Non-linear process specifications in hierarchical spatio-temporal models

Document Type

Presentation Abstract

Presentation Date

2-21-2006

Abstract

Natural systems exhibiting complex and highly non-linear behavior can often be characterized by scientifically-based deterministic models. However, such models are only approximations to the real process of interest and contain uncertainties in parameters and representativeness. Thus, statistical inference (i.e., parameter estimation and process prediction) for such natural processes can be achieved through the hierarchical incorporation of conventional deterministic spatio-temporal models (e.g., differential and integral equation models). For example, when discretized for implementation in a computational setting, many such models suggest a first order Markovian specification (termed "matrix models" in the ecological literature). Parameterizations motivated by partial differential equations and integro-difference models are effective but can be awkward in non-Gaussian settings. More intuitive, and thus, more accessible specifications are possible by parameterizing the process model directly based on scientifically meaningful dynamical components. When considered in this context, such specifications imply a very general class of models capable of accommodating many different types of spatio-temporal processes. The utility of these hierarchical "matrix" models in an ecological setting is illustrated with an application focusing on characterizing the spread of invasive species in the presence of sampling uncertainty.

Additional Details

Tuesday, 21 February 2006
4:10 p.m. in Math 109

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