# Posts tagged mixture model

## Gaussian Mixture Model

A mixture model allows us to make inferences about the component contributors to a distribution of data. More specifically, a Gaussian Mixture Model allows us to make inferences about the means and standard deviations of a specified number of underlying component Gaussian distributions.

## Dirichlet mixtures of multinomials

This example notebook demonstrates the use of a Dirichlet mixture of multinomials (a.k.a Dirichlet-multinomial or DM) to model categorical count data. Models like this one are important in a variety of areas, including natural language processing, ecology, bioinformatics, and more.

## Marginalized Gaussian Mixture Model

Gaussian mixtures are a flexible class of models for data that exhibits subpopulation heterogeneity. A toy example of such a data set is shown below.

The Dirichlet process is a flexible probability distribution over the space of distributions. Most generally, a probability distribution, $$P$$, on a set $$\Omega$$ is a [measure](https://en.wikipedia.org/wiki/Measure_(mathematics%29) that assigns measure one to the entire space ($$P(\Omega) = 1$$). A Dirichlet process $$P \sim \textrm{DP}(\alpha, P_0)$$ is a measure that has the property that, for every finite disjoint partition $$S_1, \ldots, S_n$$ of $$\Omega$$,