlation between different entities' measurements based on high-throughput sequencing data. These entities could be different genes or miRNAs whose expression is measured by RNA-seq, different transcription factors or histone marks whose expression is measured by ChIP-seq, or even combinations of different types of entities. Our Bayesian formulation accounts for both measured signal levels and uncertainty in those levels, due to varying sequencing depth in different experiments and to varying absolute levels of individual entities, both of which affect the precision of the measurements. In comparison with a traditional Pearson correlation analysis, we show that our Bayesian correlation analysis retains high correlations when measurement confidence is high, but suppresses correlations when measurement confidence is low-especially for entities with low signal levels. In addition, we consider the influence of priors on the Bayesian correlation estimate. Perhaps surprisingly, we show that naive, uniform priors on entities' signal levels can lead to highly biased correlation estimates, particularly when different experiments have widely varying sequencing depths. However, we propose two alternative priors that provably mitigate this problem. We also prove that, like traditional Pearson correlation, our Bayesian correlation calculation constitutes a kernel in the machine learning sense, and thus can be used as a similarity measure in any kernel-based machine learning algorithm. We demonstrate our approach on two RNA-seq datasets and one miRNA-seq dataset.
Logistics Group - FI Department
2005-01-01
The Farnell catalogue can now be accessed from the Material Request form on EDH in addition to the CERN Stores catalogue. Users can order Farnell equipment as well as standard Stores equipment at the same time using a single document, the EDH Materials Request form. The Materials Request form offers users items from both the internal 'Stores' catalogue and the external 'Farnell' catalogue, all of which may be ordered on the same form. The system automatically forwards orders for standard Stores equipment to the CERN Stores and those for Farnell equipment to Farnell. The delivery time is 48 hours in both cases. Requests for materials are routed for approval in accordance with the standard EDH routing procedures. Logistics Group FI Department
Optimal Detection under the Restricted Bayesian Criterion
Directory of Open Access Journals (Sweden)
Shujun Liu
2017-07-01
Full Text Available This paper aims to find a suitable decision rule for a binary composite hypothesis-testing problem with a partial or coarse prior distribution. To alleviate the negative impact of the information uncertainty, a constraint is considered that the maximum conditional risk cannot be greater than a predefined value. Therefore, the objective of this paper becomes to find the optimal decision rule to minimize the Bayes risk under the constraint. By applying the Lagrange duality, the constrained optimization problem is transformed to an unconstrained optimization problem. In doing so, the restricted Bayesian decision rule is obtained as a classical Bayesian decision rule corresponding to a modified prior distribution. Based on this transformation, the optimal restricted Bayesian decision rule is analyzed and the corresponding algorithm is developed. Furthermore, the relation between the Bayes risk and the predefined value of the constraint is also discussed. The Bayes risk obtained via the restricted Bayesian decision rule is a strictly decreasing and convex function of the constraint on the maximum conditional risk. Finally, the numerical results including a detection example are presented and agree with the theoretical results.
Albert, Jim
2009-01-01
There has been a dramatic growth in the development and application of Bayesian inferential methods. Some of this growth is due to the availability of powerful simulation-based algorithms to summarize posterior distributions. There has been also a growing interest in the use of the system R for statistical analyses. R's open source nature, free availability, and large number of contributor packages have made R the software of choice for many statisticians in education and industry. Bayesian Computation with R introduces Bayesian modeling by the use of computation using the R language. The earl
The use of conflicts in searching Bayesian networks
Poole, David L.
2013-01-01
This paper discusses how conflicts (as used by the consistency-based diagnosis community) can be adapted to be used in a search-based algorithm for computing prior and posterior probabilities in discrete Bayesian Networks. This is an "anytime" algorithm, that at any stage can estimate the probabilities and give an error bound. Whereas the most popular Bayesian net algorithms exploit the structure of the network for efficiency, we exploit probability distributions for efficiency; this algorith...
Progress on Bayesian Inference of the Fast Ion Distribution Function
DEFF Research Database (Denmark)
Stagner, L.; Heidbrink, W.W,; Chen, X.
2013-01-01
. However, when theory and experiment disagree (for one or more diagnostics), it is unclear how to proceed. Bayesian statistics provides a framework to infer the DF, quantify errors, and reconcile discrepant diagnostic measurements. Diagnostic errors and weight functions that describe the phase space...... sensitivity of the measurements are incorporated into Bayesian likelihood probabilities. Prior probabilities describe physical constraints. This poster will show reconstructions of classically described, low-power, MHD-quiescent distribution functions from actual FIDA measurements. A description of the full...
Daniel Goodman’s empirical approach to Bayesian statistics
Gerrodette, Tim; Ward, Eric; Taylor, Rebecca L.; Schwarz, Lisa K.; Eguchi, Tomoharu; Wade, Paul; Himes Boor, Gina
2016-01-01
Bayesian statistics, in contrast to classical statistics, uses probability to represent uncertainty about the state of knowledge. Bayesian statistics has often been associated with the idea that knowledge is subjective and that a probability distribution represents a personal degree of belief. Dr. Daniel Goodman considered this viewpoint problematic for issues of public policy. He sought to ground his Bayesian approach in data, and advocated the construction of a prior as an empirical histogram of “similar” cases. In this way, the posterior distribution that results from a Bayesian analysis combined comparable previous data with case-specific current data, using Bayes’ formula. Goodman championed such a data-based approach, but he acknowledged that it was difficult in practice. If based on a true representation of our knowledge and uncertainty, Goodman argued that risk assessment and decision-making could be an exact science, despite the uncertainties. In his view, Bayesian statistics is a critical component of this science because a Bayesian analysis produces the probabilities of future outcomes. Indeed, Goodman maintained that the Bayesian machinery, following the rules of conditional probability, offered the best legitimate inference from available data. We give an example of an informative prior in a recent study of Steller sea lion spatial use patterns in Alaska.
Comprehension and computation in Bayesian problem solving
Directory of Open Access Journals (Sweden)
Eric D. Johnson
2015-07-01
Full Text Available Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian reasoning relative to normalized formats (e.g. probabilities, percentages, both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on transparent Bayesian problems varies widely, and generally remains rather unimpressive. We suggest there has been an over-focus on this representational facilitator (i.e. transparent problem structures at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct versus incorrect reasoners depart, and how individual difference might influence this time point.
Attentional and Contextual Priors in Sound Perception.
Wolmetz, Michael; Elhilali, Mounya
2016-01-01
Behavioral and neural studies of selective attention have consistently demonstrated that explicit attentional cues to particular perceptual features profoundly alter perception and performance. The statistics of the sensory environment can also provide cues about what perceptual features to expect, but the extent to which these more implicit contextual cues impact perception and performance, as well as their relationship to explicit attentional cues, is not well understood. In this study, the explicit cues, or attentional prior probabilities, and the implicit cues, or contextual prior probabilities, associated with different acoustic frequencies in a detection task were simultaneously manipulated. Both attentional and contextual priors had similarly large but independent impacts on sound detectability, with evidence that listeners tracked and used contextual priors for a variety of sound classes (pure tones, harmonic complexes, and vowels). Further analyses showed that listeners updated their contextual priors rapidly and optimally, given the changing acoustic frequency statistics inherent in the paradigm. A Bayesian Observer model accounted for both attentional and contextual adaptations found with listeners. These results bolster the interpretation of perception as Bayesian inference, and suggest that some effects attributed to selective attention may be a special case of contextual prior integration along a feature axis.
2007-01-01
From next week, the SFS UNIMARKET (tooling) catalogue will be accessible using the Material Request form on EDH in addition to the CERN Stores catalogue and those of existing suppliers. Users will now be able to place orders from the SFS catalogue using the Material Request form on EDH. Note: The system automatically forwards orders for standard Stores equipment and those for SFS equipment, placed using the same Material Request form, to the CERN Stores and SFS respectively. In both cases, the maximum delivery time will be 48 hours. Requests for equipment will be routed for approval in accordance with standard EDH routing procedures. Logistics Group FI Department
2007-01-01
From next week, the SFS UNIMARKET (tooling) catalogue will be accessible using the Material Request form on EDH in addition to the CERN Stores catalogue and those of existing suppliers. Users will now be able to place orders from the SFS catalogue using the Material Request form on EDH. Note: The system automatically forwards orders for standard Stores equipment and those for SFS equipment, placed using the same Material Request form, to the CERN Stores and SFS respectively. In both cases, the maximum delivery time will be 48 hours. Requests for equipment will be routed for approval in accordance with standard EDH routing procedures. Logistics Group FI Department
2006-01-01
The Radiospares Catalogue is now accessible from the Material Request page on EDH in the same way as the CERN Stores Catalogue. This means that users can order Radiospares equipment by completing an EDH Materials Request form. N.B.: The system will automatically forward orders for standard Stores equipment to the CERN Stores and those for Radiospares equipment to Radiospares. In both cases the delivery time will be a maximum of 48 hours. Requests for materials will be routed for approval in accordance with the standard EDH routing procedures. Logistics Group FI Department
SPL Division
1999-01-01
You can now make Material Request from CERN Stores over the WEB :CERN Home/Administrative Tools/EDH/Material Requestor https://edh.cern.ch/Document/MAGVia the Stores Catalogue : CERN Home/Administrative Tools/Stores Catalogueor http://edhcat.cern.ch/In both cases, you need to enter your EDH login and password.For more details, you can consult the Quick Reference Guide on :http://edh.cern.ch/doc/quickrefguides.htmlor obtain a printed version from AIS Support at tel: 79933or e-mail to: ais.support@cern.chSPL DivisionLogistics Group
Bayesian phylogeography finds its roots.
Directory of Open Access Journals (Sweden)
Philippe Lemey
2009-09-01
Full Text Available As a key factor in endemic and epidemic dynamics, the geographical distribution of viruses has been frequently interpreted in the light of their genetic histories. Unfortunately, inference of historical dispersal or migration patterns of viruses has mainly been restricted to model-free heuristic approaches that provide little insight into the temporal setting of the spatial dynamics. The introduction of probabilistic models of evolution, however, offers unique opportunities to engage in this statistical endeavor. Here we introduce a Bayesian framework for inference, visualization and hypothesis testing of phylogeographic history. By implementing character mapping in a Bayesian software that samples time-scaled phylogenies, we enable the reconstruction of timed viral dispersal patterns while accommodating phylogenetic uncertainty. Standard Markov model inference is extended with a stochastic search variable selection procedure that identifies the parsimonious descriptions of the diffusion process. In addition, we propose priors that can incorporate geographical sampling distributions or characterize alternative hypotheses about the spatial dynamics. To visualize the spatial and temporal information, we summarize inferences using virtual globe software. We describe how Bayesian phylogeography compares with previous parsimony analysis in the investigation of the influenza A H5N1 origin and H5N1 epidemiological linkage among sampling localities. Analysis of rabies in West African dog populations reveals how virus diffusion may enable endemic maintenance through continuous epidemic cycles. From these analyses, we conclude that our phylogeographic framework will make an important asset in molecular epidemiology that can be easily generalized to infer biogeogeography from genetic data for many organisms.
Noncausal Bayesian Vector Autoregression
DEFF Research Database (Denmark)
Lanne, Markku; Luoto, Jani
We propose a Bayesian inferential procedure for the noncausal vector autoregressive (VAR) model that is capable of capturing nonlinearities and incorporating effects of missing variables. In particular, we devise a fast and reliable posterior simulator that yields the predictive distribution...
Statistics: a Bayesian perspective
National Research Council Canada - National Science Library
Berry, Donald A
1996-01-01
...: it is the only introductory textbook based on Bayesian ideas, it combines concepts and methods, it presents statistics as a means of integrating data into the significant process, it develops ideas...
Fox, Gerardus J.A.; van den Berg, Stéphanie Martine; Veldkamp, Bernard P.; Irwing, P.; Booth, T.; Hughes, D.
2015-01-01
In educational and psychological studies, psychometric methods are involved in the measurement of constructs, and in constructing and validating measurement instruments. Assessment results are typically used to measure student proficiency levels and test characteristics. Recently, Bayesian item
Bayesian estimation of Weibull distribution parameters
International Nuclear Information System (INIS)
Bacha, M.; Celeux, G.; Idee, E.; Lannoy, A.; Vasseur, D.
1994-11-01
In this paper, we expose SEM (Stochastic Expectation Maximization) and WLB-SIR (Weighted Likelihood Bootstrap - Sampling Importance Re-sampling) methods which are used to estimate Weibull distribution parameters when data are very censored. The second method is based on Bayesian inference and allow to take into account available prior informations on parameters. An application of this method, with real data provided by nuclear power plants operation feedback analysis has been realized. (authors). 8 refs., 2 figs., 2 tabs
A theory of Bayesian decision making
Karni, Edi
2009-01-01
This paper presents a complete, choice-based, axiomatic Bayesian decision theory. It introduces a new choice set consisting of information-contingent plans for choosing actions and bets and subjective expected utility model with effect-dependent utility functions and action-dependent subjective probabilities which, in conjunction with the updating of the probabilities using Bayes’ rule, gives rise to a unique prior and a set of action-dependent posterior probabilities representing the decisio...
Bayesian Networks An Introduction
Koski, Timo
2009-01-01
Bayesian Networks: An Introduction provides a self-contained introduction to the theory and applications of Bayesian networks, a topic of interest and importance for statisticians, computer scientists and those involved in modelling complex data sets. The material has been extensively tested in classroom teaching and assumes a basic knowledge of probability, statistics and mathematics. All notions are carefully explained and feature exercises throughout. Features include:.: An introduction to Dirichlet Distribution, Exponential Families and their applications.; A detailed description of learni
Maeda, Shin-ichi
2014-01-01
Dropout is one of the key techniques to prevent the learning from overfitting. It is explained that dropout works as a kind of modified L2 regularization. Here, we shed light on the dropout from Bayesian standpoint. Bayesian interpretation enables us to optimize the dropout rate, which is beneficial for learning of weight parameters and prediction after learning. The experiment result also encourages the optimization of the dropout.
2006-01-01
The Bossard catalogue is now accessible alongside the CERN Stores catalogue from the Material Request form on EDH. Users will thus be able to order Bossard equipment using the EDH Materials Request form. As a reminder, the system automatically forwards orders for standard Stores equipment to the CERN Stores and those for Bossard equipment to Bossard. In both cases the delivery time will be a maximum of 48 hours. Requests for materials will be routed for approval in accordance with the standard EDH routing procedures. Some items will remain available from the emergency desk in the event of urgent requests. These items will be visible in the Stores catalogue even if they cannot be purchased via the EDH material request form. Logistics Group FI Department
Energy Technology Data Exchange (ETDEWEB)
Paulson, Patrick R.; Gibson, Tara D.; Schuchardt, Karen L.; Stephan, Eric G.
2008-03-01
Requirements for the provenance store and access API are developed. Existing RDF stores and APIs are evaluated against the requirements and performance benchmarks. The team’s conclusion is to use MySQL as a database backend, with a possible move to Oracle in the near-term future. Both Jena and Sesame’s APIs will be supported, but new code will use the Jena API
Attention in a bayesian framework
DEFF Research Database (Denmark)
Whiteley, Louise Emma; Sahani, Maneesh
2012-01-01
, 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...... 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....
Bayesian Kernel Mixtures for Counts.
Canale, Antonio; Dunson, David B
2011-12-01
Although Bayesian nonparametric mixture models for continuous data are well developed, there is a limited literature on related approaches for count data. A common strategy is to use a mixture of Poissons, which unfortunately is quite restrictive in not accounting for distributions having variance less than the mean. Other approaches include mixing multinomials, which requires finite support, and using a Dirichlet process prior with a Poisson base measure, which does not allow smooth deviations from the Poisson. As a broad class of alternative models, we propose to use nonparametric mixtures of rounded continuous kernels. An efficient Gibbs sampler is developed for posterior computation, and a simulation study is performed to assess performance. Focusing on the rounded Gaussian case, we generalize the modeling framework to account for multivariate count data, joint modeling with continuous and categorical variables, and other complications. The methods are illustrated through applications to a developmental toxicity study and marketing data. This article has supplementary material online.
International Nuclear Information System (INIS)
Leushacke, D.F.; Rittscher, D.
1996-01-01
In line with the decision taken in 1990 to shut down and decommission the Greifswald and Rheinsberg Nuclear Power Stations, the waste management concept of the Energiewerke Nord is based on direct and complete decommissioning of the six shut down reactor units within the next fifteen years. One key element of this concept is the construction and use of the Zwischenlager Nord (Nord Interim Store, ZLN) for holding the existing nuclear fuels and for interim and decay storage of the radioactive materials arising in decommissioning and demolition. The owner and operator of the store is Energiewerke Nord GmbH. The interim store has the functions of a processing and Energiewerke Nord GmbH. The interim store has the functions of a processing and treatment station and buffer store for the flows of residues arising. As a radioactive waste management station, it accommodates nuclear fuels, radioactive waste or residues which are not treated any further. It is used as a buffer store to allow the materials accumulating in disassembly to be stored temporarily before or after treatment in order to ensure continuous loading of the treatment plants. When operated as a processing station, the ZLN is able to handle nearly all types of radioactive waste and residues arising, except for nuclear fuels. These installations allow the treatment of radioactive residues to be separated from the demolition work both physically and in time. The possibilities of interium storage and buffer storage of untreated waste and waste packages make for high flexibility in logistics and waste management strategy. (orig.) [de
Polynomial Chaos Surrogates for Bayesian Inference
Le Maitre, Olivier
2016-01-06
The Bayesian inference is a popular probabilistic method to solve inverse problems, such as the identification of field parameter in a PDE model. The inference rely on the Bayes rule to update the prior density of the sought field, from observations, and derive its posterior distribution. In most cases the posterior distribution has no explicit form and has to be sampled, for instance using a Markov-Chain Monte Carlo method. In practice the prior field parameter is decomposed and truncated (e.g. by means of Karhunen- Lo´eve decomposition) to recast the inference problem into the inference of a finite number of coordinates. Although proved effective in many situations, the Bayesian inference as sketched above faces several difficulties requiring improvements. First, sampling the posterior can be a extremely costly task as it requires multiple resolutions of the PDE model for different values of the field parameter. Second, when the observations are not very much informative, the inferred parameter field can highly depends on its prior which can be somehow arbitrary. These issues have motivated the introduction of reduced modeling or surrogates for the (approximate) determination of the parametrized PDE solution and hyperparameters in the description of the prior field. Our contribution focuses on recent developments in these two directions: the acceleration of the posterior sampling by means of Polynomial Chaos expansions and the efficient treatment of parametrized covariance functions for the prior field. We also discuss the possibility of making such approach adaptive to further improve its efficiency.
Penalised Complexity Priors for Stationary Autoregressive Processes
Sø rbye, Sigrunn Holbek; Rue, Haavard
2017-01-01
The autoregressive (AR) process of order p(AR(p)) is a central model in time series analysis. A Bayesian approach requires the user to define a prior distribution for the coefficients of the AR(p) model. Although it is easy to write down some prior, it is not at all obvious how to understand and interpret the prior distribution, to ensure that it behaves according to the users' prior knowledge. In this article, we approach this problem using the recently developed ideas of penalised complexity (PC) priors. These prior have important properties like robustness and invariance to reparameterisations, as well as a clear interpretation. A PC prior is computed based on specific principles, where model component complexity is penalised in terms of deviation from simple base model formulations. In the AR(1) case, we discuss two natural base model choices, corresponding to either independence in time or no change in time. The latter case is illustrated in a survival model with possible time-dependent frailty. For higher-order processes, we propose a sequential approach, where the base model for AR(p) is the corresponding AR(p-1) model expressed using the partial autocorrelations. The properties of the new prior distribution are compared with the reference prior in a simulation study.
Penalised Complexity Priors for Stationary Autoregressive Processes
Sørbye, Sigrunn Holbek
2017-05-25
The autoregressive (AR) process of order p(AR(p)) is a central model in time series analysis. A Bayesian approach requires the user to define a prior distribution for the coefficients of the AR(p) model. Although it is easy to write down some prior, it is not at all obvious how to understand and interpret the prior distribution, to ensure that it behaves according to the users\\' prior knowledge. In this article, we approach this problem using the recently developed ideas of penalised complexity (PC) priors. These prior have important properties like robustness and invariance to reparameterisations, as well as a clear interpretation. A PC prior is computed based on specific principles, where model component complexity is penalised in terms of deviation from simple base model formulations. In the AR(1) case, we discuss two natural base model choices, corresponding to either independence in time or no change in time. The latter case is illustrated in a survival model with possible time-dependent frailty. For higher-order processes, we propose a sequential approach, where the base model for AR(p) is the corresponding AR(p-1) model expressed using the partial autocorrelations. The properties of the new prior distribution are compared with the reference prior in a simulation study.
International Nuclear Information System (INIS)
Nandagopan, V.
2017-01-01
A new Inflammable Materials Stores has been constructed by A and SED, BARC near Gamma Field for storage of inflammable materials falling into Petroleum Class ‘A’ ‘B’ and “C” mainly comprising of oils and lubricants, Chemicals like Acetone, Petroleum Ether etc. which are regularly procured by Central Stores Unit (CSU) for issue to the various divisions of BARC. The design of the shed done by A and SED, BARC was duly got approved from Petroleum and Explosive Safety Organization (PESO) which is a mandatory requirement before commencement of the construction. The design had taken into account various safety factors which is ideally required for an inflammable materials stores
A Bayesian Optimal Design for Sequential Accelerated Degradation Testing
Directory of Open Access Journals (Sweden)
Xiaoyang Li
2017-07-01
Full Text Available When optimizing an accelerated degradation testing (ADT plan, the initial values of unknown model parameters must be pre-specified. However, it is usually difficult to obtain the exact values, since many uncertainties are embedded in these parameters. Bayesian ADT optimal design was presented to address this problem by using prior distributions to capture these uncertainties. Nevertheless, when the difference between a prior distribution and actual situation is large, the existing Bayesian optimal design might cause some over-testing or under-testing issues. For example, the implemented ADT following the optimal ADT plan consumes too much testing resources or few accelerated degradation data are obtained during the ADT. To overcome these obstacles, a Bayesian sequential step-down-stress ADT design is proposed in this article. During the sequential ADT, the test under the highest stress level is firstly conducted based on the initial prior information to quickly generate degradation data. Then, the data collected under higher stress levels are employed to construct the prior distributions for the test design under lower stress levels by using the Bayesian inference. In the process of optimization, the inverse Gaussian (IG process is assumed to describe the degradation paths, and the Bayesian D-optimality is selected as the optimal objective. A case study on an electrical connector’s ADT plan is provided to illustrate the application of the proposed Bayesian sequential ADT design method. Compared with the results from a typical static Bayesian ADT plan, the proposed design could guarantee more stable and precise estimations of different reliability measures.
Approximate Bayesian evaluations of measurement uncertainty
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.
Basics of Bayesian reliability estimation from attribute test data
International Nuclear Information System (INIS)
Martz, H.F. Jr.; Waller, R.A.
1975-10-01
The basic notions of Bayesian reliability estimation from attribute lifetest data are presented in an introductory and expository manner. Both Bayesian point and interval estimates of the probability of surviving the lifetest, the reliability, are discussed. The necessary formulas are simply stated, and examples are given to illustrate their use. In particular, a binomial model in conjunction with a beta prior model is considered. Particular attention is given to the procedure for selecting an appropriate prior model in practice. Empirical Bayes point and interval estimates of reliability are discussed and examples are given. 7 figures, 2 tables
Bayesian networks with examples in R
Scutari, Marco
2014-01-01
Introduction. The Discrete Case: Multinomial Bayesian Networks. The Continuous Case: Gaussian Bayesian Networks. More Complex Cases. Theory and Algorithms for Bayesian Networks. Real-World Applications of Bayesian Networks. Appendices. Bibliography.
FI Department
2008-01-01
The DISTRELEC catalogue (IT) is now available in EDH in addition to the CERN Stores catalogue and the catalogues of existing suppliers. Using an EDH materials request form, users can now order DISTRELEC equipment from amongst the following product groups: peripherals, multimedia, PC components, data media, communication and data cables and adapters. Non-authorised materials will be clearly indicated. As a reminder, the system automatically manages the distribution of standard Stores equipment and punch out equipment ordered on the same request form. In both cases, delivery will take a maximum of 48 hours. The approval of the EDH document will follow the usual EDH routing procedures. Logistics Group FI Department
Store separation trajectory predictions for maritime Search and Rescue (SAR)
CSIR Research Space (South Africa)
Akroyd, G
2017-06-01
Full Text Available tunnel testing, Computational Fluid Dynamics (CFD) nor Six Degree-of-Freedom (SDOF) trajectory simulations prior to flight testing. This might have been since the released stores were relatively light weight, the airspeeds low, and incidental contact...
Shaktismen - hinduismens store gudindetradition
DEFF Research Database (Denmark)
Olesen, Bjarne Wernicke
2008-01-01
Artiklen giver en introduktion til shaktismen - hinduismens store gudindetradition. Den ser på de vigtigste gudinder, begreber, traditioner og forestillinger, ligesom den giver et vue over forskningssituationen. Shaktismens opståen i sin klassiske form, dens hovedretninger, virkelighedsforståelse...
FI Department
2008-01-01
From the beginning of March onwards, the LYRECO (stationery) catalogue will be accessible from the Material Request form on EDH in the same way as the CERN Stores catalogue and the existing individual supplier catalogues. Items will be delivered within a maximum of 48 hours. Logistics Group FI Department
Store Security: Reducing Shoplifting.
Minsel, Robert; Garman, Jerry
The major purpose of the course outline presented in the document is the reduction of stealing in retail stores. The teaching outline is formatted by juxtaposing the content outline of each substantive area next to relevant activities and methods. Some of the topics covered are psychology of shoplifting, tools used by shoplifters, Ohio's law on…
DEFF Research Database (Denmark)
Iglesias, J. E.; Sabuncu, M. R.; Van Leemput, Koen
2012-01-01
Many successful segmentation algorithms are based on Bayesian models in which prior anatomical knowledge is combined with the available image information. However, these methods typically have many free parameters that are estimated to obtain point estimates only, whereas a faithful Bayesian anal...
CSIR Research Space (South Africa)
Rosman, Benjamin
2016-02-01
Full Text Available Keywords Policy Reuse · Reinforcement Learning · Online Learning · Online Bandits · Transfer Learning · Bayesian Optimisation · Bayesian Decision Theory. 1 Introduction As robots and software agents are becoming more ubiquitous in many applications.... The agent has access to a library of policies (pi1, pi2 and pi3), and has previously experienced a set of task instances (τ1, τ2, τ3, τ4), as well as samples of the utilities of the library policies on these instances (the black dots indicate the means...
Bayesian outcome-based strategy classification.
Lee, Michael D
2016-03-01
Hilbig and Moshagen (Psychonomic Bulletin & Review, 21, 1431-1443, 2014) recently developed a method for making inferences about the decision processes people use in multi-attribute forced choice tasks. Their paper makes a number of worthwhile theoretical and methodological contributions. Theoretically, they provide an insightful psychological motivation for a probabilistic extension of the widely-used "weighted additive" (WADD) model, and show how this model, as well as other important models like "take-the-best" (TTB), can and should be expressed in terms of meaningful priors. Methodologically, they develop an inference approach based on the Minimum Description Length (MDL) principles that balances both the goodness-of-fit and complexity of the decision models they consider. This paper aims to preserve these useful contributions, but provide a complementary Bayesian approach with some theoretical and methodological advantages. We develop a simple graphical model, implemented in JAGS, that allows for fully Bayesian inferences about which models people use to make decisions. To demonstrate the Bayesian approach, we apply it to the models and data considered by Hilbig and Moshagen (Psychonomic Bulletin & Review, 21, 1431-1443, 2014), showing how a prior predictive analysis of the models, and posterior inferences about which models people use and the parameter settings at which they use them, can contribute to our understanding of human decision making.
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.
A Bayesian alternative for multi-objective ecohydrological model specification
Tang, Yating; Marshall, Lucy; Sharma, Ashish; Ajami, Hoori
2018-01-01
Recent studies have identified the importance of vegetation processes in terrestrial hydrologic systems. Process-based ecohydrological models combine hydrological, physical, biochemical and ecological processes of the catchments, and as such are generally more complex and parametric than conceptual hydrological models. Thus, appropriate calibration objectives and model uncertainty analysis are essential for ecohydrological modeling. In recent years, Bayesian inference has become one of the most popular tools for quantifying the uncertainties in hydrological modeling with the development of Markov chain Monte Carlo (MCMC) techniques. The Bayesian approach offers an appealing alternative to traditional multi-objective hydrologic model calibrations by defining proper prior distributions that can be considered analogous to the ad-hoc weighting often prescribed in multi-objective calibration. Our study aims to develop appropriate prior distributions and likelihood functions that minimize the model uncertainties and bias within a Bayesian ecohydrological modeling framework based on a traditional Pareto-based model calibration technique. In our study, a Pareto-based multi-objective optimization and a formal Bayesian framework are implemented in a conceptual ecohydrological model that combines a hydrological model (HYMOD) and a modified Bucket Grassland Model (BGM). Simulations focused on one objective (streamflow/LAI) and multiple objectives (streamflow and LAI) with different emphasis defined via the prior distribution of the model error parameters. Results show more reliable outputs for both predicted streamflow and LAI using Bayesian multi-objective calibration with specified prior distributions for error parameters based on results from the Pareto front in the ecohydrological modeling. The methodology implemented here provides insight into the usefulness of multiobjective Bayesian calibration for ecohydrologic systems and the importance of appropriate prior
A Bayesian approach to particle identification in ALICE
CERN. Geneva
2016-01-01
Among the LHC experiments, ALICE has unique particle identification (PID) capabilities exploiting different types of detectors. During Run 1, a Bayesian approach to PID was developed and intensively tested. It facilitates the combination of information from different sub-systems. The adopted methodology and formalism as well as the performance of the Bayesian PID approach for charged pions, kaons and protons in the central barrel of ALICE will be reviewed. Results are presented with PID performed via measurements of specific energy loss (dE/dx) and time-of-flight using information from the TPC and TOF detectors, respectively. Methods to extract priors from data and to compare PID efficiencies and misidentification probabilities in data and Monte Carlo using high-purity samples of identified particles will be presented. Bayesian PID results were found consistent with previous measurements published by ALICE. The Bayesian PID approach gives a higher signal-to-background ratio and a similar or larger statist...
STORE IN STORE FRANCHISING STRATEGY: THE TREND IN FRANCHISING NEGOTIATION
Rosado-Serrano, Alexander; Universidad de Puerto Rico
2016-01-01
The literature on franchising has traditionally focused on the effects and transformation it has promoted in the service sector, retailing, restaurants, hotels and other service-related industries. Store within a store research has been focused on the perspective of the manufacturer entering department stores. To date, little research has been carried out for the store in store strategy from the franchising perspective. This paper explores why big box retailers such as Walmart are adopting th...
Bayesian calibration : past achievements and future challenges
International Nuclear Information System (INIS)
Christen, J.A.
2001-01-01
Due to variations of the radiocarbon content in the biosphere over time, radiocarbon determinations need to be calibrated to obtain calendar years. Over the past decade a series of researchers have investigated the possibility of using Bayesian statistics to calibrate radiocarbon determinations, the main feature being the inclusion of contextual information into the calibration process. This allows for a coherent calibration of groups of determinations arising from related contexts (stratigraphical layers, peat cores, cultural events, ect.). Moreover, the 'related contexts' are also dated, and not only the material radiocarbon dated itself. We review Bayesian Calibration and state some of its current challenges like: software development, prior specification, robustness, etc. (author). 14 refs., 4 figs
Bayesian methods for hackers probabilistic programming and Bayesian inference
Davidson-Pilon, Cameron
2016-01-01
Bayesian methods of inference are deeply natural and extremely powerful. However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice–freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples a...
Bayesian logistic regression analysis
Van Erp, H.R.N.; Van Gelder, P.H.A.J.M.
2012-01-01
In this paper we present a Bayesian logistic regression analysis. It is found that if one wishes to derive the posterior distribution of the probability of some event, then, together with the traditional Bayes Theorem and the integrating out of nuissance parameters, the Jacobian transformation is an
Korattikara, A.; Rathod, V.; Murphy, K.; Welling, M.; Cortes, C.; Lawrence, N.D.; Lee, D.D.; Sugiyama, M.; Garnett, R.
