Efficient Approximate Bayesian Computation Coupled With Markov Chain Monte Carlo Without Likelihood

ABC techniques permit inferences in complex demographic models, but are computationally inefficient. An 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 sub-sampling the output and regression adjustment. We also propose to use a Partial Least Squares (PLS) transformation to choose informative statistics. The accuracy 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.

Key Words: Approximate Bayesian Computation, Human Evolution, Markov Chain Monte Carlo, Partial Least Squares

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