Computing the confidence in a medical decision obtained from an influence diagram

Willard and Critchfield [31] assume that uncertainty exists as to the values of the probabilities which need to be assessed for a decision tree, and that the uncertainty in each probability is represented by a continuous probability distribution. If the probability itself is thought of as an objective limit of a relative frequency, then this distribution represents our degree of belief concerning the 'true' value of the probability. Willard and Critchfield [31] obtain a method which is able to determine the probability that the recommended decision is the one which would be obtained using the objective relative frequencies. This probability is called the confidence in the decision. These same results are obtained here for the case where a problem is represented in an influence diagram. There is also a discussion concerning the importance of the confidence measure in the evaluation of the quality of a medical expert system and in the instance of a single decision.