A Bayesian method for classification and discrimination

We discuss Bayesian analyses of traditional normal‐mixture models for classification and discrimination. The development involves application of an iterative resampling approach to Monte Carlo inference, commonly called Gibbs sampling, and demonstrates routine application. We stress the benefits of exact analyses over traditional classification and discrimination techniques, including the ease with which such analyses may be performed in a quite general setting, with possibly several normal‐mixture components having different covariance matrices, the computation of exact posterior classification probabilities for observed data and for future cases to be classified, and posterior distributions for these probabilities that allow for assessment of second‐level uncertainties in classification.