On the choice of MCMC kernels for approximate Bayesian computation with SMC samplers

Approximate Bayesian computation (ABC) is a class of simulation-based statistical inference procedures that are increasingly being applied in scenarios where the likelihood function is either analytically unavailable or computationally prohibitive. These methods use, in a principled manner, simulations of the output of a parametrized system in lieu of computing the likelihood to perform parametric Bayesian inference. Such methods have wide applicability when the data generating mechanism can be simulated. While approximate, they can usually be made arbitrarily accurate at the cost of computational resources. In fact, computational issues are central to the successful use of ABC in practice. We focus here on the use of sequential Monte Carlo samplers for ABC and in particular on the choice of Markov chain Monte Carlo kernels used to drive their performance, investigating the use of kernels whose mixing properties are less sensitive to the quality of the approximation than standard kernels.