Open Access
October 2005 On adaptive Markov chain Monte Carlo algorithms
Yves F. Atchadé, Jeffrey S. Rosenthal
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Bernoulli 11(5): 815-828 (October 2005). DOI: 10.3150/bj/1130077595


We look at adaptive Markov chain Monte Carlo algorithms that generate stochastic processes based on sequences of transition kernels, where each transition kernel is allowed to depend on the history of the process. We show under certain conditions that the stochastic process generated is ergodic, with appropriate stationary distribution. We use this result to analyse an adaptive version of the random walk Metropolis algorithm where the scale parameter σ is sequentially adapted using a Robbins-Monro type algorithm in order to find the optimal scale parameter σopt. We close with a simulation example.


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Yves F. Atchadé. Jeffrey S. Rosenthal. "On adaptive Markov chain Monte Carlo algorithms." Bernoulli 11 (5) 815 - 828, October 2005.


Published: October 2005
First available in Project Euclid: 23 October 2005

zbMATH: 1085.62097
MathSciNet: MR2172842
Digital Object Identifier: 10.3150/bj/1130077595

Keywords: Adaptive Markov chain Monte Carlo , Metropolis algorithm , mixingales , parameter tuning , Robbins-Monro algorithm

Rights: Copyright © 2005 Bernoulli Society for Mathematical Statistics and Probability

Vol.11 • No. 5 • October 2005
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