<< Click to Display Table of Contents >> Navigation:  Decision-theoretic modeling > Solving decision models

In brief, solving decision-theoretic models amounts to computation of the expected utility of each of the possible decision alternatives (or strategies in case of multiple decision stages) and selecting the alternative or the strategy with the highest expected utility. The first algorithm for inference in influence diagrams was proposed by Olmsted (1983) and later refined by Shachter (1988). This algorithm reverses arcs and removes nodes in the network structure until the answer to the given probabilistic query can be read directly from the graph. Cooper (1988) proposed an algorithm for inference in influence diagrams that transforms an influence diagrams into a Bayesian network and finds the expected utilities of each of the decision alternatives by performing repeated inference in this network.

Decision-theoretic models can be also studied with respect to the value of information, i.e., the value of observing a variable (reducing its uncertainty to zero) before making a decision. Another set of questions that can be asked of a decision model involve sensitivity analysis, i.e., the impact of imprecision in the model's numerical parameters on the solution.

It is important to realize that the insight into a decision problem, including the qualitative structure of the problem, available decision alternatives, expected utility of choosing any of them, importance of various sources of uncertainty, the value of reducing this uncertainty, are by far more important than the actual recommendation.