2015-01-01
We consider the problem of Bayesian parameter estimation for deep neural networks, which is important in problem settings where we may have little data, and/ or where we need accurate posterior predictive densities p(y|x, D), e.g., for applications involving bandits or active learning. One simple
Bayesian Geostatistical Design
DEFF Research Database (Denmark)
Diggle, Peter; Lophaven, Søren Nymand
2006-01-01
locations to, or deletion of locations from, an existing design, and prospective design, which consists of choosing positions for a new set of sampling locations. We propose a Bayesian design criterion which focuses on the goal of efficient spatial prediction whilst allowing for the fact that model...
Bayesian statistical inference
Directory of Open Access Journals (Sweden)
Bruno De Finetti
2017-04-01
Full Text Available This work was translated into English and published in the volume: Bruno De Finetti, Induction and Probability, Biblioteca di Statistica, eds. P. Monari, D. Cocchi, Clueb, Bologna, 1993.Bayesian statistical Inference is one of the last fundamental philosophical papers in which we can find the essential De Finetti's approach to the statistical inference.
Bayesian Exponential Smoothing.
Forbes, C.S.; Snyder, R.D.; Shami, R.S.
2000-01-01
In this paper, a Bayesian version of the exponential smoothing method of forecasting is proposed. The approach is based on a state space model containing only a single source of error for each time interval. This model allows us to improve current practices surrounding exponential smoothing by providing both point predictions and measures of the uncertainty surrounding them.
Elsheikh, Ahmed H.; Wheeler, Mary Fanett; Hoteit, Ibrahim
2014-01-01
A Hybrid Nested Sampling (HNS) algorithm is proposed for efficient Bayesian model calibration and prior model selection. The proposed algorithm combines, Nested Sampling (NS) algorithm, Hybrid Monte Carlo (HMC) sampling and gradient estimation using
International Nuclear Information System (INIS)
Wieser, R.
1987-01-01
The spherical fuel elements are stored dry in cans. The cans themselves are stacked in parallel storage shafts, which are combined into a rectangular storage space. The storage space is made earthquake-proof by surrounding it with concrete. It consists of a ceiling assembled from several steel parts, which is connected to the floor by support elements. A cooling air ventilation station supplies the individual storage shaft and therefore the cans with cooling air via incoming and outgoing pipes. (DG) [de
International Nuclear Information System (INIS)
Mazaudier, F.; Feron, D.; Baklouti, M.; Midoux, N.
2001-01-01
The air corrosiveness of a radioactive waste package has been estimated in a store inside which the environmental conditions are supposed to be rather close to the outside ones. It is expressed according to the ISO 9223 standard, from the humidification value and the amounts of sulfur dioxide and chlorine ions. A computer code has been perfected too; the thermal behaviour of the package can then been determined. (O.M.)
Spatial and spatio-temporal bayesian models with R - INLA
Blangiardo, Marta
2015-01-01
Dedication iiiPreface ix1 Introduction 11.1 Why spatial and spatio-temporal statistics? 11.2 Why do we use Bayesian methods for modelling spatial and spatio-temporal structures? 21.3 Why INLA? 31.4 Datasets 32 Introduction to 212.1 The language 212.2 objects 222.3 Data and session management 342.4 Packages 352.5 Programming in 362.6 Basic statistical analysis with 393 Introduction to Bayesian Methods 533.1 Bayesian Philosophy 533.2 Basic Probability Elements 573.3 Bayes Theorem 623.4 Prior and Posterior Distributions 643.5 Working with the Posterior Distribution 663.6 Choosing the Prior Distr
Store and forward teledermatology
Directory of Open Access Journals (Sweden)
Kanthraj Garehatty
2007-01-01
Full Text Available Store and forward and real time or videoconferences are the two types of teledermatology services practiced. Dermatology and radio-diagnosis are visual specialties suited for store-and-forward teledermatology (SAFT. Advances in information technology, electronic instruments and biotechnology have revolutionized and brought changes in SAFT. Cellular phone, digital camera, personal digital assistants, Wi-Fi, Wi-Max and computer- aided-design software are incorporated to deliver the quality health care to remote geographic regions. Complete SAFT care equivalent to face-to-face consultation (Gold standard is essential. Health care providers in rural areas are the ′eyes′ for the consultants. Consultants to guide them should have a rapid periodic audit of visual parameters and dimensions of lesions. Given this background, this article reviews advances in 1 capture, store and transfer of images. 2 Computer Aided measurements of generalized and localized lesions and 3 the integration model to meet all the above two requirements in a centralized location. This process enables diagnosis, management, periodic assessment and complete follow-up care to achieve patient and physician satisfaction. Preservation of privacy and confidentiality of digital images is important. Uniform rules and regulations are required. Indian space research organization (ISRO, Government of India has demonstrated telemedicine pilot projects utilizing the satellite communication and mobile telemedicine units to be useful in meeting the health care needs of remote and rural India. we have to join hands with them to meet dermatology problems in rural areas.
Comparison Between Bayesian and Maximum Entropy Analyses of Flow Networks†
Directory of Open Access Journals (Sweden)
Steven H. Waldrip
2017-02-01
Full Text Available We compare the application of Bayesian inference and the maximum entropy (MaxEnt method for the analysis of ﬂow networks, such as water, electrical and transport networks. The two methods have the advantage of allowing a probabilistic prediction of ﬂow rates and other variables, when there is insufﬁcient information to obtain a deterministic solution, and also allow the effects of uncertainty to be included. Both methods of inference update a prior to a posterior probability density function (pdf by the inclusion of new information, in the form of data or constraints. The MaxEnt method maximises an entropy function subject to constraints, using the method of Lagrange multipliers,to give the posterior, while the Bayesian method ﬁnds its posterior by multiplying the prior with likelihood functions incorporating the measured data. In this study, we examine MaxEnt using soft constraints, either included in the prior or as probabilistic constraints, in addition to standard moment constraints. We show that when the prior is Gaussian,both Bayesian inference and the MaxEnt method with soft prior constraints give the same posterior means, but their covariances are different. In the Bayesian method, the interactions between variables are applied through the likelihood function, using second or higher-order cross-terms within the posterior pdf. In contrast, the MaxEnt method incorporates interactions between variables using Lagrange multipliers, avoiding second-order correlation terms in the posterior covariance. The MaxEnt method with soft prior constraints, therefore, has a numerical advantage over Bayesian inference, in that the covariance terms are avoided in its integrations. The second MaxEnt method with soft probabilistic constraints is shown to give posterior means of similar, but not identical, structure to the other two methods, due to its different formulation.
Bayesian optimization for materials science
Packwood, Daniel
2017-01-01
This book provides a short and concise introduction to Bayesian optimization specifically for experimental and computational materials scientists. After explaining the basic idea behind Bayesian optimization and some applications to materials science in Chapter 1, the mathematical theory of Bayesian optimization is outlined in Chapter 2. Finally, Chapter 3 discusses an application of Bayesian optimization to a complicated structure optimization problem in computational surface science. Bayesian optimization is a promising global optimization technique that originates in the field of machine learning and is starting to gain attention in materials science. For the purpose of materials design, Bayesian optimization can be used to predict new materials with novel properties without extensive screening of candidate materials. For the purpose of computational materials science, Bayesian optimization can be incorporated into first-principles calculations to perform efficient, global structure optimizations. While re...
Directory of Open Access Journals (Sweden)
Tarcisio de Moraes Gonçalves
2008-02-01
19 for body weight gain (BWG, g/day from 25 to 90 kg of live weight. QTL analyses using Bayesian methodology were applied to genetic model combining the marker-linked QTL, Finite Polygenic (FPM and Infinite Polygenic (IPM effects. The summaries of estimated parameters were based on Marginal posterior distributions obtained by Markov chain Monte Carlo (MCMC methods. In general, the results indicated one QTL for BT, independent of the prior. It was not possible to detect QTL for IMF or BWG probably due to non-informative markers or to the absence of QTL segregating in the studied chromosomes. This study suggested the advantage of using a combination of genetic models to analyze experimental data instead of fitting only the polygenic or the oligogenic model.
Crowdsourcing prior information to improve study design and data analysis.
Directory of Open Access Journals (Sweden)
Jeffrey S Chrabaszcz
Full Text Available Though Bayesian methods are being used more frequently, many still struggle with the best method for setting priors with novel measures or task environments. We propose a method for setting priors by eliciting continuous probability distributions from naive participants. This allows us to include any relevant information participants have for a given effect. Even when prior means are near-zero, this method provides a principle way to estimate dispersion and produce shrinkage, reducing the occurrence of overestimated effect sizes. We demonstrate this method with a number of published studies and compare the effect of different prior estimation and aggregation methods.
Bayesian Analysis for EMP Survival Probability of Solid State Relay
International Nuclear Information System (INIS)
Sun Beiyun; Zhou Hui; Cheng Xiangyue; Mao Congguang
2009-01-01
The principle to estimate the parameter p of binomial distribution by Bayesian method and the several non-informative prior are introduced. The survival probability of DC solid state relay under current injection at certain amplitude is obtained by this method. (authors)
Bayesian recovery of the initial condition for the heat equation
Knapik, B.T.; Vaart, van der A.W.; Zanten, van J.H.
2011-01-01
We study a Bayesian approach to recovering the initial condition for the heat equation from noisy observations of the solution at a later time. We consider a class of prior distributions indexed by a parameter quantifying "smoothness" and show that the corresponding posterior distributions contract
Nonparametric Bayesian models through probit stick-breaking processes.
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.
Probability and Bayesian statistics
1987-01-01
This book contains selected and refereed contributions to the "Inter national Symposium on Probability and Bayesian Statistics" which was orga nized to celebrate the 80th birthday of Professor Bruno de Finetti at his birthplace Innsbruck in Austria. Since Professor de Finetti died in 1985 the symposium was dedicated to the memory of Bruno de Finetti and took place at Igls near Innsbruck from 23 to 26 September 1986. Some of the pa pers are published especially by the relationship to Bruno de Finetti's scientific work. The evolution of stochastics shows growing importance of probability as coherent assessment of numerical values as degrees of believe in certain events. This is the basis for Bayesian inference in the sense of modern statistics. The contributions in this volume cover a broad spectrum ranging from foundations of probability across psychological aspects of formulating sub jective probability statements, abstract measure theoretical considerations, contributions to theoretical statistics an...
DEFF Research Database (Denmark)
Mørup, Morten; Schmidt, Mikkel N
2012-01-01
Many networks of scientific interest naturally decompose into clusters or communities with comparatively fewer external than internal links; however, current Bayesian models of network communities do not exert this intuitive notion of communities. We formulate a nonparametric Bayesian model...... for community detection consistent with an intuitive definition of communities and present a Markov chain Monte Carlo procedure for inferring the community structure. A Matlab toolbox with the proposed inference procedure is available for download. On synthetic and real networks, our model detects communities...... consistent with ground truth, and on real networks, it outperforms existing approaches in predicting missing links. This suggests that community structure is an important structural property of networks that should be explicitly modeled....
Approximate Bayesian recursive estimation
Czech Academy of Sciences Publication Activity Database
Kárný, Miroslav
2014-01-01
Roč. 285, č. 1 (2014), s. 100-111 ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf
Energy Technology Data Exchange (ETDEWEB)
Andrews, Stephen A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Sigeti, David E. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-11-15
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}.
Introduction to Bayesian statistics
Koch, Karl-Rudolf
2007-01-01
This book presents Bayes' theorem, the estimation of unknown parameters, the determination of confidence regions and the derivation of tests of hypotheses for the unknown parameters. It does so in a simple manner that is easy to comprehend. The book compares traditional and Bayesian methods with the rules of probability presented in a logical way allowing an intuitive understanding of random variables and their probability distributions to be formed.
Default Bayesian Estimation of the Fundamental Frequency
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Jensen, Søren Holdt
2013-01-01
Joint fundamental frequency and model order esti- mation is an important problem in several applications. In this paper, a default estimation algorithm based on a minimum of prior information is presented. The algorithm is developed in a Bayesian framework, and it can be applied to both real....... Moreover, several approximations of the posterior distributions on the fundamental frequency and the model order are derived, and one of the state-of-the-art joint fundamental frequency and model order estimators is demonstrated to be a special case of one of these approximations. The performance...
Bayesian estimation of core-melt probability
International Nuclear Information System (INIS)
Lewis, H.W.
1984-01-01
A very simple application of the canonical Bayesian algorithm is made to the problem of estimation of the probability of core melt in a commercial power reactor. An approximation to the results of the Rasmussen study on reactor safety is used as the prior distribution, and the observation that there has been no core melt yet is used as the single experiment. The result is a substantial decrease in the mean probability of core melt--factors of 2 to 4 for reasonable choices of parameters. The purpose is to illustrate the procedure, not to argue for the decrease
Bayesian Predictive Models for Rayleigh Wind Speed
DEFF Research Database (Denmark)
Shahirinia, Amir; Hajizadeh, Amin; Yu, David C
2017-01-01
predictive model of the wind speed aggregates the non-homogeneous distributions into a single continuous distribution. Therefore, the result is able to capture the variation among the probability distributions of the wind speeds at the turbines’ locations in a wind farm. More specifically, instead of using...... a wind speed distribution whose parameters are known or estimated, the parameters are considered as random whose variations are according to probability distributions. The Bayesian predictive model for a Rayleigh which only has a single model scale parameter has been proposed. Also closed-form posterior...... and predictive inferences under different reasonable choices of prior distribution in sensitivity analysis have been presented....
International Nuclear Information System (INIS)
Trinks, U.
1978-12-01
The applied method makes use of the interaction between the magnetic moment μ vector of the neutron and a magnetic field B vector. By means of superconducting magnets there can easily be achieved potential walls of μ B approximately 2 x 10 -7 eV. The principle of magnetic storing was first used for the storage ring NESTOR and showed immediate success: the stored neutrons decreased exponentially with a time constant tau = (907 +- 70) sec corresponding to the natural lifetime of the neutrons within the statistical errors. This means that there occurred no measurable additional losses (e.g. by resonance excitation) Neutrons therefore could be observed in the storage ring during about 5 half-lives (in principle of course longer, too). The orbit dynamics for neutrons in the storage ring is smilar to that in circular accelerators for charged particles. It is so well understood that the problem of the storage ring for uncharged particles (with magnetic moment) may be considered to e solved. (orig./HSI) [de
Numerical methods for Bayesian inference in the face of aging
International Nuclear Information System (INIS)
Clarotti, C.A.; Villain, B.; Procaccia, H.
1996-01-01
In recent years, much attention has been paid to Bayesian methods for Risk Assessment. Until now, these methods have been studied from a theoretical point of view. Researchers have been mainly interested in: studying the effectiveness of Bayesian methods in handling rare events; debating about the problem of priors and other philosophical issues. An aspect central to the Bayesian approach is numerical computation because any safety/reliability problem, in a Bayesian frame, ends with a problem of numerical integration. This aspect has been neglected until now because most Risk studies assumed the Exponential model as the basic probabilistic model. The existence of conjugate priors makes numerical integration unnecessary in this case. If aging is to be taken into account, no conjugate family is available and the use of numerical integration becomes compulsory. EDF (National Board of Electricity, of France) and ENEA (National Committee for Energy, New Technologies and Environment, of Italy) jointly carried out a research program aimed at developing quadrature methods suitable for Bayesian Interference with underlying Weibull or gamma distributions. The paper will illustrate the main results achieved during the above research program and will discuss, via some sample cases, the performances of the numerical algorithms which on the appearance of stress corrosion cracking in the tubes of Steam Generators of PWR French power plants. (authors)
Bayesian ARTMAP for regression.
Sasu, L M; Andonie, R
2013-10-01
Bayesian ARTMAP (BA) is a recently introduced neural architecture which uses a combination of Fuzzy ARTMAP competitive learning and Bayesian learning. Training is generally performed online, in a single-epoch. During training, BA creates input data clusters as Gaussian categories, and also infers the conditional probabilities between input patterns and categories, and between categories and classes. During prediction, BA uses Bayesian posterior probability estimation. So far, BA was used only for classification. The goal of this paper is to analyze the efficiency of BA for regression problems. Our contributions are: (i) we generalize the BA algorithm using the clustering functionality of both ART modules, and name it BA for Regression (BAR); (ii) we prove that BAR is a universal approximator with the best approximation property. In other words, BAR approximates arbitrarily well any continuous function (universal approximation) and, for every given continuous function, there is one in the set of BAR approximators situated at minimum distance (best approximation); (iii) we experimentally compare the online trained BAR with several neural models, on the following standard regression benchmarks: CPU Computer Hardware, Boston Housing, Wisconsin Breast Cancer, and Communities and Crime. Our results show that BAR is an appropriate tool for regression tasks, both for theoretical and practical reasons. Copyright © 2013 Elsevier Ltd. All rights reserved.
Bayesian theory and applications
Dellaportas, Petros; Polson, Nicholas G; Stephens, David A
2013-01-01
The development of hierarchical models and Markov chain Monte Carlo (MCMC) techniques forms one of the most profound advances in Bayesian analysis since the 1970s and provides the basis for advances in virtually all areas of applied and theoretical Bayesian statistics. This volume guides the reader along a statistical journey that begins with the basic structure of Bayesian theory, and then provides details on most of the past and present advances in this field. The book has a unique format. There is an explanatory chapter devoted to each conceptual advance followed by journal-style chapters that provide applications or further advances on the concept. Thus, the volume is both a textbook and a compendium of papers covering a vast range of topics. It is appropriate for a well-informed novice interested in understanding the basic approach, methods and recent applications. Because of its advanced chapters and recent work, it is also appropriate for a more mature reader interested in recent applications and devel...
Inventory model using bayesian dynamic linear model for demand forecasting
Directory of Open Access Journals (Sweden)
Marisol Valencia-Cárdenas
2014-12-01
Full Text Available An important factor of manufacturing process is the inventory management of terminated product. Constantly, industry is looking for better alternatives to establish an adequate plan of production and stored quantities, with optimal cost, getting quantities in a time horizon, which permits to define resources and logistics with anticipation, needed to distribute products on time. Total absence of historical data, required by many statistical models to forecast, demands the search for other kind of accurate techniques. This work presents an alternative that not only permits to forecast, in an adjusted way, but also, to provide optimal quantities to produce and store with an optimal cost, using Bayesian statistics. The proposal is illustrated with real data. Palabras clave: estadística bayesiana, optimización, modelo de inventarios, modelo lineal dinámico bayesiano. Keywords: Bayesian statistics, opti
Network structure exploration via Bayesian nonparametric models
International Nuclear Information System (INIS)
Chen, Y; Wang, X L; Xiang, X; Tang, B Z; Bu, J Z
2015-01-01
Complex networks provide a powerful mathematical representation of complex systems in nature and society. To understand complex networks, it is crucial to explore their internal structures, also called structural regularities. The task of network structure exploration is to determine how many groups there are in a complex network and how to group the nodes of the network. Most existing structure exploration methods need to specify either a group number or a certain type of structure when they are applied to a network. In the real world, however, the group number and also the certain type of structure that a network has are usually unknown in advance. To explore structural regularities in complex networks automatically, without any prior knowledge of the group number or the certain type of structure, we extend a probabilistic mixture model that can handle networks with any type of structure but needs to specify a group number using Bayesian nonparametric theory. We also propose a novel Bayesian nonparametric model, called the Bayesian nonparametric mixture (BNPM) model. Experiments conducted on a large number of networks with different structures show that the BNPM model is able to explore structural regularities in networks automatically with a stable, state-of-the-art performance. (paper)
Bayesian Recurrent Neural Network for Language Modeling.
Chien, Jen-Tzung; Ku, Yuan-Chu
2016-02-01
A language model (LM) is calculated as the probability of a word sequence that provides the solution to word prediction for a variety of information systems. A recurrent neural network (RNN) is powerful to learn the large-span dynamics of a word sequence in the continuous space. However, the training of the RNN-LM is an ill-posed problem because of too many parameters from a large dictionary size and a high-dimensional hidden layer. This paper presents a Bayesian approach to regularize the RNN-LM and apply it for continuous speech recognition. We aim to penalize the too complicated RNN-LM by compensating for the uncertainty of the estimated model parameters, which is represented by a Gaussian prior. The objective function in a Bayesian classification network is formed as the regularized cross-entropy error function. The regularized model is constructed not only by calculating the regularized parameters according to the maximum a posteriori criterion but also by estimating the Gaussian hyperparameter by maximizing the marginal likelihood. A rapid approximation to a Hessian matrix is developed to implement the Bayesian RNN-LM (BRNN-LM) by selecting a small set of salient outer-products. The proposed BRNN-LM achieves a sparser model than the RNN-LM. Experiments on different corpora show the robustness of system performance by applying the rapid BRNN-LM under different conditions.
Bayesian posterior distributions without Markov chains.
Cole, Stephen R; Chu, Haitao; Greenland, Sander; Hamra, Ghassan; Richardson, David B
2012-03-01
Bayesian posterior parameter distributions are often simulated using Markov chain Monte Carlo (MCMC) methods. However, MCMC methods are not always necessary and do not help the uninitiated understand Bayesian inference. As a bridge to understanding Bayesian inference, the authors illustrate a transparent rejection sampling method. In example 1, they illustrate rejection sampling using 36 cases and 198 controls from a case-control study (1976-1983) assessing the relation between residential exposure to magnetic fields and the development of childhood cancer. Results from rejection sampling (odds ratio (OR) = 1.69, 95% posterior interval (PI): 0.57, 5.00) were similar to MCMC results (OR = 1.69, 95% PI: 0.58, 4.95) and approximations from data-augmentation priors (OR = 1.74, 95% PI: 0.60, 5.06). In example 2, the authors apply rejection sampling to a cohort study of 315 human immunodeficiency virus seroconverters (1984-1998) to assess the relation between viral load after infection and 5-year incidence of acquired immunodeficiency syndrome, adjusting for (continuous) age at seroconversion and race. In this more complex example, rejection sampling required a notably longer run time than MCMC sampling but remained feasible and again yielded similar results. The transparency of the proposed approach comes at a price of being less broadly applicable than MCMC.
Risk-sensitivity in Bayesian sensorimotor integration.
Directory of Open Access Journals (Sweden)
Jordi Grau-Moya
Full Text Available Information processing in the nervous system during sensorimotor tasks with inherent uncertainty has been shown to be consistent with Bayesian integration. Bayes optimal decision-makers are, however, risk-neutral in the sense that they weigh all possibilities based on prior expectation and sensory evidence when they choose the action with highest expected value. In contrast, risk-sensitive decision-makers are sensitive to model uncertainty and bias their decision-making processes when they do inference over unobserved variables. In particular, they allow deviations from their probabilistic model in cases where this model makes imprecise predictions. Here we test for risk-sensitivity in a sensorimotor integration task where subjects exhibit Bayesian information integration when they infer the position of a target from noisy sensory feedback. When introducing a cost associated with subjects' response, we found that subjects exhibited a characteristic bias towards low cost responses when their uncertainty was high. This result is in accordance with risk-sensitive decision-making processes that allow for deviations from Bayes optimal decision-making in the face of uncertainty. Our results suggest that both Bayesian integration and risk-sensitivity are important factors to understand sensorimotor integration in a quantitative fashion.
Netemeyer, Richard G; Maxham, James G; Lichtenstein, Donald R
2010-05-01
Based on emotional contagion theory and the value-profit chain literatures, the present study posits a number of hypotheses that show how managers in the small store, small number of employees retail context may affect store employees, customers, and potentially store performance. With data from 306 store managers, 1,615 store customer-contact employees, and 57,656 customers of a single retail chain, the authors examined relationships among store manager job satisfaction and job performance, store customer-contact employee job satisfaction and job performance, customer satisfaction with the retailer, and a customer-spending-based store performance metric (customer spending growth over a 2-year period). Via path analysis, several hypothesized direct and interaction relations among these constructs are supported. The results suggest implications for academic researchers and retail managers. PsycINFO Database Record (c) 2010 APA, all rights reserved.
International Nuclear Information System (INIS)
Elsheikh, Ahmed H.; Wheeler, Mary F.; Hoteit, Ibrahim
2014-01-01
A Hybrid Nested Sampling (HNS) algorithm is proposed for efficient Bayesian model calibration and prior model selection. The proposed algorithm combines, Nested Sampling (NS) algorithm, Hybrid Monte Carlo (HMC) sampling and gradient estimation using Stochastic Ensemble Method (SEM). NS is an efficient sampling algorithm that can be used for Bayesian calibration and estimating the Bayesian evidence for prior model selection. Nested sampling has the advantage of computational feasibility. Within the nested sampling algorithm, a constrained sampling step is performed. For this step, we utilize HMC to reduce the correlation between successive sampled states. HMC relies on the gradient of the logarithm of the posterior distribution, which we estimate using a stochastic ensemble method based on an ensemble of directional derivatives. SEM only requires forward model runs and the simulator is then used as a black box and no adjoint code is needed. The developed HNS algorithm is successfully applied for Bayesian calibration and prior model selection of several nonlinear subsurface flow problems
Energy Technology Data Exchange (ETDEWEB)
Elsheikh, Ahmed H., E-mail: aelsheikh@ices.utexas.edu [Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, TX (United States); Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom); Wheeler, Mary F. [Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, TX (United States); Hoteit, Ibrahim [Department of Earth Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal (Saudi Arabia)
2014-02-01
A Hybrid Nested Sampling (HNS) algorithm is proposed for efficient Bayesian model calibration and prior model selection. The proposed algorithm combines, Nested Sampling (NS) algorithm, Hybrid Monte Carlo (HMC) sampling and gradient estimation using Stochastic Ensemble Method (SEM). NS is an efficient sampling algorithm that can be used for Bayesian calibration and estimating the Bayesian evidence for prior model selection. Nested sampling has the advantage of computational feasibility. Within the nested sampling algorithm, a constrained sampling step is performed. For this step, we utilize HMC to reduce the correlation between successive sampled states. HMC relies on the gradient of the logarithm of the posterior distribution, which we estimate using a stochastic ensemble method based on an ensemble of directional derivatives. SEM only requires forward model runs and the simulator is then used as a black box and no adjoint code is needed. The developed HNS algorithm is successfully applied for Bayesian calibration and prior model selection of several nonlinear subsurface flow problems.
International Nuclear Information System (INIS)
Elsel, W.
1986-01-01
The advantages obtained by the energy store device according to the invention with a superconducting solenoid system consist of the fact that only relatively short superconducting forward and return leads are required, which are collected into cables as far as possible. This limits the coolant losses of the cables. Only one relatively expensive connecting part with a transition of its conductors from room temperature to a low temperature is required, which, like the normal conducting current switch, is easily accessible. As the continuation has to be cooled independently of the upper part solenoid, cooling of this continuation part can prevent the introduction of large quantities of heat into the connected part solenoid. Due to the cooling of the forward and return conductors of the connecting cable with the coolant of the lower part solenoid, there are relatively few separations between the coolant spaces of the part solenoids. (orig./MM) [de
DEFF Research Database (Denmark)
Zielke, Stephan
2014-01-01
quarters of intentions to shop in discount stores. Value perception has the strongest total effect, which is partly mediated by enjoyment, shame and guilt. Attributions influence the shopping intention indirectly via value perception and emotions. The inferior quality attribution has the strongest total......This paper analyzes the impact of price-related attributions, emotions and value perception on the intention to shop at grocery discounters in an integrated framework. Moderating effects of price consciousness are also analyzed. The results show that the proposed model explains almost three...... effect, followed by the efficiency of the business model attribution. The unfairness to stakeholders and the tricks in price communication attribution mostly influence the shopping intention for less price-conscious customers....
Bayesian tomographic reconstruction of microsystems
International Nuclear Information System (INIS)
Salem, Sofia Fekih; Vabre, Alexandre; Mohammad-Djafari, Ali
2007-01-01
The microtomography by X ray transmission plays an increasingly dominating role in the study and the understanding of microsystems. Within this framework, an experimental setup of high resolution X ray microtomography was developed at CEA-List to quantify the physical parameters related to the fluids flow in microsystems. Several difficulties rise from the nature of experimental data collected on this setup: enhanced error measurements due to various physical phenomena occurring during the image formation (diffusion, beam hardening), and specificities of the setup (limited angle, partial view of the object, weak contrast).To reconstruct the object we must solve an inverse problem. This inverse problem is known to be ill-posed. It therefore needs to be regularized by introducing prior information. The main prior information we account for is that the object is composed of a finite known number of different materials distributed in compact regions. This a priori information is introduced via a Gauss-Markov field for the contrast distributions with a hidden Potts-Markov field for the class materials in the Bayesian estimation framework. The computations are done by using an appropriate Markov Chain Monte Carlo (MCMC) technique.In this paper, we present first the basic steps of the proposed algorithms. Then we focus on one of the main steps in any iterative reconstruction method which is the computation of forward and adjoint operators (projection and backprojection). A fast implementation of these two operators is crucial for the real application of the method. We give some details on the fast computation of these steps and show some preliminary results of simulations
Bayesian analysis in plant pathology.
Mila, A L; Carriquiry, A L
2004-09-01
ABSTRACT Bayesian methods are currently much discussed and applied in several disciplines from molecular biology to engineering. Bayesian inference is the process of fitting a probability model to a set of data and summarizing the results via probability distributions on the parameters of the model and unobserved quantities such as predictions for new observations. In this paper, after a short introduction of Bayesian inference, we present the basic features of Bayesian methodology using examples from sequencing genomic fragments and analyzing microarray gene-expressing levels, reconstructing disease maps, and designing experiments.
Parametric Bayesian Estimation of Differential Entropy and Relative Entropy
Directory of Open Access Journals (Sweden)
Maya Gupta
2010-04-01
Full Text Available Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian estimates, depend on the accuracy of the prior parameters, but example simulations show that the performance can be substantially improved compared to maximum likelihood or state-of-the-art nonparametric estimators.
Bayesian inference for disease prevalence using negative binomial group testing
Pritchard, Nicholas A.; Tebbs, Joshua M.
2011-01-01
Group testing, also known as pooled testing, and inverse sampling are both widely used methods of data collection when the goal is to estimate a small proportion. Taking a Bayesian approach, we consider the new problem of estimating disease prevalence from group testing when inverse (negative binomial) sampling is used. Using different distributions to incorporate prior knowledge of disease incidence and different loss functions, we derive closed form expressions for posterior distributions and resulting point and credible interval estimators. We then evaluate our new estimators, on Bayesian and classical grounds, and apply our methods to a West Nile Virus data set. PMID:21259308
Hierarchical Bayesian sparse image reconstruction with application to MRFM.
Dobigeon, Nicolas; Hero, Alfred O; Tourneret, Jean-Yves
2009-09-01
This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument.
A Bayesian Model of the Memory Colour Effect.
Witzel, Christoph; Olkkonen, Maria; Gegenfurtner, Karl R
2018-01-01
According to the memory colour effect, the colour of a colour-diagnostic object is not perceived independently of the object itself. Instead, it has been shown through an achromatic adjustment method that colour-diagnostic objects still appear slightly in their typical colour, even when they are colourimetrically grey. Bayesian models provide a promising approach to capture the effect of prior knowledge on colour perception and to link these effects to more general effects of cue integration. Here, we model memory colour effects using prior knowledge about typical colours as priors for the grey adjustments in a Bayesian model. This simple model does not involve any fitting of free parameters. The Bayesian model roughly captured the magnitude of the measured memory colour effect for photographs of objects. To some extent, the model predicted observed differences in memory colour effects across objects. The model could not account for the differences in memory colour effects across different levels of realism in the object images. The Bayesian model provides a particularly simple account of memory colour effects, capturing some of the multiple sources of variation of these effects.
Source Localization by Entropic Inference and Backward Renormalization Group Priors
Directory of Open Access Journals (Sweden)
Nestor Caticha
2015-04-01
Full Text Available A systematic method of transferring information from coarser to finer resolution based on renormalization group (RG transformations is introduced. It permits building informative priors in finer scales from posteriors in coarser scales since, under some conditions, RG transformations in the space of hyperparameters can be inverted. These priors are updated using renormalized data into posteriors by Maximum Entropy. The resulting inference method, backward RG (BRG priors, is tested by doing simulations of a functional magnetic resonance imaging (fMRI experiment. Its results are compared with a Bayesian approach working in the finest available resolution. Using BRG priors sources can be partially identified even when signal to noise ratio levels are up to ~ -25dB improving vastly on the single step Bayesian approach. For low levels of noise the BRG prior is not an improvement over the single scale Bayesian method. Analysis of the histograms of hyperparameters can show how to distinguish if the method is failing, due to very high levels of noise, or if the identification of the sources is, at least partially possible.
