Testing for Differences Among Discrete Distributions: An Application of Model-Based Clustering

We consider the problem of testing for differences among a number of discrete distributions. Our approach is based on viewing the different samples as drawn from a mixture distribution where each mixture component represents a different group or cluster. We adapt the methodology of Dasgupta and Raftery (1998) to this problem, giving explicit details in the case of multinomial and first-order Markov chain distributions. The resulting method is computationally efficient and easy to implement. Applications to two datasets are discussed.