A diagnostic method that uses causal knowledge and linear programming in the application of Bayes' formula

Bayes' formula has been applied extensively in computer-based medical diagnostic systems. One assumption that is often made in the application of the formula is that the findings in a case are conditionally independent. This assumption is often invalid and leads to inaccurate posterior probability assignments to the diagnostic hypotheses. This paper discusses a method for using causal knowledge to structure findings according to their probabilistic dependencies. An inference procedure is discussed which propagates probabilities within a network of causally related findings in order to calculate posterior probabilities of diagnostic hypotheses. A linear programming technique is described that bounds the values of the propagated probabilities subject to known probabilistic constraints.