BURD, Bayesian estimation in data analysis of Probabilistic Safety Assessment
International Nuclear Information System (INIS)
Jang, Seung-cheol; Park, Jin-Kyun
2008-01-01
1 - Description of program or function: BURD (Bayesian Update for Reliability Data) is a simple code that can be used to obtain a Bayesian estimate easily in the data analysis of PSA (Probabilistic Safety Assessment). According to the Bayes' theorem, basically, the code facilitates calculations of posterior distribution given the prior and the likelihood (evidence) distributions. The distinctive features of the program, BURD, are the following: - The input consists of the prior and likelihood functions that can be chosen from the built-in statistical distributions. - The available prior distributions are uniform, Jeffrey's non informative, beta, gamma, and log-normal that are most-frequently used in performing PSA. - For likelihood function, the user can choose from four statistical distributions, e.g., beta, gamma, binomial and poisson. - A simultaneous graphic display of the prior and posterior distributions facilitate an intuitive interpretation of the results. - Export facilities for the graphic display screen and text-type outputs are available. - Three options for treating zero-evidence data are provided. - Automatic setup of an integral calculus section for a Bayesian updating. 2 - Methods: The posterior distribution is estimated in accordance with the Bayes' theorem, given the prior and the likelihood (evidence) distributions. 3 - Restrictions on the complexity of the problem: The accuracy of the results depends on the calculational error of the statistical function library in MS Excel
Bayesian image reconstruction for improving detection performance of muon tomography.
Wang, Guobao; Schultz, Larry J; Qi, Jinyi
2009-05-01
Muon tomography is a novel technology that is being developed for detecting high-Z materials in vehicles or cargo containers. Maximum likelihood methods have been developed for reconstructing the scattering density image from muon measurements. However, the instability of maximum likelihood estimation often results in noisy images and low detectability of high-Z targets. In this paper, we propose using regularization to improve the image quality of muon tomography. We formulate the muon reconstruction problem in a Bayesian framework by introducing a prior distribution on scattering density images. An iterative shrinkage algorithm is derived to maximize the log posterior distribution. At each iteration, the algorithm obtains the maximum a posteriori update by shrinking an unregularized maximum likelihood update. Inverse quadratic shrinkage functions are derived for generalized Laplacian priors and inverse cubic shrinkage functions are derived for generalized Gaussian priors. Receiver operating characteristic studies using simulated data demonstrate that the Bayesian reconstruction can greatly improve the detection performance of muon tomography.
Constrained noninformative priors
International Nuclear Information System (INIS)
Atwood, C.L.
1994-10-01
The Jeffreys noninformative prior distribution for a single unknown parameter is the distribution corresponding to a uniform distribution in the transformed model where the unknown parameter is approximately a location parameter. To obtain a prior distribution with a specified mean but with diffusion reflecting great uncertainty, a natural generalization of the noninformative prior is the distribution corresponding to the constrained maximum entropy distribution in the transformed model. Examples are given
The importance of store windows in creating store identity and store attractiveness
Directory of Open Access Journals (Sweden)
Renko Sanda
2012-01-01
Full Text Available While choosing the store, customer first notices the store window and it plays an important role in retailing strategy. Store's window is what customers see first in meeting with the store. Store window design can lead customer to enter the store, and can give a lot of information about store brands and products. Besides the analysis of the way how specific elements of the window design affect customers and their perception, the explanation of their attraction and rejection to customers is given. If we consider the importance of the topics, we can point out the lack of literature about store windows as the communication tool which allow store to communicate with its customers and to create its retailing strategy as well. There is the scientific contribution of this paper. The paper gives theoretical comprehensions completed with the results of the study about the importance of store windows for retailers as well as for customers. Therefore, for the purpose of this paper, a two-phase research study, including a qualitative and a quantitative approach, was used: 1 the qualitative study among retailers which indicated the most important elements of store windows, the level of financial sources invested in the window design, the basis for the decisions about store window design, etc.; 2 the quantitative study on the sample of consumers conducted with on-line questionnaire. Findings suggest that store window attractiveness is the main motif for store visits. The results of the research confirm that by means of store window and its elements (with special emphasis on price and pricing actions retail store sends messages to its consumers.
Bayesian nonparametric data analysis
Müller, Peter; Jara, Alejandro; Hanson, Tim
2015-01-01
This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the book’s structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in on-line software pages.
Congdon, Peter
2014-01-01
This book provides an accessible approach to Bayesian computing and data analysis, with an emphasis on the interpretation of real data sets. Following in the tradition of the successful first edition, this book aims to make a wide range of statistical modeling applications accessible using tested code that can be readily adapted to the reader's own applications. The second edition has been thoroughly reworked and updated to take account of advances in the field. A new set of worked examples is included. The novel aspect of the first edition was the coverage of statistical modeling using WinBU
Bayesian estimation of isotopic age differences
International Nuclear Information System (INIS)
Curl, R.L.
1988-01-01
Isotopic dating is subject to uncertainties arising from counting statistics and experimental errors. These uncertainties are additive when an isotopic age difference is calculated. If large, they can lead to no significant age difference by classical statistics. In many cases, relative ages are known because of stratigraphic order or other clues. Such information can be used to establish a Bayes estimate of age difference which will include prior knowledge of age order. Age measurement errors are assumed to be log-normal and a noninformative but constrained bivariate prior for two true ages in known order is adopted. True-age ratio is distributed as a truncated log-normal variate. Its expected value gives an age-ratio estimate, and its variance provides credible intervals. Bayesian estimates of ages are different and in correct order even if measured ages are identical or reversed in order. For example, age measurements on two samples might both yield 100 ka with coefficients of variation of 0.2. Bayesian estimates are 22.7 ka for age difference with a 75% credible interval of [4.4, 43.7] ka
A Robust Bayesian Truth Serum for Small Populations
Parkes, David C.; Witkowski, Jens
2012-01-01
Peer prediction mechanisms allow the truthful elicitation of private signals (e.g., experiences, or opinions) in regard to a true world state when this ground truth is unobservable. The original peer prediction method is incentive compatible for any number of agents n >= 2, but relies on a common prior, shared by all agents and the mechanism. The Bayesian Truth Serum (BTS) relaxes this assumption. While BTS still assumes that agents share a common prior, this prior need not be known to the me...
Inference in hybrid Bayesian networks
DEFF Research Database (Denmark)
Lanseth, Helge; Nielsen, Thomas Dyhre; Rumí, Rafael
2009-01-01
Since the 1980s, Bayesian Networks (BNs) have become increasingly popular for building statistical models of complex systems. This is particularly true for boolean systems, where BNs often prove to be a more efficient modelling framework than traditional reliability-techniques (like fault trees...... decade's research on inference in hybrid Bayesian networks. The discussions are linked to an example model for estimating human reliability....
Searching Algorithm Using Bayesian Updates
Caudle, Kyle
2010-01-01
In late October 1967, the USS Scorpion was lost at sea, somewhere between the Azores and Norfolk Virginia. Dr. Craven of the U.S. Navy's Special Projects Division is credited with using Bayesian Search Theory to locate the submarine. Bayesian Search Theory is a straightforward and interesting application of Bayes' theorem which involves searching…
Bayesian Group Bridge for Bi-level Variable Selection.
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.
Bayesian log-periodic model for financial crashes
DEFF Research Database (Denmark)
Rodríguez-Caballero, Carlos Vladimir; Knapik, Oskar
2014-01-01
This paper introduces a Bayesian approach in econophysics literature about financial bubbles in order to estimate the most probable time for a financial crash to occur. To this end, we propose using noninformative prior distributions to obtain posterior distributions. Since these distributions...... cannot be performed analytically, we develop a Markov Chain Monte Carlo algorithm to draw from posterior distributions. We consider three Bayesian models that involve normal and Student’s t-distributions in the disturbances and an AR(1)-GARCH(1,1) structure only within the first case. In the empirical...... part of the study, we analyze a well-known example of financial bubble – the S&P 500 1987 crash – to show the usefulness of the three methods under consideration and crashes of Merval-94, Bovespa-97, IPCMX-94, Hang Seng-97 using the simplest method. The novelty of this research is that the Bayesian...
Bayesian dynamic mediation analysis.
Huang, Jing; Yuan, Ying
2017-12-01
Most existing methods for mediation analysis assume that mediation is a stationary, time-invariant process, which overlooks the inherently dynamic nature of many human psychological processes and behavioral activities. In this article, we consider mediation as a dynamic process that continuously changes over time. We propose Bayesian multilevel time-varying coefficient models to describe and estimate such dynamic mediation effects. By taking the nonparametric penalized spline approach, the proposed method is flexible and able to accommodate any shape of the relationship between time and mediation effects. Simulation studies show that the proposed method works well and faithfully reflects the true nature of the mediation process. By modeling mediation effect nonparametrically as a continuous function of time, our method provides a valuable tool to help researchers obtain a more complete understanding of the dynamic nature of the mediation process underlying psychological and behavioral phenomena. We also briefly discuss an alternative approach of using dynamic autoregressive mediation model to estimate the dynamic mediation effect. The computer code is provided to implement the proposed Bayesian dynamic mediation analysis. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Approximate Bayesian computation.
Directory of Open Access Journals (Sweden)
Mikael Sunnåker
Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.
Tobacco advertising in retail stores.
Cummings, K M; Sciandra, R; Lawrence, J
1991-01-01
Recent studies have described tobacco advertising in the print media, on billboards, and through sponsorship of cultural and sporting events. However, little attention has been given to another common and unavoidable source of tobacco advertising, that which is encountered in retail stores. In July 1987, we conducted a survey of 61 packaged goods retail stores in Buffalo, NY, to assess the prevalence and type of point-of-sale tobacco advertising. In addition, store owners or managers were surveyed to determine their store's policy regarding tobacco advertising, receipt of monetary incentives from distributors for displaying tobacco ads, and willingness to display antitobacco ads. Six types of stores were involved in the study: 10 supermarkets, 10 privately owned grocery stores, 9 chain convenience food stores that do not sell gasoline, 11 chain convenience food stores that sell gasoline, 11 chain pharmacies, and 10 private pharmacies. Two-thirds of the stores displayed tobacco posters, and 87 percent had promotional items advertising tobacco products, primarily cigarettes. Larger stores, and those that were privately owned, tended to display more posters and promotional items. Eighty percent of tobacco product displays were for cigarettes, 16 percent for smokeless tobacco products, and 4 percent for cigars and pipe tobacco. Convenience stores selling gasoline had the most separate tobacco product displays. Of tobacco product displays, 24 percent were located adjacent to candy and snack displays. Twenty-nine of the 61 store owners or managers indicated that their store had a policy regulating the display of tobacco ads and tobacco product displays.(ABSTRACT TRUNCATED AT 250 WORDS) PMID:1910192
Bayesian inference with ecological applications
Link, William A
2009-01-01
This text is written to provide a mathematically sound but accessible and engaging introduction to Bayesian inference specifically for environmental scientists, ecologists and wildlife biologists. It emphasizes the power and usefulness of Bayesian methods in an ecological context. The advent of fast personal computers and easily available software has simplified the use of Bayesian and hierarchical models . One obstacle remains for ecologists and wildlife biologists, namely the near absence of Bayesian texts written specifically for them. The book includes many relevant examples, is supported by software and examples on a companion website and will become an essential grounding in this approach for students and research ecologists. Engagingly written text specifically designed to demystify a complex subject Examples drawn from ecology and wildlife research An essential grounding for graduate and research ecologists in the increasingly prevalent Bayesian approach to inference Companion website with analyt...
Bayesian Inference on Gravitational Waves
Directory of Open Access Journals (Sweden)
Asad Ali
2015-12-01
Full Text Available The Bayesian approach is increasingly becoming popular among the astrophysics data analysis communities. However, the Pakistan statistics communities are unaware of this fertile interaction between the two disciplines. Bayesian methods have been in use to address astronomical problems since the very birth of the Bayes probability in eighteenth century. Today the Bayesian methods for the detection and parameter estimation of gravitational waves have solid theoretical grounds with a strong promise for the realistic applications. This article aims to introduce the Pakistan statistics communities to the applications of Bayesian Monte Carlo methods in the analysis of gravitational wave data with an overview of the Bayesian signal detection and estimation methods and demonstration by a couple of simplified examples.
Acquisition of multiple prior distributions in tactile temporal order judgment
Directory of Open Access Journals (Sweden)
Yasuhito eNagai
2012-08-01
Full Text Available The Bayesian estimation theory proposes that the brain acquires the prior distribution of a task and integrates it with sensory signals to minimize the effect of sensory noise. Psychophysical studies have demonstrated that our brain actually implements Bayesian estimation in a variety of sensory-motor tasks. However, these studies only imposed one prior distribution on participants within a task period. In this study, we investigated the conditions that enable the acquisition of multiple prior distributions in temporal order judgment (TOJ of two tactile stimuli across the hands. In Experiment 1, stimulation intervals were randomly selected from one of two prior distributions (biased to right hand earlier and biased to left hand earlier in association with color cues (green and red, respectively. Although the acquisition of the two priors was not enabled by the color cues alone, it was significant when participants shifted their gaze (above or below in response to the color cues. However, the acquisition of multiple priors was not significant when participants moved their mouths (opened or closed. In Experiment 2, the spatial cues (above and below were used to identify which eye position or retinal cue position was crucial for the eye-movement-dependent acquisition of multiple priors in Experiment 1. The acquisition of the two priors was significant when participants moved their gaze to the cues (i.e., the cue positions on the retina were constant across the priors, as well as when participants did not shift their gazes (i.e., the cue positions on the retina changed according to the priors. Thus, both eye and retinal cue positions were effective in acquiring multiple priors. Based on previous neurophysiological reports, we discuss possible neural correlates that contribute to the acquisition of multiple priors.
Borsboom, D.; Haig, B.D.
2013-01-01
Unlike most other statistical frameworks, Bayesian statistical inference is wedded to a particular approach in the philosophy of science (see Howson & Urbach, 2006); this approach is called Bayesianism. Rather than being concerned with model fitting, this position in the philosophy of science
Tobacco advertising in retail stores.
Cummings, K M; Sciandra, R; Lawrence, J
1991-01-01
Recent studies have described tobacco advertising in the print media, on billboards, and through sponsorship of cultural and sporting events. However, little attention has been given to another common and unavoidable source of tobacco advertising, that which is encountered in retail stores. In July 1987, we conducted a survey of 61 packaged goods retail stores in Buffalo, NY, to assess the prevalence and type of point-of-sale tobacco advertising. In addition, store owners or managers were sur...
Deriving proper uniform priors for regression coefficients, Parts I, II, and III
van Erp, H.R.N.; Linger, R.O.; van Gelder, P.H.A.J.M.
2017-01-01
It is a relatively well-known fact that in problems of Bayesian model selection, improper priors should, in general, be avoided. In this paper we will derive and discuss a collection of four proper uniform priors which lie on an ascending scale of informativeness. It will turn out that these
Bayesian inference of chemical kinetic models from proposed reactions
Galagali, Nikhil
2015-02-01
© 2014 Elsevier Ltd. Bayesian inference provides a natural framework for combining experimental data with prior knowledge to develop chemical kinetic models and quantify the associated uncertainties, not only in parameter values but also in model structure. Most existing applications of Bayesian model selection methods to chemical kinetics have been limited to comparisons among a small set of models, however. The significant computational cost of evaluating posterior model probabilities renders traditional Bayesian methods infeasible when the model space becomes large. We present a new framework for tractable Bayesian model inference and uncertainty quantification using a large number of systematically generated model hypotheses. The approach involves imposing point-mass mixture priors over rate constants and exploring the resulting posterior distribution using an adaptive Markov chain Monte Carlo method. The posterior samples are used to identify plausible models, to quantify rate constant uncertainties, and to extract key diagnostic information about model structure-such as the reactions and operating pathways most strongly supported by the data. We provide numerical demonstrations of the proposed framework by inferring kinetic models for catalytic steam and dry reforming of methane using available experimental data.
Testability evaluation using prior information of multiple sources
Directory of Open Access Journals (Sweden)
Wang Chao
2014-08-01
Full Text Available Testability plays an important role in improving the readiness and decreasing the life-cycle cost of equipment. Testability demonstration and evaluation is of significance in measuring such testability indexes as fault detection rate (FDR and fault isolation rate (FIR, which is useful to the producer in mastering the testability level and improving the testability design, and helpful to the consumer in making purchase decisions. Aiming at the problems with a small sample of testability demonstration test data (TDTD such as low evaluation confidence and inaccurate result, a testability evaluation method is proposed based on the prior information of multiple sources and Bayes theory. Firstly, the types of prior information are analyzed. The maximum entropy method is applied to the prior information with the mean and interval estimate forms on the testability index to obtain the parameters of prior probability density function (PDF, and the empirical Bayesian method is used to get the parameters for the prior information with a success-fail form. Then, a parametrical data consistency check method is used to check the compatibility between all the sources of prior information and TDTD. For the prior information to pass the check, the prior credibility is calculated. A mixed prior distribution is formed based on the prior PDFs and the corresponding credibility. The Bayesian posterior distribution model is acquired with the mixed prior distribution and TDTD, based on which the point and interval estimates are calculated. Finally, examples of a flying control system are used to verify the proposed method. The results show that the proposed method is feasible and effective.
Testability evaluation using prior information of multiple sources
Institute of Scientific and Technical Information of China (English)
Wang Chao; Qiu Jing; Liu Guanjun; Zhang Yong
2014-01-01
Testability plays an important role in improving the readiness and decreasing the life-cycle cost of equipment. Testability demonstration and evaluation is of significance in measuring such testability indexes as fault detection rate (FDR) and fault isolation rate (FIR), which is useful to the producer in mastering the testability level and improving the testability design, and helpful to the consumer in making purchase decisions. Aiming at the problems with a small sample of testabil-ity demonstration test data (TDTD) such as low evaluation confidence and inaccurate result, a test-ability evaluation method is proposed based on the prior information of multiple sources and Bayes theory. Firstly, the types of prior information are analyzed. The maximum entropy method is applied to the prior information with the mean and interval estimate forms on the testability index to obtain the parameters of prior probability density function (PDF), and the empirical Bayesian method is used to get the parameters for the prior information with a success-fail form. Then, a parametrical data consistency check method is used to check the compatibility between all the sources of prior information and TDTD. For the prior information to pass the check, the prior credibility is calculated. A mixed prior distribution is formed based on the prior PDFs and the corresponding credibility. The Bayesian posterior distribution model is acquired with the mixed prior distribution and TDTD, based on which the point and interval estimates are calculated. Finally, examples of a flying control system are used to verify the proposed method. The results show that the proposed method is feasible and effective.
PET reconstruction via nonlocal means induced prior.
Hou, Qingfeng; Huang, Jing; Bian, Zhaoying; Chen, Wufan; Ma, Jianhua
2015-01-01
The traditional Bayesian priors for maximum a posteriori (MAP) reconstruction methods usually incorporate local neighborhood interactions that penalize large deviations in parameter estimates for adjacent pixels; therefore, only local pixel differences are utilized. This limits their abilities of penalizing the image roughness. To achieve high-quality PET image reconstruction, this study investigates a MAP reconstruction strategy by incorporating a nonlocal means induced (NLMi) prior (NLMi-MAP) which enables utilizing global similarity information of image. The present NLMi prior approximates the derivative of Gibbs energy function by an NLM filtering process. Specially, the NLMi prior is obtained by subtracting the current image estimation from its NLM filtered version and feeding the residual error back to the reconstruction filter to yield the new image estimation. We tested the present NLMi-MAP method with simulated and real PET datasets. Comparison studies with conventional filtered backprojection (FBP) and a few iterative reconstruction methods clearly demonstrate that the present NLMi-MAP method performs better in lowering noise, preserving image edge and in higher signal to noise ratio (SNR). Extensive experimental results show that the NLMi-MAP method outperforms the existing methods in terms of cross profile, noise reduction, SNR, root mean square error (RMSE) and correlation coefficient (CORR).
Objective Bayesian Analysis of Skew- t Distributions
BRANCO, MARCIA D'ELIA
2012-02-27
We study the Jeffreys prior and its properties for the shape parameter of univariate skew-t distributions with linear and nonlinear Student\\'s t skewing functions. In both cases, we show that the resulting priors for the shape parameter are symmetric around zero and proper. Moreover, we propose a Student\\'s t approximation of the Jeffreys prior that makes an objective Bayesian analysis easy to perform. We carry out a Monte Carlo simulation study that demonstrates an overall better behaviour of the maximum a posteriori estimator compared with the maximum likelihood estimator. We also compare the frequentist coverage of the credible intervals based on the Jeffreys prior and its approximation and show that they are similar. We further discuss location-scale models under scale mixtures of skew-normal distributions and show some conditions for the existence of the posterior distribution and its moments. Finally, we present three numerical examples to illustrate the implications of our results on inference for skew-t distributions. © 2012 Board of the Foundation of the Scandinavian Journal of Statistics.
Bayesian analogy with relational transformations.
Lu, Hongjing; Chen, Dawn; Holyoak, Keith J
2012-07-01
How can humans acquire relational representations that enable analogical inference and other forms of high-level reasoning? Using comparative relations as a model domain, we explore the possibility that bottom-up learning mechanisms applied to objects coded as feature vectors can yield representations of relations sufficient to solve analogy problems. We introduce Bayesian analogy with relational transformations (BART) and apply the model to the task of learning first-order comparative relations (e.g., larger, smaller, fiercer, meeker) from a set of animal pairs. Inputs are coded by vectors of continuous-valued features, based either on human magnitude ratings, normed feature ratings (De Deyne et al., 2008), or outputs of the topics model (Griffiths, Steyvers, & Tenenbaum, 2007). Bootstrapping from empirical priors, the model is able to induce first-order relations represented as probabilistic weight distributions, even when given positive examples only. These learned representations allow classification of novel instantiations of the relations and yield a symbolic distance effect of the sort obtained with both humans and other primates. BART then transforms its learned weight distributions by importance-guided mapping, thereby placing distinct dimensions into correspondence. These transformed representations allow BART to reliably solve 4-term analogies (e.g., larger:smaller::fiercer:meeker), a type of reasoning that is arguably specific to humans. Our results provide a proof-of-concept that structured analogies can be solved with representations induced from unstructured feature vectors by mechanisms that operate in a largely bottom-up fashion. We discuss potential implications for algorithmic and neural models of relational thinking, as well as for the evolution of abstract thought. Copyright 2012 APA, all rights reserved.
Neutrino masses and their ordering: global data, priors and models
Gariazzo, S.; Archidiacono, M.; de Salas, P. F.; Mena, O.; Ternes, C. A.; Tórtola, M.
2018-03-01
We present a full Bayesian analysis of the combination of current neutrino oscillation, neutrinoless double beta decay and Cosmic Microwave Background observations. Our major goal is to carefully investigate the possibility to single out one neutrino mass ordering, namely Normal Ordering or Inverted Ordering, with current data. Two possible parametrizations (three neutrino masses versus the lightest neutrino mass plus the two oscillation mass splittings) and priors (linear versus logarithmic) are exhaustively examined. We find that the preference for NO is only driven by neutrino oscillation data. Moreover, the values of the Bayes factor indicate that the evidence for NO is strong only when the scan is performed over the three neutrino masses with logarithmic priors; for every other combination of parameterization and prior, the preference for NO is only weak. As a by-product of our Bayesian analyses, we are able to (a) compare the Bayesian bounds on the neutrino mixing parameters to those obtained by means of frequentist approaches, finding a very good agreement; (b) determine that the lightest neutrino mass plus the two mass splittings parametrization, motivated by the physical observables, is strongly preferred over the three neutrino mass eigenstates scan and (c) find that logarithmic priors guarantee a weakly-to-moderately more efficient sampling of the parameter space. These results establish the optimal strategy to successfully explore the neutrino parameter space, based on the use of the oscillation mass splittings and a logarithmic prior on the lightest neutrino mass, when combining neutrino oscillation data with cosmology and neutrinoless double beta decay. We also show that the limits on the total neutrino mass ∑ mν can change dramatically when moving from one prior to the other. These results have profound implications for future studies on the neutrino mass ordering, as they crucially state the need for self-consistent analyses which explore the
Book review: Bayesian analysis for population ecology
Link, William A.
2011-01-01
Brian Dennis described the field of ecology as “fertile, uncolonized ground for Bayesian ideas.” He continued: “The Bayesian propagule has arrived at the shore. Ecologists need to think long and hard about the consequences of a Bayesian ecology. The Bayesian outlook is a successful competitor, but is it a weed? I think so.” (Dennis 2004)
DEFF Research Database (Denmark)
Michelsen, Jimmi
2017-01-01
Tekstgennemgang og undervisningsforløb til Dorte Nors "Den store tomat". Undervisningsforløbet er henvendt til elever i folkeskolens udskoling......Tekstgennemgang og undervisningsforløb til Dorte Nors "Den store tomat". Undervisningsforløbet er henvendt til elever i folkeskolens udskoling...
Consumers’ preferences regarding department stores
van Laarhoven, W.; Borgers, A.W.J.; van den Berg, P.E.W.
2017-01-01
The main reason for this research was the bankruptcy of one the Dutch oldest and largest chain of department stores at the end of 2015. The main goal of this research is to find what, from a consumers’ perspective, a department store should look like. A four storey (1500 m2 each) building was
Forhastet regulering af de store
DEFF Research Database (Denmark)
Thomsen, Steen
2013-01-01
Christiansborg gennemfører sandsynligvis en markant skærpet regulering af de store finansielle virksomheder. Det vil virke kontraktivt og medvirke til erhvervslivets kredittørke.......Christiansborg gennemfører sandsynligvis en markant skærpet regulering af de store finansielle virksomheder. Det vil virke kontraktivt og medvirke til erhvervslivets kredittørke....
Example-driven manifold priors for image deconvolution.
Ni, Jie; Turaga, Pavan; Patel, Vishal M; Chellappa, Rama
2011-11-01
Image restoration methods that exploit prior information about images to be estimated have been extensively studied, typically using the Bayesian framework. In this paper, we consider the role of prior knowledge of the object class in the form of a patch manifold to address the deconvolution problem. Specifically, we incorporate unlabeled image data of the object class, say natural images, in the form of a patch-manifold prior for the object class. The manifold prior is implicitly estimated from the given unlabeled data. We show how the patch-manifold prior effectively exploits the available sample class data for regularizing the deblurring problem. Furthermore, we derive a generalized cross-validation (GCV) function to automatically determine the regularization parameter at each iteration without explicitly knowing the noise variance. Extensive experiments show that this method performs better than many competitive image deconvolution methods.
Bayesian inference in processing experimental data: principles and basic applications
International Nuclear Information System (INIS)
D'Agostini, G
2003-01-01
This paper introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as the following: model comparison (including the automatic Ockham's Razor filter provided by the Bayesian approach); parametric inference; quantification of the uncertainty about the value of physical quantities, also taking into account systematic effects; role of marginalization; posterior characterization; predictive distributions; hierarchical modelling and hyperparameters; Gaussian approximation of the posterior and recovery of conventional methods, especially maximum likelihood and chi-square fits under well-defined conditions; conjugate priors, transformation invariance and maximum entropy motivated priors; and Monte Carlo (MC) estimates of expectation, including a short introduction to Markov Chain MC methods
Sparse Bayesian Learning for DOA Estimation with Mutual Coupling
Directory of Open Access Journals (Sweden)
Jisheng Dai
2015-10-01
Full Text Available Sparse Bayesian learning (SBL has given renewed interest to the problem of direction-of-arrival (DOA estimation. It is generally assumed that the measurement matrix in SBL is precisely known. Unfortunately, this assumption may be invalid in practice due to the imperfect manifold caused by unknown or misspecified mutual coupling. This paper describes a modified SBL method for joint estimation of DOAs and mutual coupling coefficients with uniform linear arrays (ULAs. Unlike the existing method that only uses stationary priors, our new approach utilizes a hierarchical form of the Student t prior to enforce the sparsity of the unknown signal more heavily. We also provide a distinct Bayesian inference for the expectation-maximization (EM algorithm, which can update the mutual coupling coefficients more efficiently. Another difference is that our method uses an additional singular value decomposition (SVD to reduce the computational complexity of the signal reconstruction process and the sensitivity to the measurement noise.
On a full Bayesian inference for force reconstruction problems
Aucejo, M.; De Smet, O.
2018-05-01
In a previous paper, the authors introduced a flexible methodology for reconstructing mechanical sources in the frequency domain from prior local information on both their nature and location over a linear and time invariant structure. The proposed approach was derived from Bayesian statistics, because of its ability in mathematically accounting for experimenter's prior knowledge. However, since only the Maximum a Posteriori estimate was computed, the posterior uncertainty about the regularized solution given the measured vibration field, the mechanical model and the regularization parameter was not assessed. To answer this legitimate question, this paper fully exploits the Bayesian framework to provide, from a Markov Chain Monte Carlo algorithm, credible intervals and other statistical measures (mean, median, mode) for all the parameters of the force reconstruction problem.
Analysis of lifespan monitoring data using Bayesian logic
International Nuclear Information System (INIS)
Pozzi, M; Zonta, D; Glisic, B; Inaudi, D; Lau, J M; Fong, C C
2011-01-01
In this contribution, we use a Bayesian approach to analyze the data from a 19-storey building block, which is part of the Punggol EC26 construction project undertaken by the Singapore Housing and Development Board in the early 2000s. The building was instrumented during construction with interferometric fiber optic average strain sensors, embedded in ten of the first story columns during construction. The philosophy driving the design of the monitoring system was to instrument a representative number of structural elements, while maintaining the cost at a reasonable level. The analysis of the data, along with prior experience, allowed the engineer to recognize at early stage an ongoing differential settlement of one base column. We show how the whole cognitive process followed by the engineer can be reproduced using Bayesian logic. Particularly, we discuss to what extent the prior knowledge and potential evidence from inspection, can alter the perception of the building response based solely on instrumental data.
DEFF Research Database (Denmark)
Choi, Sang-Hyeon; Lee, Ikjin; Jeong, Cheol-Ho
2016-01-01
Sabine absorption coefficient is a widely used one deduced from reverberation time measurements via the Sabine equation. First- and second-level Bayesian analysis are used to estimate the flow resistivity of a sound absorber and the influences of the test chambers from Sabine absorption...... coefficients measured in 13 different reverberation chambers. The first-level Bayesian analysis is more general than the second-level Bayesian analysis. Sharper posterior distribution can be acquired by the second-level Bayesian analysis than the one by the first-level Bayesian analysis because more data...... are used to set more reliable prior distribution. The estimated room’s influences by the first- and the second-level Bayesian analyses are similar to the estimated results by the mean absolute error minimization....
Current trends in Bayesian methodology with applications
Upadhyay, Satyanshu K; Dey, Dipak K; Loganathan, Appaia
2015-01-01
Collecting Bayesian material scattered throughout the literature, Current Trends in Bayesian Methodology with Applications examines the latest methodological and applied aspects of Bayesian statistics. The book covers biostatistics, econometrics, reliability and risk analysis, spatial statistics, image analysis, shape analysis, Bayesian computation, clustering, uncertainty assessment, high-energy astrophysics, neural networking, fuzzy information, objective Bayesian methodologies, empirical Bayes methods, small area estimation, and many more topics.Each chapter is self-contained and focuses on
Bayesian Statistics: Concepts and Applications in Animal Breeding – A Review
Directory of Open Access Journals (Sweden)
Lsxmikant-Sambhaji Kokate
2011-07-01
Full Text Available Statistics uses two major approaches- conventional (or frequentist and Bayesian approach. Bayesian approach provides a complete paradigm for both statistical inference and decision making under uncertainty. Bayesian methods solve many of the difficulties faced by conventional statistical methods, and extend the applicability of statistical methods. It exploits the use of probabilistic models to formulate scientific problems. To use Bayesian statistics, there is computational difficulty and secondly, Bayesian methods require specifying prior probability distributions. Markov Chain Monte-Carlo (MCMC methods were applied to overcome the computational difficulty, and interest in Bayesian methods was renewed. In Bayesian statistics, Bayesian structural equation model (SEM is used. It provides a powerful and flexible approach for studying quantitative traits for wide spectrum problems and thus it has no operational difficulties, with the exception of some complex cases. In this method, the problems are solved at ease, and the statisticians feel it comfortable with the particular way of expressing the results and employing the software available to analyze a large variety of problems.
