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
A Bayesian Approach to Inferring the Phylogenetic Structure of Communities from Metagenomic Data
TL;DR: This work presents a Bayesian method for inferring the phylogenetic relationship among related organisms found within metagenomic samples that exploits variation in the frequency of taxa among samples to simultaneously infer each lineage haplotype, the phylogenetics tree connecting them, and their frequency within each sample.
Journal ArticleDOI
Amyotrophic lateral sclerosis in Piedmont (Italy): A Bayesian spatial analysis of the incident cases
TL;DR: The aim of this study was to depict the spatial risk distribution of ALS in Piedmont's resident population during the period 1995−2004, and results appear coherent with literature data, stimulating other in-depth analysis in this field of research.
Journal ArticleDOI
Dynamic Reliability Models for Software Using Time-Dependent Covariates
TL;DR: A Bayesian framework for inference and model assessment, using Markov chain Monte Carlo techniques, that allows for incorporation of subjective information about the parameters through the assumed prior distributions is described.
Journal ArticleDOI
A Bayesian analysis of a proportion under non-ignorable non-response
Balgobin Nandram,Jai Won Choi +1 more
TL;DR: The main result is that for some of the states the non‐response mechanism can be considered non‐ignorable, and that 95 per cent credible intervals of the probability for a household doctor visit and the probability that a household responds shed important light on the NHIS data.
Posted Content
Fixed-width output analysis for Markov chain Monte Carlo
TL;DR: In this article, the authors consider a method that stops the simulation when the width of a confidence interval based on an ergodic average is less than a user-specified value.
References
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Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
Stuart Geman,Donald Geman +1 more
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Monte Carlo Sampling Methods Using Markov Chains and Their Applications
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Journal ArticleDOI
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.