On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo

摘要

Approximate Bayesian computation (ABC) has gained popularity over the pastfew years for the analysis of complex models arising in population genetic,epidemiology and system biology. Sequential Monte Carlo (SMC) approaches havebecome work horses in ABC. Here we discuss how to construct the perturbationkernels that are required in ABC SMC approaches, in order to construct a set ofdistributions that start out from a suitably defined prior and converge towardsthe unknown posterior. We derive optimality criteria for different kernels,which are based on the Kullback-Leibler divergence between a distribution andthe distribution of the perturbed particles. We will show that for manycomplicated posterior distributions, locally adapted kernels tend to show thebest performance. In cases where it is possible to estimate the Fisherinformation we can construct particularly efficient perturbation kernels. Wefind that the added moderate cost of adapting kernel functions is easilyregained in terms of the higher acceptance rate. We demonstrate thecomputational efficiency gains in a range of toy-examples which illustrate someof the challenges faced in real-world applications of ABC, before turning totwo demanding parameter inference problem in molecular biology, which highlightthe huge increases in efficiency that can be gained from choice of optimalmodels. We conclude with a general discussion of rational choice ofperturbation kernels in ABC SMC settings.