HIERARCHICAL BAYESIAN SPACE-TIME MODELS

Space-time data are ubiquitous in the environmental sciences. Often, a s is the case with atmospheric and oceanographic processes, these data contain many different scales of spatial and temporal variability. Su ch data are often non-stationary in space and time and may involve man y observation/prediction locations. These factors can limit the effect iveness of traditional spacetime statistical models and methods. In th is article, we propose the use of hierarchical space-time models to ac hieve more flexible models and methods for the analysis of environment al data distributed in space and time. The first stage of the hierarch ical model specifies a measurement-error process for the observational data in terms of some 'state' process. The second stage allows for si te-specific time series models for this state variable. This stage inc ludes large-scale (e.g. seasonal) variability plus a space-time dynami c process for the 'anomalies'. Much of our interest is with this anoma ly process. In the third stage, the parameters of these time series mo dels, which are distributed in space, are themselves given a joint dis tribution with spatial dependence (Markov random fields). The Bayesian formulation is completed in the last two stages by specifying priors on parameters. We implement the model in a Markov chain Monte Carlo fr amework and apply it to an atmospheric data set of monthly maximum tem perature.