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
Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo
TL;DR: In this paper, general methods for analyzing the convergence of discrete-time, general state-space Markov chains, such as those used in stochastic simulation algorithms including the Gibbs sampler, are provided.
Journal ArticleDOI
Efficient parametrisations for normal linear mixed models
TL;DR: In this paper, the authors present simple hierarchical centring reparametrisations that often give improved convergence for a broad class of normal linear mixed models, including the Laird-Ware model, and a general structure for hierarchically nested linear models.
Journal ArticleDOI
Regeneration in Markov chain samplers
TL;DR: In this paper, the use of Markov chain splitting, originally developed for the theoretical analysis of general state-space Markov chains, was introduced into regenerative methods for analyzing the output of these samplers.
Journal ArticleDOI
Detecting Initialization Bias in Simulation Output
TL;DR: A general approach to testing for initialization bias in the mean of a simulation output series is presented and an initialization bias test is developed.