## ABC à l’X

**T**omorrow, there is a series of seminars at École Polytechnique (** X**) on random models for ecology, genetics and evolution. The first one is on ABC,

*Approximate Bayesian Computations Done Exactly*, by Razeesh Shainudin and I plan to attend. Here is the abstract:

Evaluating the likelihood function of parameters in highly-structured population genetic models from extant deoxyribonucleic acid (DNA) sequences is computationally prohibitive. In such cases, one may approximately infer the parameters from summary statistics of the data such as the site-frequency-spectrum (SFS) or its linear combinations. Such methods are known as approximate likelihood or Bayesian computations. Using a controlled lumped Markov chain and computational commutative algebraic methods we compute the exact likelihood of the SFS and many classical linear combinations of it at a non-recombining locus that is neutrally evolving under the infi™nitely-many-sites mutation model. Using a partially ordered graph of coalescent experiments around the SFS we provide a decision-theoretic framework for approximate sufficiency. We also extend a family of classical hypothesis tests of standard neutrality at a non-recombining locus based on the SFS to a more powerful version that conditions on the topological information provided by the SFS.Keywords: controlled lumped Markov chain, unlabelled coalescent, random integer partition sequences, partially ordered experiments, population genomic inference population genetic Markov bases, approximate Bayesian computation done exactly.

February 9, 2011 at 12:14 am

[…] 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 […]