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

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 ...

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

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

Monday 3/2
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
Tuesday 4/2
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
Wednesday 26/2
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
Thursday 27/2
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
Friday 28/2
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.