likelihood-free parallel tempering

Meïli Baragatti, Agnès Grimaud, and Denys Pommeret posted an ABC paper on arXiv entitled Likelihood-free parallel tempering. While most ABC methods essentially are tempering methods, in that the tolerance level acts like an energy level, this paper uses parallel chains at various tolerance levels, with an exchange mechanism derived from Geyer and Thomson (1995, JASA). As with regular ABC-MCMC, the acceptance probability is such that the likelihood needs not be computed. On the mixture example of Sisson et al. (2007, PNAS) and on the tuberculosis example of Tanaka et al. (2006, Genetics), the authors report better performances than ABC-PMC, ABC-MCMC and ABC. (In a bimodal toy example,  ABC-PMC does not identify a second mode, which should not be the case with a large enough initial tolerance and a small enough tempering decrease step.) The paper introduces a sequence of temperatures in addition to a sequence of tolerances and it is only through an example that I understood the (unusual) role of the temperatures as scale factors in the  random walk proposal. It seems to me that an annealing step should be added as the chains with larger tolerances are less interesting as time goes on.

Ps-Scott Sisson just signaled on his twitter account the publication of several papers using ABC in monkey evolution. As well as a fourth paper by Wegman et al.. estimating the size of the initial American settlers to be around 100, about 13,000 years ago, all using standard ABC model choice techniques. Scott also pointed out a conference held in Bristol next April 16-19.

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