Bernoulli

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  • Volume 11, Number 5 (2005), 815-828.

On adaptive Markov chain Monte Carlo algorithms

Yves F. Atchadé and Jeffrey S. Rosenthal

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Abstract

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.

Article information

Source
Bernoulli Volume 11, Number 5 (2005), 815-828.

Dates
First available in Project Euclid: 23 October 2005

Permanent link to this document
https://projecteuclid.org/euclid.bj/1130077595

Digital Object Identifier
doi:10.3150/bj/1130077595

Mathematical Reviews number (MathSciNet)
MR2172842

Zentralblatt MATH identifier
1085.62097

Keywords
adaptive Markov chain Monte Carlo Metropolis algorithm mixingales parameter tuning Robbins-Monro algorithm

Citation

Atchadé, Yves F.; Rosenthal, Jeffrey S. On adaptive Markov chain Monte Carlo algorithms. Bernoulli 11 (2005), no. 5, 815--828. doi:10.3150/bj/1130077595. https://projecteuclid.org/euclid.bj/1130077595


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