Computational Tools and Theory of Multivariate Spatial Models

University Of Alaska Fairbanks Campus, Fairbanks AK

Investigators

Abstract

ABSTRACT: PI: Barry, Ronald Award ID: DMS - 0505748 Institution: University of Alaska, Fairbanks Program: STATISTICS Title: Computational Tools and Theory of Multivariate Spatial Models A research group is developing software and theory for hierarchical and multivariable spatial models. As such models involve unobserved, spatially-correlated variables, modeling these processes will require the development of flexible variogram models that will conform to a wide variety of random processes. These are approached through process-convolution models. The investigators are considering a variety of special cases, including cokriging, generalized (hierarchical) spatial models, spatial compositional data and Poisson process models. They are exploring several computational approaches, including generalized estimating equations, MCMC and expectation-maximization. They are also identifying spectral, sparse matrix and other approaches to reduce the computational burden of the analysis. The software they are developing will allow researchers in many fields to analyze multivariable spatial models. Many research projects produce data that is associated with locations on a map. For instance, an epidemiological study might consist of air pollution measurements taken at several fixed locations, along with the locations of households where an occupant was hospitalized with a pollution-related ailment. In this case the air pollution measurement is a geostatistical variable (it could, in theory, be measured at any location on the map) and the households are a point process. Other examples might include multiple geostatistical variables: for instance, soil nitrogen and soil moisture measured at multiple locations in an ecological study. Multiple geostatistical variables and point process variables are special cases of what are called multivariate or hierarchical spatial models. The investigators are developing the general theory of these models, and are producing software that can efficiently analyze these models. Dissemination of the software will allow the development of more sophisticated models for mapped data in many applied fields.