Entropy methods for joint distributions in decision analysis

A fundamental step in decision analysis is the elicitation of the decision maker's information about the uncertainties of the decision situation in the form of a joint probability distribution. This paper presents a method based on the maximum entropy principle to obtain a joint probability distribution using lower order joint probability assessments. The approach reduces the number of assessments significantly and also reduces the number of conditioning variables in these assessments. We discuss the order of the approximation provided by the maximum entropy distribution with each lower order assessment using a Monte Carlo simulation and discuss the implications of using the maximum entropy distribution in Bayesian inference. We present an application to a practical decision situation faced by a semiconductor testing company in the Silicon Valley.