Posterior concentration rates for infinite dimensional exponential families

Vincent Rivoirard (1, 2) , Judith Rousseau (1, 3, 2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Université Paris Dauphine-PSL
3 CREST - Centre de Recherche en Économie et Statistique

In this paper we derive adaptive non-parametric rates of concentration of the posterior distributions for the density model on the class of Sobolev and Besov spaces. For this purpose, we build prior models based on wavelet or Fourier expansions of the logarithm of the density. The prior models are not necessarily Gaussian

Mots clés: Bayesian non-parametric; rates of convergence; adaptive estimation; wavelets; Fourier Bases; Sobolev balls; Besov balls

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

Vincent Rivoirard, Judith Rousseau. Posterior concentration rates for infinite dimensional exponential families. Bayesian Analysis, 2012, 07 (02), pp.311 - 334. ⟨10.1214/12-BA710⟩. ⟨hal-00634432⟩