## Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review (1996)

Venue: | Journal of the American Statistical Association |

Citations: | 234 - 6 self |

### BibTeX

@ARTICLE{Cowles96markovchain,

author = {Mary Kathryn Cowles and Bradley P. Carlin},

title = {Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review},

journal = {Journal of the American Statistical Association},

year = {1996},

volume = {91},

pages = {883--904}

}

### Years of Citing Articles

### OpenURL

### 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 currently has yielded relatively little that is 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 thirteen convergence diagnostics, describing the theoretical basis and practical implementation of each. We then compare their performance in two simple models and conclude that all the methods can fail to detect the sorts of convergence failure they were designed to identify. We thus recommend a combination of strategies aimed at evaluating and accelerating MCMC sampler conver...

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