DMS-9704934 BAYESIAN PREPOSTERIOR SIMULATION Peter Mueller Duke Univiversity We expand the ambit of methods and programs developed for posterior simulation to expected utility maximization. The main tool is simulation in an augmented probability model. For expected utility maximization the original probability model on parameters and data is augmented to an artificial probability model on decision variables, model parameters and data. The augmented probability model is chosen such that the marginal distribution on the decision parameters is proportional to expected utility, and thus the mode of this marginal distribution corresponds to the optimal design. We develop novel Markov chain Monte Carlo techniques amenable to simulation from this auxiliary probability model and investigate algorithms for mode estimation in a possibly high dimensional distribution based on a simulated Monte Carlo sample. The Bayesian framework provides coherent support for decision making through an iterative cycle of problem structuring, uncertainty modeling, preference modeling, expected utility maximization and sensitivity analysis. Recent computational developments in statistics (the Gibbs sampler, stochastic substitution sampling) have significantly widened the range of models used for uncertainty modeling. We study the use of these methods in other parts of the decision making cycle, in particular expected utility maximization and preference modeling. The investigated methods are simulation based and highly computational intensive and require state of the art computer simulation, relating to the Federal Strategic Area of high performance computing. The impact of the research is to widen the class of problems where expected utility maximization, i.e., formal solution of decision problems, is practically feasible in a way similar to how Gibbs sampling and related techniques have made complex probability models accessible for uncertainty model ing.
