A new strategy for speeding Markov chain Monte Carlo algorithms
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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.
Key wordsAsymptotic variance Efficiency Gibbs sampler Metropolis Hastings algorithms Rao-Blackwellization
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- 1.Abrams D I, Goldman A I, Launer C, Korvick J A, Neaton J D, Crane L R et al. (1994) Comparative trial of didanosine and zalcitabine in patients with human immunodeficiency virus infection who are intolerant or have failed zidovudine therapy. New England Journal of Medicine330: 657–662CrossRefGoogle Scholar
- 8.Gilks W R, Roberts G O (1996) Strategies for improving MCMC. In: Gilks W R, Richardson S, Spiegelhalter D J (eds.) Markov Chain Monte Carlo in Practice, pp. 89–114. Chapman and Hall, LondonGoogle Scholar
- 11.Hills S E, Smith AFM (1992) Parametrization issues in Bayesian inference. In: Bernardo J M, Berger J O, Dawid, A P, Smith A F M (eds.) Bayesian statistics 4, pp. 641–649. Oxford University Press, OxfordGoogle Scholar
- 17.Sargent D J, Hodges J S (1997) Smoothed ANOVA with application to subgroup analysis. Research Report 97-002, Division of Biostatistics, University of MinnesotaGoogle Scholar
- 19.Spiegelhalter D J, Thomas A, Best N, Gilks W R (1995) BUGS: Bayesian Inference Using Gibbs Sampling, Version 0.50. Technical report, Medical Research Council Biostatistics Unit, Institute of Public Health, Cambridge UniversityGoogle Scholar