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.



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 ...


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.


Exercises help list


The course is free to attend, subject to space availability. Register by contacting Johan Alenlöv at


All activities will take place on Zoom, link to Zoom meeting will be distributed to registered students. All times are in CEST.

Monday 16/8
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
13:15 - 15:00 L4 : The bootstrap particle filter
L5 : Convergence of bootstrap PF
15:15 - 17:00 Exercise session 1
Tuesday 17/8
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
Wednesday 18/8
Time Content Material
10:15 - 12:00 Discussion Seminar 1 Discussion1.pdf
13:15 - 15:00 L11 : Metropolis-Hastings
L12 : Particle Metropolis-Hastings
15:15 - 17:00 Exercise session 3
Thursday 19/8
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
Friday 20/8
Time Content Material
10:15 - 12:00 Exercise session 4
13:15 - 16:00 Discussion seminar 2
Guest lecture
Guest Lecture


Any questions about the course can be sent to