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Selecting between different dependency structures of hidden Markov randomfield can be very challenging, due to the intractable normalizing constant inthe likelihood. We answer this question with approximate Bayesian computation(ABC) which provides a model choice method in the Bayesian paradigm. This comesafter the work of Grelaud et al. (2009) who exhibited sufficient statistics ondirectly observed Gibbs random fields. But when the random field is latent, thesufficiency falls and we complement the set with geometric summary statistics.The general approach to construct these intuitive statistics relies on aclustering analysis of the sites based on the observed colors and plausiblelatent graphs. The efficiency of ABC model choice based on these statistics isevaluated via a local error rate which may be of independent interest. As abyproduct we derived an ABC algorithm that adapts the dimension of the summarystatistics to the dataset without distorting the model selection.

Adaptive ABC model choice and geometric summary statistics for hidden Gibbs random fields