Bayesian maximum posterior probability method for interpreting plutonium urinalysis data
International Nuclear Information System (INIS)
Miller, G.; Inkret, W.C.
1996-01-01
A new internal dosimetry code for interpreting urinalysis data in terms of radionuclide intakes is described for the case of plutonium. The mathematical method is to maximise the Bayesian posterior probability using an entropy function as the prior probability distribution. A software package (MEMSYS) developed for image reconstruction is used. Some advantages of the new code are that it ensures positive calculated dose, it smooths out fluctuating data, and it provides an estimate of the propagated uncertainty in the calculated doses. (author)
A Bayesian Model of the Memory Colour Effect
Witzel, Christoph; Olkkonen, Maria; Gegenfurtner, Karl R.
2018-01-01
According to the memory colour effect, the colour of a colour-diagnostic object is not perceived independently of the object itself. Instead, it has been shown through an achromatic adjustment method that colour-diagnostic objects still appear slightly in their typical colour, even when they are colourimetrically grey. Bayesian models provide a promising approach to capture the effect of prior knowledge on colour perception and to link these effects to more general effects of cue integration....
A Bayesian model of the memory colour effect.
Witzel, Christoph; Olkkonen, Maria; Gegenfurtner, Karl R.
2018-01-01
According to the memory colour effect, the colour of a colour-diagnostic object is not perceived independently of the object itself. Instead, it has been shown through an achromatic adjustment method that colour-diagnostic objects still appear slightly in their typical colour, even when they are colourimetrically grey. Bayesian models provide a promising approach to capture the effect of prior knowledge on colour perception and to link these effects to more general effects of cue integration....
DEFF Research Database (Denmark)
Engerer, Volkmar Paul; Roued-Cunliffe, Henriette; Albretsen, Jørgen
digitisation of Arthur Prior’s Nachlass kept in the Bodleian Library, Oxford. The DH infrastructure in question is the Prior Virtual Lab (PVL). PVL was established in 2011 in order to provide researchers in the field of temporal logic easy access to the papers of Arthur Norman Prior (1914-1969), and officially......In this paper, we present a DH research infrastructure which relies heavily on a combination of domain knowledge with information technology. The general goal is to develop tools to aid scholars in their interpretations and understanding of temporal logic. This in turn is based on an extensive...
Bayesian Networks and Influence Diagrams
DEFF Research Database (Denmark)
Kjærulff, Uffe Bro; Madsen, Anders Læsø
Probabilistic networks, also known as Bayesian networks and influence diagrams, have become one of the most promising technologies in the area of applied artificial intelligence, offering intuitive, efficient, and reliable methods for diagnosis, prediction, decision making, classification......, troubleshooting, and data mining under uncertainty. Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. Intended...
MEASURING GROCERY STORES SERVICE QUALITY IN INDONESIA: A RETAIL SERVICE QUALITY SCALE APPROACH
Directory of Open Access Journals (Sweden)
Leonnard Leonnard
2017-12-01
Full Text Available The growing number of modern grocery stores in Indonesia is a challenge for each grocery store to maintain and increase their number of consumers. The success of maintaining and improving service quality will affect long-term profitability and business sustainability. Therefore, in this study, we examined consumer perceptions of service quality in one of modern grocery stores in Indonesia. Data were collected from 387 consumers of grocery stores in Jakarta, Bogor, Depok, Bekasi, Cibubur, and Subang. Structural Equation Modeling (SEM through Maximum likelihood and Bayesian estimation was employed to analyze the data. The finding indicated that the five indicators of the retail service quality scale consisting of physical aspects, reliability, personal interactions, problem solving and policies provided valid multi-item instruments in measuring consumer perceptions of service quality in grocery stores.
A Bayesian approach to person perception.
Clifford, C W G; Mareschal, I; Otsuka, Y; Watson, T L
2015-11-01
Here we propose a Bayesian approach to person perception, outlining the theoretical position and a methodological framework for testing the predictions experimentally. We use the term person perception to refer not only to the perception of others' personal attributes such as age and sex but also to the perception of social signals such as direction of gaze and emotional expression. The Bayesian approach provides a formal description of the way in which our perception combines current sensory evidence with prior expectations about the structure of the environment. Such expectations can lead to unconscious biases in our perception that are particularly evident when sensory evidence is uncertain. We illustrate the ideas with reference to our recent studies on gaze perception which show that people have a bias to perceive the gaze of others as directed towards themselves. We also describe a potential application to the study of the perception of a person's sex, in which a bias towards perceiving males is typically observed. Copyright © 2015 Elsevier Inc. All rights reserved.
Bayesian nonparametric adaptive control using Gaussian processes.
Chowdhary, Girish; Kingravi, Hassan A; How, Jonathan P; Vela, Patricio A
2015-03-01
Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element is radial basis function networks (RBFNs), with RBF centers preallocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become noneffective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semiglobal in nature. This paper investigates a Gaussian process-based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. The GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed-loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.
Robustifying Bayesian nonparametric mixtures for count data.
Canale, Antonio; Prünster, Igor
2017-03-01
Our motivating application stems from surveys of natural populations and is characterized by large spatial heterogeneity in the counts, which makes parametric approaches to modeling local animal abundance too restrictive. We adopt a Bayesian nonparametric approach based on mixture models and innovate with respect to popular Dirichlet process mixture of Poisson kernels by increasing the model flexibility at the level both of the kernel and the nonparametric mixing measure. This allows to derive accurate and robust estimates of the distribution of local animal abundance and of the corresponding clusters. The application and a simulation study for different scenarios yield also some general methodological implications. Adding flexibility solely at the level of the mixing measure does not improve inferences, since its impact is severely limited by the rigidity of the Poisson kernel with considerable consequences in terms of bias. However, once a kernel more flexible than the Poisson is chosen, inferences can be robustified by choosing a prior more general than the Dirichlet process. Therefore, to improve the performance of Bayesian nonparametric mixtures for count data one has to enrich the model simultaneously at both levels, the kernel and the mixing measure. © 2016, The International Biometric Society.
Classical-Equivalent Bayesian Portfolio Optimization for Electricity Generation Planning
Directory of Open Access Journals (Sweden)
Hellinton H. Takada
2018-01-01
Full Text Available There are several electricity generation technologies based on different sources such as wind, biomass, gas, coal, and so on. The consideration of the uncertainties associated with the future costs of such technologies is crucial for planning purposes. In the literature, the allocation of resources in the available technologies has been solved as a mean-variance optimization problem assuming knowledge of the expected values and the covariance matrix of the costs. However, in practice, they are not exactly known parameters. Consequently, the obtained optimal allocations from the mean-variance optimization are not robust to possible estimation errors of such parameters. Additionally, it is usual to have electricity generation technology specialists participating in the planning processes and, obviously, the consideration of useful prior information based on their previous experience is of utmost importance. The Bayesian models consider not only the uncertainty in the parameters, but also the prior information from the specialists. In this paper, we introduce the classical-equivalent Bayesian mean-variance optimization to solve the electricity generation planning problem using both improper and proper prior distributions for the parameters. In order to illustrate our approach, we present an application comparing the classical-equivalent Bayesian with the naive mean-variance optimal portfolios.
DEFF Research Database (Denmark)
Blackburn, Patrick Rowan; Jørgensen, Klaus Frovin
2016-01-01
’s search led him through the work of Castañeda, and back to his own work on hybrid logic: the first made temporal reference philosophically respectable, the second made it technically feasible in a modal framework. With the aid of hybrid logic, Prior built a bridge from a two-dimensional UT calculus...
Prior Knowledge Assessment Guide
2014-12-01
assessment in a reasonable amount of time. Hands-on assessments can be extremely diverse in makeup and administration depending on the subject matter...DEVELOPING AND USING PRIOR KNOWLEDGE ASSESSMENTS TO TAILOR TRAINING D-3 ___ Brush and scrub ___ Orchards ___ Rice
Extended Linear Models with Gaussian Priors
DEFF Research Database (Denmark)
Quinonero, Joaquin
2002-01-01
In extended linear models the input space is projected onto a feature space by means of an arbitrary non-linear transformation. A linear model is then applied to the feature space to construct the model output. The dimension of the feature space can be very large, or even infinite, giving the model...... a very big flexibility. Support Vector Machines (SVM's) and Gaussian processes are two examples of such models. In this technical report I present a model in which the dimension of the feature space remains finite, and where a Bayesian approach is used to train the model with Gaussian priors...... on the parameters. The Relevance Vector Machine, introduced by Tipping, is a particular case of such a model. I give the detailed derivations of the expectation-maximisation (EM) algorithm used in the training. These derivations are not found in the literature, and might be helpful for newcomers....
Numerical Methods for Bayesian Inverse Problems
Ernst, Oliver
2014-01-06
We present recent results on Bayesian inversion for a groundwater flow problem with an uncertain conductivity field. In particular, we show how direct and indirect measurements can be used to obtain a stochastic model for the unknown. The main tool here is Bayes’ theorem which merges the indirect data with the stochastic prior model for the conductivity field obtained by the direct measurements. Further, we demonstrate how the resulting posterior distribution of the quantity of interest, in this case travel times of radionuclide contaminants, can be obtained by Markov Chain Monte Carlo (MCMC) simulations. Moreover, we investigate new, promising MCMC methods which exploit geometrical features of the posterior and which are suited to infinite dimensions.
Numerical Methods for Bayesian Inverse Problems
Ernst, Oliver; Sprungk, Bjorn; Cliffe, K. Andrew; Starkloff, Hans-Jorg
2014-01-01
We present recent results on Bayesian inversion for a groundwater flow problem with an uncertain conductivity field. In particular, we show how direct and indirect measurements can be used to obtain a stochastic model for the unknown. The main tool here is Bayes’ theorem which merges the indirect data with the stochastic prior model for the conductivity field obtained by the direct measurements. Further, we demonstrate how the resulting posterior distribution of the quantity of interest, in this case travel times of radionuclide contaminants, can be obtained by Markov Chain Monte Carlo (MCMC) simulations. Moreover, we investigate new, promising MCMC methods which exploit geometrical features of the posterior and which are suited to infinite dimensions.
Variational Bayesian Inference of Line Spectra
DEFF Research Database (Denmark)
Badiu, Mihai Alin; Hansen, Thomas Lundgaard; Fleury, Bernard Henri
2017-01-01
parameters. We propose an accurate representation of the pdfs of the frequencies by mixtures of von Mises pdfs, which yields closed-form expectations. We define the algorithm VALSE in which the estimates of the pdfs and parameters are iteratively updated. VALSE is a gridless, convergent method, does......; and the coefficients are governed by a Bernoulli-Gaussian prior model turning model order selection into binary sequence detection. Unlike earlier works which retain only point estimates of the frequencies, we undertake a more complete Bayesian treatment by estimating the posterior probability density functions (pdfs......) of the frequencies and computing expectations over them. Thus, we additionally capture and operate with the uncertainty of the frequency estimates. Aiming to maximize the model evidence, variational optimization provides analytic approximations of the posterior pdfs and also gives estimates of the additional...
Bayesian Age-Period-Cohort Modeling and Prediction - BAMP
Directory of Open Access Journals (Sweden)
Volker J. Schmid
2007-10-01
Full Text Available The software package BAMP provides a method of analyzing incidence or mortality data on the Lexis diagram, using a Bayesian version of an age-period-cohort model. A hierarchical model is assumed with a binomial model in the first-stage. As smoothing priors for the age, period and cohort parameters random walks of first and second order, with and without an additional unstructured component are available. Unstructured heterogeneity can also be included in the model. In order to evaluate the model fit, posterior deviance, DIC and predictive deviances are computed. By projecting the random walk prior into the future, future death rates can be predicted.
Bayesian modeling to paired comparison data via the Pareto distribution
Directory of Open Access Journals (Sweden)
Nasir Abbas
2017-12-01
Full Text Available A probabilistic approach to build models for paired comparison experiments based on the comparison of two Pareto variables is considered. Analysis of the proposed model is carried out in classical as well as Bayesian frameworks. Informative and uninformative priors are employed to accommodate the prior information. Simulation study is conducted to assess the suitablily and performance of the model under theoretical conditions. Appropriateness of fit of the is also carried out. Entire inferential procedure is illustrated by comparing certain cricket teams using real dataset.
Allegheny County Supermarkets & Convenience Stores
Allegheny County / City of Pittsburgh / Western PA Regional Data Center — Location information for all Supermarkets and Convenience Stores in Allegheny County was produced using the Allegheny County Fee and Permit Data for 2016.
Information from the central stores
GS Department
2010-01-01
All items sold in the CERN shop (Bldg. 33) are now available in the central stores (Bldg. 73) and can be purchased on-line via EDH “Material Request” or at the “Emergency Desk” of the stores on the ground floor of Bldg. 73. These items are visible in the CERN catalogue under the “SCEM” codes beginning with 92. Department of General Infrastructure Services (GS) GS-SEM Group
Hemoglobin Function in Stored Blood.
1974-08-01
States during 1973. Several advantages over ACA) are important. Blood stored in CPD maintains higher ./ levels of 2,3-DPG (2,3- diphosphoglycerate ) and a...survival and ATP levels in stored blood is explained by the several functions of ATP which are necessary for cell viability. However, ATP levels do...not correlate with oxygen affinity during storage. Levels of 2,3-DPG determine oxygen affinity and thus hemoglobin function. (12,13) When normal levels
Bayesian exploration for intelligent identification of textures
Directory of Open Access Journals (Sweden)
Jeremy A. Fishel
2012-06-01
Full Text Available In order to endow robots with humanlike abilities to characterize and identify objects, they must be provided with tactile sensors and intelligent algorithms to select, control and interpret data from useful exploratory movements. Humans make informed decisions on the sequence of exploratory movements that would yield the most information for the task, depending on what the object may be and prior knowledge of what to expect from possible exploratory movements. This study is focused on texture discrimination, a subset of a much larger group of exploratory movements and percepts that humans use to discriminate, characterize, and identify objects. Using a testbed equipped with a biologically inspired tactile sensor (the BioTac® we produced sliding movements similar to those that humans make when exploring textures. Measurement of tactile vibrations and reaction forces when exploring textures were used to extract measures of textural properties inspired from psychophysical literature (traction, roughness, and fineness. Different combinations of normal force and velocity were identified to be useful for each of these three properties. A total of 117 textures were explored with these three movements to create a database of prior experience to use for identifying these same textures in future encounters. When exploring a texture, the discrimination algorithm adaptively selects the optimal movement to make and property to measure based on previous experience to differentiate the texture from a set of plausible candidates, a process we call Bayesian exploration. Performance of 99.6% in correctly discriminating pairs of similar textures was found to exceed human capabilities. Absolute classification from the entire set of 117 textures generally required a small number of well-chosen exploratory movements (median=5 and yielded a 95.4% success rate. The method of Bayesian exploration developed and tested in this paper may generalize well to other
A Noninformative Prior on a Space of Distribution Functions
Directory of Open Access Journals (Sweden)
Alexander Terenin
2017-07-01
Full Text Available In a given problem, the Bayesian statistical paradigm requires the specification of a prior distribution that quantifies relevant information about the unknowns of main interest external to the data. In cases where little such information is available, the problem under study may possess an invariance under a transformation group that encodes a lack of information, leading to a unique prior—this idea was explored at length by E.T. Jaynes. Previous successful examples have included location-scale invariance under linear transformation, multiplicative invariance of the rate at which events in a counting process are observed, and the derivation of the Haldane prior for a Bernoulli success probability. In this paper we show that this method can be extended, by generalizing Jaynes, in two ways: (1 to yield families of approximately invariant priors; and (2 to the infinite-dimensional setting, yielding families of priors on spaces of distribution functions. Our results can be used to describe conditions under which a particular Dirichlet Process posterior arises from an optimal Bayesian analysis, in the sense that invariances in the prior and likelihood lead to one and only one posterior distribution.
Development of uncertainty-based work injury model using Bayesian structural equation modelling.
Chatterjee, Snehamoy
2014-01-01
This paper proposed a Bayesian method-based structural equation model (SEM) of miners' work injury for an underground coal mine in India. The environmental and behavioural variables for work injury were identified and causal relationships were developed. For Bayesian modelling, prior distributions of SEM parameters are necessary to develop the model. In this paper, two approaches were adopted to obtain prior distribution for factor loading parameters and structural parameters of SEM. In the first approach, the prior distributions were considered as a fixed distribution function with specific parameter values, whereas, in the second approach, prior distributions of the parameters were generated from experts' opinions. The posterior distributions of these parameters were obtained by applying Bayesian rule. The Markov Chain Monte Carlo sampling in the form Gibbs sampling was applied for sampling from the posterior distribution. The results revealed that all coefficients of structural and measurement model parameters are statistically significant in experts' opinion-based priors, whereas, two coefficients are not statistically significant when fixed prior-based distributions are applied. The error statistics reveals that Bayesian structural model provides reasonably good fit of work injury with high coefficient of determination (0.91) and less mean squared error as compared to traditional SEM.
CORPORATE REBRANDING OF GRAMEDIA STORE (CORPORATE REBRANDING DI GRAMEDIA STORE
Directory of Open Access Journals (Sweden)
Natasha Helena Kairupan
2016-10-01
Full Text Available Abstract. The purposes of this research are to determine the stages of analysis, planning, and evaluation of corporate rebranding process of Gramedia Book Store to be Gramedia Store to rise stakeholder’s awareness. The method used is descriptive qualitative with positivism paradigm. The technique of collecting data through in-depth interview, observation, and literature study. The result of this research showed the analysis stage by analyzing the market through insights and foresights, brand audit through SWOT analysis, and identifying opportunities. The planning stage is by determine the purpose of the planning process and then determine the target audience, consist of external and internal customer. The planning of external customer by renaming and change of corporate identity, and marketing planning using communication channel (above the line and below the line. The planning of internal customer by Brand Induction, training, inspiration briefing at store, and innovation competition. The evaluation of rebranding process of Gramedia Store is having a focus group discussion with customer, media monitoring, and presentation to BOD. Keywords : Process, Corporate Rebranding, Stakeholder Awareness, Corporate Identity, Gramedia Store Abstrak.Tujuan penelitian ini adalah untuk mengetahui bagaimana tahapan analisis, perencanaan, dan evaluasi proses corporate rebranding Gramedia Book Store menjadi Gramedia Store untuk meningkatkan stakeholder awareness. Pendekatan yang digunakan adalah kualitatif dengan paradigma positivisme dan jenis studi deksriptif. Teknik pengumpulan data yang dilakukan melalui wawancara mendalam, observasi, dan studi pustaka. Berdasarkan hasil penelitian, tahapan analisis dilakukan dengan menganalisis pasar melalui insights dan foresights, audit merek dengan analisis SWOT, dan mengidentifikasi peluang. Dalam tahapan perencanaan dengan menentukan tujuan kemudian menentukan target audiens, yaitu eksternal dan internal. Perencanaan
Bayesian seismic AVO inversion
Energy Technology Data Exchange (ETDEWEB)
Buland, Arild
2002-07-01
A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P-wave velocity, S-wave velocity and density. Distributions for other elastic parameters can also be assessed, for example acoustic impedance, shear impedance and P-wave to S-wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance, hence exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3-D dataset from the Sleipner Field. The results show good agreement with well logs but the uncertainty is high. The stochastic model includes uncertainties of both the elastic parameters, the wavelet and the seismic and well log data. The posterior distribution is explored by Markov chain Monte Carlo simulation using the Gibbs sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The uncertainty of the estimated wavelet is low. In the Heidrun examples the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results. We have developed a 3-D linearized AVO inversion method with spatially coupled model parameters where the objective is to obtain posterior distributions for P-wave velocity, S
A Bayesian approach to meta-analysis of plant pathology studies.
Mila, A L; Ngugi, H K
2011-01-01
Bayesian statistical methods are used for meta-analysis in many disciplines, including medicine, molecular biology, and engineering, but have not yet been applied for quantitative synthesis of plant pathology studies. In this paper, we illustrate the key concepts of Bayesian statistics and outline the differences between Bayesian and classical (frequentist) methods in the way parameters describing population attributes are considered. We then describe a Bayesian approach to meta-analysis and present a plant pathological example based on studies evaluating the efficacy of plant protection products that induce systemic acquired resistance for the management of fire blight of apple. In a simple random-effects model assuming a normal distribution of effect sizes and no prior information (i.e., a noninformative prior), the results of the Bayesian meta-analysis are similar to those obtained with classical methods. Implementing the same model with a Student's t distribution and a noninformative prior for the effect sizes, instead of a normal distribution, yields similar results for all but acibenzolar-S-methyl (Actigard) which was evaluated only in seven studies in this example. Whereas both the classical (P = 0.28) and the Bayesian analysis with a noninformative prior (95% credibility interval [CRI] for the log response ratio: -0.63 to 0.08) indicate a nonsignificant effect for Actigard, specifying a t distribution resulted in a significant, albeit variable, effect for this product (CRI: -0.73 to -0.10). These results confirm the sensitivity of the analytical outcome (i.e., the posterior distribution) to the choice of prior in Bayesian meta-analyses involving a limited number of studies. We review some pertinent literature on more advanced topics, including modeling of among-study heterogeneity, publication bias, analyses involving a limited number of studies, and methods for dealing with missing data, and show how these issues can be approached in a Bayesian framework
Estimating Functions with Prior Knowledge, (EFPK) for diffusions
DEFF Research Database (Denmark)
Nolsøe, Kim; Kessler, Mathieu; Madsen, Henrik
2003-01-01
In this paper a method is formulated in an estimating function setting for parameter estimation, which allows the use of prior information. The main idea is to use prior knowledge of the parameters, either specified as moments restrictions or as a distribution, and use it in the construction of a...... of an estimating function. It may be useful when the full Bayesian analysis is difficult to carry out for computational reasons. This is almost always the case for diffusions, which is the focus of this paper, though the method applies in other settings.......In this paper a method is formulated in an estimating function setting for parameter estimation, which allows the use of prior information. The main idea is to use prior knowledge of the parameters, either specified as moments restrictions or as a distribution, and use it in the construction...
The Bayesian Approach to Association
Arora, N. S.
2017-12-01
The Bayesian approach to Association focuses mainly on quantifying the physics of the domain. In the case of seismic association for instance let X be the set of all significant events (above some threshold) and their attributes, such as location, time, and magnitude, Y1 be the set of detections that are caused by significant events and their attributes such as seismic phase, arrival time, amplitude etc., Y2 be the set of detections that are not caused by significant events, and finally Y be the set of observed detections We would now define the joint distribution P(X, Y1, Y2, Y) = P(X) P(Y1 | X) P(Y2) I(Y = Y1 + Y2) ; where the last term simply states that Y1 and Y2 are a partitioning of Y. Given the above joint distribution the inference problem is simply to find the X, Y1, and Y2 that maximizes posterior probability P(X, Y1, Y2| Y) which reduces to maximizing P(X) P(Y1 | X) P(Y2) I(Y = Y1 + Y2). In this expression P(X) captures our prior belief about event locations. P(Y1 | X) captures notions of travel time, residual error distributions as well as detection and mis-detection probabilities. While P(Y2) captures the false detection rate of our seismic network. The elegance of this approach is that all of the assumptions are stated clearly in the model for P(X), P(Y1|X) and P(Y2). The implementation of the inference is merely a by-product of this model. In contrast some of the other methods such as GA hide a number of assumptions in the implementation details of the inference - such as the so called "driver cells." The other important aspect of this approach is that all seismic knowledge including knowledge from other domains such as infrasound and hydroacoustic can be included in the same model. So, we don't need to separately account for misdetections or merge seismic and infrasound events as a separate step. Finally, it should be noted that the objective of automatic association is to simplify the job of humans who are publishing seismic bulletins based on this
Bayesian networks improve causal environmental ...
Rule-based weight of evidence approaches to ecological risk assessment may not account for uncertainties and generally lack probabilistic integration of lines of evidence. Bayesian networks allow causal inferences to be made from evidence by including causal knowledge about the problem, using this knowledge with probabilistic calculus to combine multiple lines of evidence, and minimizing biases in predicting or diagnosing causal relationships. Too often, sources of uncertainty in conventional weight of evidence approaches are ignored that can be accounted for with Bayesian networks. Specifying and propagating uncertainties improve the ability of models to incorporate strength of the evidence in the risk management phase of an assessment. Probabilistic inference from a Bayesian network allows evaluation of changes in uncertainty for variables from the evidence. The network structure and probabilistic framework of a Bayesian approach provide advantages over qualitative approaches in weight of evidence for capturing the impacts of multiple sources of quantifiable uncertainty on predictions of ecological risk. Bayesian networks can facilitate the development of evidence-based policy under conditions of uncertainty by incorporating analytical inaccuracies or the implications of imperfect information, structuring and communicating causal issues through qualitative directed graph formulations, and quantitatively comparing the causal power of multiple stressors on value
Bayesian Latent Class Analysis Tutorial.
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.
Kernel Bayesian ART and ARTMAP.
Masuyama, Naoki; Loo, Chu Kiong; Dawood, Farhan
2018-02-01
Adaptive Resonance Theory (ART) is one of the successful approaches to resolving "the plasticity-stability dilemma" in neural networks, and its supervised learning model called ARTMAP is a powerful tool for classification. Among several improvements, such as Fuzzy or Gaussian based models, the state of art model is Bayesian based one, while solving the drawbacks of others. However, it is known that the Bayesian approach for the high dimensional and a large number of data requires high computational cost, and the covariance matrix in likelihood becomes unstable. This paper introduces Kernel Bayesian ART (KBA) and ARTMAP (KBAM) by integrating Kernel Bayes' Rule (KBR) and Correntropy Induced Metric (CIM) to Bayesian ART (BA) and ARTMAP (BAM), respectively, while maintaining the properties of BA and BAM. The kernel frameworks in KBA and KBAM are able to avoid the curse of dimensionality. In addition, the covariance-free Bayesian computation by KBR provides the efficient and stable computational capability to KBA and KBAM. Furthermore, Correntropy-based similarity measurement allows improving the noise reduction ability even in the high dimensional space. The simulation experiments show that KBA performs an outstanding self-organizing capability than BA, and KBAM provides the superior classification ability than BAM, respectively. Copyright © 2017 Elsevier Ltd. All rights reserved.
Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach
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.
Bayesian logistic regression approaches to predict incorrect DRG assignment.
Suleiman, Mani; Demirhan, Haydar; Boyd, Leanne; Girosi, Federico; Aksakalli, Vural
2018-05-07
Episodes of care involving similar diagnoses and treatments and requiring similar levels of resource utilisation are grouped to the same Diagnosis-Related Group (DRG). In jurisdictions which implement DRG based payment systems, DRGs are a major determinant of funding for inpatient care. Hence, service providers often dedicate auditing staff to the task of checking that episodes have been coded to the correct DRG. The use of statistical models to estimate an episode's probability of DRG error can significantly improve the efficiency of clinical coding audits. This study implements Bayesian logistic regression models with weakly informative prior distributions to estimate the likelihood that episodes require a DRG revision, comparing these models with each other and to classical maximum likelihood estimates. All Bayesian approaches had more stable model parameters than maximum likelihood. The best performing Bayesian model improved overall classification per- formance by 6% compared to maximum likelihood, with a 34% gain compared to random classification, respectively. We found that the original DRG, coder and the day of coding all have a significant effect on the likelihood of DRG error. Use of Bayesian approaches has improved model parameter stability and classification accuracy. This method has already lead to improved audit efficiency in an operational capacity.
Bayesian estimation of the discrete coefficient of determination.
Chen, Ting; Braga-Neto, Ulisses M
2016-12-01
The discrete coefficient of determination (CoD) measures the nonlinear interaction between discrete predictor and target variables and has had far-reaching applications in Genomic Signal Processing. Previous work has addressed the inference of the discrete CoD using classical parametric and nonparametric approaches. In this paper, we introduce a Bayesian framework for the inference of the discrete CoD. We derive analytically the optimal minimum mean-square error (MMSE) CoD estimator, as well as a CoD estimator based on the Optimal Bayesian Predictor (OBP). For the latter estimator, exact expressions for its bias, variance, and root-mean-square (RMS) are given. The accuracy of both Bayesian CoD estimators with non-informative and informative priors, under fixed or random parameters, is studied via analytical and numerical approaches. We also demonstrate the application of the proposed Bayesian approach in the inference of gene regulatory networks, using gene-expression data from a previously published study on metastatic melanoma.
A Bayesian Markov geostatistical model for estimation of hydrogeological properties
International Nuclear Information System (INIS)
Rosen, L.; Gustafson, G.
1996-01-01
A geostatistical methodology based on Markov-chain analysis and Bayesian statistics was developed for probability estimations of hydrogeological and geological properties in the siting process of a nuclear waste repository. The probability estimates have practical use in decision-making on issues such as siting, investigation programs, and construction design. The methodology is nonparametric which makes it possible to handle information that does not exhibit standard statistical distributions, as is often the case for classified information. Data do not need to meet the requirements on additivity and normality as with the geostatistical methods based on regionalized variable theory, e.g., kriging. The methodology also has a formal way for incorporating professional judgments through the use of Bayesian statistics, which allows for updating of prior estimates to posterior probabilities each time new information becomes available. A Bayesian Markov Geostatistical Model (BayMar) software was developed for implementation of the methodology in two and three dimensions. This paper gives (1) a theoretical description of the Bayesian Markov Geostatistical Model; (2) a short description of the BayMar software; and (3) an example of application of the model for estimating the suitability for repository establishment with respect to the three parameters of lithology, hydraulic conductivity, and rock quality designation index (RQD) at 400--500 meters below ground surface in an area around the Aespoe Hard Rock Laboratory in southeastern Sweden
TruStore: Implementing a Trusted Store for Android
Yury, Zhauniarovich; Olga, Gadyatskaya; Bruno, Crispo
2013-01-01
In the Android ecosystem, the process of verifying the integrity of downloaded apps is left to the user. Different from other systems, e.g., Apple, App Store, Google does not provide any certified vetting process for the Android apps. This choice has a lot of advantages but it is also the open door to possible attacks as the recent one shown by Bluebox. To address this issue, we present how to enable the deployment of application certification service, we called TruStores, for the Android pla...
Zollanvari, Amin; Dougherty, Edward R
2016-12-01
In classification, prior knowledge is incorporated in a Bayesian framework by assuming that the feature-label distribution belongs to an uncertainty class of feature-label distributions governed by a prior distribution. A posterior distribution is then derived from the prior and the sample data. An optimal Bayesian classifier (OBC) minimizes the expected misclassification error relative to the posterior distribution. From an application perspective, prior construction is critical. The prior distribution is formed by mapping a set of mathematical relations among the features and labels, the prior knowledge, into a distribution governing the probability mass across the uncertainty class. In this paper, we consider prior knowledge in the form of stochastic differential equations (SDEs). We consider a vector SDE in integral form involving a drift vector and dispersion matrix. Having constructed the prior, we develop the optimal Bayesian classifier between two models and examine, via synthetic experiments, the effects of uncertainty in the drift vector and dispersion matrix. We apply the theory to a set of SDEs for the purpose of differentiating the evolutionary history between two species.
Interactive Instruction in Bayesian Inference
DEFF Research Database (Denmark)
Khan, Azam; Breslav, Simon; Hornbæk, Kasper
2018-01-01
An instructional approach is presented to improve human performance in solving Bayesian inference problems. Starting from the original text of the classic Mammography Problem, the textual expression is modified and visualizations are added according to Mayer’s principles of instruction. These pri......An instructional approach is presented to improve human performance in solving Bayesian inference problems. Starting from the original text of the classic Mammography Problem, the textual expression is modified and visualizations are added according to Mayer’s principles of instruction....... These principles concern coherence, personalization, signaling, segmenting, multimedia, spatial contiguity, and pretraining. Principles of self-explanation and interactivity are also applied. Four experiments on the Mammography Problem showed that these principles help participants answer the questions...... that an instructional approach to improving human performance in Bayesian inference is a promising direction....
Probability biases as Bayesian inference
Directory of Open Access Journals (Sweden)
Andre; C. R. Martins
2006-11-01
Full Text Available In this article, I will show how several observed biases in human probabilistic reasoning can be partially explained as good heuristics for making inferences in an environment where probabilities have uncertainties associated to them. Previous results show that the weight functions and the observed violations of coalescing and stochastic dominance can be understood from a Bayesian point of view. We will review those results and see that Bayesian methods should also be used as part of the explanation behind other known biases. That means that, although the observed errors are still errors under the be understood as adaptations to the solution of real life problems. Heuristics that allow fast evaluations and mimic a Bayesian inference would be an evolutionary advantage, since they would give us an efficient way of making decisions. %XX In that sense, it should be no surprise that humans reason with % probability as it has been observed.
