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
Bayesian meta-analysis of fMRI image data.
Hyemin Han,Joonsuk Park +1 more
TL;DR: Bayesian meta-analysis provides neuroscientists with an alternativeMeta-analysis method for fMRI studies given the improved overlap with the NeuroSynth result and the practical and epistemological value of Bayes Factors that can directly test the presence of an effect.
Journal ArticleDOI
On the use of MCMC computerized adaptive testing with empirical prior information to improve efficiency
TL;DR: By using both simulated and real data, it is proved that the introduction of empirical prior information in the estimation of candidate's ability within computerized adaptive testing produces more accurate ability estimates, especially for short tests and when reproducing boundary abilities.
Journal ArticleDOI
Sampling frequent and minimal boolean patterns: theory and application in classification
Geng Li,Mohammed J. Zaki +1 more
TL;DR: This work develops effective sampling methods to extract a representative subset of the minimal Boolean patterns in disjunctive normal form (DNF), and proposes a novel theoretical characterization of the minimum DNF expressions, which allows us to prune the pattern search space effectively.
Journal ArticleDOI
A new class of regression model for a bounded response with application in the study of the incidence rate of colorectal cancer.
TL;DR: A new class of regression models for bounded response by considering a new distribution in the open unit interval which includes a new parameter to make a more flexible distribution, and inferential procedures based on the Bayesian methodology are presented.
Journal ArticleDOI
Response to Cho and Liu, “Sampling from complicated and unknown distributions: Monte Carlo and Markov chain Monte Carlo methods for redistricting”
TL;DR: The goal of the present commentary is to draw attention to two facts omitted by Cho and Liu that, if included, would have severely weakened their conclusions.
References
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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.
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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.
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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.