The River Plate (also known as La Plata River or Río de la Plata) is the widest river on Earth and a natural border between Argentina and Uruguay. During the late 19th century, the port area along this river was a place were natives mixed with Africans (most of them slaves) and European immigrants. One consequence of this encounter was the mix of European music, such as the Waltz and Mazurka, with the African Candombe and Argentinian Milonga (which, in turn, is a mix of Afro-American rhythms), giving origin to a dance and music we now call the Tango.
Mixing previous existing elements is a great way to create new stuff, not only music. In statistics, mixture models are one common approach to model building. These models are built by mixing simpler distributions to obtain more complex ones. For example, we can combine two Gaussians to describe a bimodal distribution or many Gaussians to describe arbitrary distributions. While using Gaussians is very common, we can mix, in principle, any family of distributions we want. Mixture models are used for different purposes, such as directly modeling sub-populations or as a useful trick for handling complicated distributions that cannot be described with simpler distributions.
In this chapter, we will cover the following topics:
- Finite mixture models
- Infinite mixture models
- Continuous mixture models