PROPRIETY OF THE REFERENCE POSTERIOR DISTRIBUTION IN GAUSSIAN PROCESS MODELING

• 成果类型: Article
• 署名作者: Mure, Joseph
• 署名单位: Electricite de France (EDF); Universite Paris Cite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/20-AOS2040
• 发表日期: 2021
• 页码: 2356-2377
• 关键词: objective bayesian-analysis; rates

摘要

In a seminal article, Berger, De Oliveira and Sanso [J. Amer. Statist. Assoc. 96 (2001) 1361-1374] compare several objective prior distributions for the parameters of Gaussian process models with isotropic correlation kernel. The reference prior distribution stands out among them insofar as it always leads to a proper posterior. They prove this result for rough correlation kernels: Spherical, Exponential with power rho < 2, Matern with smoothness nu < 1. This paper provides a proof for smooth correlation kernels: Exponential with power rho = 2, Matern with smoothness nu >= 1, Rational Quadratic, along with tail rates of the reference prior for these kernels.