Peter Müller, Ph.D.
Professor of Biostatistics
The University of Texas M. D. Anderson Cancer Center
Houston, Texas U.S.A.

Many Bayesian design problems require the solution of analytically intractable integration and optimization problems. We will discuss three related approaches. The first is optimal design by curve fitting of Monte Carlo samples. Second, we will propose an approach to exploring expected utility surfaces by pre-posterior simulation.  By artificially augmenting the usual statistical model, p (theta, y) for a parameter, theta, and data, y, to a probability model h (d, theta, y) that includes the decision vector, d, the optimal design problem is recast as a problem of simulating from this augmented distribution. We will also discuss a generalization of this augmented probability model that is similar to the power transformation in simulated annealing.  Another practically important but notoriously difficult class of problems is sequential decision-making. We will discuss some recent simulation-based methods for approximate solutions to sequential design problems.  We will begin with a general review of simulation-based methods in Bayesian inference, including designs based on inference loss, expected utility optimization, and stylized Bayesian design. Biostatistical applications will include adaptive dose allocation in phase I/II trials, dose individualization, and optimal sampling for longitudinal data.