A new strategy for speeding Markov chain Monte Carlo algorithms |
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Authors: | Antonietta Mira Daniel J Sargent |
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Institution: | (1) Department of Economics, University of Insubria, Via Ravasi 2, Varese, Italy;(2) Mayo Clinic, Rochester, MN, USA |
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Abstract: | Markov chain Monte Carlo (MCMC) methods have become popular as a basis for drawing inference from complex statistical models.
Two common difficulties with MCMC algorithms are slow mixing and long run-times, which are frequently closely related. Mixing
over the entire state space can often be aided by careful tuning of the chain's transition kernel. In order to preserve the
algorithm's stationary distribution, however, care must be taken when updating a chain's transition kernel based on that same
chain's history. In this paper we introduce a technique that allows the transition kernel of the Gibbs sampler to be updated
at user specified intervals, while preserving the chain's stationary distribution. This technique seems to be beneficial both
in increasing efficiency of the resulting estimates (via Rao-Blackwellization) and in reducing the run-time. A reinterpretation
of the modified Gibbs sampling scheme introduced in terms of auxiliary samples allows its extension to the more general Metropolis-Hastings
framework. The strategies we develop are particularly helpful when calculation of the full conditional (for a Gibbs algorithm)
or of the proposal distribution (for a Metropolis-Hastings algorithm) is computationally expensive.
Partial financial support from FAR 2002-3, University of Insubria is gratefully acknowledged. |
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Keywords: | Asymptotic variance Efficiency Gibbs sampler Metropolis Hastings algorithms Rao-Blackwellization |
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