Graduate Course · Winter 2025
This course studies modern methods for sampling from complex, multi-modal distributions at scale. Emphasis is placed on both theoretical foundations and practical implementations.
↓ Syllabus (PDF)Topics and schedule are subject to change.
| Date | Topic | Slides |
|---|---|---|
| Feb 23 | Lecture 1: Introduction | Slides PDF |
| Feb 25 |
Lecture 2: MCMC foundations
Geyer (1998) — See Chapter 2 for further reading on Markov Kernels in an MCMC context.
Roberts & Rosenthal (2004) — Rigorous treatment of ergodicity and CLTs for Markov chains relevant for MCMC.
|
Slides PDF |
| Mar 2 |
Lecture 3: Metropolis-Hastings
MCMC interactive gallery — Play around with some of the methods discussed .
| Slides PDF |
| Mar 4 |
Lecture 4: Local inference algorithms
MCMC using Hamiltonian dynamics — Review of HMC methods .
| Slides PDF |
| Mar 9 | Lecture 5: Multi-modal distributions | Slides PDF |
| Mar 11 | Lecture 6: Annealing | Slides PDF |
| Mar 16 | Lecture 7: Statistical mechanics for statisticians | Slides PDF |
| Mar 18 | Lecture 8: Introduction to parallel annealing | Slides PDF |
| Mar 23 | Lecture 9: Non-reversible parallel tempering | Slides PDF |
Assignment notebooks are written in Julia. To get started, install Julia and open the template notebook in VS Code:
.ipynb file, open it in VS Code,
and select your Julia kernel when prompted.
New to Julia? The official Getting Started guide is the best first stop. For a gentler introduction aimed at scientists, Introduction to Julia (Julia Academy, free) and the community MIT Julia tutorials are both excellent. The full documentation is also very readable.
The project involves an in-depth review of a method related to the course, and is expected to take approximately one week of effort. Deliverables are a 5-page write-up (excluding code) and a 30-minute presentation during the week of April 13 (date TBD).
You are encouraged to find topics of interest to you and relevant to your research. Here are some examples of topics if you want inspirations.