The effect of assuming independence in applying Bayes' theorem to risk estimation and classification in diagnosis.

The effect of assuming independence in the use of Bayes' Theorem for classification and estimation of risk is examined. Analytic results are provided for two specific multivariate normal models and for a model involving binary variables. Monte Carlo results are presented for the former. In these specific cases and an example from medical research, the (false) independence assumption results in classification error rates comparable or better than rates obtained by using the correct model. For a number of covariance structures selected, the a posteriori distribution becomes more U-shaped as the number of variables increases, thus biasing the estimate of risk toward zero or one.