Introduction to mixture models
Weixin Yao, Sijia Xiang · 2024
Mixture models are flexible and natural models for analyzing heterogeneous populations consisting of homogeneous sub-populations. They can be used for cluster analysis, latent class analysis, and more. The resulting finite mixture models are commonly used for exploratory data analysis and clustering. Chapter 1 starts with an introduction to mixture models, their formulations, identifiability, maximum likelihood estimation, and the EM algorithm. The chapter then discusses some applications of the EM algorithm, including mode estimation and robust generalized M estimator for linear regression. The topography of finite normal mixture models, unboundedness of normal mixture likelihood, and consistent root selections for mixture models are also covered. Finite mixtures of skewed distributions, semi-supervised mixture models, nonparametric maximum likelihood estimate, and mixture models for matrix data are also discussed.