Hierarchical modeling of nonlinear multivariate spatio-temporal dynamical systems in the presence of uncertainty
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Dynamic spatio-temporal models are statistical models that specify the joint distribution of a spatio-temporal process as the product of a series of conditional models whereby the current value of the process is conditioned on the process at the previous time point. Spatio-temporal dynamical models are often truer to the underlying scientific etiology of the process than their descriptive, covariance-based, counterpart, but are overparameterized even in simple linear settings (the curse of dimensionality). This problem is even worse in nonlinear settings. The use of mechanistic models to motivate the parameterization of a dynamical spatio-temporal model provides a way of reducing the dimensionality of the parameter space while still including important dynamics. However, in certain situations the numerical solutions to the mechanistic models are computationally expensive, and so using them within a Bayesian hierarchical model is not feasible. For these situations, one can use computer model emulators, computationally inexpensive statistical surrogates for the complex mechanistic model. In this dissertation, we provide several examples of using mechanistic models to motivate the parameterization of Bayesian hierarchical models for multivariate, nonlinear spatio-temporal models describing lower trophic level marine ecosystem dynamics. These examples include the use of a forest of one-dimensional computer model emulators to model a three-dimensional scientific process, emulator-assisted data assimilation, and the use of mechanistic models to motivate the parameterization of multivariate dynamical spatio-temporal models that exhibit quadratic nonlinearity.
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