A seminar in the Statistics Department

Abstract

With accessibility to geo-coded locations where scientific data are collected through Geographical Information Systems (GIS), investigators in diverse fields such as environmental sciences, ecology and forestry and public health are increasingly turning to spatial process models for modeling associations and relationships over space. Over the last decade hierarchical models implemented through Markov Chain Monte Carlo (MCMC) methods have become especially popular for spatial modeling, given their flexibility and power to estimate models (and hence address scientific hypothesis) that would be infeasible otherwise. However, estimation in hierarchical spatial models often involves expensive matrix decompositions whose computational complexity increases exponentially with the number of spatial locations, rendering them infeasible for large spatial data sets. Recently much attention has been devoted to this problem. In this talk we primarily focus upon the use of a predictive process derived from the original spatial process that projects process realizations to a lower-dimensional subspace thereby reducing the computational burden.  This approach can be looked upon as a process-based approach to reduced-rank methods for "kriging" but offers additional complexities. We discuss attractive theoretical properties of this predictive process as well as its greater modeling flexibility compared to existing methods. In particular, we show how the predictive process seamlessly adapts to settings with non-stationary processes, with richer and more complex space-varying regression models and with multivariate spatial models. We also discuss some pitfalls of this and other reduced-rank methods and offer remedies. A computationally feasible template that encompasses these diverse settings will be presented and illustrated. Author(s):  Banerjee Sudipto; Finley Andrew O.; Waldmann Patrick; Ericsson Tore.