Evaluating statistic appropriateness for Bayesian model choice

Jean-Michel Marin (1) , Natesh Pillai (2) , Christian Robert (3, 4) , Judith Rousseau (3, 4)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 Department of Statistics
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
4 CREST - Centre de Recherche en Économie et Statistique

The choice of the summary statistics in Bayesian inference and in particular in ABC is paramount to produce a valid outcome. We examine necessary and sufficient conditions on those statistics for a corresponding Bayes factor to be convergent. The conditions thus obtained are then usable in ABC settings to determine which summary statistics are appropriate, following a standard Monte Carlo validation.

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

Jean-Michel Marin, Natesh Pillai, Christian Robert, Judith Rousseau. Evaluating statistic appropriateness for Bayesian model choice. 2011. ⟨hal-00641487⟩