Science‐based parameterizations for dynamical spatiotemporal models

Abstract

AbstractMost real‐world processes change with time, and the manner in which they change through time often depends on their location in space. Statistical models for such spatiotemporal processes fall into one of two broad categories: descriptive spatiotemporal models and dynamic spatiotemporal models. Descriptive spatiotemporal models are based on the joint specification of first‐order and second‐order moments (i.e., mean and covariance, respectively). Dynamical spatiotemporal models specify the joint distribution through a series of conditional probability models that model the current process conditioned on the process at the previous time point(s). A common pitfall with dynamic spatiotemporal models is the so‐called curse of dimensionality, where the number of parameters in the model can increase by orders of magnitude as the number of spatial locations increase. As a result, dynamic spatiotemporal models are over‐parameterized in most situations. However, dynamical models being truer to the etiology of the scientific process than descriptive models, it is typically easier to use a priori knowledge of the process dynamics to motivate statistical parameterization, reducing the dimensionality of the parameter space and overcoming the curse of dimensionality. We provide an overview of several methods of using a priori scientific knowledge to motivate the parameterization of a dynamic spatiotemporal model, including mechanistically motivated statistical modeling, computer models, and computer model emulation. WIREs Comput Stat 2012, 4:554–560. doi: 10.1002/wics.1227This article is categorized under: Applications of Computational Statistics > Computational Physics and Computational Geophysics