A comfort measure for diagnostic problem solving

In order to apply Bayes' theorem for diagnostic problem solving when multiple disorders can occur simultaneously, several previous proposals have suggested using the ratio of posterior probabilities to rank diagnostic hypotheses. Approaches using such relative likelihoods lose the measure of absolute strengths of hypotheses, and thus are incapable of evaluating the “quality” of a problem solution. In this paper, we propose to impose a quantity called a “comfort measure” on the solution: a solution of a diagnostic problem is a minimal-size set of hypotheses such that the sum of their posterior probabilities exceeds a given comfort measure. Based on a probabilistic causal model developed previously, a problem-solving strategy is presented which does not require the manifestation independence assumption required with direct Bayesian classification, and which is applicable to multimembership classification problems. This strategy selectively generates diagnostic hypotheses and calculates both their relative likelihood and the lower and upper bounds of their posterior probabilities. These bounds are successively refined as more hypotheses are generated. Using these bounds, not the real posterior probabilities, the problem-solving strategy identifies a solution satisfying the given comfort measure, usually after only a small portion of all possible hypotheses have been generated.