Many problems can be described as an overall populations composed of distinct sub-populations. When we know to which sub-population each observation belongs, we can specifically model each sub-population as a separate group. However, many times we do not have direct access to this information, thus it may be more appropriate to model that data using mixture models. We can use mixture models, to try to capture true sub-populations in the data or as a general statistical trick to model complex distributions by combining simpler distributions. We may even try to do something in the middle.

In this chapter we divide mixture models into three classes—finite mixture models, infinite mixture models, and continuous mixture models. A finite mixture model is a finite weighted mixture of two or more distributions, each distribution or component representing a subgroup of the...