Bayesian analysis of CCDM models
Jesus, J. F.; Valentim, R.; Andrade-Oliveira, F.
2017-09-01
Creation of Cold Dark Matter (CCDM), in the context of Einstein Field Equations, produces a negative pressure term which can be used to explain the accelerated expansion of the Universe. In this work we tested six different spatially flat models for matter creation using statistical criteria, in light of SNe Ia data: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Bayesian Evidence (BE). These criteria allow to compare models considering goodness of fit and number of free parameters, penalizing excess of complexity. We find that JO model is slightly favoured over LJO/ΛCDM model, however, neither of these, nor Γ = 3αH0 model can be discarded from the current analysis. Three other scenarios are discarded either because poor fitting or because of the excess of free parameters. A method of increasing Bayesian evidence through reparameterization in order to reducing parameter degeneracy is also developed.
Bayesian analysis of CCDM models
Energy Technology Data Exchange (ETDEWEB)
Jesus, J.F. [Universidade Estadual Paulista (Unesp), Câmpus Experimental de Itapeva, Rua Geraldo Alckmin 519, Vila N. Sra. de Fátima, Itapeva, SP, 18409-010 Brazil (Brazil); Valentim, R. [Departamento de Física, Instituto de Ciências Ambientais, Químicas e Farmacêuticas—ICAQF, Universidade Federal de São Paulo (UNIFESP), Unidade José Alencar, Rua São Nicolau No. 210, Diadema, SP, 09913-030 Brazil (Brazil); Andrade-Oliveira, F., E-mail: jfjesus@itapeva.unesp.br, E-mail: valentim.rodolfo@unifesp.br, E-mail: felipe.oliveira@port.ac.uk [Institute of Cosmology and Gravitation—University of Portsmouth, Burnaby Road, Portsmouth, PO1 3FX United Kingdom (United Kingdom)
2017-09-01
Creation of Cold Dark Matter (CCDM), in the context of Einstein Field Equations, produces a negative pressure term which can be used to explain the accelerated expansion of the Universe. In this work we tested six different spatially flat models for matter creation using statistical criteria, in light of SNe Ia data: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Bayesian Evidence (BE). These criteria allow to compare models considering goodness of fit and number of free parameters, penalizing excess of complexity. We find that JO model is slightly favoured over LJO/ΛCDM model, however, neither of these, nor Γ = 3α H {sub 0} model can be discarded from the current analysis. Three other scenarios are discarded either because poor fitting or because of the excess of free parameters. A method of increasing Bayesian evidence through reparameterization in order to reducing parameter degeneracy is also developed.
Learning Bayesian networks for discrete data
Liang, Faming; Zhang, Jian
2009-01-01
Bayesian networks have received much attention in the recent literature. In this article, we propose an approach to learn Bayesian networks using the stochastic approximation Monte Carlo (SAMC) algorithm. Our approach has two nice features. Firstly
Bayesian Network Induction via Local Neighborhoods
National Research Council Canada - National Science Library
Margaritis, Dimitris
1999-01-01
.... We present an efficient algorithm for learning Bayesian networks from data. Our approach constructs Bayesian networks by first identifying each node's Markov blankets, then connecting nodes in a consistent way...
Can a significance test be genuinely Bayesian?
Pereira, Carlos A. de B.; Stern, Julio Michael; Wechsler, Sergio
2008-01-01
The Full Bayesian Significance Test, FBST, is extensively reviewed. Its test statistic, a genuine Bayesian measure of evidence, is discussed in detail. Its behavior in some problems of statistical inference like testing for independence in contingency tables is discussed.
Bayesian modeling using WinBUGS
Ntzoufras, Ioannis
2009-01-01
A hands-on introduction to the principles of Bayesian modeling using WinBUGS Bayesian Modeling Using WinBUGS provides an easily accessible introduction to the use of WinBUGS programming techniques in a variety of Bayesian modeling settings. The author provides an accessible treatment of the topic, offering readers a smooth introduction to the principles of Bayesian modeling with detailed guidance on the practical implementation of key principles. The book begins with a basic introduction to Bayesian inference and the WinBUGS software and goes on to cover key topics, including: Markov Chain Monte Carlo algorithms in Bayesian inference Generalized linear models Bayesian hierarchical models Predictive distribution and model checking Bayesian model and variable evaluation Computational notes and screen captures illustrate the use of both WinBUGS as well as R software to apply the discussed techniques. Exercises at the end of each chapter allow readers to test their understanding of the presented concepts and all ...
Method of storing solidification products
International Nuclear Information System (INIS)
Tani, Yutaro.
1985-01-01
Purpose: To enable to efficiently and satisfactorily cool and store solidification products of liquid wastes generated from the reactor spent fuel reprocessing process by a simple facility. Method: Liquid wastes generated from the reactor spent fuel reprocessing process are caused to flow from the upper opening to the inside of a spherical canistor. The opening of the spherical canistor is welded with a lid by a remote control and the liquid wastes are tightly sealed within the spherical canistor as glass solidification products. Spherical canistors having the solidification products tightly sealed therein are sent into and stored in a hopper by the remote control. Further, a blower is driven upon storing to suck cooling air from the cooling air intake port to the inside of the hopper to absorb the decay heat of radioactive materials in the solidification products and the air is discharged from the duct and through the stack to the atmosphere. (Kawakami, Y.)
CytoBayesJ: software tools for Bayesian analysis of cytogenetic radiation dosimetry data.
Ainsbury, Elizabeth A; Vinnikov, Volodymyr; Puig, Pedro; Maznyk, Nataliya; Rothkamm, Kai; Lloyd, David C
2013-08-30
A number of authors have suggested that a Bayesian approach may be most appropriate for analysis of cytogenetic radiation dosimetry data. In the Bayesian framework, probability of an event is described in terms of previous expectations and uncertainty. Previously existing, or prior, information is used in combination with experimental results to infer probabilities or the likelihood that a hypothesis is true. It has been shown that the Bayesian approach increases both the accuracy and quality assurance of radiation dose estimates. New software entitled CytoBayesJ has been developed with the aim of bringing Bayesian analysis to cytogenetic biodosimetry laboratory practice. CytoBayesJ takes a number of Bayesian or 'Bayesian like' methods that have been proposed in the literature and presents them to the user in the form of simple user-friendly tools, including testing for the most appropriate model for distribution of chromosome aberrations and calculations of posterior probability distributions. The individual tools are described in detail and relevant examples of the use of the methods and the corresponding CytoBayesJ software tools are given. In this way, the suitability of the Bayesian approach to biological radiation dosimetry is highlighted and its wider application encouraged by providing a user-friendly software interface and manual in English and Russian. Copyright © 2013 Elsevier B.V. All rights reserved.
A systematic review of Bayesian articles in psychology: The last 25 years.
van de Schoot, Rens; Winter, Sonja D; Ryan, Oisín; Zondervan-Zwijnenburg, Mariëlle; Depaoli, Sarah
2017-06-01
Although the statistical tools most often used by researchers in the field of psychology over the last 25 years are based on frequentist statistics, it is often claimed that the alternative Bayesian approach to statistics is gaining in popularity. In the current article, we investigated this claim by performing the very first systematic review of Bayesian psychological articles published between 1990 and 2015 (n = 1,579). We aim to provide a thorough presentation of the role Bayesian statistics plays in psychology. This historical assessment allows us to identify trends and see how Bayesian methods have been integrated into psychological research in the context of different statistical frameworks (e.g., hypothesis testing, cognitive models, IRT, SEM, etc.). We also describe take-home messages and provide "big-picture" recommendations to the field as Bayesian statistics becomes more popular. Our review indicated that Bayesian statistics is used in a variety of contexts across subfields of psychology and related disciplines. There are many different reasons why one might choose to use Bayes (e.g., the use of priors, estimating otherwise intractable models, modeling uncertainty, etc.). We found in this review that the use of Bayes has increased and broadened in the sense that this methodology can be used in a flexible manner to tackle many different forms of questions. We hope this presentation opens the door for a larger discussion regarding the current state of Bayesian statistics, as well as future trends. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Inference in hybrid Bayesian networks
International Nuclear Information System (INIS)
Langseth, Helge; Nielsen, Thomas D.; Rumi, Rafael; Salmeron, Antonio
2009-01-01
Since the 1980s, Bayesian networks (BNs) have become increasingly popular for building statistical models of complex systems. This is particularly true for boolean systems, where BNs often prove to be a more efficient modelling framework than traditional reliability techniques (like fault trees and reliability block diagrams). However, limitations in the BNs' calculation engine have prevented BNs from becoming equally popular for domains containing mixtures of both discrete and continuous variables (the so-called hybrid domains). In this paper we focus on these difficulties, and summarize some of the last decade's research on inference in hybrid Bayesian networks. The discussions are linked to an example model for estimating human reliability.
Prior indigenous technological species
Wright, Jason T.
2018-01-01
One of the primary open questions of astrobiology is whether there is extant or extinct life elsewhere the solar system. Implicit in much of this work is that we are looking for microbial or, at best, unintelligent life, even though technological artefacts might be much easier to find. Search for Extraterrestrial Intelligence (SETI) work on searches for alien artefacts in the solar system typically presumes that such artefacts would be of extrasolar origin, even though life is known to have existed in the solar system, on Earth, for eons. But if a prior technological, perhaps spacefaring, species ever arose in the solar system, it might have produced artefacts or other technosignatures that have survived to present day, meaning solar system artefact SETI provides a potential path to resolving astrobiology's question. Here, I discuss the origins and possible locations for technosignatures of such a prior indigenous technological species, which might have arisen on ancient Earth or another body, such as a pre-greenhouse Venus or a wet Mars. In the case of Venus, the arrival of its global greenhouse and potential resurfacing might have erased all evidence of its existence on the Venusian surface. In the case of Earth, erosion and, ultimately, plate tectonics may have erased most such evidence if the species lived Gyr ago. Remaining indigenous technosignatures might be expected to be extremely old, limiting the places they might still be found to beneath the surfaces of Mars and the Moon, or in the outer solar system.
Bayesian experts in exploring reaction kinetics of transcription circuits.
Yoshida, Ryo; Saito, Masaya M; Nagao, Hiromichi; Higuchi, Tomoyuki
2010-09-15
Biochemical reactions in cells are made of several types of biological circuits. In current systems biology, making differential equation (DE) models simulatable in silico has been an appealing, general approach to uncover a complex world of biochemical reaction dynamics. Despite of a need for simulation-aided studies, our research field has yet provided no clear answers: how to specify kinetic values in models that are difficult to measure from experimental/theoretical analyses on biochemical kinetics. We present a novel non-parametric Bayesian approach to this problem. The key idea lies in the development of a Dirichlet process (DP) prior distribution, called Bayesian experts, which reflects substantive knowledge on reaction mechanisms inherent in given models and experimentally observable kinetic evidences to the subsequent parameter search. The DP prior identifies significant local regions of unknown parameter space before proceeding to the posterior analyses. This article reports that a Bayesian expert-inducing stochastic search can effectively explore unknown parameters of in silico transcription circuits such that solutions of DEs reproduce transcriptomic time course profiles. A sample source code is available at the URL http://daweb.ism.ac.jp/~yoshidar/lisdas/.
Method of storing fissile mateiral
International Nuclear Information System (INIS)
Onoshita, Toshio; Ishitobi, Masuhiro
1989-01-01
Upon storing nuclear fissile materials in a storing building, vessels packed with fissile materials are inserted into a containing chamber divided with partition walls comprising neutron absorbers and neutron moderators. Thus, released neutrons permeating the vessel are moderated by the neutron moderators and then absorbed by the neutron absorbers. Accordingly, the neutron absorbing effect by the neutron absorbers is improved, and irradiation of neutrons released from one of vessels to the other of vessels can be suppressed. Accordingly, it is possible to shorten the distance between the vessels in a contained state as much as possible, while securing the critical safety, to improve the containing density during storage. (T.M.)
Bayesian methods for proteomic biomarker development
Directory of Open Access Journals (Sweden)
Belinda Hernández
2015-12-01
In this review we provide an introduction to Bayesian inference and demonstrate some of the advantages of using a Bayesian framework. We summarize how Bayesian methods have been used previously in proteomics and other areas of bioinformatics. Finally, we describe some popular and emerging Bayesian models from the statistical literature and provide a worked tutorial including code snippets to show how these methods may be applied for the evaluation of proteomic biomarkers.
Eliciting hyperparameters of prior distributions for the parameters of paired comparison models
Directory of Open Access Journals (Sweden)
Nasir Abbas
2013-02-01
Full Text Available Normal 0 false false false EN-US X-NONE AR-SA In the study of paired comparisons (PC, items may be ranked or issues may be prioritized through subjective assessment of certain judges. PC models are developed and then used to serve the purpose of ranking. The PC models may be studied through classical or Bayesian approach. Bayesian inference is a modern statistical technique used to draw conclusions about the population parameters. Its beauty lies in incorporating prior information about the parameters into the analysis in addition to current information (i.e. data. The prior and current information are formally combined to yield a posterior distribution about the population parameters, which is the work bench of the Bayesian statisticians. However, the problems the Bayesians face correspond to the selection and formal utilization of prior distribution. Once the type of prior distribution is decided to be used, the problem of estimating the parameters of the prior distribution (i.e. elicitation still persists. Different methods are devised to serve the purpose. In this study an attempt is made to use Minimum Chi-square (hence forth MCS for the elicitation purpose. Though it is a classical estimation technique, but is used here for the election purpose. The entire elicitation procedure is illustrated through a numerical data set.
Breastfeeding FAQs: Safely Storing Breast Milk
... Search English Español Breastfeeding FAQs: Safely Storing Breast Milk KidsHealth / For Parents / Breastfeeding FAQs: Safely Storing Breast ... may have. How do I store my breast milk? You can freeze and/or refrigerate your pumped ( ...
Objective Bayesian analysis of neutrino masses and hierarchy
Heavens, Alan F.; Sellentin, Elena
2018-04-01
Given the precision of current neutrino data, priors still impact noticeably the constraints on neutrino masses and their hierarchy. To avoid our understanding of neutrinos being driven by prior assumptions, we construct a prior that is mathematically minimally informative. Using the constructed uninformative prior, we find that the normal hierarchy is favoured but with inconclusive posterior odds of 5.1:1. Better data is hence needed before the neutrino masses and their hierarchy can be well constrained. We find that the next decade of cosmological data should provide conclusive evidence if the normal hierarchy with negligible minimum mass is correct, and if the uncertainty in the sum of neutrino masses drops below 0.025 eV. On the other hand, if neutrinos obey the inverted hierarchy, achieving strong evidence will be difficult with the same uncertainties. Our uninformative prior was constructed from principles of the Objective Bayesian approach. The prior is called a reference prior and is minimally informative in the specific sense that the information gain after collection of data is maximised. The prior is computed for the combination of neutrino oscillation data and cosmological data and still applies if the data improve.
Bayesian networks and food security - An introduction
Stein, A.
2004-01-01
This paper gives an introduction to Bayesian networks. Networks are defined and put into a Bayesian context. Directed acyclical graphs play a crucial role here. Two simple examples from food security are addressed. Possible uses of Bayesian networks for implementation and further use in decision
Plug & Play object oriented Bayesian networks
DEFF Research Database (Denmark)
Bangsø, Olav; Flores, J.; Jensen, Finn Verner
2003-01-01
been shown to be quite suitable for dynamic domains as well. However, processing object oriented Bayesian networks in practice does not take advantage of their modular structure. Normally the object oriented Bayesian network is transformed into a Bayesian network and, inference is performed...... dynamic domains. The communication needed between instances is achieved by means of a fill-in propagation scheme....
A Bayesian framework for risk perception
van Erp, H.R.N.
2017-01-01
We present here a Bayesian framework of risk perception. This framework encompasses plausibility judgments, decision making, and question asking. Plausibility judgments are modeled by way of Bayesian probability theory, decision making is modeled by way of a Bayesian decision theory, and relevancy
Improving medical stores management through automation and effective communication.
Kumar, Ashok; Cariappa, M P; Marwaha, Vishal; Sharma, Mukti; Arora, Manu
2016-01-01
Medical stores management in hospitals is a tedious and time consuming chore with limited resources tasked for the purpose and poor penetration of Information Technology. The process of automation is slow paced due to various inherent factors and is being challenged by the increasing inventory loads and escalating budgets for procurement of drugs. We carried out an indepth case study at the Medical Stores of a tertiary care health care facility. An iterative six step Quality Improvement (QI) process was implemented based on the Plan-Do-Study-Act (PDSA) cycle. The QI process was modified as per requirement to fit the medical stores management model. The results were evaluated after six months. After the implementation of QI process, 55 drugs of the medical store inventory which had expired since 2009 onwards were replaced with fresh stock by the suppliers as a result of effective communication through upgraded database management. Various pending audit objections were dropped due to the streamlined documentation and processes. Inventory management improved drastically due to automation, with disposal orders being initiated four months prior to the expiry of drugs and correct demands being generated two months prior to depletion of stocks. The monthly expense summary of drugs was now being done within ten days of the closing month. Improving communication systems within the hospital with vendor database management and reaching out to clinicians is important. Automation of inventory management requires to be simple and user-friendly, utilizing existing hardware. Physical stores monitoring is indispensable, especially due to the scattered nature of stores. Staff training and standardized documentation protocols are the other keystones for optimal medical store management.
Using literature and data to learn Bayesian networks as clinical models of ovarian tumors.
Antal, Peter; Fannes, Geert; Timmerman, Dirk; Moreau, Yves; De Moor, Bart
2004-03-01
Thanks to its increasing availability, electronic literature has become a potential source of information for the development of complex Bayesian networks (BN), when human expertise is missing or data is scarce or contains much noise. This opportunity raises the question of how to integrate information from free-text resources with statistical data in learning Bayesian networks. Firstly, we report on the collection of prior information resources in the ovarian cancer domain, which includes "kernel" annotations of the domain variables. We introduce methods based on the annotations and literature to derive informative pairwise dependency measures, which are derived from the statistical cooccurrence of the names of the variables, from the similarity of the "kernel" descriptions of the variables and from a combined method. We perform wide-scale evaluation of these text-based dependency scores against an expert reference and against data scores (the mutual information (MI) and a Bayesian score). Next, we transform the text-based dependency measures into informative text-based priors for Bayesian network structures. Finally, we report the benefit of such informative text-based priors on the performance of a Bayesian network for the classification of ovarian tumors from clinical data.
Store operations to maintain cache coherence
Energy Technology Data Exchange (ETDEWEB)
Evangelinos, Constantinos; Nair, Ravi; Ohmacht, Martin
2017-08-01
In one embodiment, a computer-implemented method includes encountering a store operation during a compile-time of a program, where the store operation is applicable to a memory line. It is determined, by a computer processor, that no cache coherence action is necessary for the store operation. A store-without-coherence-action instruction is generated for the store operation, responsive to determining that no cache coherence action is necessary. The store-without-coherence-action instruction specifies that the store operation is to be performed without a cache coherence action, and cache coherence is maintained upon execution of the store-without-coherence-action instruction.
Store operations to maintain cache coherence
Energy Technology Data Exchange (ETDEWEB)
Evangelinos, Constantinos; Nair, Ravi; Ohmacht, Martin
2017-09-12
In one embodiment, a computer-implemented method includes encountering a store operation during a compile-time of a program, where the store operation is applicable to a memory line. It is determined, by a computer processor, that no cache coherence action is necessary for the store operation. A store-without-coherence-action instruction is generated for the store operation, responsive to determining that no cache coherence action is necessary. The store-without-coherence-action instruction specifies that the store operation is to be performed without a cache coherence action, and cache coherence is maintained upon execution of the store-without-coherence-action instruction.
Stores, Weight and Inertial System Facility
Federal Laboratory Consortium — This facility provides stores weight, center of gravity, and inertia measurements in support of weapon/aircraft compatibility testing. System provides store weight...
Storing XML Documents in Databases
A.R. Schmidt; S. Manegold (Stefan); M.L. Kersten (Martin); L.C. Rivero; J.H. Doorn; V.E. Ferraggine
2005-01-01
textabstractThe authors introduce concepts for loading large amounts of XML documents into databases where the documents are stored and maintained. The goal is to make XML databases as unobtrusive in multi-tier systems as possible and at the same time provide as many services defined by the XML
A study was executed to determine the potential of storing farmers stock peanuts and shelled peanuts for crushing in hermetically sealed grain bags. The objectives of the study were to evaluate equipment for loading and unloading the grain bags, the capacity of the grain bags, and the changes in qu...
Storing biomass in round bales
Energy Technology Data Exchange (ETDEWEB)
Summer, H.R.; Hellwig, R.E.; Monroe, G.E.
1984-09-01
Biomass fuels, in the form of crop residues, were stored outside in large round bales. The influence of rainfall on bale mass and the change in apparent average moisture content (A.A.M.C) was studied. Covering the bales with large sheets of polyethylene was found to be the most effective way of reducing moisture penetration.
African Journals Online (AJOL)
olufunke oyedokun
2015-04-22
Apr 22, 2015 ... theobromine levels decrease, which in turn affects the colour, flavor (aroma) of the beans (Lagunes et al., 2007;. Rodriguez-Campos et al., 2011) and the organoleptic properties of the dried cocoa beans in store (Camu et al.,. 2008). Freshly harvested cocoa beans require fermentation for 5 - 7 days before ...
Bayesian tomography and integrated data analysis in fusion diagnostics
Li, Dong; Dong, Y. B.; Deng, Wei; Shi, Z. B.; Fu, B. Z.; Gao, J. M.; Wang, T. B.; Zhou, Yan; Liu, Yi; Yang, Q. W.; Duan, X. R.
2016-11-01
In this article, a Bayesian tomography method using non-stationary Gaussian process for a prior has been introduced. The Bayesian formalism allows quantities which bear uncertainty to be expressed in the probabilistic form so that the uncertainty of a final solution can be fully resolved from the confidence interval of a posterior probability. Moreover, a consistency check of that solution can be performed by checking whether the misfits between predicted and measured data are reasonably within an assumed data error. In particular, the accuracy of reconstructions is significantly improved by using the non-stationary Gaussian process that can adapt to the varying smoothness of emission distribution. The implementation of this method to a soft X-ray diagnostics on HL-2A has been used to explore relevant physics in equilibrium and MHD instability modes. This project is carried out within a large size inference framework, aiming at an integrated analysis of heterogeneous diagnostics.
Uncertainty, reward, and attention in the Bayesian brain
DEFF Research Database (Denmark)
Whiteley, Louise Emma
2008-01-01
results suggest that value a¿ects a fronto-striatal action selection network rather than directly impacting on sensory processing. Finally, we consider a major theoretical problem – the demonstrations of optimality that dominate the ¿eld have been obtained in tasks with a small number of objects...... in the focus of attention. When faced instead with a complex scene, the brain can’t be Bayes-optimal everywhere. We suggest that a general limitation on the representation of complex posteriors causes the brain to make approximations, which are then locally re¿ned by attention. This framework extends ideas...... of attention as Bayesian prior, and uni¿es apparently disparate attentional ‘bottlenecks’. We present simulations of three key paradigms, and discuss how such modelling could be extended to more detailed, neurally inspired settings. Broadening the Bayesian picture of perception and strengthening its connection...
Bayesian non parametric modelling of Higgs pair production
Directory of Open Access Journals (Sweden)
Scarpa Bruno
2017-01-01
Full Text Available Statistical classification models are commonly used to separate a signal from a background. In this talk we face the problem of isolating the signal of Higgs pair production using the decay channel in which each boson decays into a pair of b-quarks. Typically in this context non parametric methods are used, such as Random Forests or different types of boosting tools. We remain in the same non-parametric framework, but we propose to face the problem following a Bayesian approach. A Dirichlet process is used as prior for the random effects in a logit model which is fitted by leveraging the Polya-Gamma data augmentation. Refinements of the model include the insertion in the simple model of P-splines to relate explanatory variables with the response and the use of Bayesian trees (BART to describe the atoms in the Dirichlet process.
To P or Not to P: Backing Bayesian Statistics.
Buchinsky, Farrel J; Chadha, Neil K
2017-12-01
In biomedical research, it is imperative to differentiate chance variation from truth before we generalize what we see in a sample of subjects to the wider population. For decades, we have relied on null hypothesis significance testing, where we calculate P values for our data to decide whether to reject a null hypothesis. This methodology is subject to substantial misinterpretation and errant conclusions. Instead of working backward by calculating the probability of our data if the null hypothesis were true, Bayesian statistics allow us instead to work forward, calculating the probability of our hypothesis given the available data. This methodology gives us a mathematical means of incorporating our "prior probabilities" from previous study data (if any) to produce new "posterior probabilities." Bayesian statistics tell us how confidently we should believe what we believe. It is time to embrace and encourage their use in our otolaryngology research.
Bayesian image restoration for medical images using radon transform
International Nuclear Information System (INIS)
Shouno, Hayaru; Okada, Masato
2010-01-01
We propose an image reconstruction algorithm using Bayesian inference for Radon transformed observation data, which often appears in the field of medical image reconstruction known as computed tomography (CT). In order to apply our Bayesian reconstruction method, we introduced several hyper-parameters that control the ratio between prior information and the fidelity of the observation process. Since the quality of the reconstructed image is influenced by the estimation accuracy of these hyper-parameters, we propose an inference method for them based on the marginal likelihood maximization principle as well as the image reconstruction method. We are able to demonstrate a reconstruction result superior to that obtained using the conventional filtered back projection method. (author)
Sparse reconstruction using distribution agnostic bayesian matching pursuit
Masood, Mudassir
2013-11-01
A fast matching pursuit method using a Bayesian approach is introduced for sparse signal recovery. This method performs Bayesian estimates of sparse signals even when the signal prior is non-Gaussian or unknown. It is agnostic on signal statistics and utilizes a priori statistics of additive noise and the sparsity rate of the signal, which are shown to be easily estimated from data if not available. The method utilizes a greedy approach and order-recursive updates of its metrics to find the most dominant sparse supports to determine the approximate minimum mean-square error (MMSE) estimate of the sparse signal. Simulation results demonstrate the power and robustness of our proposed estimator. © 2013 IEEE.
Bayesian detection of causal rare variants under posterior consistency.
Liang, Faming
2013-07-26
Identification of causal rare variants that are associated with complex traits poses a central challenge on genome-wide association studies. However, most current research focuses only on testing the global association whether the rare variants in a given genomic region are collectively associated with the trait. Although some recent work, e.g., the Bayesian risk index method, have tried to address this problem, it is unclear whether the causal rare variants can be consistently identified by them in the small-n-large-P situation. We develop a new Bayesian method, the so-called Bayesian Rare Variant Detector (BRVD), to tackle this problem. The new method simultaneously addresses two issues: (i) (Global association test) Are there any of the variants associated with the disease, and (ii) (Causal variant detection) Which variants, if any, are driving the association. The BRVD ensures the causal rare variants to be consistently identified in the small-n-large-P situation by imposing some appropriate prior distributions on the model and model specific parameters. The numerical results indicate that the BRVD is more powerful for testing the global association than the existing methods, such as the combined multivariate and collapsing test, weighted sum statistic test, RARECOVER, sequence kernel association test, and Bayesian risk index, and also more powerful for identification of causal rare variants than the Bayesian risk index method. The BRVD has also been successfully applied to the Early-Onset Myocardial Infarction (EOMI) Exome Sequence Data. It identified a few causal rare variants that have been verified in the literature.
Bayesian molecular dating: opening up the black box.
Bromham, Lindell; Duchêne, Sebastián; Hua, Xia; Ritchie, Andrew M; Duchêne, David A; Ho, Simon Y W
2018-05-01
Molecular dating analyses allow evolutionary timescales to be estimated from genetic data, offering an unprecedented capacity for investigating the evolutionary past of all species. These methods require us to make assumptions about the relationship between genetic change and evolutionary time, often referred to as a 'molecular clock'. Although initially regarded with scepticism, molecular dating has now been adopted in many areas of biology. This broad uptake has been due partly to the development of Bayesian methods that allow complex aspects of molecular evolution, such as variation in rates of change across lineages, to be taken into account. But in order to do this, Bayesian dating methods rely on a range of assumptions about the evolutionary process, which vary in their degree of biological realism and empirical support. These assumptions can have substantial impacts on the estimates produced by molecular dating analyses. The aim of this review is to open the 'black box' of Bayesian molecular dating and have a look at the machinery inside. We explain the components of these dating methods, the important decisions that researchers must make in their analyses, and the factors that need to be considered when interpreting results. We illustrate the effects that the choices of different models and priors can have on the outcome of the analysis, and suggest ways to explore these impacts. We describe some major research directions that may improve the reliability of Bayesian dating. The goal of our review is to help researchers to make informed choices when using Bayesian phylogenetic methods to estimate evolutionary rates and timescales. © 2017 Cambridge Philosophical Society.
Bayesian detection of causal rare variants under posterior consistency.
Directory of Open Access Journals (Sweden)
Faming Liang
Full Text Available Identification of causal rare variants that are associated with complex traits poses a central challenge on genome-wide association studies. However, most current research focuses only on testing the global association whether the rare variants in a given genomic region are collectively associated with the trait. Although some recent work, e.g., the Bayesian risk index method, have tried to address this problem, it is unclear whether the causal rare variants can be consistently identified by them in the small-n-large-P situation. We develop a new Bayesian method, the so-called Bayesian Rare Variant Detector (BRVD, to tackle this problem. The new method simultaneously addresses two issues: (i (Global association test Are there any of the variants associated with the disease, and (ii (Causal variant detection Which variants, if any, are driving the association. The BRVD ensures the causal rare variants to be consistently identified in the small-n-large-P situation by imposing some appropriate prior distributions on the model and model specific parameters. The numerical results indicate that the BRVD is more powerful for testing the global association than the existing methods, such as the combined multivariate and collapsing test, weighted sum statistic test, RARECOVER, sequence kernel association test, and Bayesian risk index, and also more powerful for identification of causal rare variants than the Bayesian risk index method. The BRVD has also been successfully applied to the Early-Onset Myocardial Infarction (EOMI Exome Sequence Data. It identified a few causal rare variants that have been verified in the literature.
Bayesian detection of causal rare variants under posterior consistency.
Liang, Faming; Xiong, Momiao
2013-01-01
Identification of causal rare variants that are associated with complex traits poses a central challenge on genome-wide association studies. However, most current research focuses only on testing the global association whether the rare variants in a given genomic region are collectively associated with the trait. Although some recent work, e.g., the Bayesian risk index method, have tried to address this problem, it is unclear whether the causal rare variants can be consistently identified by them in the small-n-large-P situation. We develop a new Bayesian method, the so-called Bayesian Rare Variant Detector (BRVD), to tackle this problem. The new method simultaneously addresses two issues: (i) (Global association test) Are there any of the variants associated with the disease, and (ii) (Causal variant detection) Which variants, if any, are driving the association. The BRVD ensures the causal rare variants to be consistently identified in the small-n-large-P situation by imposing some appropriate prior distributions on the model and model specific parameters. The numerical results indicate that the BRVD is more powerful for testing the global association than the existing methods, such as the combined multivariate and collapsing test, weighted sum statistic test, RARECOVER, sequence kernel association test, and Bayesian risk index, and also more powerful for identification of causal rare variants than the Bayesian risk index method. The BRVD has also been successfully applied to the Early-Onset Myocardial Infarction (EOMI) Exome Sequence Data. It identified a few causal rare variants that have been verified in the literature.
Bayesian NL interpretation and learning
Zeevat, H.
2011-01-01
Everyday natural language communication is normally successful, even though contemporary computational linguistics has shown that NL is characterised by very high degree of ambiguity and the results of stochastic methods are not good enough to explain the high success rate. Bayesian natural language
Bayesian Networks and Influence Diagrams
DEFF Research Database (Denmark)
Kjærulff, Uffe Bro; Madsen, Anders Læsø
Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, Second Edition, provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. This new edition contains six new...
