Moment methods for decision analysis

Decision models involving continuous probability distributions almost always require some form of approximation. The usual approach to evaluating these kinds of models is to construct a discrete approximation for each continuous distribution and compute value lotteries and certain equivalents using these discrete approximations. Although decision analysts are quite comfortable with this approach, there has been relatively little consideration of how these discrete approximations affect the results of the analysis. In the first part of this paper, three common methods of constructing discrete approximations are reviewed and their performance in a simple example compared. The results of the example suggest a different approach that offers potential improvements in accuracy and efficiency over the usual approach. The basic idea is that given discrete approximations that accurately represent the moments of assessed ‘input’ distributions, the moments of the ‘output’ distribution or value lotteries may be easily and accurately computed. These moments than summarize what is known about the value lottery and certain equivalent, and provide the basis for computing approximate value lotteries and certain equivalents. This paper discusses the methods supporting this moment approach and evaluates their performance in the context of the example.