grisaitis/bayesian-multilevel-modeling

A tutorial on Bayesian multilevel linear regression for analyzing grouped data

An Introduction to Bayesian Multilevel Modeling

In this repo I give a tutorial of fitting multilevel probabilistic models. I explain what problems they're useful for and give implementations with TensorFlow Probability.

Scope:

• What is multilevel modeling? (Aka "mixed effects" or "hierarchical" models)
  • Why is it Bayesian? How is different from classical regression, and how does it work?
• What problems is this useful for? (Hint: most problems!)
• How does one implement it? Here I use TensorFlow Probability (aka tfp), a project related to but separate from TensorFlow with modules for probabilistic modeling (e.g. Hamiltonian Monte Carlo sampling, etc).

Running the examples

1. Install docker version 18.06 or later (or perhaps a little earlier)

2. Execute in a terminal:

    $ cd this-repo
    $ docker-compose up --force-recreate --build

3. Go to http://localhost:11000.

To-do

1. Add a basic example of a multilevel model. Use the radon dataset, and fit a model with probabilistic county-level intercepts.
   1. Add a working implementation.
   2. Improve analysis and discussion. Add metrics for evaluating model accuracy, and improve visualizations of parameters and errors.
2. Add a classical regression for comparison. Analyze the results and motivate the probabilistic multilevel approach.
3. Add an example of a multilevel model that uses group-level covariates. (Use county-level Uranium data to improve county-level intercepts in the radon example).
4. Add example with multilevel slopes (not just intercepts)
5. Documentation
6. docker instructions
7. Add references, other helpful tutorials