Bayesian Discrimination between Two Multivariate Normal Populations with Equal Covariance Matrices
Abstract Here Bayesian and classical estimates of P, the probability that a new observation belongs to one of two multivariate normal populations with equal covariance matrices, are compared. In particular, the regions of location of a new observation for which the estimates differ are shown. The Bayesian and classical allocation rule contours are given and their differences highlighted. The posterior moments of L, the log-density ratio for a new observation, are given, and the distribution of L is approximated using Johnson curves. The posterior distribution and interval for P are obtained by transformation. An example is given that demonstrates their use.