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
emcee: The MCMC Hammer
TL;DR: The emcee algorithm as mentioned in this paper is a Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman & Weare (2010).
Book
Discrete Choice Methods with Simulation
TL;DR: In this paper, the authors describe the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation, and compare simulation-assisted estimation procedures, including maximum simulated likelihood, method of simulated moments, and methods of simulated scores.
Journal ArticleDOI
Generalized linear mixed models: a practical guide for ecology and evolution
Benjamin M. Bolker,Mollie Elizabeth Brooks,Connie J. Clark,Shane W. Geange,John R. Poulsen,M. Henry H. Stevens,Jada-Simone S. White +6 more
TL;DR: The use (and misuse) of GLMMs in ecology and evolution are reviewed, estimation and inference are discussed, and 'best-practice' data analysis procedures for scientists facing this challenge are summarized.
Journal ArticleDOI
General methods for monitoring convergence of iterative simulations
Stephen P. Brooks,Andrew Gelman +1 more
TL;DR: This work generalizes the method proposed by Gelman and Rubin (1992a) for monitoring the convergence of iterative simulations by comparing between and within variances of multiple chains, in order to obtain a family of tests for convergence.
Posted Content
Making the Most Of Statistical Analyses: Improving Interpretation and Presentation
TL;DR: This article offers an approach, built on the technique of statistical simulation, to extract the currently overlooked information from any statistical method and to interpret and present it in a reader-friendly manner.
References
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Journal ArticleDOI
[Practical Markov Chain Monte Carlo]: Rejoinder: Replication without Contrition
Andrew Gelman,Donald B. Rubin +1 more
TL;DR: In this paper, the convergence of MCMC samples is discussed and a complete list of the commentaries on these articles is shown on the next page, along with a list of commentaries for each article.
Book ChapterDOI
Bayesian Estimation of Fuel Economy Potential Due to Technology Improvements
TL;DR: In this paper, a key question is how much of an increase in fuel efficiency is possible through implementation of existing technology, and the answer is that it is not necessarily the case.