Sequential Monte Carlo without likelihoods
While peeping at the slides of the working groups of the 2008-09 Program on Sequential Monte Carlo Methods, I came upon a short presentation of the ABC-PRC version of Sisson, Fan and Tanaka of the ABC algorithm that does not seem to be aware the bias exhibited in our paper with Marc Beaumont, Jean-Marie Cornuet and Jean-Michel Marin, following a first exchange of Marc with the authors. Since this appears to be the case for many people using ABC, I recap here our point.
The difficulty with the method centers at the acceptance probability above, that is derived from the SMC sampler of Del Moral, Doucet and Jasra (2006, JRSS B), with the difference that the likelihood is removed in a standard ABC fashion. However, the missing likelihood in the denominator is not compensated for and this creates the bias. The difficulty is not acknowledged in PNAS (which rejected our submission on the ground that the problem was “well-known”, which is apparently not that true). The update published on Scott Sisson’s webpage does not acknowledge the bias but rather puts the blame for poor performances on the fact that “poor choices of backward kernels such as L = K can in some cases result in importance weights with a very large or infinite variance“. Rather interestingly, the solution put forward in the update for the backward kernel L ends up with a form that is identical with the population Monte Carlo solution we propose, but for the wrong reason altogether!