This is a small demo using PyMC3 to model distributions of movie ratings. The goal is to demonstrate hierarchical Bayesian techniques for pooling data observations for smoothing individual estimates. This hierarchical pooling concept is explained in Gelman et al. (2013) and this post using the radon dataset.

Some useful links include Ted Dunning's post on sampling a prior for a Dirichlet and the Wikipedia page on Dirichlet compound multinomial distributions.

The notebook below can be downloaded here.