Bayesian perspective on inference for space-time processes

I begin with a very brief review of selected issues and approaches to space-time statistical analysis. I then transition through three basic motivations of the Bayesian perspective. The first of these involves clarification of the Bayesian interpretation of some common procedures (e.g., the Kalman filter). The second is the traditional Bayesian method of endowing model parameters with prior distributions and applying Bayes' Theorem. The third component of the discussion is the development of Bayesian models which actively rely on physical reasoning. To motivate these physical-statistical approaches, a brief review of stochastic modeling of climate and weather processes in presented. Selected examples are presented.