Séminaire des Doctorant·e·s :

Le 09 octobre 2013 à 17h15 - Salle 9.11

Présentée par Stoehr Julien - Université Paris Dauphine

Model choice for hidden Gibbs random fields using Approximate Bayesian Computation

Gibbs random fields (GRF) are widely used statistical models to analyse different types of dependence, like for spatially correlated data. However, when those models are faced with the challenge of selecting a dependence structure from many, the use of standard model choice methods is hampered by the intractibility of the normalising constant in the Gibbs likelihood. Likelihood-free simulation techniques like the Approximate Bayesian Computation (ABC) algorithm have been developped to face that problem. Grelaud, et al. show how to implement this algorithm for model selection in the general setting of Gibbs Random Fields. When the random field is directly observed, Grelaud et al. provide sufficient summary statistics for selecting models. But, when the random field is hidden, those statistics are not sufficient anymore. During this presentation, an explanation of ABC algorithm will be given and I will provide new summary statistics, especially one based on pixels clusters, and assess their efficiency for an ABC model choice between hidden random fields models.