Bayesian inference with rescaled Gaussian process priors

TL;DR

This paper investigates how rescaling Gaussian process priors affects the convergence rates of posterior distributions in nonparametric Bayesian inference, demonstrating optimal contraction rates through probabilistic bounds.

Contribution

It introduces rescaled Gaussian process priors that achieve optimal posterior contraction rates in nonparametric Bayesian models.

Findings

Rescaling influences the rate of posterior contraction.

Rescaled priors can attain optimal convergence rates.

Bounds on small deviation probabilities are established.

Abstract

We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit rescaled Gaussian process priors yielding posteriors that contract around the true parameter at optimal convergence rates. To derive our results we establish bounds on small deviation probabilities for smooth stationary Gaussian processes.