Some covariance models based on normal scale mixtures

摘要

Modelling spatio-temporal processes has become an important issue in currentresearch. Since Gaussian processes are essentially determined by their secondorder structure, broad classes of covariance functions are of interest. Here, anew class is described that merges and generalizes various models presented inthe literature, in particular models in Gneiting (J. Amer. Statist. Assoc. 97(2002) 590--600) and Stein (Nonstationary spatial covariance functions (2005)Univ. Chicago). Furthermore, new models and a multivariate extension areintroduced.