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21
Simulating Normalized Constants: From Importance Sampling to Bridge Sampling to Path Sampling
 Statistical Science, 13, 163–185. COMPARISON OF METHODS FOR COMPUTING BAYES FACTORS 435
, 1998
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Cited by 153 (4 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Simulating ratios of normalizing constants via a simple identity: A theoretical exploration
 Statistica Sinica
, 1996
"... Abstract: Let pi(w),i =1, 2, be two densities with common support where each density is known up to a normalizing constant: pi(w) =qi(w)/ci. We have draws from each density (e.g., via Markov chain Monte Carlo), and we want to use these draws to simulate the ratio of the normalizing constants, c1/c2. ..."
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Cited by 121 (4 self)
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Abstract: Let pi(w),i =1, 2, be two densities with common support where each density is known up to a normalizing constant: pi(w) =qi(w)/ci. We have draws from each density (e.g., via Markov chain Monte Carlo), and we want to use these draws to simulate the ratio of the normalizing constants, c1/c2. Such a computational problem is often encountered in likelihood and Bayesian inference, and arises in fields such as physics and genetics. Many methods proposed in statistical and other literature (e.g., computational physics) for dealing with this problem are based on various special cases of the following simple identity: c1 c2 = E2[q1(w)α(w)] E1[q2(w)α(w)]. Here Ei denotes the expectation with respect to pi (i =1, 2), and α is an arbitrary function such that the denominator is nonzero. A main purpose of this paper is to provide a theoretical study of the usefulness of this identity, with focus on (asymptotically) optimal and practical choices of α. Using a simple but informative example, we demonstrate that with sensible (not necessarily optimal) choices of α, we can reduce the simulation error by orders of magnitude when compared to the conventional importance sampling method, which corresponds to α =1/q2. We also introduce several generalizations of this identity for handling more complicated settings (e.g., estimating several ratios simultaneously) and pose several open problems that appear to have practical as well as theoretical value. Furthermore, we discuss related theoretical and empirical work.
H: Computing Bayes factors using thermodynamic integration
 Syst Biol
"... Abstract.—In the Bayesian paradigm, a common method for comparing two models is to compute the Bayes factor, defined as the ratio of their respective marginal likelihoods. In recent phylogenetic works, the numerical evaluation of marginal likelihoods has often been performed using the harmonic mean ..."
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Abstract.—In the Bayesian paradigm, a common method for comparing two models is to compute the Bayes factor, defined as the ratio of their respective marginal likelihoods. In recent phylogenetic works, the numerical evaluation of marginal likelihoods has often been performed using the harmonic mean estimation procedure. In the present article, we propose to employ another method, based on an analogy with statistical physics, called thermodynamic integration. We describe the method, propose an implementation, and show on two analytical examples that this numerical method yields reliable estimates. In contrast, the harmonic mean estimator leads to a strong overestimation of the marginal likelihood, which is all the more pronounced as the model is higher dimensional. As a result, the harmonic mean estimator systematically favors more parameterrich models, an artefact that might explain some recent puzzling observations, based on harmonic mean estimates, suggesting that Bayes factors tend to overscore complex models. Finally, we apply our method to the comparison of several alternative models of aminoacid replacement. We confirm our previous observations, indicating that modeling pattern heterogeneity across sites tends to yield better models than standard empirical matrices. [Bayes factor; harmonic mean; mixture model; path sampling; phylogeny; thermodynamic integration.] Bayesian methods have become popular in molecular phylogenetics over the recent years. The simple and intuitive interpretation of the concept of probabilities
Fully Bayesian Estimation of Gibbs Hyperparameters for Emission Computed Tomography Data
 IEEE Transactions on Medical Imaging
, 1997
"... In recent years, many investigators have proposed Gibbs prior models to regularize images reconstructed from emission computed tomography data. Unfortunately, hyperparameters used to specify Gibbs priors can greatly influence the degree of regularity imposed by such priors, and as a result, numerous ..."
