Kernel Approximate Bayesian Computation for Population Genetic Inferences
Shigeki Nakagome, Kenji Fukumizu, Shuhei Mano
(Submitted on 15 May 2012)

As genomic data accumulate, Bayesian inferences can be applied to estimate evolutionary parameters. However, the complexity of stochastic models used in population genetics makes it difficult to derive the likelihoods needed for Bayesian inferences. Approximate Bayesian Computation (ABC) is an alternative approach for obtaining Bayesian inferences without likelihoods. ABC is a rejection-based method that applies a tolerance of dissimilarity between sets of summary statistics from observed and simulated data. ABC gives an exact sampler from the posterior density in the limit of zero tolerance. However, the choices for summary statistics and metrics of dissimilarity are ambiguous, and acceptance rates decrease with an increasing number of summary statistics. Therefore, it is difficult to maintain estimator consistency using ABC. In this study, we apply the kernel Bayes’ rule proposed by Fukumizu et al. (2011) to ABC. We report that kernel ABC (i) avoids the need for tolerance, (ii) upholds the consistency of estimators, and (iii) is tractable for a large number of summary statistics. We demonstrate these advantages by comparing kernel ABC with conventional ABC for population genetic inferences.