[Tutorial] Deep dive into MCMC

[b-remy]

What is the main topic of this tutorial: Explain what are MCMC, Metropolis-Hastings, Hamiltonian Monte Carlo, and how to use them in practice.

One line description This tutorial would help to understand what are the different variants of MCMC, what they have in common, how they differ, and provide examples of usage.

Level

• [x] Beginner
• [x] Intermediate
• [ ] Advanced

Learning goals

• What's a MCMC
• Metropolis-Hastings
• Hamiltonian Monte Carlo
• How to run MCMC with Tensorflow Probability

[tobias-liaudat]

@b-remy Some questions that might be good to motivate the tutorial or some discussion:

• [ ] I have a high dimensional problem. Can I still use Bayesian inference and sampling techniques? Which technique would be appropriate and why?

• [ ] Help! The posterior I'm interested in is multimodal! What should I do and consider?

• [ ] How can I know that the chains I am running have converged?

• [ ] How can I estimate the number of samples needed for my chain to converge? On what does this number usually depends?

• [ ] In sampling algorithms, it is common to have some proposal sample that is accepted or rejected given some condition. What properties should the proposal have to guarantee the convergence of the chain to the desired stationary distribution?

• [ ] Some people talk about a "funnel" distribution. Where do these originate, and what are the problems associated with them?

• [ ] Are there some off the shelf codes I could use in a project where I need to do MCMC?