A correction of the bias in the ABC-PRC algorithm

When Sisson et al. (2007) introduced the ABC-PRC algorithm, the goal was to improve upon existing ABC-MCMC algorithms (Marjoram et al., 2003). While the ABC-PRC method is based upon the theoretical developments of Del Moral et al. (2006), the application to the setting of approximate Bayesian computation induces a bias in the approximation to the posterior distribution of interest, as we demonstrate in this paper via both theoretical reasoning and exper- imental results. A correction based on genuine importance sampling arguments is however implementable and we demonstrate here its applicability.