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A new strategy for speeding Markov chain Monte Carlo algorithms

Author

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  • Antonietta Mira

    (University of Insubria)

  • Daniel J. Sargent

    (Mayo Clinic)

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.

Suggested Citation

  • Antonietta Mira & Daniel J. Sargent, 2003. "A new strategy for speeding Markov chain Monte Carlo algorithms," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 12(1), pages 49-60, February.
    • Handle: RePEc:spr:stmapp:v:12:y:2003:i:1:d:10.1007_bf02511583
    DOI: 10.1007/BF02511583
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    References listed on IDEAS

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    1. P. Damlen & J. Wakefield & S. Walker, 1999. "Gibbs sampling for Bayesian non‐conjugate and hierarchical models by using auxiliary variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 331-344, April.
    2. J. S. Hodges, 1998. "Some algebra and geometry for hierarchical models, applied to diagnostics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 497-536.
    3. Antonietta Mira & Luke Tierney, 2002. "Efficiency and Convergence Properties of Slice Samplers," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 1-12, March.
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    Cited by:

    1. Pasanisi, Alberto & Fu, Shuai & Bousquet, Nicolas, 2012. "Estimating discrete Markov models from various incomplete data schemes," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2609-2625.
    2. Rigat, F. & Mira, A., 2012. "Parallel hierarchical sampling: A general-purpose interacting Markov chains Monte Carlo algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1450-1467.

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