On the distribution of posterior probabilities in finite mixture models with application in clustering

The paper discusses an approach based on the multivariate Delta method for approximating the distribution of posterior probabilities in finite mixture models. It can be used for developing distributions of many other characteristics involving posterior probabilities such as the entropy of fuzzy classification or expected cluster sizes. An application of the proposed methodology to clustering through merging mixture components is proposed and discussed. The methodology is studied and illustrated on simulated and well-known classification datasets with good results.