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Research Article

Markov chain Monte Carlo without likelihoods

Paul Marjoram, John Molitor, Vincent Plagnol, and Simon Tavaré
  1. *Biostatistics Division, Department of Preventive Medicine, Keck School of Medicine, and †Molecular and Computational Biology, Department of Biological Sciences, University of Southern California, Los Angeles, CA 90089

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PNAS December 23, 2003 100 (26) 15324-15328; https://doi.org/10.1073/pnas.0306899100
Paul Marjoram
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John Molitor
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Vincent Plagnol
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Simon Tavaré
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  1. Communicated by Michael S. Waterman, University of Southern California, Los Angeles, CA, October 24, 2003 (received for review June 20, 2003)

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Abstract

Many stochastic simulation approaches for generating observations from a posterior distribution depend on knowing a likelihood function. However, for many complex probability models, such likelihoods are either impossible or computationally prohibitive to obtain. Here we present a Markov chain Monte Carlo method for generating observations from a posterior distribution without the use of likelihoods. It can also be used in frequentist applications, in particular for maximum-likelihood estimation. The approach is illustrated by an example of ancestral inference in population genetics. A number of open problems are highlighted in the discussion.

Footnotes

    • ↵‡ To whom correspondence should be addressed at: Program in Molecular and Computational Biology, Department of Biological Sciences, SHS 172, University of Southern California, 835 West 37th Street, Los Angeles, CA 90089-1340. E-mail: stavare{at}usc.edu.

    • Abbreviations: MCMC, Markov chain Monte Carlo; MRCA, most recent common ancestor.

    • Received June 20, 2003.
    • Copyright © 2003, The National Academy of Sciences
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    Markov chain Monte Carlo without likelihoods
    Paul Marjoram, John Molitor, Vincent Plagnol, Simon Tavaré
    Proceedings of the National Academy of Sciences Dec 2003, 100 (26) 15324-15328; DOI: 10.1073/pnas.0306899100

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    Markov chain Monte Carlo without likelihoods
    Paul Marjoram, John Molitor, Vincent Plagnol, Simon Tavaré
    Proceedings of the National Academy of Sciences Dec 2003, 100 (26) 15324-15328; DOI: 10.1073/pnas.0306899100
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    Proceedings of the National Academy of Sciences: 100 (26)
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    • Article
      • Abstract
      • Examples from Evolutionary Biology
      • MCMC Methods
      • An Example from Population Genetics
      • Implementing Algorithm F
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      • Discussion
      • Acknowledgments
      • Footnotes
      • References
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