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Parallel hierarchical sampling:a general-purpose class of multiple-chains MCMC algorithms

Author

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  • Antonietta Mira

    (Department of Economics, University of Insubria, Italy)

  • Fabio Rigat

    (Department of Statistics and Centre for analytical Science, University of Warwick, UK)

Abstract

This paper introduces the Parallel Hierarchical Sampler (PHS), a class of Markov chain Monte Carlo algorithms using several interacting chains having the same target distribution but different mixing properties. Unlike any single-chain MCMC algorithm, upon reaching stationarity one of the PHS chains, which we call the “mother” chain, attains exact Monte Carlo sampling of the target distribution of interest. We empirically show that this translates in a dramatic improvement in the sampler’s performance with respect to single-chain MCMC algorithms. Convergence of the PHS joint transition kernel is proved and its relationships with single-chain samplers, Parallel Tempering (PT) and variable augmentation algorithms are discussed. We then provide two illustrative examples comparing the accuracy of PHS with

Suggested Citation

  • Antonietta Mira & Fabio Rigat, 2009. "Parallel hierarchical sampling:a general-purpose class of multiple-chains MCMC algorithms," Economics and Quantitative Methods qf0903, Department of Economics, University of Insubria.
    • Handle: RePEc:ins:quaeco:qf0903
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    File URL: https://www.eco.uninsubria.it/RePEc/pdf/QF2009_5.pdf
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    References listed on IDEAS

    as
    1. Olivier Cappé & Christian P. Robert & Tobias Rydén, 2003. "Reversible jump, birth‐and‐death and more general continuous time Markov chain Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 679-700, August.
    2. repec:dau:papers:123456789/6040 is not listed on IDEAS
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