This week's Joint CAM/DSS Statistics Seminar Speaker will be Christopher Wikle from the University of Missouri.
Title: An Overview of Mechanistically-Motivated Dynamic Spatio-Temporal Statistical Models
Abstract: 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. Correspondingly, in recent years there has been a significant amount of research on new statistical methodology for such models. Although descriptive models that approach the problem from the second-order (covariance) perspective are important, and innovative work is being done in this regard, many real-world processes are dynamic, and it can be more efficient in some cases to characterize the associated spatio-temporal dependence by the use of dynamic models. The chief challenge with the specification of such dynamical models has been related to the curse of dimensionality and the specification of realistic dependence. Even in fairly simple linear, first-order Markovian settings with Gaussian errors, 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. In addition, this framework has allowed for the specification of science-based parameterizations (and associated prior distributions) in which classes of mechanistic dynamical models (e.g., partial differential equations (PDEs), integro-difference equations (IDEs), and agent-based models (ABMs)) are used to motivate specific parameterizations. Most of the focus for the application of such models in statistics has been in the linear case. The problems mentioned above with linear dynamic models are compounded in the case of nonlinear models, yet these are the processes that govern environmental science. In this sense, the need for coherent and sensible model parameterizations is not only helpful, it is essential. Here, we present on overview of recent research for accommodating realistic “science-based” linear and nonlinear motivating structure in spatio-temporal dynamical models as well as some discussion of dimension reduction, model selection and the use of emulators or model surrogates for prior elicitation. Examples will be presented from atmospheric science, oceanography, and ecology.