Sequential Monte Carlo Methods
PhD Course, 6 credits, 16 - 20 August 2021.
The aim of this course is to provide an introduction to the theory and application of sequential Monte Carlo (SMC) methods. To this end we will start by studying the use of SMC for inference in nonlinear dynamical systems. It will be shown how SMC can be used to solve challenging parameter (system identification) and state inference problems in nonlinear dynamical systems. Importantly, we will also discuss SMC in a more general context, showing how it can be used as a generic tool for sampling from complex probability distributions.
Syllabus
Contents
- Probabilistic modelling of dynamical systems
- The Monte Carlo idea and importance sampling
- Sequential Monte Carlo / Particle filtering
- Basic convergence theory for particle filters
- Likelihood estimation and maximum likelihood parameter inference
- Particle Markov chain Monte Carlo
- Probabilistic programming
- General SMC / SMC Samplers
Course Structure
The course consists of lecture and homework assignments. The homeworks will to a large extent be computer based, please bring your own laptop with some programming environment of your choice installed, e.g. Python, Julia, R, Matlab ...
- Lectures: 18h
- Practicals: 8h (+ time on your own)
- Discussion seminars: 4h
- 1 hand-in assignment
Examination
Via successfully completing and handing in the hand-in assignments.
Course literature
Lecture notes will be made available to the course participants.
Thomas B. Schön and Fredrik Lindsten. Learning of dynamical systems - Particle filters and Markov chain methods, Lecture notes, 2017. Available here.
Chrisitan A. Naesseth, Fredrik Lindsten and Thomas B. Schön. Elements of Sequential Monte Carlo, Available here.
Material
- Preparatory exercises
- Exercises 1
- Exercises 2
- Exercises 3
- Exercises 4
- seOMXlogreturns2012to2014.csv
- Hand-in assignments
- Updated 2021-08-26: Removed mention of unit square in H.4
Exercises help list
Registration
The course is free to attend, subject to space availability. Register by contacting Johan Alenlöv at johan.alenlov@liu.se.
Schedule
All activities will take place on Zoom, link to Zoom meeting will be distributed to registered students. All times are in CEST.
| Time | Content | Material |
|---|---|---|
| 9:15 - 12:00 | L1 : Introduction and probabilistic modelling L2 : Probabilistic modelling of dynamical systems and the filtering problem L3 : Monte Carlo and importance sampling |
lecture1.pdf lecture2.pdf lecture3.pdf |
| 13:15 - 15:00 | L4 : The bootstrap particle filter L5 : Convergence of bootstrap PF |
lecture4.pdf lecture5.pdf |
| 15:15 - 17:00 | Exercise session 1 |
| Time | Content | Material |
|---|---|---|
| 9:15 - 12:00 | L6 : Auxiliary variables and the auxiliary PF L7 : The fully adapted PF L8 : Path space view, path degeneracy and ESS |
lecture6.pdf lecture7.pdf lecture8.pdf |
| 13:15 - 15:00 | Exercise session 2 | |
| 15:15 - 17:00 | L9 : Parameter learning and likelihood estimation L10 : The particle filter as a likelihood estimator |
lecture9.pdf lecture10.pdf |
| Time | Content | Material |
|---|---|---|
| 10:15 - 12:00 | Discussion Seminar 1 | Discussion1.pdf |
| 13:15 - 15:00 | L11 : Metropolis-Hastings L12 : Particle Metropolis-Hastings |
lecture11.pdf lecture12.pdf |
| 15:15 - 17:00 | Exercise session 3 |
| Time | Content | Material |
|---|---|---|
| 10:15 - 12:00 | L13 : Gibbs sampling L14 : Particle Gibbs |
lecture13.pdf mwg_example.m lecture14.pdf |
| 14:15 - 17:00 | L15 : General SMC L16 : SMC samplers L17 : SMC for probabilistic programming |
lecture15.pdf lecture16.pdf lecture17.pdf |
| Time | Content | Material |
|---|---|---|
| 10:15 - 12:00 | Exercise session 4 | |
| 13:15 - 16:00 | Discussion seminar 2 Guest lecture |
discussion2.pdf Guest Lecture |
Contact
Any questions about the course can be sent to johan.alenlov@liu.se.