The Spatial Random Effects Model and Its Role in Spatial and Spatio-Temporal Statistics

• Activity Number: 317
• Type: Invited
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Statistical and Applied Mathematical Sciences Institute
• Author(s): Noel A. Cressie*+
• Companies: The Ohio State University
• Keywords: Fixed Rank Kriging ; Fixed Rank Filtering ; STRE model ; VAR process ; remote sensing

Abstract

The spatial random effects (SRE) model specifies that small-scale spatial variation has a smooth component that is an inner product of known spatial basis functions (fixed in number) and random coefficients. Importantly, the coefficients are generally correlated, and their fixed-rank covariance matrix has to be inferred, along with the hidden spatial process. There is also a non-smooth, fine-scale variation component that is analogous to the nugget effect in geostatistics. When time is included, an evolutionary component can be incorporated into the SRE model, resulting in a spatio-temporal random effects (STRE) model. These models allow fast optimal prediction (kriging, filtering, smoothing, forecasting) of the hidden process; we illustrate their effectiveness on a large remote-sensing dataset.