PROPRIETY OF THE REFERENCE POSTERIOR DISTRIBUTION IN GAUSSIAN PROCESS MODELING

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.

Automated summary

In this paper, various objective prior distributions for the parameters of Gaussian process models with isotropic correlation kernels were compared. The reference prior distribution was shown to always lead to a proper posterior, with proof provided for specific correlation kernels.