Séminaire de Probabilités et Statistique

Le lundi 12 octobre 2009 à 14:30 - UM2 - Bât 09 - Salle 431 (4ème étage)

Jean-Michel Marin
ABC methods for model choice in Gibbs random fields

The core idea is that, for Gibbs random fields and in particular for Ising models, when comparing several neighbourhood structures, the computation of the posterior probabilities of the models under competition can be operated by likelihood-free simulation techniques (ABC). The turning point for this resolution is that, due to the specific structure of Gibbs random field distributions, there exists a sufficient statistic across models which allows for an exact (rather than Approximate) simulation from the posterior probabilities of the models. Obviously, when the structures grow more complex, it becomes necessary to introduce a true ABC step with a tolerance threshold in order to avoid running the algorithm for too long. Our toy example shows that the accuracy of the approximation of the Bayes factor can be greatly improved by resorting to the original ABC approach, since it allows for the inclusion of many more simulations. In a biophysical application to the choice of a folding structure for two proteins, we also demonstrate that we can implement the ABC solution on realistic datasets and, in the examples processed there, that the Bayes factors allow for a ranking more standard methods (FROST, TM-score) do not.

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