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Cited by 23 (3 self)
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In recent years, many investigators have proposed Gibbs prior models to regularize images reconstructed from emission computed tomography data. Unfortunately, hyperparameters used to specify Gibbs priors can greatly influence the degree of regularity imposed by such priors, and as a result, numerous procedures have been proposed to estimate hyperparameter values from observed image data. Many of these procedures attempt to maximize the joint posterior distribution on the image scene. To implement these methods, approximations to the joint posterior densities are required, because the dependence of the Gibbs partition function on the hyperparameter values is unknown. In this paper, we use recent results in Markov Chain Monte Carlo sampling to estimate the relative values of Gibbs partition functions, and using these values, sample from joint posterior distributions on image scenes. This allows for a fully Bayesian procedure which does not fix the hyperparameters at some estimated or spe...
Probabilistic Reasoning and Inference for Systems Biology
, 2007
"... One of the important challenges in Systems Biology is reasoning and performing hypotheses testing in uncertain conditions, when available knowledge may be incomplete and the experimental data may contain substantial noise. In this thesis we develop methods of probabilistic reasoning and inference th ..."
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One of the important challenges in Systems Biology is reasoning and performing hypotheses testing in uncertain conditions, when available knowledge may be incomplete and the experimental data may contain substantial noise. In this thesis we develop methods of probabilistic reasoning and inference that operate consistently within an environment of uncertain knowledge and data. Mechanistic mathematical models are used to describe hypotheses about biological systems. We consider both deductive model based reasoning and model inference from data. The main contributions are a novel modelling approach using continuous time Markov chains that enables deductive derivation of model behaviours and their properties, and the application of Bayesian inferential methods to solve the inverse problem of model inference and comparison, given uncertain knowledge and noisy data. In the first part of the thesis, we consider both individual and population
unknown title
, 2000
"... Efficient calculation of the normalizing constant of the autologistic and related models on the cylinder and lattice A. N. Pettitt, ..."
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Efficient calculation of the normalizing constant of the autologistic and related models on the cylinder and lattice A. N. Pettitt,
Approximating the marginal likelihood using copula
, 810
"... Model selection is an important activity in modern data analysis and the conventional Bayesian approach to this problem involves calculation of marginal likelihoods for different models, together with diagnostics which examine specific aspects of model fit. Calculating the marginal likelihood is a d ..."
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Model selection is an important activity in modern data analysis and the conventional Bayesian approach to this problem involves calculation of marginal likelihoods for different models, together with diagnostics which examine specific aspects of model fit. Calculating the marginal likelihood is a difficult computational problem. Our article proposes some extensions of the Laplace approximation for this task that are related to copula models and which are easy to apply. Variations which can be used both with and without simulation from the posterior distribution are considered, as well as use of the approximations with bridge sampling and in random effects models with a large number of latent variables. The use of a tcopula to obtain higher accuracy when multivariate dependence is not well captured by a Gaussian copula is also discussed.
BMC Bioinformatics BioMed Central Methodology article A maximum likelihood framework for protein design
, 2006
"... This is an Open Access article distributed under the terms of the Creative Commons Attribution License ..."
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This is an Open Access article distributed under the terms of the Creative Commons Attribution License
The ConditionalPotts Clustering Model
"... A Bayesian kernelbased clustering method is presented. The associated model arises as an embedding of the Potts density for label membership probabilities into an extended Bayesian model for joint data and label membership probabilities. The method may be seen as a principled extension of the soca ..."
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A Bayesian kernelbased clustering method is presented. The associated model arises as an embedding of the Potts density for label membership probabilities into an extended Bayesian model for joint data and label membership probabilities. The method may be seen as a principled extension of the socalled superparamagnetic clustering. The model depends on three parameters: the temperature, the kernel bandwidth and the joint pairmembership probability threshold. We elucidate an informative prior based on random graph theory and kernel density estimation. The clustering is estimated automatically by setting the parameters at the modes of their posteriors. Two stochastic WangLandaulike algorithms are presented to estimate the posteriors. We also develop an efficient clustering procedure based only on the modes of our informative prior.