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
Markov Chain Monte Carlo Convergence Assessment via Two-Way Analysis of Variance
Stephen P. Brooks,Paolo Giudici +1 more
TL;DR: This article extends the original ideas of Gelman and Rubin and, more recently, Brooks and Gelman, to problems where they are able to split the variation inherent within the MCMC simulation output into two distinct groups, and shows how a diagnostic may be useful in assessing the performance of MCMC samplers addressing model choice problems.
Journal ArticleDOI
Disaggregating the Distal, Proximal, and Time-Varying Effects of Parent Alcoholism on Children’s Internalizing Symptoms
TL;DR: An integrative data analysis combined observations over ages 2 through 17 from two longitudinal studies of children of alcoholic parents and matched controls recruited from the community found no support for time-varying effects, but proximal effects of mothers’ alcohol-related consequences on child-reported internalizing symptoms were found and distal effects of mother and father alcoholism predicted greaterinternalizing symptoms among children of alcoholism parents.
Posted Content
A Meta-Analysis of the Determinants of Organic Sales Growth
TL;DR: In this paper, the authors present the results of a meta-analysis on drivers of organic sales growth, conducted using a Hierarchical Bayes estimation technique, based on a comprehensive review of a diverse set of literatures.
A Measurement Model for Synthesizing Multiple Comparative Indicators: The Case of Judicial Independence
Drew A. Linzer,Jeffrey K. Staton +1 more
TL;DR: In this paper, the authors introduce a statistical measurement model for uncovering latent concepts commonly encountered in time series, cross-sectional analyses in comparative politics and international relations, which is applicable to a wide variety of latent concepts in the study of international relations.
Journal ArticleDOI
Bayesian CART: Prior Specification and Posterior Simulation
TL;DR: The core computational innovations involve a novel Metropolis–Hastings method that can dramatically improve the convergence and mixing properties of MCMC methods of Bayesian CART analysis.
References
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Journal ArticleDOI
Equation of state calculations by fast computing machines
TL;DR: In this article, a modified Monte Carlo integration over configuration space is used to investigate the properties of a two-dimensional rigid-sphere system with a set of interacting individual molecules, and the results are compared to free volume equations of state and a four-term virial coefficient expansion.
Journal ArticleDOI
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.
Journal ArticleDOI
Monte Carlo Sampling Methods Using Markov Chains and Their Applications
TL;DR: A generalization of the sampling method introduced by Metropolis et al. as mentioned in this paper is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates.
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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.