Bayesian Analysis

Some Aspects of Symmetric Gamma Process Mixtures

Zacharie Naulet and Éric Barat

Full-text: Open access

Abstract

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 Hölder classes, and in the case of location-modulation mixtures are nearly optimal.

Article information

Source
Bayesian Anal., Volume 13, Number 3 (2018), 703-720.

Dates
First available in Project Euclid: 7 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.ba/1507341640

Digital Object Identifier
doi:10.1214/17-BA1058

Mathematical Reviews number (MathSciNet)
MR3807863

Subjects
Primary: 62G08: Nonparametric regression 62G20: Asymptotic properties
Secondary: 60G57: Random measures

Keywords
Bayesian nonparameterics nonparametric regression signed random measures

Rights
Creative Commons Attribution 4.0 International License.

Citation

Naulet, Zacharie; Barat, Éric. Some Aspects of Symmetric Gamma Process Mixtures. Bayesian Anal. 13 (2018), no. 3, 703--720. doi:10.1214/17-BA1058. https://projecteuclid.org/euclid.ba/1507341640


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