Properties of the Posterior Distribution of a Regression Model Based on Gaussian Random Fields

A. Zaytsev, E. Burnaev, V. Spokoiny

Abstract:

We consider the regression problem based on Gaussian processes. We assume that
the prior distribution on the vector of parameters in the corresponding model of the covariance
function is non-informative. Under this assumption, we prove the Bernstein–von Mises theorem
that states that the posterior distribution on the parameters vector is close to the corresponding
normal distribution. We show results of numerical experiments that indicate that our results
apply in practically important cases.