Modern perspectives on statistics for spatio-temporal data

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 dynamical 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. This problem is compounded when the spatio-temporal dynamical processes are nonlinear or multivariate. 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. Such models are best considered from a Bayesian perspective, with associated computational challenges. Spatio-temporal statistics remains an active and vibrant area of research. (C) 2014 Wiley Periodicals, Inc.