Decision analysis by augmented probability simulation

We provide a generic Monte Carlo method to find the alternative of maximum expected utility in a decision analysis. We define an artificial distribution on the product space of alternatives and states, and show that the optimal alternative is the mode of the implied marginal distribution on the alternatives. After drawing a sample from the artificial distribution, we may use exploratory data analysis tools to approximately identify the optimal alternative. We illustrate our method for some important types of influence diagrams.