Analysis of imprecise decision models

This work introduces the Optimizing Multivariate Sensitivity Analysis method for examining decision models whose probabilities and utilities are not precisely known and which offer the decision maker many alternate plans of action. It is an approach to many-way sensitivity analysis that enables powerful decision analysis without all the numbers. Each decision model input to the method is a Bayesian influence diagram whose conditional probabilities and utilities for outcomes are specified by the user as polynomial functions of bounded symbolic variables. The expected utility of each allowed decision strategy is likewise a polynomial function. Polynomial constraints supplied by the user limit the possible values of the variables to a finite feasible set; these constraints can concern complete expected utilities as well as individual variables.; From the constraints in the decision model the method makes mathematical inferences about the differences between the expected utilities of the possible decision strategies. The method determines which strategies have symbolic expected utilities that are similar enough to be clustered into groups; which strategies have symbolic expected utilities that are significantly different so that they should be considered competitors; and what is the largest possible increase or decrease in expected utility that each strategy offers the decision maker over its significantly different competitors. Each basic comparison between symbolic expected utilities uses nonlinear optimization to compute the maximum difference between one symbolic expected utility and a set of others. The user can trade off explicitly the time spent solving each optimization problem against the precision of its interval result.; Comparison of their symbolic expected utilities allows the method to assign each possible decision strategy to a recommendation category that indicates whether that strategy offers the decision maker at least a given increase in expected utility over its competitors for all feasible values of the symbolic variables; for some feasible values; or for none. The method computes explicitly the set of variable values for which each decision strategy belongs to each recommendation category as a system of polynomial inequalities; the method summarizes these sets of values to make them more comprehensible to the user.