## Sequential Monte Carlo without likelihoods

**W**hile 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!

March 30, 2009 at 1:18 am

[…] Incredibly ugly squalid pictures… Well, this is not a common teaser to attract readers, but a comment on one of my graphs in the second revision of our paper Adaptivity for approximate Bayesian computation algorithms: a population Monte Carlo approach, written with Marc Beaumont, Jean-Marie Cornuet, and Jean-Michel Marin, and (re-re-)submitted to Biometrika… Not something I’d like to hear about my graphs, thank you!, as the pdf version of the graph on the right actually looks better than than one…. Anyway, we revised the paper towards less squalidness, replacing histogram with density using the “h” type in R. The major request on the revision was to get under eight pages in order to fit inside the Miscelanea section of Biometrika. Changes are thus mostly cosmetic compared with the earlier version, as you can check on the arXiv list of versions. The background for the paper and the earlier paper of Sisson, Fan, and Tanaka (2007, PNAS) it analyses, is described in this earlier post. […]

February 11, 2009 at 4:58 pm

[…] going on at the Université de Montpellier II, I will (hopefully) give a seminar there tomorrow on ABC methods. Here are my slides for those interested (or on […]

February 11, 2009 at 1:23 pm

[…] a second round of reviews from Biometrika where the referees validated our analysis of the bias in ABC-PRC. The changes are quite minor, compared with the previous version and include an […]

February 5, 2009 at 3:30 pm

[…] Marc Beaumont, University of Reading (whose paper is discussed on that post); […]

January 9, 2009 at 8:14 am

[…] the supplementary material in the Appendix of Sisson et al. (2007b) yesterday, I found I have an additional difficulty with the ABC-PRC algorithm that is related with the partial rejection control (PRC) […]

January 7, 2009 at 10:42 am

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December 12, 2008 at 4:37 pm

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November 21, 2008 at 11:09 pm

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November 21, 2008 at 12:36 pm

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