Adaptive design of experiments for spatio-temporal models

Recall the last weather forecast map you saw on television. The map shows how aspects of the weather vary both in space and time. It is important to be able to predict and understand, such response variables that describe the weather, for example the amount of rainfall, sunshine and air pollution. There are many other important areas that affect our day-to-day lives in which spatio-temporal data are used to detect recognisable and meaningful patterns as well as to make predictions. Examples include the study of house prices, ecology, geology and many areas of medicine such as brain imaging.In order to obtain high accuracy in predictions of a response variable and to gain scientific insights into how the response is varying with space and time, mathematical models that are statistical in nature are employed which explicitly include the underlying uncertainty in the data. This research is concerned with such models and how to plan experiments to gather data in the most effective and efficient way. Designs are considered which are adaptive in the sense that data gathered at previous time points and locations are used to inform the choice of locations where observations are to be made at the next time point. A number of requirements on such a design are investigated, such as high accuracy of predictions and sound interpretation of the model that will be fitted to the data. These requirements are translated into criteria, including multi-objective criteria, for selecting the locations for the next time point using a Bayesian framework. Algorithms for finding the design are developed and implemented.