Covariate-Based Parameterization of Time-Varying Spatial Covariances

• Activity Number: 184
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Daniel W. Gladish*+ and Christopher K. Wikle and Scott H. Holan
• Companies: University of Missouri and University of Missouri and University of Missouri
• Keywords: Bayesian Hierarchical modeling ; Covariance parameterization ; Spatio-temporal process ; Exponential spectral representation ; Environmental modeling

Abstract

Environmental spatio-temporal modeling is commonly approached from a dynamic first-order (mean) perspective due to the typical assumption that the true underlying process is best thought of as spatial process evolving through time. Thus, these processes are dynamic in time with a spatial error structure. This spatial covariance structure may be affected by time varying factors exogenous to the mean structure of the model. As such, our modeling approach is to incorporate these factors within the parameterization of a time-varying spatial covariance structure. A concern resides in parameterizing these exogenous covariate factors in a manner such that the covariance structure remains valid. The exponential spectral representation developed by Bloomfield (1973) provides a parsimonious framework for such parameterization, allowing for no direct restrictions on the covariate parameters. Under this time-varying error covariance framework, we develop a spatio-temporal model within the Bayesian hierarchical state-space paradigm. We illustrate this methodology using examples from the lower-trophic ocean ecosystem.