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Using Parallel Computation to Improve Independent Metropolis-Hastings Based Estimation

Author

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  • Pierre Jacob

    (Crest)

  • Christian P. Robert

    (Crest)

  • Murray H. Smith

    (Crest)

Abstract

In this paper, we consider the implications of the fact that parallel raw-power can be exploited by a generic Metropolis--Hastings algorithm if the proposed values are independent. In particular, we present improvements to the independent Metropolis--Hastings algorithm that significantly decrease the variance of any estimator derived from the MCMC output, for a null computing cost since those improvements are based on a fixed number of target density evaluations. Furthermore, the techniques developed in this paper do not jeopardize the Markovian convergence properties of the algorithm, since they are based on the Rao--Blackwell principles of Gelfand and Smith (1990), already exploited in Casella and Robert (1996), Atchade and Perron (2005) and Douc and Robert (2010). We illustrate those improvements both on a toy normal example and on a classical probit regression model, but stress the fact that they are applicable in any case where the independent Metropolis-Hastings is applicable.

Suggested Citation

  • Pierre Jacob & Christian P. Robert & Murray H. Smith, 2010. "Using Parallel Computation to Improve Independent Metropolis-Hastings Based Estimation," Working Papers 2010-44, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2010-44
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    References listed on IDEAS

    as
    1. James P. Hobert, 2002. "On the applicability of regenerative simulation in Markov chain Monte Carlo," Biometrika, Biometrika Trust, vol. 89(4), pages 731-743, December.
    2. Craiu, Radu V. & Rosenthal, Jeffrey & Yang, Chao, 2009. "Learn From Thy Neighbor: Parallel-Chain and Regional Adaptive MCMC," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1454-1466.
    3. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
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