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The Bayesian decision-theoretic approach to design of experiments involvesspecifying a design (values of all controllable variables) to maximise theexpected utility function (expectation with respect to the distribution ofresponses and parameters). For most common utility functions, the expectedutility is rarely available in closed form and requires a computationallyexpensive approximation which then needs to be maximised over the space of allpossible designs. This hinders practical use of the Bayesian approach to findexperimental designs. However, recently, a new utility called Fisherinformation gain has been proposed. The resulting expected Fisher informationgain reduces to the prior expectation of the trace of the Fisher informationmatrix. Since the Fisher information is often available in closed form, thissignificantly simplifies approximation and subsequent identification of optimaldesigns. In this paper, it is shown that for exponential family models,maximising the expected Fisher information gain is equivalent to maximising analternative objective function over a reduced-dimension space, simplifying evenfurther the identification of optimal designs. However, if this function doesnot have enough global maxima, then designs that maximise the expected Fisherinformation gain lead to non-identifiablility.

Properties of using Fisher information gain for Bayesian design of experiments