Sequential Monte Carlo Methods
PhD Course, 6 credits, February 2025.
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
- 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: 17h
- Practicals: 7h (+ time on your own)
- Discussion seminars: 2h
- 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
- Hand-in assignments Work with exercise H.2 before the session 26/2
- seOMXlogreturns2012to2014.csv
Registration
The course is free to attend, subject to space availability. For PhD students at IDA, register through the portal. For other PhD students, register by contacting Johan Alenlöv at johan.alenlov@liu.se, provide your name, email and home university.
Schedule
- Schedule is now updated.
Time | Content | Material | Location |
---|---|---|---|
10:15 - 12:00 | L1 : Introduction and probabilistic modelling L2 : Probabilistic modelling of dynamical systems and the filtering problem |
lecture1.pdf lecture2.pdf |
Planck |
13:15 - 15:00 | L3 : Monte Carlo and importance sampling L4 : The bootstrap particle filter |
lecture3.pdf lecture4.pdf |
Planck |
15:15 - 17:00 | L5 : Convergence of bootstrap PF Exercise Session 1 |
lecture5.pdf | E324 |
Time | Content | Material | Location |
---|---|---|---|
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 | KY23 |
13:15 - 15:00 | Exercise Session 2 | KY31 |
Time | Content | Material | Location |
---|---|---|---|
10:15 - 12:00 | Discussion Seminar | Ada Lovelace | |
13:15 - 15:00 | L9 : Parameter learning and likelihood estimation L10 : The particle filter as a likelihood estimator |
lecture9.pdf lecture10.pdf |
Ada Lovelace |
15:15 - 17:00 | Exercise Session 3 | Ada Lovelace |
Time | Content | Material | Location |
---|---|---|---|
10:15 - 12:00 | L11 : Metropolis-Hastings L12 : Particle Metropolis-Hastings |
lecture11.pdf lecture12.pdf |
KY31 |
13:15 - 15:00 | L13 : Gibbs sampling L14 : Particle Gibbs |
lecture13.pdf mwg_example.m lecture14.pdf | KY34 |
15:15 - 17:00 | Exercise Session 4 | KY34 |
Time | Content | Material | Location |
---|---|---|---|
9:15 - 12:00 | L15 : General SMC L16 : SMC samplers L17 : TBD |
lecture15.pdf lecture16.pdf lecture17.pdf |
KY34 |
Contact
Any questions about the course can be sent to johan.alenlov@liu.se.