I recently needed to do some work with the multivariate Gaussian distribution, in a fully Bayesian context. Surprisingly, I could not find a good reference for what I would consider a fairly basic subject area, so I wrote one (The book Bayesian Data Analysis has it all, but its hardly easy to tease out the relevant details.). By good I mean all equations given, with consistent notation throughout and, most importantly considering my use (Gibbs sampling, where I want to collapse out everything possible.), how to integrate out a Gaussian drawn from the conjugate prior, to determine the probability of a newly presented sample having been drawn from the Gaussian being estimated.

Gaussian Conjugate Prior Cheat Sheet.


Additionally, I wrote some python code to demonstrate it in action.

Gaussian Conjugate Prior Example.


Now I have gone to the effort of writing this I am going to have to sit down at some point and implement a Dirichlet process Gaussian mixture model, which is a pretty dam good density estimation method, and it would be nice to have it in my tool box. When I do I will of course upload it to my Google code repository.