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The generation of decision-theoretic Bayesian optimal designs is complicatedby the significant computational challenge of minimising an analyticallyintractable expected loss function over a, potentially, high-dimensional designspace. A new general approach for approximately finding Bayesian optimaldesigns is proposed which uses computationally efficient normal-basedapproximations to posterior summaries to aid in approximating the expectedloss. This new approach is demonstrated on illustrative, yet challenging,examples including hierarchical models for blocked experiments, andexperimental aims of parameter estimation and model discrimination. Wherepossible, the results of the proposed methodology are compared, both in termsof performance and computing time, to results from using computationally moreexpensive, but potentially more accurate, Monte Carlo approximations. Moreoverthe methodology is also applied to problems where the use of Monte Carloapproximations is computationally infeasible.

An approach for finding fully Bayesian optimal designs using normal-based approximations to loss functions