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Proc Natl Acad Sci U S A. 2003 Dec 23;100(26):15324-8. Epub 2003 Dec 8.

Markov chain Monte Carlo without likelihoods.

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  • 1Department of Preventive Medicine, Keck School of Medicine, University of Southern California, Los Angeles, CA 90089, USA.


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.

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