Two population classification in Gaussian process

The problem is to classify an individual into one of two populations based on an observation on the individual which follows a stationary Gaussian process and the populations are two distinct time points. Plug-in likelihood ratio rules are considered using samples from the process. The distribution of associated classification statistics are derived. For the special case when the mis-classification probabilities are equal, the nature of dependence between the population distributions on the probability of correct classification is studied. Lower bounds and iterative method of evaluation of the optimal correlation between the populations are obtained.