  This paper derives a formula for computing the conditional probability of a
set of candidates, where a candidate is a set of disorders that explain a given
set of positive findings. Such candidate sets are produced by a recent method
for multidisorder diagnosis called symptom clustering. A symptom clustering
represents a set of candidates compactly as a cartesian product of differential
diagnoses. By evaluating the probability of a candidate set, then, a large set
of candidates can be validated or pruned simultaneously. The probability of a
candidate set is then specialized to obtain the probability of a single
candidate. Unlike earlier results, the equation derived here allows the
specification of positive, negative, and unknown symptoms and does not make
assumptions about disorders not in the candidate.
