Geometric summary statistics for ABC model choice between hidden Gibbs random fields

Julien Stoehr (1) , Pierre Pudlo (1) , Lionel Cucala (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

Selecting between different dependence structures of a hidden Markov random field can be very challenging, due to the intractable normalizing constants in the likelihoods and the sum over all possible latent random fields. 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. When the Gibbs random field is directly observed, Grelaud et al. (2009) exhibit sufficient summary statistics that immediately guarantee the consistency of the ABC algorithm. But, when the random field is hidden, those statistics are not sufficient anymore. We provide new summary statistics based on the geometry of the image, more precisely a clustering analysis of pixels. To assess their efficiency, we also derive a conditional misclassification rate evaluating the power of ABC algorithms which may be of independent interest.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Calcul [stat.CO]

Julien Stoehr, Pierre Pudlo, Lionel Cucala. Geometric summary statistics for ABC model choice between hidden Gibbs random fields. 2014. ⟨hal-00942797v1⟩