ABC-SMC redux (2)

The ABC paper entitled “An Adaptive Sequential Monte Carlo Method for Approximate Bayesian Computation” by Pierre Del Moral, Arnaud Doucet and Ajay Jasra and discussed in that earlier post is now available on-line. In addition to this discussion, I note (and regret) here that the paper does not analyse Sisson et al. (2007) besides remarking that the computational cost of the ABC-PRC algorithm is quadratic in the number of particles. Re-reading the paper, I find an important feature there is that the update in the weights is reduced to the ratio of the proportions of surviving particles (and nothing else!), due to the choice of the reversal backward kernel L_n-1 and to the use of an (MCMC) invariant transition forward kernel K_n (which can be a standard Metropolis-Hastings kernel for instance).