Reparametrized Dynamic Space-Time Models and Spatial Model Selection

Abstract

Researchers in diverse areas such as environmental and health sciences are increasingly facing working with space-time data. Often the dimension of space-time data sets can be very large and moreover, space-time processes are often complicated in that the dependence structure across space and time is non-trivial, often non-separable and non-stationary in space and/or time. Hence, space-time modeling is a challenging task and in particular parameter estimation can be problematic due to the high dimensionality. We propose a reparametrization approach to fit dynamic space-time models with an unstructured covariance function. Our modeling contribution is to present unconstrained reparametrization for a covariance matrix in dynamic space-time models. Using this unconstrained reparametrization method, we are able to implement the modeling of a high dimensional covariance matrix that automatically maintains the positive definiteness constraint. We illustrate the use of this reparametrization method by applying our model to a set of atmospheric nitrate concentration data. We also consider the problem of model selection for spatial data. The issue of model selection in spatial models has rarely been addressed in the literature, though it is very important. To address this problem, we consider selection criteria such as the Akaike Information Criterion (AIC), Corrected Akaike Information Criterion (AICc) and Bayesian Information Criterion (BIC). The performance of these selection criteria are examined using Monte Carlo simulations. In particular, the ability of these criteria to select the correct model is evaluated.