Adaptive Sampling Design for Spatio-Temporal Prediction
Fanshawe TR., Diggle PJ.
Environmental monitoring provides a typical setting that gives rise to spatio-temporal design problems. This chapter considers the model-based design, in which the optimal design problem requires two key features to be specified: (i) a statistical or mathematical model for the process under consideration; and, (ii) a criterion with respect to which the design is required to be optimized. After reviewing spatial and spatio-temporal adaptive designs it considers the performance of adaptive design-finding algorithms with respect to these for two different models for stochastic process S: the stationary Gaussian model; and a dynamic process convolution model. The chapter uses the second of these models to consider adaptive designs for the Upper Austria rainfall data. It concludes that adaptive designs should be constructed by a criterion that directly measures the extent to which the primary scientific goal of the analysis is being met, and should therefore be strongly context-dependent.