The Annals of Applied Probability

Adaptive Gibbs samplers and related MCMC methods

Krzysztof Łatuszyński, Gareth O. Roberts, and Jeffrey S. Rosenthal

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We consider various versions of adaptive Gibbs and Metropolis-within-Gibbs samplers, which update their selection probabilities (and perhaps also their proposal distributions) on the fly during a run by learning as they go in an attempt to optimize the algorithm. We present a cautionary example of how even a simple-seeming adaptive Gibbs sampler may fail to converge. We then present various positive results guaranteeing convergence of adaptive Gibbs samplers under certain conditions.

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Ann. Appl. Probab., Volume 23, Number 1 (2013), 66-98.

First available in Project Euclid: 25 January 2013

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Zentralblatt MATH identifier

Primary: 60J05: Discrete-time Markov processes on general state spaces 65C05: Monte Carlo methods
Secondary: 62F15: Bayesian inference

MCMC estimation adaptive MCMC Gibbs sampling


Łatuszyński, Krzysztof; Roberts, Gareth O.; Rosenthal, Jeffrey S. Adaptive Gibbs samplers and related MCMC methods. Ann. Appl. Probab. 23 (2013), no. 1, 66--98. doi:10.1214/11-AAP806.

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