Hierarchical models for Large Geostatistical Datasets with Application

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

This proposal lays down a comprehensive framework for carrying out statistical inference on point-referenced high-dimensional spatial data available from a large number of locations. The focus of the proposal is methodological rather than purely theoretical or purely applied. Thus, statistical theory is used to develop mathematically formal but computationally feasible methods that can have a broad range of applications. Theoretical derivations and new results that will enhance current methods (including findings by the PI in prior NSF-funded research) will be explored, but always keeping in mind the practicing spatial analyst. The basic framework is to use a low-rank spatial process obtained by projecting the original process onto a lower-dimensional subspace. The PI intends to explore approximation properties of the low rank spatial process with regard to different metrics. The long-term goal of the PI is to develop a full suite of statistical methods that estimate spatial models in a wide variety of experiments in forestry, ecology and the broader environmental sciences. A recurrent underlying theme of the proposed methods that makes it different from existing methods is that the modeler does not need to sacrifice richness in modeling as a compromise for the large datasets. This resolves the statistical irony that large datasets are precisely where complex relationships can be detected effectively. Modern spatial technologies such as Geographical Information Systems (GIS) and Global Positioning Systems (GPS) routinely identify geographical coordinates with a simple hand-held device. Consequently, scientists and researchers in a variety of disciplines today have access to geocoded data as never before. With data becoming increasingly high-dimensional both in terms of number of observed locations and the number of observations per location, scientists are seeking to hypothesize complex relationships. These, in turn, yield rather complex hierarchical models that are computationally expensive even for moderately sized datasets. This team recognises a need for statistical modeling of large multivariate spatial data and proposes a model-based setup to tackle a wide variety of large geostatistical datasets. Although some of the more serious statistical modeling will require multi-processor capabilities, the emphasis on this project is on methodology implementable with moderately powerful computing tools. The proposed methodologies would, therefore, be accessible to a large number of researchers. The broader impact of the proposed methods is best assessed by connecting the outcome of this research with the widely recognized impact of GIS on human society. From identifying spatial disparities in health standards to more precise weather predictions, GIS technology is used today in almost every sphere of society and the proposed methods can have far reaching beneficial effects in environmental research that potentially touch unexpected corners of society.