Designs for spatial and spatio-temporal models

This thesis determines optimal experimental designs for geostatistical models, under various frequentist and Bayesian setups. For simple and ordinary kriging and cokriging, equispaced designs minimize some functions of the prediction error and are proved to be G-optimal and I-optimal. G-optimal designs for universal kriging models are found to be symmetric and concentrated near the boundaries. To address a more practical scenario, deterministic algorithms are proposed for finding retrospective optimal designs by the addition or deletion of points from an already existing design. The theory is illustrated by designing an optimal water monitoring network for an Indian river.