Bayesian Sampling using Condition Indicators
DEFF Research Database (Denmark)
Faber, Michael H.; Sørensen, John Dalsgaard
2002-01-01
of condition indicators introduced by Benjamin and Cornell (1970) a Bayesian approach to quality control is formulated. The formulation is then extended to the case where the quality control is based on sampling of indirect information about the condition of the components, i.e. condition indicators...
Bayesian Classification of Image Structures
DEFF Research Database (Denmark)
Goswami, Dibyendu; Kalkan, Sinan; Krüger, Norbert
2009-01-01
In this paper, we describe work on Bayesian classi ers for distinguishing between homogeneous structures, textures, edges and junctions. We build semi-local classiers from hand-labeled images to distinguish between these four different kinds of structures based on the concept of intrinsic dimensi...
3-D contextual Bayesian classifiers
DEFF Research Database (Denmark)
Larsen, Rasmus
In this paper we will consider extensions of a series of Bayesian 2-D contextual classification pocedures proposed by Owen (1984) Hjort & Mohn (1984) and Welch & Salter (1971) and Haslett (1985) to 3 spatial dimensions. It is evident that compared to classical pixelwise classification further...
Bayesian Alternation During Tactile Augmentation
Directory of Open Access Journals (Sweden)
Caspar Mathias Goeke
2016-10-01
Full Text Available A large number of studies suggest that the integration of multisensory signals by humans is well described by Bayesian principles. However, there are very few reports about cue combination between a native and an augmented sense. In particular, we asked the question whether adult participants are able to integrate an augmented sensory cue with existing native sensory information. Hence for the purpose of this study we build a tactile augmentation device. Consequently, we compared different hypotheses of how untrained adult participants combine information from a native and an augmented sense. In a two-interval forced choice (2 IFC task, while subjects were blindfolded and seated on a rotating platform, our sensory augmentation device translated information on whole body yaw rotation to tactile stimulation. Three conditions were realized: tactile stimulation only (augmented condition, rotation only (native condition, and both augmented and native information (bimodal condition. Participants had to choose one out of two consecutive rotations with higher angular rotation. For the analysis, we fitted the participants’ responses with a probit model and calculated the just notable difference (JND. Then we compared several models for predicting bimodal from unimodal responses. An objective Bayesian alternation model yielded a better prediction (χred2 = 1.67 than the Bayesian integration model (χred2= 4.34. Slightly higher accuracy showed a non-Bayesian winner takes all model (χred2= 1.64, which either used only native or only augmented values per subject for prediction. However the performance of the Bayesian alternation model could be substantially improved (χred2= 1.09 utilizing subjective weights obtained by a questionnaire. As a result, the subjective Bayesian alternation model predicted bimodal performance most accurately among all tested models. These results suggest that information from augmented and existing sensory modalities in
Bayesian models for comparative analysis integrating phylogenetic uncertainty
Directory of Open Access Journals (Sweden)
Villemereuil Pierre de
2012-06-01
Full Text Available Abstract Background Uncertainty in comparative analyses can come from at least two sources: a phylogenetic uncertainty in the tree topology or branch lengths, and b uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow and inflated significance in hypothesis testing (e.g. p-values will be too small. Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable. Methods We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses. Results We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS. Conclusions Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible
Bayesian models for comparative analysis integrating phylogenetic uncertainty
2012-01-01
Background Uncertainty in comparative analyses can come from at least two sources: a) phylogenetic uncertainty in the tree topology or branch lengths, and b) uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow) and inflated significance in hypothesis testing (e.g. p-values will be too small). Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable. Methods We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses. Results We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS. Conclusions Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible general purpose tool for
Merging Digital Surface Models Implementing Bayesian Approaches
Sadeq, H.; Drummond, J.; Li, Z.
2016-06-01
In this research different DSMs from different sources have been merged. The merging is based on a probabilistic model using a Bayesian Approach. The implemented data have been sourced from very high resolution satellite imagery sensors (e.g. WorldView-1 and Pleiades). It is deemed preferable to use a Bayesian Approach when the data obtained from the sensors are limited and it is difficult to obtain many measurements or it would be very costly, thus the problem of the lack of data can be solved by introducing a priori estimations of data. To infer the prior data, it is assumed that the roofs of the buildings are specified as smooth, and for that purpose local entropy has been implemented. In addition to the a priori estimations, GNSS RTK measurements have been collected in the field which are used as check points to assess the quality of the DSMs and to validate the merging result. The model has been applied in the West-End of Glasgow containing different kinds of buildings, such as flat roofed and hipped roofed buildings. Both quantitative and qualitative methods have been employed to validate the merged DSM. The validation results have shown that the model was successfully able to improve the quality of the DSMs and improving some characteristics such as the roof surfaces, which consequently led to better representations. In addition to that, the developed model has been compared with the well established Maximum Likelihood model and showed similar quantitative statistical results and better qualitative results. Although the proposed model has been applied on DSMs that were derived from satellite imagery, it can be applied to any other sourced DSMs.
MERGING DIGITAL SURFACE MODELS IMPLEMENTING BAYESIAN APPROACHES
Directory of Open Access Journals (Sweden)
H. Sadeq
2016-06-01
Full Text Available In this research different DSMs from different sources have been merged. The merging is based on a probabilistic model using a Bayesian Approach. The implemented data have been sourced from very high resolution satellite imagery sensors (e.g. WorldView-1 and Pleiades. It is deemed preferable to use a Bayesian Approach when the data obtained from the sensors are limited and it is difficult to obtain many measurements or it would be very costly, thus the problem of the lack of data can be solved by introducing a priori estimations of data. To infer the prior data, it is assumed that the roofs of the buildings are specified as smooth, and for that purpose local entropy has been implemented. In addition to the a priori estimations, GNSS RTK measurements have been collected in the field which are used as check points to assess the quality of the DSMs and to validate the merging result. The model has been applied in the West-End of Glasgow containing different kinds of buildings, such as flat roofed and hipped roofed buildings. Both quantitative and qualitative methods have been employed to validate the merged DSM. The validation results have shown that the model was successfully able to improve the quality of the DSMs and improving some characteristics such as the roof surfaces, which consequently led to better representations. In addition to that, the developed model has been compared with the well established Maximum Likelihood model and showed similar quantitative statistical results and better qualitative results. Although the proposed model has been applied on DSMs that were derived from satellite imagery, it can be applied to any other sourced DSMs.
Bayesian phylogenetic estimation of fossil ages.
Drummond, Alexei J; Stadler, Tanja
2016-07-19
Recent advances have allowed for both morphological fossil evidence and molecular sequences to be integrated into a single combined inference of divergence dates under the rule of Bayesian probability. In particular, the fossilized birth-death tree prior and the Lewis-Mk model of discrete morphological evolution allow for the estimation of both divergence times and phylogenetic relationships between fossil and extant taxa. We exploit this statistical framework to investigate the internal consistency of these models by producing phylogenetic estimates of the age of each fossil in turn, within two rich and well-characterized datasets of fossil and extant species (penguins and canids). We find that the estimation accuracy of fossil ages is generally high with credible intervals seldom excluding the true age and median relative error in the two datasets of 5.7% and 13.2%, respectively. The median relative standard error (RSD) was 9.2% and 7.2%, respectively, suggesting good precision, although with some outliers. In fact, in the two datasets we analyse, the phylogenetic estimate of fossil age is on average less than 2 Myr from the mid-point age of the geological strata from which it was excavated. The high level of internal consistency found in our analyses suggests that the Bayesian statistical model employed is an adequate fit for both the geological and morphological data, and provides evidence from real data that the framework used can accurately model the evolution of discrete morphological traits coded from fossil and extant taxa. We anticipate that this approach will have diverse applications beyond divergence time dating, including dating fossils that are temporally unconstrained, testing of the 'morphological clock', and for uncovering potential model misspecification and/or data errors when controversial phylogenetic hypotheses are obtained based on combined divergence dating analyses.This article is part of the themed issue 'Dating species divergences using
Bayesian modeling of ChIP-chip data using latent variables.
Wu, Mingqi
2009-10-26
BACKGROUND: The ChIP-chip technology has been used in a wide range of biomedical studies, such as identification of human transcription factor binding sites, investigation of DNA methylation, and investigation of histone modifications in animals and plants. Various methods have been proposed in the literature for analyzing the ChIP-chip data, such as the sliding window methods, the hidden Markov model-based methods, and Bayesian methods. Although, due to the integrated consideration of uncertainty of the models and model parameters, Bayesian methods can potentially work better than the other two classes of methods, the existing Bayesian methods do not perform satisfactorily. They usually require multiple replicates or some extra experimental information to parametrize the model, and long CPU time due to involving of MCMC simulations. RESULTS: In this paper, we propose a Bayesian latent model for the ChIP-chip data. The new model mainly differs from the existing Bayesian models, such as the joint deconvolution model, the hierarchical gamma mixture model, and the Bayesian hierarchical model, in two respects. Firstly, it works on the difference between the averaged treatment and control samples. This enables the use of a simple model for the data, which avoids the probe-specific effect and the sample (control/treatment) effect. As a consequence, this enables an efficient MCMC simulation of the posterior distribution of the model, and also makes the model more robust to the outliers. Secondly, it models the neighboring dependence of probes by introducing a latent indicator vector. A truncated Poisson prior distribution is assumed for the latent indicator variable, with the rationale being justified at length. CONCLUSION: The Bayesian latent method is successfully applied to real and ten simulated datasets, with comparisons with some of the existing Bayesian methods, hidden Markov model methods, and sliding window methods. The numerical results indicate that the
Topics in Bayesian statistics and maximum entropy
International Nuclear Information System (INIS)
Mutihac, R.; Cicuttin, A.; Cerdeira, A.; Stanciulescu, C.
1998-12-01
Notions of Bayesian decision theory and maximum entropy methods are reviewed with particular emphasis on probabilistic inference and Bayesian modeling. The axiomatic approach is considered as the best justification of Bayesian analysis and maximum entropy principle applied in natural sciences. Particular emphasis is put on solving the inverse problem in digital image restoration and Bayesian modeling of neural networks. Further topics addressed briefly include language modeling, neutron scattering, multiuser detection and channel equalization in digital communications, genetic information, and Bayesian court decision-making. (author)
Bayesian analysis of rare events
Energy Technology Data Exchange (ETDEWEB)
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 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.
Directory of Open Access Journals (Sweden)
Mihaela Simionescu
2014-12-01
Full Text Available There are many types of econometric models used in predicting the inflation rate, but in this study we used a Bayesian shrinkage combination approach. This methodology is used in order to improve the predictions accuracy by including information that is not captured by the econometric models. Therefore, experts’ forecasts are utilized as prior information, for Romania these predictions being provided by Institute for Economic Forecasting (Dobrescu macromodel, National Commission for Prognosis and European Commission. The empirical results for Romanian inflation show the superiority of a fixed effects model compared to other types of econometric models like VAR, Bayesian VAR, simultaneous equations model, dynamic model, log-linear model. The Bayesian combinations that used experts’ predictions as priors, when the shrinkage parameter tends to infinite, improved the accuracy of all forecasts based on individual models, outperforming also zero and equal weights predictions and naïve forecasts.
40 CFR 266.101 - Management prior to burning.
2010-07-01
... storage units that store mixtures of hazardous waste and the primary fuel to the boiler or industrial... MANAGEMENT FACILITIES Hazardous Waste Burned in Boilers and Industrial Furnaces § 266.101 Management prior to burning. (a) Generators. Generators of hazardous waste that is burned in a boiler or industrial furnace...
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.
On selecting a prior for the precision parameter of Dirichlet process mixture models
Dorazio, R.M.
2009-01-01
In hierarchical mixture models the Dirichlet process is used to specify latent patterns of heterogeneity, particularly when the distribution of latent parameters is thought to be clustered (multimodal). The parameters of a Dirichlet process include a precision parameter ?? and a base probability measure G0. In problems where ?? is unknown and must be estimated, inferences about the level of clustering can be sensitive to the choice of prior assumed for ??. In this paper an approach is developed for computing a prior for the precision parameter ?? that can be used in the presence or absence of prior information about the level of clustering. This approach is illustrated in an analysis of counts of stream fishes. The results of this fully Bayesian analysis are compared with an empirical Bayes analysis of the same data and with a Bayesian analysis based on an alternative commonly used prior.
Model/School Store Management Guide.
North Dakota State Board for Vocational Education, Bismarck.
This teacher-coordinator manual assists in planning, organizing, directing, and evaluating student learning experiences associated with either a model store, school store, or combination. (A model store in a marketing laboratory simulates marketing functions; the school store markets merchandise to fellow students, faculty, and/or the public.)…
Neutrino mass priors for cosmology from random matrices
Long, Andrew J.; Raveri, Marco; Hu, Wayne; Dodelson, Scott
2018-02-01
Cosmological measurements of structure are placing increasingly strong constraints on the sum of the neutrino masses, Σ mν, through Bayesian inference. Because these constraints depend on the choice for the prior probability π (Σ mν), we argue that this prior should be motivated by fundamental physical principles rather than the ad hoc choices that are common in the literature. The first step in this direction is to specify the prior directly at the level of the neutrino mass matrix Mν, since this is the parameter appearing in the Lagrangian of the particle physics theory. Thus by specifying a probability distribution over Mν, and by including the known squared mass splittings, we predict a theoretical probability distribution over Σ mν that we interpret as a Bayesian prior probability π (Σ mν). Assuming a basis-invariant probability distribution on Mν, also known as the anarchy hypothesis, we find that π (Σ mν) peaks close to the smallest Σ mν allowed by the measured mass splittings, roughly 0.06 eV (0.1 eV) for normal (inverted) ordering, due to the phenomenon of eigenvalue repulsion in random matrices. We consider three models for neutrino mass generation: Dirac, Majorana, and Majorana via the seesaw mechanism; differences in the predicted priors π (Σ mν) allow for the possibility of having indications about the physical origin of neutrino masses once sufficient experimental sensitivity is achieved. We present fitting functions for π (Σ mν), which provide a simple means for applying these priors to cosmological constraints on the neutrino masses or marginalizing over their impact on other cosmological parameters.
Storing XML Documents in Databases
Schmidt, A.R.; Manegold, Stefan; Kersten, Martin; Rivero, L.C.; Doorn, J.H.; Ferraggine, V.E.
2005-01-01
textabstractThe authors introduce concepts for loading large amounts of XML documents into databases where the documents are stored and maintained. The goal is to make XML databases as unobtrusive in multi-tier systems as possible and at the same time provide as many services defined by the XML standards as possible. The ubiquity of XML has sparked great interest in deploying concepts known from Relational Database Management Systems such as declarative query languages, transactions, indexes ...
Method of storing radioactive wastes
International Nuclear Information System (INIS)
Adachi, Toshio; Hiratake, Susumu.
1980-01-01
Purpose: To reduce the radiation doses externally irradiated from treated radioactive waste and also reduce the separation of radioactive nuclide due to external environmental factors such as air, water or the like. Method: Radioactive waste adhered with radioactive nuclide to solid material is molten to mix and submerge the radioactive nuclide adhered to the surface of the solid material into molten material. Then, the radioactive nuclide thus mixed is solidified to store the waste in solidified state. (Aizawa, K.)
Directory of Open Access Journals (Sweden)
Lisa V Hampson
Full Text Available Definitive sample sizes for clinical trials in rare diseases are usually infeasible. Bayesian methodology can be used to maximise what is learnt from clinical trials in these circumstances. We elicited expert prior opinion for a future Bayesian randomised controlled trial for a rare inflammatory paediatric disease, polyarteritis nodosa (MYPAN, Mycophenolate mofetil for polyarteritis nodosa.A Bayesian prior elicitation meeting was convened. Opinion was sought on the probability that a patient in the MYPAN trial treated with cyclophosphamide would achieve disease remission within 6-months, and on the relative efficacies of mycophenolate mofetil and cyclophosphamide. Expert opinion was combined with previously unseen data from a recently completed randomised controlled trial in ANCA associated vasculitis.A pan-European group of fifteen experts participated in the elicitation meeting. Consensus expert prior opinion was that the most likely rates of disease remission within 6 months on cyclophosphamide or mycophenolate mofetil were 74% and 71%, respectively. This prior opinion will now be taken forward and will be modified to formulate a Bayesian posterior opinion once the MYPAN trial data from 40 patients randomised 1:1 to either CYC or MMF become available.We suggest that the methodological template we propose could be applied to trial design for other rare diseases.
Specialty Store and Multi-Brand Store loyalty: An Indian consumer perspective
Directory of Open Access Journals (Sweden)
Sarabjot Singh
2013-12-01
Full Text Available In the competitive era of retailing, retailers need to understand the importance of store format preferences. The study aimed to understand consumer store loyalty; in-depth interview was conducted to examine consumer store loyalty antecedents for two retail formats: specialty stores and multi brand stores. The study conceptualizes store loyalty factors like program loyalty, trust and brand commitment. Trust and brand commitment act as mediating factors between store image and store loyalty formats, and also between brand image and store loyalty formats. The findings highlight how consumer store loyalty preference differ for these two formats.
Bayesian analysis of spatial point processes in the neighbourhood of Voronoi networks
DEFF Research Database (Denmark)
Skare, Øivind; Møller, Jesper; Jensen, Eva Bjørn Vedel
2007-01-01
A model for an inhomogeneous Poisson process with high intensity near the edges of a Voronoi tessellation in 2D or 3D is proposed. The model is analysed in a Bayesian setting with priors on nuclei of the Voronoi tessellation and other model parameters. An MCMC algorithm is constructed to sample...
Bayesian analysis of spatial point processes in the neighbourhood of Voronoi networks
DEFF Research Database (Denmark)
Skare, Øivind; Møller, Jesper; Vedel Jensen, Eva B.
A model for an inhomogeneous Poisson process with high intensity near the edges of a Voronoi tessellation in 2D or 3D is proposed. The model is analysed in a Bayesian setting with priors on nuclei of the Voronoi tessellation and other model parameters. An MCMC algorithm is constructed to sample...
Bayesian prediction of spatial count data using generalized linear mixed models
DEFF Research Database (Denmark)
Christensen, Ole Fredslund; Waagepetersen, Rasmus Plenge
2002-01-01
Spatial weed count data are modeled and predicted using a generalized linear mixed model combined with a Bayesian approach and Markov chain Monte Carlo. Informative priors for a data set with sparse sampling are elicited using a previously collected data set with extensive sampling. Furthermore, ...
Adaptive Bayesian inference on the mean of an infinite-dimensional normal distribution
Belitser, E.; Ghosal, S.
2003-01-01
We consider the problem of estimating the mean of an infinite-break dimensional normal distribution from the Bayesian perspective. Under the assumption that the unknown true mean satisfies a "smoothness condition," we first derive the convergence rate of the posterior distribution for a prior that
Czech Academy of Sciences Publication Activity Database
Fernandes, R.; Millard, A.R.; Brabec, Marek; Nadeau, M.J.; Grootes, P.
2014-01-01
Roč. 9, č. 2 (2014), Art . no. e87436 E-ISSN 1932-6203 Institutional support: RVO:67985807 Keywords : ancienit diet reconstruction * stable isotope measurements * mixture model * Bayesian estimation * Dirichlet prior Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 3.234, year: 2014
A non-parametric Bayesian approach to decompounding from high frequency data
Gugushvili, Shota; van der Meulen, F.H.; Spreij, Peter
2016-01-01
Given a sample from a discretely observed compound Poisson process, we consider non-parametric estimation of the density f0 of its jump sizes, as well as of its intensity λ0. We take a Bayesian approach to the problem and specify the prior on f0 as the Dirichlet location mixture of normal densities.
Bayesian Statistics in Educational Research: A Look at the Current State of Affairs
König, Christoph; van de Schoot, Rens
2018-01-01
The ability of a scientific discipline to build cumulative knowledge depends on its predominant method of data analysis. A steady accumulation of knowledge requires approaches which allow researchers to consider results from comparable prior research. Bayesian statistics is especially relevant for establishing a cumulative scientific discipline,…
Festa, Roberto
1992-01-01
According to the Bayesian view, scientific hypotheses must be appraised in terms of their posterior probabilities relative to the available experimental data. Such posterior probabilities are derived from the prior probabilities of the hypotheses by applying Bayes'theorem. One of the most important
Bayesian Ranging for Radio Localization with and without Line-of-Sight Detection
DEFF Research Database (Denmark)
Jing, Lishuai; Pedersen, Troels; Fleury, Bernard Henri
2015-01-01
We consider Bayesian ranging methods for local- ization in wireless communication systems. Based on a channel model and given priors for the range and the line-of-sight (LOS) condition, we propose range estimators with and without LOS detection. Since the pdf of the received frequency...
Rens van de Schoot; Joris J. Broere; Koen H. Perryck; Mariëlle Zondervan-Zwijnenburg; Nancy E. van Loey
2015-01-01
Background: The analysis of small data sets in longitudinal studies can lead to power issues and often suffers from biased parameter values. These issues can be solved by using Bayesian estimation in conjunction with informative prior distributions. By means of a simulation study and an empirical example concerning posttraumatic stress symptoms (PTSS) following mechanical ventilation in burn survivors, we demonstrate the advantages and potential pitfalls of using Bayesian estimation.Methods: ...
Negative price-image effects of appealing store architecture
DEFF Research Database (Denmark)
Zielke, Stephan; Toporowski, Waldemar
2012-01-01
Retailers often worry about the negative effects of appealing exterior architecture on their store's price image, especially the price-level perception and the ease of price evaluation. Findings from prior laboratory experiments support these concerns, while field studies find no such effects. Th....... The availability of price information neutralizes the negative effects of appealing architecture on the price-level perception, but not on the ease of price evaluation....
Understanding Retailers’ Acceptance of Virtual Stores
Irene Y.L. Chen
2010-01-01
The acceptance of e-commerce among consumers has stimulated the rise of virtual stores. Increasing traditional retailers or people who do not have sufficient capital for maintaining a brick-and-mortar store have considered using virtual stores to reach global market. In the e-commerce literature, there has been rich research evidence concerning consumers’ acceptance of virtual stores. However, rigorous academic research on retailers’ acceptance of virtual stores is relatively scarce today. Th...
Prior Elicitation, Assessment and Inference with a Dirichlet Prior
Directory of Open Access Journals (Sweden)
Michael Evans
2017-10-01
Full Text Available Methods are developed for eliciting a Dirichlet prior based upon stating bounds on the individual probabilities that hold with high prior probability. This approach to selecting a prior is applied to a contingency table problem where it is demonstrated how to assess the prior with respect to the bias it induces as well as how to check for prior-data conflict. It is shown that the assessment of a hypothesis via relative belief can easily take into account what it means for the falsity of the hypothesis to correspond to a difference of practical importance and provide evidence in favor of a hypothesis.
Bayesian selective response-adaptive design using the historical control.
Kim, Mi-Ok; Harun, Nusrat; Liu, Chunyan; Khoury, Jane C; Broderick, Joseph P
2018-06-13
High quality historical control data, if incorporated, may reduce sample size, trial cost, and duration. A too optimistic use of the data, however, may result in bias under prior-data conflict. Motivated by well-publicized two-arm comparative trials in stroke, we propose a Bayesian design that both adaptively incorporates historical control data and selectively adapt the treatment allocation ratios within an ongoing trial responsively to the relative treatment effects. The proposed design differs from existing designs that borrow from historical controls. As opposed to reducing the number of subjects assigned to the control arm blindly, this design does so adaptively to the relative treatment effects only if evaluation of cumulated current trial data combined with the historical control suggests the superiority of the intervention arm. We used the effective historical sample size approach to quantify borrowed information on the control arm and modified the treatment allocation rules of the doubly adaptive biased coin design to incorporate the quantity. The modified allocation rules were then implemented under the Bayesian framework with commensurate priors addressing prior-data conflict. Trials were also more frequently concluded earlier in line with the underlying truth, reducing trial cost, and duration and yielded parameter estimates with smaller standard errors. © 2018 The Authors. Statistics in Medicine Published by John Wiley & Sons, Ltd.
Bayesian approach in MN low dose of radiation counting
International Nuclear Information System (INIS)
Serna Berna, A.; Alcaraz, M.; Acevedo, C.; Navarro, J. L.; Alcanzar, M. D.; Canteras, M.
2006-01-01
The Micronucleus assay in lymphocytes is a well established technique for the assessment of genetic damage induced by ionizing radiation. Due to the presence of a natural background of MN the net MN is obtained by subtracting this value to the gross value. When very low doses of radiation are given the induced MN is close even lower than the predetermined background value. Furthermore, the damage distribution induced by the radiation follows a Poisson probability distribution. These two facts pose a difficult task to obtain the net counting rate in the exposed situations. It is possible to overcome this problem using a bayesian approach, in which the selection of a priori distributions for the background and net counting rate plays an important role. In the present work we make a detailed analysed using bayesian theory to infer the net counting rate in two different situations: a) when the background is known for an individual sample, using exact value value for the background and Jeffreys prior for the net counting rate, and b) when the background is not known and we make use of a population background distribution as background prior function and constant prior for the net counting rate. (Author)
Bayesian estimation methods in metrology
International Nuclear Information System (INIS)
Cox, M.G.; Forbes, A.B.; Harris, P.M.
2004-01-01
In metrology -- the science of measurement -- a measurement result must be accompanied by a statement of its associated uncertainty. The degree of validity of a measurement result is determined by the validity of the uncertainty statement. In recognition of the importance of uncertainty evaluation, the International Standardization Organization in 1995 published the Guide to the Expression of Uncertainty in Measurement and the Guide has been widely adopted. The validity of uncertainty statements is tested in interlaboratory comparisons in which an artefact is measured by a number of laboratories and their measurement results compared. Since the introduction of the Mutual Recognition Arrangement, key comparisons are being undertaken to determine the degree of equivalence of laboratories for particular measurement tasks. In this paper, we discuss the possible development of the Guide to reflect Bayesian approaches and the evaluation of key comparison data using Bayesian estimation methods
Deep Learning and Bayesian Methods
Directory of Open Access Journals (Sweden)
Prosper Harrison B.
2017-01-01
Full Text Available A revolution is underway in which deep neural networks are routinely used to solve diffcult problems such as face recognition and natural language understanding. Particle physicists have taken notice and have started to deploy these methods, achieving results that suggest a potentially significant shift in how data might be analyzed in the not too distant future. We discuss a few recent developments in the application of deep neural networks and then indulge in speculation about how such methods might be used to automate certain aspects of data analysis in particle physics. Next, the connection to Bayesian methods is discussed and the paper ends with thoughts on a significant practical issue, namely, how, from a Bayesian perspective, one might optimize the construction of deep neural networks.
Bayesian inference on proportional elections.
Directory of Open Access Journals (Sweden)
Gabriel Hideki Vatanabe Brunello
Full Text Available Polls for majoritarian voting systems usually show estimates of the percentage of votes for each candidate. However, proportional vote systems do not necessarily guarantee the candidate with the most percentage of votes will be elected. Thus, traditional methods used in majoritarian elections cannot be applied on proportional elections. In this context, the purpose of this paper was to perform a Bayesian inference on proportional elections considering the Brazilian system of seats distribution. More specifically, a methodology to answer the probability that a given party will have representation on the chamber of deputies was developed. Inferences were made on a Bayesian scenario using the Monte Carlo simulation technique, and the developed methodology was applied on data from the Brazilian elections for Members of the Legislative Assembly and Federal Chamber of Deputies in 2010. A performance rate was also presented to evaluate the efficiency of the methodology. Calculations and simulations were carried out using the free R statistical software.
Multiview Bayesian Correlated Component Analysis
DEFF Research Database (Denmark)
Kamronn, Simon Due; Poulsen, Andreas Trier; Hansen, Lars Kai
2015-01-01
are identical. Here we propose a hierarchical probabilistic model that can infer the level of universality in such multiview data, from completely unrelated representations, corresponding to canonical correlation analysis, to identical representations as in correlated component analysis. This new model, which...... we denote Bayesian correlated component analysis, evaluates favorably against three relevant algorithms in simulated data. A well-established benchmark EEG data set is used to further validate the new model and infer the variability of spatial representations across multiple subjects....
Optimal design of priors constrained by external predictors
Czech Academy of Sciences Publication Activity Database
Quinn, A.; Kárný, Miroslav; Guy, Tatiana Valentine
2017-01-01
Roč. 84, č. 1 (2017), s. 150-158 ISSN 0888-613X R&D Projects: GA ČR(CZ) GA16-09848S Institutional support: RVO:67985556 Keywords : Fully probabilistic design * Parameter prior * External predictive distribution * Bayesian transfer learning * Kullback–Leibler divergence Subject RIV: BC - Control Systems Theory OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 2.845, year: 2016 http://library.utia.cas.cz/separaty/2017/AS/guy-0473911.pdf
Bayesian approach to analyzing holograms of colloidal particles.
Dimiduk, Thomas G; Manoharan, Vinothan N
2016-10-17
We demonstrate a Bayesian approach to tracking and characterizing colloidal particles from in-line digital holograms. We model the formation of the hologram using Lorenz-Mie theory. We then use a tempered Markov-chain Monte Carlo method to sample the posterior probability distributions of the model parameters: particle position, size, and refractive index. Compared to least-squares fitting, our approach allows us to more easily incorporate prior information about the parameters and to obtain more accurate uncertainties, which are critical for both particle tracking and characterization experiments. Our approach also eliminates the need to supply accurate initial guesses for the parameters, so it requires little tuning.
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.
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.
Directory of Open Access Journals (Sweden)
Moritz eBoos
2016-05-01
Full Text Available Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modelling 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 behaviour. 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 modelling 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 modelling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision.
Saffian, Shamin M; Duffull, Stephen B; Roberts, Rebecca L; Tait, Robert C; Black, Leanne; Lund, Kirstin A; Thomson, Alison H; Wright, Daniel F B
2016-12-01
A previously established Bayesian dosing tool for warfarin was found to produce biased maintenance dose predictions. In this study, we aimed (1) to determine whether the biased warfarin dose predictions previously observed could be replicated in a new cohort of patients from 2 different clinical settings, (2) to explore the influence of CYP2C9 and VKORC1 genotype on predictive performance of the Bayesian dosing tool, and (3) to determine whether the previous population used to develop the kinetic-pharmacodynamic model underpinning the Bayesian dosing tool was sufficiently different from the test (posterior) population to account for the biased dose predictions. The warfarin maintenance doses for 140 patients were predicted using the dosing tool and compared with the observed maintenance dose. The impact of genotype was assessed by predicting maintenance doses with prior parameter values known to be altered by genetic variability (eg, EC50 for VKORC1 genotype). The prior population was evaluated by fitting the published kinetic-pharmacodynamic model, which underpins the Bayesian tool, to the observed data using NONMEM and comparing the model parameter estimates with published values. The Bayesian tool produced positively biased dose predictions in the new cohort of patients (mean prediction error [95% confidence interval]; 0.32 mg/d [0.14-0.5]). The bias was only observed in patients requiring ≥7 mg/d. The direction and magnitude of the observed bias was not influenced by genotype. The prior model provided a good fit to our data, which suggests that the bias was not caused by different prior and posterior populations. Maintenance doses for patients requiring ≥7 mg/d were overpredicted. The bias was not due to the influence of genotype nor was it related to differences between the prior and posterior populations. There is a need for a more mechanistic model that captures warfarin dose-response relationship at higher warfarin doses.
Generalized multiple kernel learning with data-dependent priors.
Mao, Qi; Tsang, Ivor W; Gao, Shenghua; Wang, Li
2015-06-01
Multiple kernel learning (MKL) and classifier ensemble are two mainstream methods for solving learning problems in which some sets of features/views are more informative than others, or the features/views within a given set are inconsistent. In this paper, we first present a novel probabilistic interpretation of MKL such that maximum entropy discrimination with a noninformative prior over multiple views is equivalent to the formulation of MKL. Instead of using the noninformative prior, we introduce a novel data-dependent prior based on an ensemble of kernel predictors, which enhances the prediction performance of MKL by leveraging the merits of the classifier ensemble. With the proposed probabilistic framework of MKL, we propose a hierarchical Bayesian model to learn the proposed data-dependent prior and classification model simultaneously. The resultant problem is convex and other information (e.g., instances with either missing views or missing labels) can be seamlessly incorporated into the data-dependent priors. Furthermore, a variety of existing MKL models can be recovered under the proposed MKL framework and can be readily extended to incorporate these priors. Extensive experiments demonstrate the benefits of our proposed framework in supervised and semisupervised settings, as well as in tasks with partial correspondence among multiple views.
