Adaptivity for approximate Bayesian computation algorithms: a population Monte Carlo approach

Sequential techniques can be added to the approximate Bayesian computation (ABC) algorithm to enhance its efficiency. Sisson et al. (2007) introduced the partial rejection control version of this algorithm to improve upon existing Markov chain versions of the algorithm. While Sisson et al.’s (2007) method is based upon the theoretical developments of Del Moral et al. (2006), the application to the approximate Bayesian computation setting induces a bias in the approximation to the posterior distribution of interest. It is however possible to devise an alternative version based on genuine importance sampling arguments in connection with the population Monte Carlo method of Cappé et al. (2004). This algorithm is simpler than Sisson et al.’s (2007) algorithm, it does not suffer from the original bias, and it includes an automatic scaling of the forward kernel. Moreover, when applied to a population genetics example, its efficiency compares favourably with two other versions of the approximate Bayesian computation algorithm.