Bayes linear analysis for Bayesian optimal experimental design

In many areas of science, models are used to describe attributes of complex systems. These models are generally themselves highly complex functions of their inputs, and can be computationally expensive to evaluate. Often, these models have parameters which must be estimated using data from the real system. In this paper, we address the problem of using prior information supplied by the model, in conjunction with prior beliefs about its parameters, to design the collection of data such that it is optimal for decisions which must be made using posterior beliefs about the model parameters. Optimal design calculations do not generally have a closed form solution, so we propose a Bayes linear analysis to find an approximately optimal design. We motivate the approach by considering optimal specification of measurement locations for remote sensing of airborne species.