# Posts in advanced

## How to wrap a JAX function for use in PyMC

top-level ‘substitutions’ key is deprecated, place under ‘myst’ key instead [myst.topmatter]

## Factor analysis

top-level ‘substitutions’ key is deprecated, place under ‘myst’ key instead [myst.topmatter]

## 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.

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 $$\Omega$$,