Some Aspects of Symmetric Gamma Process Mixtures

Zacharie Naulet (1) , Eric Barat (1)

1 LM2S (CEA, LIST) - Laboratoire Modélisation et Simulation de Systèmes (CEA, LIST)

In this article, we present some specific aspects of symmetric Gamma process mixtures for use in regression models. First we propose a new Gibbs sampler for simulating the posterior. The algorithm is tested on two examples, the mean regression problem with normal errors, and the reconstruction of two dimensional CT images. In a second time, we establish posterior rates of convergence related to the mean regression problem with normal errors. For location-scale and location-modulation mixtures the rates are adaptive over Holder classes, and in the case of location-modulation mixtures are nearly optimal.

Mots clés: signed random measures; nonparametric regression; Bayesian non parametrics; nonparametric regression; signed random measures; Bayesian nonparameterics

Domaines: Statistiques [math.ST]; Analyse fonctionnelle [math.FA]

Zacharie Naulet, Eric Barat. Some Aspects of Symmetric Gamma Process Mixtures. Bayesian Analysis, 2018, 13, pp.703 - 720. ⟨10.1214/17-BA1058⟩. ⟨cea-01838175⟩