Fractional Gaussian noise: Prior specification and model comparison
Sø rbye, Sigrunn Holbek; Rue, Haavard
2017-01-01
Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ(symbol) of a first-order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.
Fractional Gaussian noise: Prior specification and model comparison
Sørbye, Sigrunn Holbek
2017-07-07
Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ(symbol) of a first-order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.
Application of a predictive Bayesian model to environmental accounting.
Anex, R P; Englehardt, J D
2001-03-30
Environmental accounting techniques are intended to capture important environmental costs and benefits that are often overlooked in standard accounting practices. Environmental accounting methods themselves often ignore or inadequately represent large but highly uncertain environmental costs and costs conditioned by specific prior events. Use of a predictive Bayesian model is demonstrated for the assessment of such highly uncertain environmental and contingent costs. The predictive Bayesian approach presented generates probability distributions for the quantity of interest (rather than parameters thereof). A spreadsheet implementation of a previously proposed predictive Bayesian model, extended to represent contingent costs, is described and used to evaluate whether a firm should undertake an accelerated phase-out of its PCB containing transformers. Variability and uncertainty (due to lack of information) in transformer accident frequency and severity are assessed simultaneously using a combination of historical accident data, engineering model-based cost estimates, and subjective judgement. Model results are compared using several different risk measures. Use of the model for incorporation of environmental risk management into a company's overall risk management strategy is discussed.
Bayesian accounts of covert selective attention: A tutorial review.
Vincent, Benjamin T
2015-05-01
Decision making and optimal observer models offer an important theoretical approach to the study of covert selective attention. While their probabilistic formulation allows quantitative comparison to human performance, the models can be complex and their insights are not always immediately apparent. Part 1 establishes the theoretical appeal of the Bayesian approach, and introduces the way in which probabilistic approaches can be applied to covert search paradigms. Part 2 presents novel formulations of Bayesian models of 4 important covert attention paradigms, illustrating optimal observer predictions over a range of experimental manipulations. Graphical model notation is used to present models in an accessible way and Supplementary Code is provided to help bridge the gap between model theory and practical implementation. Part 3 reviews a large body of empirical and modelling evidence showing that many experimental phenomena in the domain of covert selective attention are a set of by-products. These effects emerge as the result of observers conducting Bayesian inference with noisy sensory observations, prior expectations, and knowledge of the generative structure of the stimulus environment.
Bayesian Action&Perception: Representing the World in the Brain
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Gerald E. Loeb
2014-10-01
Full Text Available Theories of perception seek to explain how sensory data are processed to identify previously experienced objects, but they usually do not consider the decisions and effort that goes into acquiring the sensory data. Identification of objects according to their tactile properties requires active exploratory movements. The sensory data thereby obtained depend on the details of those movements, which human subjects change rapidly and seemingly capriciously. Bayesian Exploration is an algorithm that uses prior experience to decide which next exploratory movement should provide the most useful data to disambiguate the most likely possibilities. In previous studies, a simple robot equipped with a biomimetic tactile sensor and operated according to Bayesian Exploration performed in a manner similar to and actually better than humans on a texture identification task. Expanding on this, Bayesian Action&Perception refers to the construction and querying of an associative memory of previously experienced entities containing both sensory data and the motor programs that elicited them. We hypothesize that this memory can be queried i to identify useful next exploratory movements during identification of an unknown entity (action for perception or ii to characterize whether an unknown entity is fit for purpose (perception for action or iii to recall what actions might be feasible for a known entity (Gibsonian affordance. The biomimetic design of this mechatronic system may provide insights into the neuronal basis of biological action and perception.
Bayesian site selection for fast Gaussian process regression
Pourhabib, Arash; Liang, Faming; Ding, Yu
2014-01-01
Gaussian Process (GP) regression is a popular method in the field of machine learning and computer experiment designs; however, its ability to handle large data sets is hindered by the computational difficulty in inverting a large covariance matrix. Likelihood approximation methods were developed as a fast GP approximation, thereby reducing the computation cost of GP regression by utilizing a much smaller set of unobserved latent variables called pseudo points. This article reports a further improvement to the likelihood approximation methods by simultaneously deciding both the number and locations of the pseudo points. The proposed approach is a Bayesian site selection method where both the number and locations of the pseudo inputs are parameters in the model, and the Bayesian model is solved using a reversible jump Markov chain Monte Carlo technique. Through a number of simulated and real data sets, it is demonstrated that with appropriate priors chosen, the Bayesian site selection method can produce a good balance between computation time and prediction accuracy: it is fast enough to handle large data sets that a full GP is unable to handle, and it improves, quite often remarkably, the prediction accuracy, compared with the existing likelihood approximations. © 2014 Taylor and Francis Group, LLC.
Application of an efficient Bayesian discretization method to biomedical data
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Gopalakrishnan Vanathi
2011-07-01
Full Text Available Abstract Background Several data mining methods require data that are discrete, and other methods often perform better with discrete data. We introduce an efficient Bayesian discretization (EBD method for optimal discretization of variables that runs efficiently on high-dimensional biomedical datasets. The EBD method consists of two components, namely, a Bayesian score to evaluate discretizations and a dynamic programming search procedure to efficiently search the space of possible discretizations. We compared the performance of EBD to Fayyad and Irani's (FI discretization method, which is commonly used for discretization. Results On 24 biomedical datasets obtained from high-throughput transcriptomic and proteomic studies, the classification performances of the C4.5 classifier and the naïve Bayes classifier were statistically significantly better when the predictor variables were discretized using EBD over FI. EBD was statistically significantly more stable to the variability of the datasets than FI. However, EBD was less robust, though not statistically significantly so, than FI and produced slightly more complex discretizations than FI. Conclusions On a range of biomedical datasets, a Bayesian discretization method (EBD yielded better classification performance and stability but was less robust than the widely used FI discretization method. The EBD discretization method is easy to implement, permits the incorporation of prior knowledge and belief, and is sufficiently fast for application to high-dimensional data.
Bayesian site selection for fast Gaussian process regression
Pourhabib, Arash
2014-02-05
Gaussian Process (GP) regression is a popular method in the field of machine learning and computer experiment designs; however, its ability to handle large data sets is hindered by the computational difficulty in inverting a large covariance matrix. Likelihood approximation methods were developed as a fast GP approximation, thereby reducing the computation cost of GP regression by utilizing a much smaller set of unobserved latent variables called pseudo points. This article reports a further improvement to the likelihood approximation methods by simultaneously deciding both the number and locations of the pseudo points. The proposed approach is a Bayesian site selection method where both the number and locations of the pseudo inputs are parameters in the model, and the Bayesian model is solved using a reversible jump Markov chain Monte Carlo technique. Through a number of simulated and real data sets, it is demonstrated that with appropriate priors chosen, the Bayesian site selection method can produce a good balance between computation time and prediction accuracy: it is fast enough to handle large data sets that a full GP is unable to handle, and it improves, quite often remarkably, the prediction accuracy, compared with the existing likelihood approximations. © 2014 Taylor and Francis Group, LLC.
12th Brazilian Meeting on Bayesian Statistics
Louzada, Francisco; Rifo, Laura; Stern, Julio; Lauretto, Marcelo
2015-01-01
Through refereed papers, this volume focuses on the foundations of the Bayesian paradigm; their comparison to objectivistic or frequentist Statistics counterparts; and the appropriate application of Bayesian foundations. This research in Bayesian Statistics is applicable to data analysis in biostatistics, clinical trials, law, engineering, and the social sciences. EBEB, the Brazilian Meeting on Bayesian Statistics, is held every two years by the ISBrA, the International Society for Bayesian Analysis, one of the most active chapters of the ISBA. The 12th meeting took place March 10-14, 2014 in Atibaia. Interest in foundations of inductive Statistics has grown recently in accordance with the increasing availability of Bayesian methodological alternatives. Scientists need to deal with the ever more difficult choice of the optimal method to apply to their problem. This volume shows how Bayes can be the answer. The examination and discussion on the foundations work towards the goal of proper application of Bayesia...
Kim, Hea-Jung
2014-01-01
This paper considers a hierarchical screened Gaussian model (HSGM) for Bayesian inference of normal models when an interval constraint in the mean parameter space needs to be incorporated in the modeling but when such a restriction is uncertain. An objective measure of the uncertainty, regarding the interval constraint, accounted for by using the HSGM is proposed for the Bayesian inference. For this purpose, we drive a maximum entropy prior of the normal mean, eliciting the uncertainty regarding the interval constraint, and then obtain the uncertainty measure by considering the relationship between the maximum entropy prior and the marginal prior of the normal mean in HSGM. Bayesian estimation procedure of HSGM is developed and two numerical illustrations pertaining to the properties of the uncertainty measure are provided.
Directory of Open Access Journals (Sweden)
Hea-Jung Kim
2014-01-01
Full Text Available This paper considers a hierarchical screened Gaussian model (HSGM for Bayesian inference of normal models when an interval constraint in the mean parameter space needs to be incorporated in the modeling but when such a restriction is uncertain. An objective measure of the uncertainty, regarding the interval constraint, accounted for by using the HSGM is proposed for the Bayesian inference. For this purpose, we drive a maximum entropy prior of the normal mean, eliciting the uncertainty regarding the interval constraint, and then obtain the uncertainty measure by considering the relationship between the maximum entropy prior and the marginal prior of the normal mean in HSGM. Bayesian estimation procedure of HSGM is developed and two numerical illustrations pertaining to the properties of the uncertainty measure are provided.
Directory of Open Access Journals (Sweden)
Ron Tolmie
2014-11-01
Full Text Available Heat can be collected from local energy sources and concentrated into a relatively small volume, and at a useful working temperature, by using a heat pump as the concentrator. That heat can be stored and utilized at a later date for applications like space heating. The process is doing two things at the same time: storing heat and shifting the power demand. The concentration step can be done at night when there is normally a surplus of power and its timing can be directly controlled by the power grid operator to ensure that the power consumption occurs only when adequate power is available. The sources of heat can be the summer air, the heat extracted from buildings by their cooling systems, natural heat from the ground or solar heat, all of which are free, abundant and readily accessible. Such systems can meet the thermal needs of buildings while at the same time stabilizing the grid power demand, thus reducing the need for using fossil-fuelled peaking power generators. The heat pump maintains the temperature of the periphery at the ambient ground temperature so very little energy is lost during storage.
Method of storing radioactive wastes
Energy Technology Data Exchange (ETDEWEB)
Kikuchi, M; Kamiya, K; Sugimoto, Y
1976-01-09
A method is claimed to decrease the number of storage containers filled with radioactive wastes. A wire-netting containers having a capacity of 67 liters is filled with 60 kg of pellet-like radioactive solid material. The wire-netting container is held in the middle of a drum can, and asphalt is poured between the drum can and the wire-netting container and stored until radioactivity is attenuated. After storage, the stored body is heated to melt the asphalt and the wire-netting container is removed. Thereafter, the pellet-like radioactive solid material is taken out of the wire-netting container and combined with the other pellet-like radioactive solid material similarly taken out of the storage container, and the resultant material is filled into a wire-netting container having a capacity of 167 liters every 150 kg, and inserted again into the same drum can, into which recovered asphalt is poured for final storage.
[Occupational risks in grocery stores].
Graziosi, Francesca; Bonfiglioli, Roberta; Violante, Francesco S
2014-01-01
This work provides an overview of the spectrum of possible occupational risk factors in the retail grocery store/supermarket workplace. Literature on this theme, obtained consulting PubMed database and Google Scholar, was checked. We also exjlore results from the National bInstitute for Occupational Safety and Health (NIOSH) and the Occupational Safety and Health Administration (OSHA). RESULTs: Contacts with objects, use of dangerous equipment (cutter, food slicer) and falls to the same level (slips, trips and falls) are the mainly described workplace hazards. Exposure to chemical (flour dust, components of detergents or disinfectants, volatile organic compounds and contact with nickel) and physical agents (cold exposure, nonionizing radiation and whole bpdy vibration) are reported by many authors. Relations between biomechanical and ergonomic risk factors and musculoskeletal disorders represent the main subjects of study. Few studies are found about biological agents (particularly among butchers). Data regarding psychosocial risks factors in this setting are still limited. Musculoskeletal disorders continue to be the most recurrent health problem between the grocery store workers (particularly low back pain and carpal tunnel syndrome among cashiers). Many technical documents and international Srecommendations are present to prevent these kinds of disorders. Psychosocial risk factors and risk of workplace violence should deserve further investigation.
Putting Priors in Mixture Density Mercer Kernels
Srivastava, Ashok N.; Schumann, Johann; Fischer, Bernd
2004-01-01
This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. We describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using predefined kernels. These data adaptive kernels can en- code prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS). The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains template for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic- algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code. The results show that the Mixture Density Mercer-Kernel described here outperforms tree-based classification in distinguishing high-redshift galaxies from low- redshift galaxies by approximately 16% on test data, bagged trees by approximately 7%, and bagged trees built on a much larger sample of data by approximately 2%.
Prior expectations facilitate metacognition for perceptual decision.
Sherman, M T; Seth, A K; Barrett, A B; Kanai, R
2015-09-01
The influential framework of 'predictive processing' suggests that prior probabilistic expectations influence, or even constitute, perceptual contents. This notion is evidenced by the facilitation of low-level perceptual processing by expectations. However, whether expectations can facilitate high-level components of perception remains unclear. We addressed this question by considering the influence of expectations on perceptual metacognition. To isolate the effects of expectation from those of attention we used a novel factorial design: expectation was manipulated by changing the probability that a Gabor target would be presented; attention was manipulated by instructing participants to perform or ignore a concurrent visual search task. We found that, independently of attention, metacognition improved when yes/no responses were congruent with expectations of target presence/absence. Results were modeled under a novel Bayesian signal detection theoretic framework which integrates bottom-up signal propagation with top-down influences, to provide a unified description of the mechanisms underlying perceptual decision and metacognition. Copyright © 2015 Elsevier Inc. All rights reserved.
Bayesian nonlinear regression for large small problems
Chakraborty, Sounak; Ghosh, Malay; Mallick, Bani K.
2012-01-01
Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. This is known as large p small n problem. Furthermore, the problem is more complicated when we have multiple correlated responses. We develop multivariate nonlinear regression models in this setup for accurate prediction. In this paper, we introduce a full Bayesian support vector regression model with Vapnik's ε-insensitive loss function, based on reproducing kernel Hilbert spaces (RKHS) under the multivariate correlated response setup. This provides a full probabilistic description of support vector machine (SVM) rather than an algorithm for fitting purposes. We have also introduced a multivariate version of the relevance vector machine (RVM). Instead of the original treatment of the RVM relying on the use of type II maximum likelihood estimates of the hyper-parameters, we put a prior on the hyper-parameters and use Markov chain Monte Carlo technique for computation. We have also proposed an empirical Bayes method for our RVM and SVM. Our methods are illustrated with a prediction problem in the near-infrared (NIR) spectroscopy. A simulation study is also undertaken to check the prediction accuracy of our models. © 2012 Elsevier Inc.
Bayesian Nonparametric Clustering for Positive Definite Matrices.
Cherian, Anoop; Morellas, Vassilios; Papanikolopoulos, Nikolaos
2016-05-01
Symmetric Positive Definite (SPD) matrices emerge as data descriptors in several applications of computer vision such as object tracking, texture recognition, and diffusion tensor imaging. Clustering these data matrices forms an integral part of these applications, for which soft-clustering algorithms (K-Means, expectation maximization, etc.) are generally used. As is well-known, these algorithms need the number of clusters to be specified, which is difficult when the dataset scales. To address this issue, we resort to the classical nonparametric Bayesian framework by modeling the data as a mixture model using the Dirichlet process (DP) prior. Since these matrices do not conform to the Euclidean geometry, rather belongs to a curved Riemannian manifold,existing DP models cannot be directly applied. Thus, in this paper, we propose a novel DP mixture model framework for SPD matrices. Using the log-determinant divergence as the underlying dissimilarity measure to compare these matrices, and further using the connection between this measure and the Wishart distribution, we derive a novel DPM model based on the Wishart-Inverse-Wishart conjugate pair. We apply this model to several applications in computer vision. Our experiments demonstrate that our model is scalable to the dataset size and at the same time achieves superior accuracy compared to several state-of-the-art parametric and nonparametric clustering algorithms.
BEAST: Bayesian evolutionary analysis by sampling trees
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Drummond Alexei J
2007-11-01
Full Text Available Abstract Background The evolutionary analysis of molecular sequence variation is a statistical enterprise. This is reflected in the increased use of probabilistic models for phylogenetic inference, multiple sequence alignment, and molecular population genetics. Here we present BEAST: a fast, flexible software architecture for Bayesian analysis of molecular sequences related by an evolutionary tree. A large number of popular stochastic models of sequence evolution are provided and tree-based models suitable for both within- and between-species sequence data are implemented. Results BEAST version 1.4.6 consists of 81000 lines of Java source code, 779 classes and 81 packages. It provides models for DNA and protein sequence evolution, highly parametric coalescent analysis, relaxed clock phylogenetics, non-contemporaneous sequence data, statistical alignment and a wide range of options for prior distributions. BEAST source code is object-oriented, modular in design and freely available at http://beast-mcmc.googlecode.com/ under the GNU LGPL license. Conclusion BEAST is a powerful and flexible evolutionary analysis package for molecular sequence variation. It also provides a resource for the further development of new models and statistical methods of evolutionary analysis.
Bayesian nonlinear regression for large small problems
Chakraborty, Sounak
2012-07-01
Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. This is known as large p small n problem. Furthermore, the problem is more complicated when we have multiple correlated responses. We develop multivariate nonlinear regression models in this setup for accurate prediction. In this paper, we introduce a full Bayesian support vector regression model with Vapnik\\'s ε-insensitive loss function, based on reproducing kernel Hilbert spaces (RKHS) under the multivariate correlated response setup. This provides a full probabilistic description of support vector machine (SVM) rather than an algorithm for fitting purposes. We have also introduced a multivariate version of the relevance vector machine (RVM). Instead of the original treatment of the RVM relying on the use of type II maximum likelihood estimates of the hyper-parameters, we put a prior on the hyper-parameters and use Markov chain Monte Carlo technique for computation. We have also proposed an empirical Bayes method for our RVM and SVM. Our methods are illustrated with a prediction problem in the near-infrared (NIR) spectroscopy. A simulation study is also undertaken to check the prediction accuracy of our models. © 2012 Elsevier Inc.
Bayesian Networks for enterprise risk assessment
Bonafede, C. E.; Giudici, P.
2007-08-01
According to different typologies of activity and priority, risks can assume diverse meanings and it can be assessed in different ways. Risk, in general, is measured in terms of a probability combination of an event (frequency) and its consequence (impact). To estimate the frequency and the impact (severity) historical data or expert opinions (either qualitative or quantitative data) are used. Moreover, qualitative data must be converted in numerical values or bounds to be used in the model. In the case of enterprise risk assessment the considered risks are, for instance, strategic, operational, legal and of image, which many times are difficult to be quantified. So in most cases only expert data, gathered by scorecard approaches, are available for risk analysis. The Bayesian Networks (BNs) are a useful tool to integrate different information and in particular to study the risk's joint distribution by using data collected from experts. In this paper we want to show a possible approach for building a BN in the particular case in which only prior probabilities of node states and marginal correlations between nodes are available, and when the variables have only two states.
Bayesian data assimilation in shape registration
Cotter, C J
2013-03-28
In this paper we apply a Bayesian framework to the problem of geodesic curve matching. Given a template curve, the geodesic equations provide a mapping from initial conditions for the conjugate momentum onto topologically equivalent shapes. Here, we aim to recover the well-defined posterior distribution on the initial momentum which gives rise to observed points on the target curve; this is achieved by explicitly including a reparameterization in the formulation. Appropriate priors are chosen for the functions which together determine this field and the positions of the observation points, the initial momentum p0 and the reparameterization vector field ν, informed by regularity results about the forward model. Having done this, we illustrate how maximum likelihood estimators can be used to find regions of high posterior density, but also how we can apply recently developed Markov chain Monte Carlo methods on function spaces to characterize the whole of the posterior density. These illustrative examples also include scenarios where the posterior distribution is multimodal and irregular, leading us to the conclusion that knowledge of a state of global maximal posterior density does not always give us the whole picture, and full posterior sampling can give better quantification of likely states and the overall uncertainty inherent in the problem. © 2013 IOP Publishing Ltd.
Reliability demonstration test planning using bayesian analysis
International Nuclear Information System (INIS)
Chandran, Senthil Kumar; Arul, John A.
2003-01-01
In Nuclear Power Plants, the reliability of all the safety systems is very critical from the safety viewpoint and it is very essential that the required reliability requirements be met while satisfying the design constraints. From practical experience, it is found that the reliability of complex systems such as Safety Rod Drive Mechanism is of the order of 10 -4 with an uncertainty factor of 10. To demonstrate the reliability of such systems is prohibitive in terms of cost and time as the number of tests needed is very large. The purpose of this paper is to develop a Bayesian reliability demonstrating testing procedure for exponentially distributed failure times with gamma prior distribution on the failure rate which can be easily and effectively used to demonstrate component/subsystem/system reliability conformance to stated requirements. The important questions addressed in this paper are: With zero failures, how long one should perform the tests and how many components are required to conclude with a given degree of confidence, that the component under test, meets the reliability requirement. The procedure is explained with an example. This procedure can also be extended to demonstrate with more number of failures. The approach presented is applicable for deriving test plans for demonstrating component failure rates of nuclear power plants, as the failure data for similar components are becoming available in existing plants elsewhere. The advantages of this procedure are the criterion upon which the procedure is based is simple and pertinent, the fitting of the prior distribution is an integral part of the procedure and is based on the use of information regarding two percentiles of this distribution and finally, the procedure is straightforward and easy to apply in practice. (author)
Bayesian inversion of refraction seismic traveltime data
Ryberg, T.; Haberland, Ch
2018-03-01
We apply a Bayesian Markov chain Monte Carlo (McMC) formalism to the inversion of refraction seismic, traveltime data sets to derive 2-D velocity models below linear arrays (i.e. profiles) of sources and seismic receivers. Typical refraction data sets, especially when using the far-offset observations, are known as having experimental geometries which are very poor, highly ill-posed and far from being ideal. As a consequence, the structural resolution quickly degrades with depth. Conventional inversion techniques, based on regularization, potentially suffer from the choice of appropriate inversion parameters (i.e. number and distribution of cells, starting velocity models, damping and smoothing constraints, data noise level, etc.) and only local model space exploration. McMC techniques are used for exhaustive sampling of the model space without the need of prior knowledge (or assumptions) of inversion parameters, resulting in a large number of models fitting the observations. Statistical analysis of these models allows to derive an average (reference) solution and its standard deviation, thus providing uncertainty estimates of the inversion result. The highly non-linear character of the inversion problem, mainly caused by the experiment geometry, does not allow to derive a reference solution and error map by a simply averaging procedure. We present a modified averaging technique, which excludes parts of the prior distribution in the posterior values due to poor ray coverage, thus providing reliable estimates of inversion model properties even in those parts of the models. The model is discretized by a set of Voronoi polygons (with constant slowness cells) or a triangulated mesh (with interpolation within the triangles). Forward traveltime calculations are performed by a fast, finite-difference-based eikonal solver. The method is applied to a data set from a refraction seismic survey from Northern Namibia and compared to conventional tomography. An inversion test
3rd Bayesian Young Statisticians Meeting
Lanzarone, Ettore; Villalobos, Isadora; Mattei, Alessandra
2017-01-01
This book is a selection of peer-reviewed contributions presented at the third Bayesian Young Statisticians Meeting, BAYSM 2016, Florence, Italy, June 19-21. The meeting provided a unique opportunity for young researchers, M.S. students, Ph.D. students, and postdocs dealing with Bayesian statistics to connect with the Bayesian community at large, to exchange ideas, and to network with others working in the same field. The contributions develop and apply Bayesian methods in a variety of fields, ranging from the traditional (e.g., biostatistics and reliability) to the most innovative ones (e.g., big data and networks).
Ensemble Bayesian forecasting system Part I: Theory and algorithms
Herr, Henry D.; Krzysztofowicz, Roman
2015-05-01
The ensemble Bayesian forecasting system (EBFS), whose theory was published in 2001, is developed for the purpose of quantifying the total uncertainty about a discrete-time, continuous-state, non-stationary stochastic process such as a time series of stages, discharges, or volumes at a river gauge. The EBFS is built of three components: an input ensemble forecaster (IEF), which simulates the uncertainty associated with random inputs; a deterministic hydrologic model (of any complexity), which simulates physical processes within a river basin; and a hydrologic uncertainty processor (HUP), which simulates the hydrologic uncertainty (an aggregate of all uncertainties except input). It works as a Monte Carlo simulator: an ensemble of time series of inputs (e.g., precipitation amounts) generated by the IEF is transformed deterministically through a hydrologic model into an ensemble of time series of outputs, which is next transformed stochastically by the HUP into an ensemble of time series of predictands (e.g., river stages). Previous research indicated that in order to attain an acceptable sampling error, the ensemble size must be on the order of hundreds (for probabilistic river stage forecasts and probabilistic flood forecasts) or even thousands (for probabilistic stage transition forecasts). The computing time needed to run the hydrologic model this many times renders the straightforward simulations operationally infeasible. This motivates the development of the ensemble Bayesian forecasting system with randomization (EBFSR), which takes full advantage of the analytic meta-Gaussian HUP and generates multiple ensemble members after each run of the hydrologic model; this auxiliary randomization reduces the required size of the meteorological input ensemble and makes it operationally feasible to generate a Bayesian ensemble forecast of large size. Such a forecast quantifies the total uncertainty, is well calibrated against the prior (climatic) distribution of
Seeded Bayesian Networks: Constructing genetic networks from microarray data
Directory of Open Access Journals (Sweden)
Quackenbush John
2008-07-01
Full Text Available Abstract Background DNA microarrays and other genomics-inspired technologies provide large datasets that often include hidden patterns of correlation between genes reflecting the complex processes that underlie cellular metabolism and physiology. The challenge in analyzing large-scale expression data has been to extract biologically meaningful inferences regarding these processes – often represented as networks – in an environment where the datasets are often imperfect and biological noise can obscure the actual signal. Although many techniques have been developed in an attempt to address these issues, to date their ability to extract meaningful and predictive network relationships has been limited. Here we describe a method that draws on prior information about gene-gene interactions to infer biologically relevant pathways from microarray data. Our approach consists of using preliminary networks derived from the literature and/or protein-protein interaction data as seeds for a Bayesian network analysis of microarray results. Results Through a bootstrap analysis of gene expression data derived from a number of leukemia studies, we demonstrate that seeded Bayesian Networks have the ability to identify high-confidence gene-gene interactions which can then be validated by comparison to other sources of pathway data. Conclusion The use of network seeds greatly improves the ability of Bayesian Network analysis to learn gene interaction networks from gene expression data. We demonstrate that the use of seeds derived from the biomedical literature or high-throughput protein-protein interaction data, or the combination, provides improvement over a standard Bayesian Network analysis, allowing networks involving dynamic processes to be deduced from the static snapshots of biological systems that represent the most common source of microarray data. Software implementing these methods has been included in the widely used TM4 microarray analysis package.
Self-consistent Bayesian analysis of space-time symmetry studies
International Nuclear Information System (INIS)
Davis, E.D.
1996-01-01
We introduce a Bayesian method for the analysis of epithermal neutron transmission data on space-time symmetries in which unique assignment of the prior is achieved by maximisation of the cross entropy and the imposition of a self-consistency criterion. Unlike the maximum likelihood method used in previous analyses of parity-violation data, our method is freed of an ad hoc cutoff parameter. Monte Carlo studies indicate that our self-consistent Bayesian analysis is superior to the maximum likelihood method when applied to the small data samples typical of symmetry studies. (orig.)
International Nuclear Information System (INIS)
Von Nessi, G T; Hole, M J
2014-01-01
We present recent results and technical breakthroughs for the Bayesian inference of tokamak equilibria using force-balance as a prior constraint. Issues surrounding model parameter representation and posterior analysis are discussed and addressed. These points motivate the recent advancements embodied in the Bayesian Equilibrium Analysis and Simulation Tool (BEAST) software being presently utilized to study equilibria on the Mega-Ampere Spherical Tokamak (MAST) experiment in the UK (von Nessi et al 2012 J. Phys. A 46 185501). State-of-the-art results of using BEAST to study MAST equilibria are reviewed, with recent code advancements being systematically presented though out the manuscript. (paper)
Using literature and data to learn Bayesian networks as clinical models of ovarian tumors
DEFF Research Database (Denmark)
Antal, P.; Fannes, G.; Timmerman, D.
2004-01-01
Thanks to its increasing availability, electronic literature has become a potential source of information for the development of complex Bayesian networks (BN), when human expertise is missing or data is scarce or contains much noise. This opportunity raises the question of how to integrate...... information from free-text resources with statistical data in learning Bayesian networks. Firstly, we report on the collection of prior information resources in the ovarian cancer domain, which includes "kernel" annotations of the domain variables. We introduce methods based on the annotations and literature...
Metis: A Pure Metropolis Markov Chain Monte Carlo Bayesian Inference Library
Energy Technology Data Exchange (ETDEWEB)
Bates, Cameron Russell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Mckigney, Edward Allen [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2018-01-09
The use of Bayesian inference in data analysis has become the standard for large scienti c experiments [1, 2]. The Monte Carlo Codes Group(XCP-3) at Los Alamos has developed a simple set of algorithms currently implemented in C++ and Python to easily perform at-prior Markov Chain Monte Carlo Bayesian inference with pure Metropolis sampling. These implementations are designed to be user friendly and extensible for customization based on speci c application requirements. This document describes the algorithmic choices made and presents two use cases.
Directory of Open Access Journals (Sweden)
Hea-Jung Kim
2017-06-01
Full Text Available This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT models with stochastic (or uncertain constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT models (such as log-normal, log-Cauchy, and log-logistic FT models as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works.
Elsheikh, Ahmed H.
2014-02-01
A Hybrid Nested Sampling (HNS) algorithm is proposed for efficient Bayesian model calibration and prior model selection. The proposed algorithm combines, Nested Sampling (NS) algorithm, Hybrid Monte Carlo (HMC) sampling and gradient estimation using Stochastic Ensemble Method (SEM). NS is an efficient sampling algorithm that can be used for Bayesian calibration and estimating the Bayesian evidence for prior model selection. Nested sampling has the advantage of computational feasibility. Within the nested sampling algorithm, a constrained sampling step is performed. For this step, we utilize HMC to reduce the correlation between successive sampled states. HMC relies on the gradient of the logarithm of the posterior distribution, which we estimate using a stochastic ensemble method based on an ensemble of directional derivatives. SEM only requires forward model runs and the simulator is then used as a black box and no adjoint code is needed. The developed HNS algorithm is successfully applied for Bayesian calibration and prior model selection of several nonlinear subsurface flow problems. © 2013 Elsevier Inc.
16-channel analog store and multiplexer unit
Energy Technology Data Exchange (ETDEWEB)
Brossard, M; Kulka, Z [Clermont-Ferrand-2 Univ., 63 - Aubiere (France). Lab. de Physique Corpusculaire
1979-03-15
A 16-channel analog store and multiplexer unit is described. The unit enables storing and selection of analog information which is then digitally encoded by single ADC. This solution becomes economically attractive particularly in multidetector pulse height analysis systems.
Store Separations From a Supersonic Cone
National Research Council Canada - National Science Library
Simko, Richard J
2006-01-01
... analyses of supersonic store separations. Also included in this research is a study of supersonic base pressure profiles, near-wake velocity profiles, wind tunnel shock interactions and force/moment studies on a conical store and parent vehicle...
DEFF Research Database (Denmark)
Strathe, Anders Bjerring; Jørgensen, Henry; Kebreab, E
2012-01-01
ABSTRACT SUMMARY The objective of the current study was to develop Bayesian simultaneous equation models for modelling energy intake and partitioning in growing pigs. A key feature of the Bayesian approach is that parameters are assigned prior distributions, which may reflect the current state...... of nature. In the models, rates of metabolizable energy (ME) intake, protein deposition (PD) and lipid deposition (LD) were treated as dependent variables accounting for residuals being correlated. Two complementary equation systems were used to model ME intake (MEI), PD and LD. Informative priors were...... developed, reflecting current knowledge about metabolic scaling and partial efficiencies of PD and LD rates, whereas flat non-informative priors were used for the reminder of the parameters. The experimental data analysed originate from a balance and respiration trial with 17 cross-bred pigs of three...
