7.9 Summary

Many problems can be described as an overall population 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 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.

In this chapter, we divided mixture models into three classes: finite mixture models, non-finite 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 data. In principle, the components can be virtually anything we may consider useful from simple distributions, such as a Gaussian or a Poisson, to more complex...