Abstract

Bayesian forecasting in time and interpolation in space is a challenging task due to the complex nature of spatio-temporal dependencies that need to be modeled for better understanding and description of the underlying processes. The problem exacerbates further when the geographical study region, such as the one in the Eastern United States considered in this chapter, is vast and the training data set for forecasting, and modelling, is rich in both space and time. This chapter develops forecasting methods for three recently This is a Book Title Name of the Author/Editor °c XXXX John Wiley & Sons, Ltd 2 Bayesian Forecasting Using Spatio-temporal Models with Applications to Ozone Concentration Levels in the Eastern United States proposed hierarchical Bayesian models for spatio-temporal data sets. The chapter also develops Markov chain Monte Carlo based computation methods for estimating a number of relevant forecast calibration measures that facilitates rigorous comparisons of the Bayesian forecasting methods. The methods are illustrated with a test data set on daily maximum eight hour average ozone concentration levels observed over a study region in the Eastern United States. Forecast validations, using several moving windows, find a model developed using an approximate Gaussian predictive process to be the best and it is the only viable method for large data sets when computing speed is also taken into account. The methods are implemented in a recently developed software package, spTimer, which is a publicly available contributed R package that has wider applicability