Dirichlet is a conjugate prior to the Multinomial likelihood. In other words our posterior distr. is also a Dirichlet distributuion with parameters incorporating observed data.
We have seen with parametric mixture models that we can assign group labels to observations using a model, but so far we have assumed that we know how many groups there are a priori. What if we don't know how many groups produced the data? We often want the choice of K to be data-driven. There are a number of approaches for allocating samples to groups where the number of groups is not pre-determined. We will look at two generative methods here.
