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The Multiple-Try Method and Local Optimization in Metropolis Sampling

Jun S. Liu, Faming Liang and Wing Hung Wong
Journal of the American Statistical Association
Vol. 95, No. 449 (Mar., 2000), pp. 121-134
DOI: 10.2307/2669532
Stable URL: http://www.jstor.org/stable/2669532
Page Count: 14
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The Multiple-Try Method and Local Optimization in Metropolis Sampling
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Abstract

This article describes a new Metropolis-like transition rule, the multiple-try Metropolis, for Markov chain Monte Carlo (MCMC) simulations. By using this transition rule together with adaptive direction sampling, we propose a novel method for incorporating local optimization steps into a MCMC sampler in continuous state-space. Numerical studies show that the new method performs significantly better than the traditional Metropolis-Hastings (M-H) sampler. With minor tailoring in using the rule, the multiple-try method can also be exploited to achieve the effect of a griddy Gibbs sampler without having to bear with griddy approximations, and the effect of a hit-and-run algorithm without having to figure out the required conditional distribution in a random direction.

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