Introducing Covariates in the Covariance Structure of Spatial and Spatio-Temporal Processes

• Activity Number: 322
• Type: Invited
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Alexandra M. Schmidt*+ and Peter Guttorp and Joaquim Henriques Neto and Anthony O'Hagan
• Companies: Federal University of Rio de Janeiro and University of Washington and Federal University of Rio de Janeiro and University of Sheffield
• Keywords: Anisotropy ; Convolution ; Manifold ; Projection

Abstract

In the analysis of most spatio-temporal processes underlying environmental studies there is little reason to expect spatial covariance structures to be stationary over the spatial scales of interest. This is because there may be local influences in the correlation structure of the spatial random process. Many alternatives to the usual stationary models have been proposed in the last decade, most of them based on highly stochastic systems. We discuss models for spatial covariance structures which relax the assumption of stationarity while keeping relative model simplicity. This is done by accounting for covariate information in the covariance structure of the spatial process. In particular, we discuss the inclusion of covariate information in the latent space approach of Sampson and Guttorp (1992) and Schmidt and O'Hagan (2003), and the convolution approach of Higdon (1998). We also developed applets to visualize better the proposed nonstationary covariance structures. This is joint work with Peter Guttorp, Joaquim H. Viana Neto, and Tony O'Hagan.