Mixture modeling is a valuable technique for representing populations with varying characteristics, allowing us to explore their heterogeneity. By utilizing well-known probability distributions such as Gaussian, Poisson, and Binomial, mixture models offer a formal and convenient statistical framework for both clustering and classification purposes. Unlike traditional clustering methods, mixture models enable us to estimate the likelihood of belonging to a specific cluster and make inferences about sub-populations. For instance, in the field of marketing, one might seek to cluster different customer groups and determine the probabilities of these groups purchasing specific products. This information can then be utilized to tailor customized promotions, effectively targeting each group. Similarly, when applying natural language processing to a large collection of documents, clustering them into distinct topics becomes crucial. Additionally, understanding the importance of each topic across the documents can provide valuable insights. Throughout this course, you will gain a comprehensive understanding of mixture models, including their estimation techniques and the appropriate scenarios for their application.