Zero Variance Markov Chain Monte Carlo for Bayesian Estimators

Antonietta Mira; Reza Solgi; Daniele Imparato

doi:10.1007/s11222-012-9344-6

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arXiv · 1012.2983

Zero Variance Markov Chain Monte Carlo for Bayesian Estimators

Antonietta Mira·Reza Solgi·Daniele Imparato

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Abstract

Interest is in evaluating, by Markov chain Monte Carlo (MCMC) simulation, the expected value of a function with respect to a, possibly unnormalized, probability distribution. A general purpose variance reduction technique for the MCMC estimator, based on the zero-variance principle introduced in the physics literature, is proposed. Conditions for asymptotic unbiasedness of the zero-variance estimator are derived. A central limit theorem is also proved under regularity conditions. The potential of the idea is illustrated with real applications to probit, logit and GARCH Bayesian models. For all these models, a central limit theorem and unbiasedness for the zero-variance estimator are proved (see the supplementary material available on-line).

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BibTeX RIS

Antonietta Mira, Reza Solgi, Daniele Imparato. 2010-12-14. Zero Variance Markov Chain Monte Carlo for Bayesian Estimators. https://doi.org/10.1007/s11222-012-9344-6

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