## ABC à l’X [back]

“It is difficult to ensure that such sophisticated battles against the ‘ε-dilemma’ that arise in the simulation based inferential approaches of ABC and ALC do not confound the true posterior.”Shainudin et al., 2010

**I**t was a very interesting talk that took place at Polytechnique last afternoon. 9Although one could argue that the title was misleading in that ABC was never truly used, except as a scarecrow!) Indeed, Razeesh Shainudin gave a lively one-hour lecture where he showed that, for the standard Wright-Fisher coalescent model, the exact likelihood of the site-frequency-spectrum statistic (SFS). Ìt would have required much more time to cover the dense material contained in the paper he coauthored on this topic (and to appear in the Bulletin of Mathematical Biology, Algebraic Biology Special Edition), but his message was quite clear, namely that a graph analysis of the distribution of the SFS statistic was permitting a closed-form representation of the likelihood. And similarly for some linear combinations of the SFS that allowed for *[great!]* Kemeny and Snell‘s (1968) lumpability criterion to apply, namely for an impoverished Markov chain defined on an aggregated state space to remain Markov. I do see the direct consequence on the quality of ABC (except when conducting Monte Carlo experiments to compare both outputs) and I have not thought long enough to spot the impact on our current research, but appreciated very much the intuition given in the talk. The idea beyond the method seems to be that improving the support of the importance sampling distribution in order to remove parameter values that could not lead to the real data (SFS) provides a clear efficiency improvement)

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