Bayesian discrimination using multiple observations

Abstract

The multiple observations model is appropriate when multiple p-variate observations are available on each individual to be classified. The classical(probability density ratio)approach to this problem has been studied by Gupta and Logan(1990). This paper concerns Bayesian predictive discrimination using a diffuse prior for the mean vector and two dispersion matrices for each of two populations. Training samples are used to classify an unknown observation into one of the two populations. This extends the work of Geisser(1964)to a model that includes the earlier work as a special case. Simulation is used to demonstrate the behavior of the procedure, and a two-stage modification is proposed which guards against some undesirable behavior when the number of multiple observations becomes large.

Keywords:

• Bayesian discrimination
• diffuse priors
• hierarchical model
• multivariate normality
• predictive discrimination
• two-stage classification