Simulation-based optimal design

We review simulation based methods in optimal design. Expected utility maximization, i.e., optimal design, is concerned with maximizing an integral expression representing expected utility with respect to some design parameter. Except in special cases neither the maximization nor the integration can be solved analytically and approximations and/or simulation based methods are needed. On one hand the integration problem is easier to solve than the integration appearing in posterior inference problems. This is because the expectation is with respect to the joint distribution of parameters and data, which typically allows efficient random variate generation. On the other hand, the problem is difficult because the integration is embedded in the maximization and has to possibly be evaluated many times for different design parameters. We discuss four related strategies: prior simulation; smoothing of Monte Carlo simulations; Markov chain Monte Carlo (MCMC) simulation in an augmented probability model; a simulated annealing type approach.