Bayesian experimental design for model discrimination

Abstract

This thesis is concerned with the situation in which there are several competing linear models for describing the dependence of a response on a set of explanatory variables. The aim of the thesis is to produce methodology by which experimental designs may be selected that allow discrimination between the possible models and enable a model to be chosen that is as close as possible to the 'true' model. A Bayesian decision theoretic framework will be used for model selection and choosing an experimental design. The Bayesian approach allows prior information from previous experimentation to be used in the selection of a design and provides a means by which a model may be selected from a set of competing models. In this thesis, the Penalised Model Discrepancy (PMD) criterion for selecting an experimental design is introduced. The criterion is first applied to the situation of screening experiments, where little prior information is available. Good designs under the PMD criterion are found for several model spaces which may be used for screening experiments. The MD, HD and F criteria are existing Bayesian criteria from the literature for selecting experimental designs for model discrimination; a comparison between these and the PMD is made via examples and a simulation study. The sensitivity of the PMD criterion to the choice of hyperparameters of the prior distribution is also investigated. The PMD criterion is then applied to the selection of follow-up runs after an initial experiment, using examples from the literature. For one example, a comparison is again made to the F, MD and HD criteria. For another example, the effect of the choice of initial design on the follow-up runs selected is investigated. Follow-up runs for a tribology experiment carried out in the School of Engineering Sciences at the University of Southampton were chosen using the PMD criterion. The results and analysis of this experiment are presented, as well as details of how the follow-up runs were chosen. In some situations, especially when interaction terms are considered, the space of possible models can become very large. As a consequence, evaluating the PMD objective function can become very computationally expensive. Methods for reducing the computational burden of evaluating the PMD objective function are investigated, and used to select good designs for large model spaces. Methodology for improving the accuracy of the evaluation of the HD and MD objective functions for large model spaces is also given.

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