  The generation of decision-theoretic Bayesian optimal designs is complicated
by the significant computational challenge of minimising an analytically
intractable expected loss function over a, potentially, high-dimensional design
space. A new general approach for approximately finding Bayesian optimal
designs is proposed which uses computationally efficient normal-based
approximations to posterior summaries to aid in approximating the expected
loss. This new approach is demonstrated on illustrative, yet challenging,
examples including hierarchical models for blocked experiments, and
experimental aims of parameter estimation and model discrimination. Where
possible, the results of the proposed methodology are compared, both in terms
of performance and computing time, to results from using computationally more
expensive, but potentially more accurate, Monte Carlo approximations. Moreover
the methodology is also applied to problems where the use of Monte Carlo
approximations is computationally infeasible.
