Revising ranked probabilities: a Bayesian approach to incomplete knowledge

Incomplete knowledge refers to situations in which a decision maker can rank the probabilities of occurrence for events of interest, but cannot specify these probabilities exactly. In this paper a Monte Carlo approach is used to investigate how physicians can arrive at revised or posterior rankings of disease probability given only rank order information about both the patient's prior probabilities of disease and the conditional probabilities of specific clinical findings for each disease. Computer-generated estimates of the expected frequencies of the posterior rankings are presented for the cases of 2, 3, and 4 disease states. The application of probability revision under conditions of incomplete knowledge to therapeutic decision making is discussed.