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Résumé 210 :

Statistical Methods for Nonlinear Dynamic Spatio-Temporal Models
Wikle, Christopher
University of Missouri

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. Although descriptive models that approach this problem from the second-order (covariance) perspective are important, many real-world processes are dynamic, and it can be more efficient in such cases to characterize the associated spatio-temporal dependence by the use of dynamic models. The challenge with the specification of such dynamical models has been related to the curse of dimensionality and the specification of realistic dependence structures. Even in fairly simple linear/Gaussian settings, spatio-temporal statistical models are often over parameterized. Hierarchical models have proven invaluable in their ability to deal to some extent with this issue by allowing dependency among groups of parameters and science-based parameterizations. The problems mentioned above 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 accommodating realistic nonlinear structure in hierarchical spatio-temporal models from multiple perspectives. Each of these perspectives represents a combination of scientific (mechanistic) knowledge, stochastic representations of uncertainty and dependence, and observations in a conditional framework. In particular, we consider (1) state-space representations using general quadratic nonlinearity structure, (2) stochastic cellular automata or "agent based" respresentations, and (3) first-order statistical emulators. Connections between these various methodologies will be presented and they will be illustrated with and motivated by various environmental applications from the geophysical and ecological sciences.