Despite the ubiquity of the Gaussian process regression model, few theoretical results are
available that account for the fact that parameters of the covariance kernel typically need to …

Monge-Kantorovich distances, otherwise known as Wasserstein distances, have received a
growing attention in statistics and machine learning as a powerful discrepancy measure for …

The manufacturing quality of industrial pieces is linked with the intrinsic concentration field of
certain chemical species. Thus, from punctual measurements sparsely distributed on the …

Gaussian process (GP) regression is a Bayesian nonparametric method for regression and
interpolation, offering a principled way of quantifying the uncertainties of predicted function …

We consider covariance parameter estimation for a Gaussian process under inequality
constraints (boundedness, monotonicity or convexity) in fixed-domain asymptotics. We …

We address uncertainty quantification for Gaussian processes (GPs) under misspecified
priors, with an eye towards Bayesian Optimization (BO). GPs are widely used in BO because …

Gaussian process modeling is a standard tool for building emulators for computer
experiments, which are usually used to study deterministic functions, for example, a solution …

In this work, we propose a way to construct Gaussian processes indexed by
multidimensional distributions. More precisely, we tackle the problem of defining positive …

We consider a one-dimensional Gaussian process having exponential covariance function.
Under fixed-domain asymptotics, we prove the strong consistency and asymptotic normality …

This article provides an introduction to the asymptotic analysis of covariance parameter
estimation for Gaussian processes. Maximum likelihood estimation is considered. The aim of …