DEVI Seminar- Agnès Lagnoux (IMT Toulouse)


10h30 - 11h30


ENAC, Building Bréguet, Amphi Boucher
7 avenue Edouard Belin, Toulouse

Event Type

On the Estimation of Covariance Parameters of Gaussian Processes

Because of their simplicity and flexibility, which make it possible to encapsulate a large class of models, Gaussian processes have become very popular in recent years, and are widely used in spatial statistics to interpolate observations and propose meta-models (for example, in kriging). Gaussian processes are characterized by their mean and covariance functions. For statistical purposes, it is a question of estimating the covariance function. In this talk, we assume that the covariance function belongs to a parametric family, and so the estimation of k is reduced to that of its parameters. Classically, estimates are found using maximum likelihood estimation (MLE), a method that has good properties and has been widely studied in the literature. However, the estimates suffer from a computational cost that can be prohibitive when the size of the sample becomes large. In some cases, MLE may also diverge. It seems appropriate then to propose alternative methods of estimation, and so we introduce composite likelihood estimators, cross-validation estimators, and variational estimators, in specific contexts for which we determine the asymptotic behavior.