Markov chain Monte Carlo (MCMC) methods make possible the use of flexible Bayesian models that would otherwise be computationally infeasible. In recent years, a great variety of such applications have been described in the literature. Applied statisticians who are new to these methods may have several questions and concerns, however: How much effort and expertise are needed to design and use a Markov chain sampler? How much confidence can one have in the answers that MCMC produces? How does the use of MCMC affect the rest of the model-building process? At the Joint Statistical Meetings in August, 1996, a panel of experienced MCMC users discussed these and other issues, as well as various “tricks of the trade. ” This article is an edited recreation of that discussion. Its purpose is to offer advice and guidance to novice users of MCMC—and to notso-novice users as well. Topics include building confidence in simulation results, methods for speeding and assessing convergence, estimating standard errors, identification of models for which good MCMC algorithms exist, and the current state of software development.
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2405
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Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images
– Geman, Geman
- 1984
|
|
1170
|
Equation of state calculations by fast computing machines
– Metropolis, Rosenbluth, et al.
- 1953
|
|
586
|
Monte Carlo Sampling Methods Using Markov Chains and Their Applications
– Hastings
- 1970
|
|
421
|
Sampling-Based Approaches to Calculating Marginal Densities
– Gelfand, Smith
- 1990
|
|
335
|
Probabilistic inference using Markov chain Monte Carlo methods (Tech
– Neal
- 1993
|
|
281
|
Stochastic Simulation
– Ripley
- 1987
|
|
259
|
Inference from Iterative Simulation Using Multiple Sequences
– Gelman, Rubin
- 1992
|
|
154
|
Bayes and empirical Bayes methods for data analysis
– Carlin, Louis
- 2000
|
|
149
|
Nonuniversal Critical Dynamics in Monte Carlo Simulations
– Swendsen, Wang
- 1987
|
|
140
|
Understanding the Metropolis–Hastings Algorithm
– Chib, Greenberg
- 1995
|
|
119
|
Markov chain Monte Carlo convergence diagnostics: a comparative study
– Cowles, Carlin
- 1996
|
|
90
|
Annealing Markov chain Monte Carlo with applications to ancestral inference
– Geyer, Thompson
- 1995
|
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81
|
A language and a program for complex Bayesian modelling. The Statistician 43
– Gilks, Thomas, et al.
- 1994
|
|
74
|
Explaining the Gibbs sampler
– Casella, George
- 1992
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69
|
Practical Markov chain Monte Carlo (with discussion
– Geyer
- 1992
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59
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Posterior Predictive Assessment of Model Fitness via Realized Discrepancies (with discussion
– Gelman, Meng, et al.
- 1996
|
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57
|
The EM algorithm - An old folk song sung to a fast new
– Meng, Dyk
- 1997
|
|
55
|
Spatial Statistics and Bayesian Computation” (with discussion
– Besag, Green
- 1993
|
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35
|
Sampling from multimodal distributions using tempered transitions
– Neal
- 1996
|
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32
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BUGS: Bayesian Inference Using Gibbs Sampling, Version 0.30
– Spiegelhalter, Thomas, et al.
- 1994
|
|
32
|
Facilitating the Gibbs Sampler: The Gibbs Stopper and the Griddy Gibbs sampler
– Ritter, Tanner
- 1992
|
|
23
|
CODA: Convergence diagnosis and output analysis software for Gibbs sampling output, Version 0.4
– Best, Cowles, et al.
- 1997
|
|
20
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Methods for approximating integrals in statistics with special emphasis on Bayesian integration problems
– Evans, Swartz
- 1995
|
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17
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Efficient parameterizations for normal linear mixed models
– Gelfand, Sahu, et al.
- 1995
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15
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Physiological Pharmacokinetic Analysis using Population Modelling and Informative Prior Distributions
– Gelman, Bois, et al.
- 1996
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13
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Subregion-adaptive Integration of Functions Having a Dominant Peak
– Genz, Kass
- 1997
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10
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Spatial Statistics and Bayesian Computation" (with discusion
– Besag, Green
- 1993
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10
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Efficient Parametrizations for Normal Linear Mixed Models
– Gelfand, Sahu, et al.
- 1995
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10
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Subsampling the Gibbs Sampler
– MacEachern, Berliner
- 1994
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7
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Bayesian Computation and Stochastic Systems" (with discussion
– Besag, Green, et al.
- 1995
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7
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Efficient parametrizations for generalized linear mixed models
– Gelfand, Sahu, et al.
- 1996
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6
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Methods for Approximating Integrals
– Evans, Swartz
- 1995
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5
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Practical Markov chain Monte Carlo" (with discussion
– Geyer
- 1992
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4
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Bayesian Analysis for some Hierarchical Linear Models," unpublished
– Boscardin
- 1996
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4
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Inference and monitoring convergence,” in Markov Chain Monte Carlo in Practice
– Gelman
- 1996
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3
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Inference and Monitoring Convergence," in Markov Chain Monte Carlo in Practice
– Gelman
- 1996
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3
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BUGS examples, Version 0.50
– Spiegelhalter, Thomas, et al.
- 1995
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2
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Comment on "Bayesian Computation and Stochastic Systems, " by
– Gelfand, Carlin
- 1995
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1
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Comment on “Computation on Bayesian Graphical Models,” by D.J
– Fienberg
- 1996
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1
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Comment on “Bayesian Computation and Stochastic Systems,” by
– Gelfand, Carlin
- 1995
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1
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Identifiability, Propriety, and Parametrization with Regard to Simulation-Based Fitting of Generalized Linear Mixed Models
– Gelfand, Sahu
- 1996
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1
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Comment on "Computation on Bayesian Graphical Models," by D.J
– Fienberg
- 1996
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