Julien Stoehr (Université Montpellier 2): ABC model choice between hidden Gibbs random fields based on geometric summary statistics

Gibbs random fields are polymorphous statistical models that are useful to analyse different types of spatially correlated data like pixels of an image. But selecting between two different dependence structures can be very challenging, due to the intractable normalizing constant in the Gibbs likelihoods. Approximate Bayesian Computation (ABC) algorithms provide a model choice method in the Bayesian paradigm. The scheme compares the observed data and many numerical simulations through summary statistics. The consistency of the ABC algorithm is obvious if the summary statistics are sufficient. Otherwise summary statistics has to be chosen carefully [2, 3]. When the Gibbs random field is directly observed, Grelaud et al. [1] exhibited sufficient summary statistics. But, when the random field is hidden, those statistics are not sufficient anymore. We provide new summary statistics based on pixels clusters, and assess their efficiency for an ABC model choice between hidden random fields models.

Keywords : Approximate Bayesian Computation, model choice, hidden Gibbs random fields, summary statistics

This is joint work with Pierre Pudlo and Lionel Cucala

References
[1] A. Grelaud, C. P. Robert, J-M. Marin, F. Rodolphe and J-F. Taly. ABC likelihood-free methods for model choice in Gibbs random fields. Bayesian Analysis, 4(2) :317–336, 2009.
[2] C. P. Robert, J-M. Cornuet, J-M. Marin and N. S. Pillai. Lack of confidence in approximate Bayesian computation model choice. Proceedings of the National Academy of Sciences of the United States of America, 108(37) :15112–15117, 2011.
[3] J-M. Marin, N. S. Pillai, C. P. Robert and J. Rousseau. Relevant statistics for Bayesian model choice. To appear in the Journal of the Royal Statistical Society, Series B, 2014.

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