Gems from a Math Collaboration: Hidden Statistical Quantities of Great Utility in Mathematical Solutions
Mevin Hooten, Department of Fish, Wildlife, & Conservation Biology, Colorado State University
Monday, September 13, 2010
4:00 p.m., room 223, Weber Bldg
An alternative, and slightly more boring, title for this talk might
be: "Change of Support in Inverse Implementations of Statistical Differential Equation Models." Statistical models using partial differential equations (PDEs) to describe dynamically evolving natural systems are appearing in the scientific literature with some regularity in recent years. Often such studies seek to characterize the dynamics of temporal or spatio-temporal phenomena such as invasive species, consumer-resource interactions, community evolution, and resource selection. Specifically, in ecological settings, data are often available at varying spatial and temporal scales. Additionally, the necessary numerical integration of a PDE may be computationally infeasible over the spatial support of interest. I will present an approach to reconcile changes of support in statistical implementations of PDE models and demonstrate its utility through simulation.