The problem of classifying each of $n$ observations to one of two sub-populations is considered. The classification rule examined chooses that classification with maximum posterior probability. Limiting behavior of the rule is given and several examples are presented which show that the rule can lead to classifying all observations to the same subpopulation. Three simulation studies are reported to indicate that this extreme behavior may occur in small samples.
"Classification by Maximum Posterior Probability." Ann. Statist. 5 (1) 185 - 190, January, 1977. https://doi.org/10.1214/aos/1176343752