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Exact likelihood-free Markov chain Monte Carlo for elliptically contoured distributions

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  • Muchmore Patrick

    (Division of Biostatistics, Department of Preventive Medicine, University of Southern California, 2001 N Soto Street, Los Angeles, CA 90089-9237, USA)

  • Marjoram Paul

    (Division of Biostatistics, Department of Preventive Medicine, University of Southern California, 2001 N Soto Street, Los Angeles, CA 90089-9237, USA)

Abstract

Recent results in Markov chain Monte Carlo (MCMC) show that a chain based on an unbiased estimator of the likelihood can have a stationary distribution identical to that of a chain based on exact likelihood calculations. In this paper we develop such an estimator for elliptically contoured distributions, a large family of distributions that includes and generalizes the multivariate normal. We then show how this estimator, combined with pseudorandom realizations of an elliptically contoured distribution, can be used to run MCMC in a way that replicates the stationary distribution of a likelihood based chain, but does not require explicit likelihood calculations. Because many elliptically contoured distributions do not have closed form densities, our simulation based approach enables exact MCMC based inference in a range of cases where previously it was impossible.

Suggested Citation

  • Muchmore Patrick & Marjoram Paul, 2015. "Exact likelihood-free Markov chain Monte Carlo for elliptically contoured distributions," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 14(4), pages 317-332, August.
    • Handle: RePEc:bpj:sagmbi:v:14:y:2015:i:4:p:317-332:n:4
    DOI: 10.1515/sagmb-2014-0063
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    References listed on IDEAS

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    1. C. C. Drovandi & A. N. Pettitt, 2011. "Estimation of Parameters for Macroparasite Population Evolution Using Approximate Bayesian Computation," Biometrics, The International Biometric Society, vol. 67(1), pages 225-233, March.
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    3. repec:dau:papers:123456789/6334 is not listed on IDEAS
    4. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    5. Mark A. Beaumont & Jean-Marie Cornuet & Jean-Michel Marin & Christian P. Robert, 2009. "Adaptive approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 96(4), pages 983-990.
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