Department of Statistics
University of Missouri
“Interaction-Based Parameterizations for Nonlinear Dynamic Spatio-Temporal Statistical Models”
Spatio-temporal statistical models are increasingly being used across a wide variety of scientific disciplines to describe and predict spatially explicit processes that evolve over time. The challenge with the specification of such dynamical models has been related to the curse of dimensionality and the specification of realistic dependence structures. Hierarchical models have proven invaluable in their ability to deal to some extent with these issues by building dependency among parameters and through mechanistic-based parameterizations in physical and “spectral” space. The problems with linear dynamic models are compounded in the case of nonlinear models, yet these are the processes that govern environmental and physical science. Here, we present some recent results for parameterizing realistic nonlinear structure in hierarchical spatio-temporal models from both a “top down” and “bottom-up” (agent-based) perspective. The notion of interaction is crucial to both of these paradigms and provides a linkage between the approaches. These methodologies will be illustrated with various environmental and ecological applications.