Statistical diagnosis based on conditional independence does not require it.
A version of Bayes' Formula (BF) obtained by treating symptom variables as conditionally independent (CI) given a patient's disease enjoys widespread popularity in computer-aided probabilistic diagnosis and other areas of statistical pattern recognition. The resulting formula (BFCI) does not, however, require the CI assumption, the latter being sufficient but not necessary for the validity of BFCI and for the consistency of the estimation scheme associated with BFCI. By drawing attention to this fact we hope to counter the often-raised objection that, symptoms being mutually dependent in practice, BFCI must necessarily produce wrong results. A "Relaxed Model", sufficient and necessary for BFCI to be valid, is worked out, and the conditions under which it is indeed less restrictive than the CI model are examined. While CI is a submodel of the Relaxed Model, the latter in turn is a submodel of the popular logistic discrimination model, i.e. the log-linear model with no second or higher order interactions involving the class (disease) variable.
D001499:Bayes Theorem; D003936:Diagnosis, Computer-Assisted; D006801:Humans; D008954:Models, Biological; D013223:Statistics as Topic