Propriety of the reference posterior distribution in Gaussian Process regression

05/23/2018

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by   Joseph Muré, et al.

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In a seminal article, Berger, De Oliveira and Sansó (2001) compare several objective prior distributions for the parameters of Gaussian Process regression 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 q<2, Matérn with smoothness ν<1. This paper provides a proof for smooth correlation kernels - Exponential with power q=2, Matérn with smoothness ν≥ 1, Rational Quadratic.