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Originally published as Genetics Published Articles Ahead of Print on June 8, 2009.
Genetics, Vol. 182, 1207-1218, August 2009, Copyright © 2009
doi:10.1534/genetics.109.102509
Efficient Approximate Bayesian Computation Coupled With Markov Chain Monte Carlo Without Likelihood
Daniel Wegmann*,
,
Christoph Leuenberger
and
Laurent Excoffier*,,1
* Computational and Molecular Population Genetics Laboratory, Institute of Ecology and Evolution, University of Bern, 3012 Bern, Switzerland and Swiss Institute of Bioinformatics, Ecole d'Ingénieurs de Fribourg, 1705 Fribourg, Switzerland
1 Corresponding author: Computational and Molecular Population Genetics Laboratory, Institute of Ecology and Evolution, University of Bern, Baltzerstrasse 6, CH-3012 Bern, Switzerland.
E-mail: laurent.excoffier{at}iee.unibe.ch
Approximate Bayesian computation (ABC) techniques permit inferences in complex demographic models, but are computationally inefficient. A Markov chain Monte Carlo (MCMC) approach has been proposed (MARJORAM et al. 2003), but it suffers from computational problems and poor mixing. We propose several methodological developments to overcome the shortcomings of this MCMC approach and hence realize substantial computational advances over standard ABC. The principal idea is to relax the tolerance within MCMC to permit good mixing, but retain a good approximation to the posterior by a combination of subsampling the output and regression adjustment. We also propose to use a partial least-squares (PLS) transformation to choose informative statistics. The accuracy of our approach is examined in the case of the divergence of two populations with and without migration. In that case, our ABC–MCMC approach needs considerably lower computation time to reach the same accuracy than conventional ABC. We then apply our method to a more complex case with the estimation of divergence times and migration rates between three African populations.
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