We consider the problem of model selection within the class of Gibbs random fields. In a Bayesian framework, this choice relies on the evaluation of the posterior probabilities of all models. We define an extended parameter setting, including the model index and show the existence of a corresponding sufficient statistic made of the conjunction of the sufficient statistics of all models. We use this statistic to derive an ABC algorithm.
On s'intéresse au problème du choix bayésien de modèles de champs de Gibbs. Ce choix repose sur l'évaluation des probabilités a posteriori des modèles. Nous montrons l'existence d'une statistique exhaustive pour l'ensemble des paramètres, incluant l'indice du modèle, constituée de la concaténation de statistiques exhaustives de chacun des modèles. Nous utilisons cette statistique pour construire un algorithme ABC.
Accepted:
Published online:
Aude Grelaud 1, 2, 3; Christian P. Robert 2, 3; Jean-Michel Marin 3, 4
@article{CRMATH_2009__347_3-4_205_0, author = {Aude Grelaud and Christian P. Robert and Jean-Michel Marin}, title = {ABC methods for model choice in {Gibbs} random fields}, journal = {Comptes Rendus. Math\'ematique}, pages = {205--210}, publisher = {Elsevier}, volume = {347}, number = {3-4}, year = {2009}, doi = {10.1016/j.crma.2008.12.009}, language = {en}, }
TY - JOUR AU - Aude Grelaud AU - Christian P. Robert AU - Jean-Michel Marin TI - ABC methods for model choice in Gibbs random fields JO - Comptes Rendus. Mathématique PY - 2009 SP - 205 EP - 210 VL - 347 IS - 3-4 PB - Elsevier DO - 10.1016/j.crma.2008.12.009 LA - en ID - CRMATH_2009__347_3-4_205_0 ER -
Aude Grelaud; Christian P. Robert; Jean-Michel Marin. ABC methods for model choice in Gibbs random fields. Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 205-210. doi : 10.1016/j.crma.2008.12.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.12.009/
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