Finite Mixture Models and Their Applications: A Review

Finite Mixture (FM) models have received increasing attention in recent years and have proven to be useful in modeling heterogeneous data with a finite number of unobserved sub-population. It has been not only widely applied to classification, clustering, and pattern identification problems for independent data, but could also be used for longitudinal data to describe differences in trajectory among these subgroups. However, due to the computational convenience, the most types of FM models are based on the normality assumption which may be violated in certain real situations. Recently, FM models with non-normal distributions, such as skew normal and skew t-distribution, have received increasing attention and showed the advantages in modeling data with non-normality and heavy tails. One of the advantages of FM models is that both maximum likelihood method and Bayesian approach can be applied to not only estimate model parameters, but also evaluate probabilities of subgroup membership simultaneously. We present a brief review of FM models for these two types of data with different scenarios.