Optimal design of experiments for multiple objectives

Abstract

The focus of this work is on developing optimality criteria corresponding to multiple inference objectives and combining them in compound criteria allowing for finding compromises between different components, especially in the cases of relatively small experiments.

In the framework of response surface factorial experiments we take into account the assumption of a potential model misspecification that is expressed in the form of extra polynomial terms that cannot be estimated. Along with obtaining quality estimates of the fitted model parameters, the contamination arising from the model disturbance is desired to be minimised. In addition, in the case of model uncertainty, the model-independent approach of making inference based on 'pure error' is to be incorporated.

We first present Generalised DP and LP criteria, the components of which correspond to maximising the precision of the fitted model estimates, minimising the joint effect of potentially missed terms and minimising the prediction bias; we also adapt the criteria for use in blocked experiments.

In Chapter 5 we develop the Mean Square Error based criteria which, instead of the prediction bias component, include the component minimising the bias of the fitted model parameters that might occur due to the model misspecification. We also provide an alternative way of estimating its value for cases where the originally suggested simulations would be too computationally expensive.

An example of a real-life blocked experiment is studied, and we present a set of optimal designs that satisfied the aims of the experimenters and the restrictions of the experimental setup. Finally, we explore the framework of multistratum experiments; together with adaptation of the MSE-based criteria we provide a flexible design construction and analysis scheme.

All of the criteria and experimental settings are accompanied by illustrative examples in order to explore the possible relationship patterns between the criterion components and optimal designs' characteristics, and produce some general practical recommendations.

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