Introduction¶

A few sentences on

mixture modeling
Bayesian n treatment of mixture models
why hierarchical mixture models
why temporal

Mixture modelling is a probabilistic representations of subpopulations (or clusters) within a population. It provides a flexible framework for statistical modeling and analysis.

Mixture Models¶

The pdf/pmf a mixture distributino is given by convex combination of the pdf/pmf of its individual components. We say a distribution $f$ is a mixture of $K$ component distributions if

$f\left(x;\Theta,\pi\right)=\sum_{k=1}^{K}\pi_{k}f\left(x;\theta_{k}\right)$

A mixture model is characterized by a set of component parameters $\Theta=\left\{ \theta_{1},\ldots,\theta_{K}\right\}$ and a prior distribution $\pi$ over these components.