In-Store Media and Channel Management
Anthony Dukes; Yunchuan Liu
2007-01-01
In this paper, we study the interesting and complicated effects of retailer in-store media on distribution channel relationships. With the help of advanced technology, retailers can open in-store media in their stores and allow manufacturers to advertise through the instore media. We show that opening in-store media is a strategic decision for a retailer, and a retailer may strategically subsidize manufacturers on their advertising through instore media to better coordinate the channel. Even ...
Consumer behaviour in Apple's App Store
Ayalew, Romel
2011-01-01
Mobile applications stores such as Apple’s App Store and Google’s Android Market revolutionized the distribution of applications for mobile devices. However, with thousands of application submissions, limited testing resources and the lack of an effective filtering mechanism, application stores suffer from information overload and a risk of releasing poor quality applications that could create confusion to consumers and may seriously affect the App store markets. Thus concern has been raised ...
Corner stores: the perspective of urban youth.
Sherman, Sandra; Grode, Gabrielle; McCoy, Tara; Vander Veur, Stephanie S; Wojtanowski, Alexis; Sandoval, Brianna Almaguer; Foster, Gary D
2015-02-01
We examined the perspectives of low-income, urban youth about the corner store experience to inform the development of corner store interventions. Focus groups were conducted to understand youth perceptions regarding their early shopping experiences, the process of store selection, reasons for shopping in a corner store, parental guidance about corner stores, and what their ideal, or "dream corner store" would look like. Thematic analysis was employed to identify themes using ATLAS.ti (version 6.1, 2010, ATLAS.ti GmbH) and Excel (version 2010, Microsoft Corp). Focus groups were conducted in nine kindergarten-through-grade 8 (K-8) public schools in low-income neighborhoods with 40 fourth- to sixth-graders with a mean age of 10.9±0.8 years. Youth report going to corner stores with family members at an early age. By second and third grades, a growing number of youth reported shopping unaccompanied by an older sibling or adult. Youth reported that the products sold in stores were the key reason they choose a specific store. A small number of youth said their parents offered guidance on their corner store purchases. When youth were asked what their dream corner store would look like, they mentioned wanting a combination of healthy and less-healthy foods. These data suggest that, among low-income, urban youth, corner store shopping starts at a very young age and that product, price, and location are key factors that affect corner store selection. The data also suggest that few parents offer guidance about corner store purchases, and youth are receptive to having healthier items in corner stores. Corner store intervention efforts should target young children and their parents/caregivers and aim to increase the availability of affordable, healthier products. Copyright © 2015 Academy of Nutrition and Dietetics. Published by Elsevier Inc. All rights reserved.
Retail brand architecture and consumer store loyalty
DEFF Research Database (Denmark)
Brunsø, Karen; Grunert, Klaus G.
is to investigate the relationship between consumers perceived retail brand architecture, their store satisfaction and loyalty. Furthermore we use perceived store image as a mediating factor in our framework. In total 772 Danish households participated in a telephone interview and returned questionnaires by mail....... The major contribution of this research is to conceptualise and empirically investigate the role of brand architecture for perceived store image, store satisfaction and loyalty....
Apparatus for storing protective suits
International Nuclear Information System (INIS)
Englemann, H.J.; Koller, J.; Schrader, H.R.; Schade, G.; Pedrerol, J.
1975-01-01
Arrangements are described for storing one or more protective suits when contaminated on the outside. In order to permit a person wearing a contaminated suit to leave a contaminated area safely, and without contaminating the environment, it has hitherto been the practice for the suit to be passed through a 'lock' and cleansed under decontaminating showers whilst still being worn. This procedure is time wasting and not always completely effective, and it may be necessary to provide a second suit for use whilst the first suit is being decontaminated. Repeated decontamination may also result in undue wear and tear. The arrangements described provide a 'lock' chamber in which a contaminated suit may be stowed away without its interior becoming contaminated, thus allowing repeated use by persons donning and shedding it. (U.K.)
Alcoholic fermentation of stored sweet potatoes
Energy Technology Data Exchange (ETDEWEB)
Yutaka, Y; One, H
1958-01-01
Sweet potatoes were ground and stored in a ground hold. The stored sweet potatoes gave about 90% fermentation efficiency by the koji process. A lower fermentation efficiency by the amylo process was improved by adding 20 to 30 mg/100 ml of organic N. Inorganic N has no effect in improving the fermentation efficiency of the stored sweet potatoes by the amylo process.
Mechanism of store-operated calcium entry
Indian Academy of Sciences (India)
Activation of receptors coupled to the phospholipase C/IP3 signalling pathway results in a rapid release of calcium from its intracellular stores, eventually leading to depletion of these stores. Calcium store depletion triggers an influx of extracellular calcium across the plasma membrane, a mechanism known as the ...
Bayesian Methods and Universal Darwinism
Campbell, John
2009-12-01
Bayesian methods since the time of Laplace have been understood by their practitioners as closely aligned to the scientific method. Indeed a recent Champion of Bayesian methods, E. T. Jaynes, titled his textbook on the subject Probability Theory: the Logic of Science. Many philosophers of science including Karl Popper and Donald Campbell have interpreted the evolution of Science as a Darwinian process consisting of a `copy with selective retention' algorithm abstracted from Darwin's theory of Natural Selection. Arguments are presented for an isomorphism between Bayesian Methods and Darwinian processes. Universal Darwinism, as the term has been developed by Richard Dawkins, Daniel Dennett and Susan Blackmore, is the collection of scientific theories which explain the creation and evolution of their subject matter as due to the Operation of Darwinian processes. These subject matters span the fields of atomic physics, chemistry, biology and the social sciences. The principle of Maximum Entropy states that Systems will evolve to states of highest entropy subject to the constraints of scientific law. This principle may be inverted to provide illumination as to the nature of scientific law. Our best cosmological theories suggest the universe contained much less complexity during the period shortly after the Big Bang than it does at present. The scientific subject matter of atomic physics, chemistry, biology and the social sciences has been created since that time. An explanation is proposed for the existence of this subject matter as due to the evolution of constraints in the form of adaptations imposed on Maximum Entropy. It is argued these adaptations were discovered and instantiated through the Operations of a succession of Darwinian processes.
iSEDfit: Bayesian spectral energy distribution modeling of galaxies
Moustakas, John
2017-08-01
iSEDfit uses Bayesian inference to extract the physical properties of galaxies from their observed broadband photometric spectral energy distribution (SED). In its default mode, the inputs to iSEDfit are the measured photometry (fluxes and corresponding inverse variances) and a measurement of the galaxy redshift. Alternatively, iSEDfit can be used to estimate photometric redshifts from the input photometry alone. After the priors have been specified, iSEDfit calculates the marginalized posterior probability distributions for the physical parameters of interest, including the stellar mass, star-formation rate, dust content, star formation history, and stellar metallicity. iSEDfit also optionally computes K-corrections and produces multiple "quality assurance" (QA) plots at each stage of the modeling procedure to aid in the interpretation of the prior parameter choices and subsequent fitting results. The software is distributed as part of the impro IDL suite.
Bayesian reliability demonstration for failure-free periods
International Nuclear Information System (INIS)
Coolen, F.P.A.; Coolen-Schrijner, P.; Rahrouh, M.
2005-01-01
We study sample sizes for testing as required for Bayesian reliability demonstration in terms of failure-free periods after testing, under the assumption that tests lead to zero failures. For the process after testing, we consider both deterministic and random numbers of tasks, including tasks arriving as Poisson processes. It turns out that the deterministic case is worst in the sense that it requires most tasks to be tested. We consider such reliability demonstration for a single type of task, as well as for multiple types of tasks to be performed by one system. We also consider the situation, where tests of different types of tasks may have different costs, aiming at minimal expected total costs, assuming that failure in the process would be catastrophic, in the sense that the process would be discontinued. Generally, these inferences are very sensitive to the choice of prior distribution, so one must be very careful with interpretation of non-informativeness of priors
Bayesian reliability demonstration for failure-free periods
Energy Technology Data Exchange (ETDEWEB)
Coolen, F.P.A. [Department of Mathematical Sciences, Science Laboratories, University of Durham, South Road, Durham, DH1 3LE (United Kingdom)]. E-mail: frank.coolen@durham.ac.uk; Coolen-Schrijner, P. [Department of Mathematical Sciences, Science Laboratories, University of Durham, South Road, Durham, DH1 3LE (United Kingdom); Rahrouh, M. [Department of Mathematical Sciences, Science Laboratories, University of Durham, South Road, Durham, DH1 3LE (United Kingdom)
2005-04-01
We study sample sizes for testing as required for Bayesian reliability demonstration in terms of failure-free periods after testing, under the assumption that tests lead to zero failures. For the process after testing, we consider both deterministic and random numbers of tasks, including tasks arriving as Poisson processes. It turns out that the deterministic case is worst in the sense that it requires most tasks to be tested. We consider such reliability demonstration for a single type of task, as well as for multiple types of tasks to be performed by one system. We also consider the situation, where tests of different types of tasks may have different costs, aiming at minimal expected total costs, assuming that failure in the process would be catastrophic, in the sense that the process would be discontinued. Generally, these inferences are very sensitive to the choice of prior distribution, so one must be very careful with interpretation of non-informativeness of priors.
An Active Lattice Model in a Bayesian Framework
DEFF Research Database (Denmark)
Carstensen, Jens Michael
1996-01-01
A Markov Random Field is used as a structural model of a deformable rectangular lattice. When used as a template prior in a Bayesian framework this model is powerful for making inferences about lattice structures in images. The model assigns maximum probability to the perfect regular lattice...... by penalizing deviations in alignment and lattice node distance. The Markov random field represents prior knowledge about the lattice structure, and through an observation model that incorporates the visual appearance of the nodes, we can simulate realizations from the posterior distribution. A maximum...... a posteriori (MAP) estimate, found by simulated annealing, is used as the reconstructed lattice. The model was developed as a central part of an algorithm for automatic analylsis of genetic experiments, positioned in a lattice structure by a robot. The algorithm has been successfully applied to many images...
Markov Chain Monte Carlo Bayesian Learning for Neural Networks
Goodrich, Michael S.
2011-01-01
Conventional training methods for neural networks involve starting al a random location in the solution space of the network weights, navigating an error hyper surface to reach a minimum, and sometime stochastic based techniques (e.g., genetic algorithms) to avoid entrapment in a local minimum. It is further typically necessary to preprocess the data (e.g., normalization) to keep the training algorithm on course. Conversely, Bayesian based learning is an epistemological approach concerned with formally updating the plausibility of competing candidate hypotheses thereby obtaining a posterior distribution for the network weights conditioned on the available data and a prior distribution. In this paper, we developed a powerful methodology for estimating the full residual uncertainty in network weights and therefore network predictions by using a modified Jeffery's prior combined with a Metropolis Markov Chain Monte Carlo method.
Uncovering Transcriptional Regulatory Networks by Sparse Bayesian Factor Model
Directory of Open Access Journals (Sweden)
Qi Yuan(Alan
2010-01-01
Full Text Available Abstract The problem of uncovering transcriptional regulation by transcription factors (TFs based on microarray data is considered. A novel Bayesian sparse correlated rectified factor model (BSCRFM is proposed that models the unknown TF protein level activity, the correlated regulations between TFs, and the sparse nature of TF-regulated genes. The model admits prior knowledge from existing database regarding TF-regulated target genes based on a sparse prior and through a developed Gibbs sampling algorithm, a context-specific transcriptional regulatory network specific to the experimental condition of the microarray data can be obtained. The proposed model and the Gibbs sampling algorithm were evaluated on the simulated systems, and results demonstrated the validity and effectiveness of the proposed approach. The proposed model was then applied to the breast cancer microarray data of patients with Estrogen Receptor positive ( status and Estrogen Receptor negative ( status, respectively.
Bayesian flood forecasting methods: A review
Han, Shasha; Coulibaly, Paulin
2017-08-01
Over the past few decades, floods have been seen as one of the most common and largely distributed natural disasters in the world. If floods could be accurately forecasted in advance, then their negative impacts could be greatly minimized. It is widely recognized that quantification and reduction of uncertainty associated with the hydrologic forecast is of great importance for flood estimation and rational decision making. Bayesian forecasting system (BFS) offers an ideal theoretic framework for uncertainty quantification that can be developed for probabilistic flood forecasting via any deterministic hydrologic model. It provides suitable theoretical structure, empirically validated models and reasonable analytic-numerical computation method, and can be developed into various Bayesian forecasting approaches. This paper presents a comprehensive review on Bayesian forecasting approaches applied in flood forecasting from 1999 till now. The review starts with an overview of fundamentals of BFS and recent advances in BFS, followed with BFS application in river stage forecasting and real-time flood forecasting, then move to a critical analysis by evaluating advantages and limitations of Bayesian forecasting methods and other predictive uncertainty assessment approaches in flood forecasting, and finally discusses the future research direction in Bayesian flood forecasting. Results show that the Bayesian flood forecasting approach is an effective and advanced way for flood estimation, it considers all sources of uncertainties and produces a predictive distribution of the river stage, river discharge or runoff, thus gives more accurate and reliable flood forecasts. Some emerging Bayesian forecasting methods (e.g. ensemble Bayesian forecasting system, Bayesian multi-model combination) were shown to overcome limitations of single model or fixed model weight and effectively reduce predictive uncertainty. In recent years, various Bayesian flood forecasting approaches have been
Bayesian Dose-Response Modeling in Sparse Data
Kim, Steven B.
This book discusses Bayesian dose-response modeling in small samples applied to two different settings. The first setting is early phase clinical trials, and the second setting is toxicology studies in cancer risk assessment. In early phase clinical trials, experimental units are humans who are actual patients. Prior to a clinical trial, opinions from multiple subject area experts are generally more informative than the opinion of a single expert, but we may face a dilemma when they have disagreeing prior opinions. In this regard, we consider compromising the disagreement and compare two different approaches for making a decision. In addition to combining multiple opinions, we also address balancing two levels of ethics in early phase clinical trials. The first level is individual-level ethics which reflects the perspective of trial participants. The second level is population-level ethics which reflects the perspective of future patients. We extensively compare two existing statistical methods which focus on each perspective and propose a new method which balances the two conflicting perspectives. In toxicology studies, experimental units are living animals. Here we focus on a potential non-monotonic dose-response relationship which is known as hormesis. Briefly, hormesis is a phenomenon which can be characterized by a beneficial effect at low doses and a harmful effect at high doses. In cancer risk assessments, the estimation of a parameter, which is known as a benchmark dose, can be highly sensitive to a class of assumptions, monotonicity or hormesis. In this regard, we propose a robust approach which considers both monotonicity and hormesis as a possibility. In addition, We discuss statistical hypothesis testing for hormesis and consider various experimental designs for detecting hormesis based on Bayesian decision theory. Past experiments have not been optimally designed for testing for hormesis, and some Bayesian optimal designs may not be optimal under a
A Nonparametric Bayesian Approach For Emission Tomography Reconstruction
International Nuclear Information System (INIS)
Barat, Eric; Dautremer, Thomas
2007-01-01
We introduce a PET reconstruction algorithm following a nonparametric Bayesian (NPB) approach. In contrast with Expectation Maximization (EM), the proposed technique does not rely on any space discretization. Namely, the activity distribution--normalized emission intensity of the spatial poisson process--is considered as a spatial probability density and observations are the projections of random emissions whose distribution has to be estimated. This approach is nonparametric in the sense that the quantity of interest belongs to the set of probability measures on R k (for reconstruction in k-dimensions) and it is Bayesian in the sense that we define a prior directly on this spatial measure. In this context, we propose to model the nonparametric probability density as an infinite mixture of multivariate normal distributions. As a prior for this mixture we consider a Dirichlet Process Mixture (DPM) with a Normal-Inverse Wishart (NIW) model as base distribution of the Dirichlet Process. As in EM-family reconstruction, we use a data augmentation scheme where the set of hidden variables are the emission locations for each observed line of response in the continuous object space. Thanks to the data augmentation, we propose a Markov Chain Monte Carlo (MCMC) algorithm (Gibbs sampler) which is able to generate draws from the posterior distribution of the spatial intensity. A difference with EM is that one step of the Gibbs sampler corresponds to the generation of emission locations while only the expected number of emissions per pixel/voxel is used in EM. Another key difference is that the estimated spatial intensity is a continuous function such that there is no need to compute a projection matrix. Finally, draws from the intensity posterior distribution allow the estimation of posterior functionnals like the variance or confidence intervals. Results are presented for simulated data based on a 2D brain phantom and compared to Bayesian MAP-EM
Transformation of Bayesian posterior distribution into a basic analytical distribution
International Nuclear Information System (INIS)
Jordan Cizelj, R.; Vrbanic, I.
2002-01-01
Bayesian estimation is well-known approach that is widely used in Probabilistic Safety Analyses for the estimation of input model reliability parameters, such as component failure rates or probabilities of failure upon demand. In this approach, a prior distribution, which contains some generic knowledge about a parameter is combined with likelihood function, which contains plant-specific data about the parameter. Depending on the type of prior distribution, the resulting posterior distribution can be estimated numerically or analytically. In many instances only a numerical Bayesian integration can be performed. In such a case the posterior is provided in the form of tabular discrete distribution. On the other hand, it is much more convenient to have a parameter's uncertainty distribution that is to be input into a PSA model to be provided in the form of some basic analytical probability distribution, such as lognormal, gamma or beta distribution. One reason is that this enables much more convenient propagation of parameters' uncertainties through the model up to the so-called top events, such as plant system unavailability or core damage frequency. Additionally, software tools used to run PSA models often require that parameter's uncertainty distribution is defined in the form of one among the several allowed basic types of distributions. In such a case the posterior distribution that came as a product of Bayesian estimation needs to be transformed into an appropriate basic analytical form. In this paper, some approaches on transformation of posterior distribution to a basic probability distribution are proposed and discussed. They are illustrated by an example from NPP Krsko PSA model.(author)
Bayesian inference for Hawkes processes
DEFF Research Database (Denmark)
Rasmussen, Jakob Gulddahl
The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...... intensity function, while the second approach is based on an underlying clustering and branching structure in the Hawkes process. For practical use, MCMC (Markov chain Monte Carlo) methods are employed. The two approaches are compared numerically using three examples of the Hawkes process....
Bayesian inference for Hawkes processes
DEFF Research Database (Denmark)
Rasmussen, Jakob Gulddahl
2013-01-01
The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...... intensity function, while the second approach is based on an underlying clustering and branching structure in the Hawkes process. For practical use, MCMC (Markov chain Monte Carlo) methods are employed. The two approaches are compared numerically using three examples of the Hawkes process....
Numeracy, frequency, and Bayesian reasoning
Directory of Open Access Journals (Sweden)
Gretchen B. Chapman
2009-02-01
Full Text Available Previous research has demonstrated that Bayesian reasoning performance is improved if uncertainty information is presented as natural frequencies rather than single-event probabilities. A questionnaire study of 342 college students replicated this effect but also found that the performance-boosting benefits of the natural frequency presentation occurred primarily for participants who scored high in numeracy. This finding suggests that even comprehension and manipulation of natural frequencies requires a certain threshold of numeracy abilities, and that the beneficial effects of natural frequency presentation may not be as general as previously believed.
Optimal inference with suboptimal models: Addiction and active Bayesian inference
Schwartenbeck, Philipp; FitzGerald, Thomas H.B.; Mathys, Christoph; Dolan, Ray; Wurst, Friedrich; Kronbichler, Martin; Friston, Karl
2015-01-01
When casting behaviour as active (Bayesian) inference, optimal inference is defined with respect to an agent’s beliefs – based on its generative model of the world. This contrasts with normative accounts of choice behaviour, in which optimal actions are considered in relation to the true structure of the environment – as opposed to the agent’s beliefs about worldly states (or the task). This distinction shifts an understanding of suboptimal or pathological behaviour away from aberrant inference as such, to understanding the prior beliefs of a subject that cause them to behave less ‘optimally’ than our prior beliefs suggest they should behave. Put simply, suboptimal or pathological behaviour does not speak against understanding behaviour in terms of (Bayes optimal) inference, but rather calls for a more refined understanding of the subject’s generative model upon which their (optimal) Bayesian inference is based. Here, we discuss this fundamental distinction and its implications for understanding optimality, bounded rationality and pathological (choice) behaviour. We illustrate our argument using addictive choice behaviour in a recently described ‘limited offer’ task. Our simulations of pathological choices and addictive behaviour also generate some clear hypotheses, which we hope to pursue in ongoing empirical work. PMID:25561321
A Bayesian perspective on Markovian dynamics and the fluctuation theorem
Virgo, Nathaniel
2013-08-01
One of E. T. Jaynes' most important achievements was to derive statistical mechanics from the maximum entropy (MaxEnt) method. I re-examine a relatively new result in statistical mechanics, the Evans-Searles fluctuation theorem, from a MaxEnt perspective. This is done in the belief that interpreting such results in Bayesian terms will lead to new advances in statistical physics. The version of the fluctuation theorem that I will discuss applies to discrete, stochastic systems that begin in a non-equilibrium state and relax toward equilibrium. I will show that for such systems the fluctuation theorem can be seen as a consequence of the fact that the equilibrium distribution must obey the property of detailed balance. Although the principle of detailed balance applies only to equilibrium ensembles, it puts constraints on the form of non-equilibrium trajectories. This will be made clear by taking a novel kind of Bayesian perspective, in which the equilibrium distribution is seen as a prior over the system's set of possible trajectories. Non-equilibrium ensembles are calculated from this prior using Bayes' theorem, with the initial conditions playing the role of the data. I will also comment on the implications of this perspective for the question of how to derive the second law.
Bayesian estimation of multicomponent relaxation parameters in magnetic resonance fingerprinting.
McGivney, Debra; Deshmane, Anagha; Jiang, Yun; Ma, Dan; Badve, Chaitra; Sloan, Andrew; Gulani, Vikas; Griswold, Mark
2018-07-01
To estimate multiple components within a single voxel in magnetic resonance fingerprinting when the number and types of tissues comprising the voxel are not known a priori. Multiple tissue components within a single voxel are potentially separable with magnetic resonance fingerprinting as a result of differences in signal evolutions of each component. The Bayesian framework for inverse problems provides a natural and flexible setting for solving this problem when the tissue composition per voxel is unknown. Assuming that only a few entries from the dictionary contribute to a mixed signal, sparsity-promoting priors can be placed upon the solution. An iterative algorithm is applied to compute the maximum a posteriori estimator of the posterior probability density to determine the magnetic resonance fingerprinting dictionary entries that contribute most significantly to mixed or pure voxels. Simulation results show that the algorithm is robust in finding the component tissues of mixed voxels. Preliminary in vivo data confirm this result, and show good agreement in voxels containing pure tissue. The Bayesian framework and algorithm shown provide accurate solutions for the partial-volume problem in magnetic resonance fingerprinting. The flexibility of the method will allow further study into different priors and hyperpriors that can be applied in the model. Magn Reson Med 80:159-170, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.
MAP estimators and their consistency in Bayesian nonparametric inverse problems
Dashti, M.
2013-09-01
We consider the inverse problem of estimating an unknown function u from noisy measurements y of a known, possibly nonlinear, map applied to u. We adopt a Bayesian approach to the problem and work in a setting where the prior measure is specified as a Gaussian random field μ0. We work under a natural set of conditions on the likelihood which implies the existence of a well-posed posterior measure, μy. Under these conditions, we show that the maximum a posteriori (MAP) estimator is well defined as the minimizer of an Onsager-Machlup functional defined on the Cameron-Martin space of the prior; thus, we link a problem in probability with a problem in the calculus of variations. We then consider the case where the observational noise vanishes and establish a form of Bayesian posterior consistency for the MAP estimator. We also prove a similar result for the case where the observation of can be repeated as many times as desired with independent identically distributed noise. The theory is illustrated with examples from an inverse problem for the Navier-Stokes equation, motivated by problems arising in weather forecasting, and from the theory of conditioned diffusions, motivated by problems arising in molecular dynamics. © 2013 IOP Publishing Ltd.
Bayesian Age-Period-Cohort Model of Lung Cancer Mortality
Directory of Open Access Journals (Sweden)
Bhikhari P. Tharu
2015-09-01
Full Text Available Background The objective of this study was to analyze the time trend for lung cancer mortality in the population of the USA by 5 years based on most recent available data namely to 2010. The knowledge of the mortality rates in the temporal trends is necessary to understand cancer burden.Methods Bayesian Age-Period-Cohort model was fitted using Poisson regression with histogram smoothing prior to decompose mortality rates based on age at death, period at death, and birth-cohort.Results Mortality rates from lung cancer increased more rapidly from age 52 years. It ended up to 325 deaths annually for 82 years on average. The mortality of younger cohorts was lower than older cohorts. The risk of lung cancer was lowered from period 1993 to recent periods.Conclusions The fitted Bayesian Age-Period-Cohort model with histogram smoothing prior is capable of explaining mortality rate of lung cancer. The reduction in carcinogens in cigarettes and increase in smoking cessation from around 1960 might led to decreasing trend of lung cancer mortality after calendar period 1993.
DPpackage: Bayesian Semi- and Nonparametric Modeling in R
Directory of Open Access Journals (Sweden)
Alejandro Jara
2011-04-01
Full Text Available Data analysis sometimes requires the relaxation of parametric assumptions in order to gain modeling flexibility and robustness against mis-specification of the probability model. In the Bayesian context, this is accomplished by placing a prior distribution on a function space, such as the space of all probability distributions or the space of all regression functions. Unfortunately, posterior distributions ranging over function spaces are highly complex and hence sampling methods play a key role. This paper provides an introduction to a simple, yet comprehensive, set of programs for the implementation of some Bayesian nonparametric and semiparametric models in R, DPpackage. Currently, DPpackage includes models for marginal and conditional density estimation, receiver operating characteristic curve analysis, interval-censored data, binary regression data, item response data, longitudinal and clustered data using generalized linear mixed models, and regression data using generalized additive models. The package also contains functions to compute pseudo-Bayes factors for model comparison and for eliciting the precision parameter of the Dirichlet process prior, and a general purpose Metropolis sampling algorithm. To maximize computational efficiency, the actual sampling for each model is carried out using compiled C, C++ or Fortran code.
MAP estimators and their consistency in Bayesian nonparametric inverse problems
International Nuclear Information System (INIS)
Dashti, M; Law, K J H; Stuart, A M; Voss, J
2013-01-01
We consider the inverse problem of estimating an unknown function u from noisy measurements y of a known, possibly nonlinear, map G applied to u. We adopt a Bayesian approach to the problem and work in a setting where the prior measure is specified as a Gaussian random field μ 0 . We work under a natural set of conditions on the likelihood which implies the existence of a well-posed posterior measure, μ y . Under these conditions, we show that the maximum a posteriori (MAP) estimator is well defined as the minimizer of an Onsager–Machlup functional defined on the Cameron–Martin space of the prior; thus, we link a problem in probability with a problem in the calculus of variations. We then consider the case where the observational noise vanishes and establish a form of Bayesian posterior consistency for the MAP estimator. We also prove a similar result for the case where the observation of G(u) can be repeated as many times as desired with independent identically distributed noise. The theory is illustrated with examples from an inverse problem for the Navier–Stokes equation, motivated by problems arising in weather forecasting, and from the theory of conditioned diffusions, motivated by problems arising in molecular dynamics. (paper)
Bayesian approach for peak detection in two-dimensional chromatography.
Vivó-Truyols, Gabriel
2012-03-20
A new method for peak detection in two-dimensional chromatography is presented. In a first step, the method starts with a conventional one-dimensional peak detection algorithm to detect modulated peaks. In a second step, a sophisticated algorithm is constructed to decide which of the individual one-dimensional peaks have been originated from the same compound and should then be arranged in a two-dimensional peak. The merging algorithm is based on Bayesian inference. The user sets prior information about certain parameters (e.g., second-dimension retention time variability, first-dimension band broadening, chromatographic noise). On the basis of these priors, the algorithm calculates the probability of myriads of peak arrangements (i.e., ways of merging one-dimensional peaks), finding which of them holds the highest value. Uncertainty in each parameter can be accounted by adapting conveniently its probability distribution function, which in turn may change the final decision of the most probable peak arrangement. It has been demonstrated that the Bayesian approach presented in this paper follows the chromatographers' intuition. The algorithm has been applied and tested with LC × LC and GC × GC data and takes around 1 min to process chromatograms with several thousands of peaks.
Maximum entropy reconstruction of spin densities involving non uniform prior
International Nuclear Information System (INIS)
Schweizer, J.; Ressouche, E.; Papoular, R.J.; Zheludev, A.I.
1997-01-01
Diffraction experiments give microscopic information on structures in crystals. A method which uses the concept of maximum of entropy (MaxEnt), appears to be a formidable improvement in the treatment of diffraction data. This method is based on a bayesian approach: among all the maps compatible with the experimental data, it selects that one which has the highest prior (intrinsic) probability. Considering that all the points of the map are equally probable, this probability (flat prior) is expressed via the Boltzman entropy of the distribution. This method has been used for the reconstruction of charge densities from X-ray data, for maps of nuclear densities from unpolarized neutron data as well as for distributions of spin density. The density maps obtained by this method, as compared to those resulting from the usual inverse Fourier transformation, are tremendously improved. In particular, any substantial deviation from the background is really contained in the data, as it costs entropy compared to a map that would ignore such features. However, in most of the cases, before the measurements are performed, some knowledge exists about the distribution which is investigated. It can range from the simple information of the type of scattering electrons to an elaborate theoretical model. In these cases, the uniform prior which considers all the different pixels as equally likely, is too weak a requirement and has to be replaced. In a rigorous bayesian analysis, Skilling has shown that prior knowledge can be encoded into the Maximum Entropy formalism through a model m(rvec r), via a new definition for the entropy given in this paper. In the absence of any data, the maximum of the entropy functional is reached for ρ(rvec r) = m(rvec r). Any substantial departure from the model, observed in the final map, is really contained in the data as, with the new definition, it costs entropy. This paper presents illustrations of model testing
The Prior Internet Resources 2017
DEFF Research Database (Denmark)
Engerer, Volkmar Paul; Albretsen, Jørgen
2017-01-01
The Prior Internet Resources (PIR) are presented. Prior’s unpublished scientific manuscripts and his wast letter correspondence with fellow researchers at the time, his Nachlass, is now subject to transcription by Prior-researchers worldwide, and form an integral part of PIR. It is demonstrated...
Bayesian analysis of magnetic island dynamics
International Nuclear Information System (INIS)
Preuss, R.; Maraschek, M.; Zohm, H.; Dose, V.
2003-01-01
We examine a first order differential equation with respect to time used to describe magnetic islands in magnetically confined plasmas. The free parameters of this equation are obtained by employing Bayesian probability theory. Additionally, a typical Bayesian change point is solved in the process of obtaining the data
Learning dynamic Bayesian networks with mixed variables
DEFF Research Database (Denmark)
Bøttcher, Susanne Gammelgaard
This paper considers dynamic Bayesian networks for discrete and continuous variables. We only treat the case, where the distribution of the variables is conditional Gaussian. We show how to learn the parameters and structure of a dynamic Bayesian network and also how the Markov order can be learned...
Using Bayesian Networks to Improve Knowledge Assessment
Millan, Eva; Descalco, Luis; Castillo, Gladys; Oliveira, Paula; Diogo, Sandra
2013-01-01
In this paper, we describe the integration and evaluation of an existing generic Bayesian student model (GBSM) into an existing computerized testing system within the Mathematics Education Project (PmatE--Projecto Matematica Ensino) of the University of Aveiro. This generic Bayesian student model had been previously evaluated with simulated…
Using Bayesian belief networks in adaptive management.
J.B. Nyberg; B.G. Marcot; R. Sulyma
2006-01-01
Bayesian belief and decision networks are relatively new modeling methods that are especially well suited to adaptive-management applications, but they appear not to have been widely used in adaptive management to date. Bayesian belief networks (BBNs) can serve many purposes for practioners of adaptive management, from illustrating system relations conceptually to...
Bayesian Decision Theoretical Framework for Clustering
Chen, Mo
2011-01-01
In this thesis, we establish a novel probabilistic framework for the data clustering problem from the perspective of Bayesian decision theory. The Bayesian decision theory view justifies the important questions: what is a cluster and what a clustering algorithm should optimize. We prove that the spectral clustering (to be specific, the…