Conjugate Bayes discrimination with infinitely many variables

The problem considered is that of discrimination between two multivariate normal populations, with common dispersion structure, when the number of variables that can be observed is unlimited. We consider a Bayesian analysis, using a natural conjugate prior for the normal distribution parameters. One implication of this is that, with prior probability 1, the parameters will be such as to allow asymptotically perfect discrimination between the populations. We also find conditions under which this perfect discrimination will be possible, even in the absence of knowledge of the parameter values.