Journal ArticleDOI
Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review
TLDR
All of the methods in this work can fail to detect the sorts of convergence failure that they were designed to identify, so a combination of strategies aimed at evaluating and accelerating MCMC sampler convergence are recommended.Abstract:
A critical issue for users of Markov chain Monte Carlo (MCMC) methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest. Research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work. Consequently, most MCMC users address the convergence problem by applying diagnostic tools to the output produced by running their samplers. After giving a brief overview of the area, we provide an expository review of 13 convergence diagnostics, describing the theoretical basis and practical implementation of each. We then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify. We thus recommend a combination of strategies aimed at evaluating and accelerating MCMC sampler convergence, including ap...read more
Citations
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Journal ArticleDOI
Updating Schemes, Correlation Structure, Blocking and Parameterization for the Gibbs Sampler
Gareth O. Roberts,Sujit K. Sahu +1 more
TL;DR: Exact computable rates of convergence for Gaussian target distributions are obtained and different random and non‐random updating strategies and blocking combinations are compared using the rates.
Journal ArticleDOI
Bayesian Mediation Analysis
Ying Yuan,David P. MacKinnon +1 more
TL;DR: This article proposes Bayesian analysis of mediation effects, which allows researchers to incorporate prior information into the mediation analysis, thus potentially improving the efficiency of estimates and conceptually simpler for multilevel mediation analysis.
Book ChapterDOI
Markov chain monte carlo methods: computation and inference
TL;DR: This chapter provides background on the relevant Markov chain theory and provides detailed information on the theory and practice of MarkovChain sampling based on the Metropolis-Hastings and Gibbs sampling algorithms.
Journal ArticleDOI
Bayesian methods in meta-analysis and evidence synthesis.
Alex J. Sutton,Keith R. Abrams +1 more
TL;DR: The Bayesian methods discussed are illustrated by means of a meta-analysis examining the evidence relating to electronic fetal heart rate monitoring and perinatal mortality in which evidence is available from a variety of sources.
Journal ArticleDOI
A self-organizing state-space model
TL;DR: In this paper, a self-organizing filter and smoother for the general nonlinear non-Gaussian state-space model is proposed, which is defined by augmenting the state vector with the unknown parameters of the original state space model.
References
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Equation of state calculations by fast computing machines
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Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
Stuart Geman,Donald Geman +1 more
TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
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Monte Carlo Sampling Methods Using Markov Chains and Their Applications
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Inference from Iterative Simulation Using Multiple Sequences
Andrew Gelman,Donald B. Rubin +1 more
TL;DR: The focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normal- ity after transformations and marginalization, and the results are derived as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations.
Journal ArticleDOI
Robust Locally Weighted Regression and Smoothing Scatterplots
TL;DR: Robust locally weighted regression as discussed by the authors is a method for smoothing a scatterplot, in which the fitted value at z k is the value of a polynomial fit to the data using weighted least squares, where the weight for (x i, y i ) is large if x i is close to x k and small if it is not.