Tapering for Prediction of Multivariate Spatial Processes

• Activity Number: 477
• Type: Invited
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Reinhard Furrer*+
• Companies: University of Zurich
• Keywords: large datasets ; sparse matrix ; asymptotics ; remote sensing

Abstract

Modeling large multivariate spatial datasets is notoriously difficult. Even if we assume - seemingly simple - Gaussian spatial fields, first and second moment models need to be specified. The second moment structure of multivariate Gaussian random fields can be characterized by a fully parameterized covariance matrix. We show that tapering the correct covariance matrix with an appropriate compactly supported positive definite function reduces the computational burden significantly and is asymptotically optimal under appropriate asymptotic setting. The effect of tapering is to create a sparse approximate linear system that can then be solved using sparse matrix algorithms.

We apply the approach to data from remotely sensed vegetation indices (VI). The model is used to attribute changes of VI to different factors such as changes in climatologies, large-scale human interventions, feedback mechanisms or natural effects, which were not captured by the climatologies.