Sequential Monte Carlo Methods

URL study guide

https://studiegids.vu.nl/en/courses/2025-2026/XM_0182

Course Objective

The aim of this master seminar is to learn how to read scientific texts at a research level, create and organise material, to give seminar talks to your fellow students, and to be able to explain the mathematical concepts and ideas involved. It is also a goal to learn how to constructively participate in a research seminar by asking questions and giving feedback. This seminar aims to provide an introduction to the theory and practice of Sequential Monte Carlo (SMC) methods, a versatile class of algorithms for Bayesian inference in dynamic and latent variable models. Based on the first ten chapters of "An Introduction to Sequential Monte Carlo Methods" by Chopin and Papaspiliopoulos, the course provides a systematic foundation in the core principles of SMC, including importance sampling, resampling, degeneracy, and variance analysis, with a focus on both discrete
- and continuous-time state-space models. The course progresses from basic SMC algorithms to more advanced topics such as backward smoothing, adaptive resampling, and effective sample size diagnostics. Students will gain hands-on experience with implementing SMC algorithms and will critically examine their theoretical properties, computational efficiency, and practical limitations.

Course Content

Learning goals:Describe the structure of state-space models and formulate inference problems within them.Learn the structure of Feynman-Kac models.Implement basic Sequential Importance Sampling (SIS) and Sequential Importance Resampling (SIR) algorithms.Explain and quantify particle degeneracy and variance in Monte Carlo estimators.Apply smoothing techniques such as backward simulation and forward-filtering backward-sampling (FFBS).Use diagnostics such as effective sample size (ESS) to monitor and adapt SMC algorithms.Analyze the convergence properties and asymptotic behavior of SMC estimators.Design and evaluate adaptive resampling strategies to improve algorithmic performance.Apply SMC methods to simple real-world or simulated data problems.Understand the theoretical assumptions and limitations of SMC in high-dimensional settings.Prepare for more advanced topics such as Particle MCMC and SMC samplers.

Teaching Methods

A seminar, for 2 hours per week during each week of periods 1 and 2. Each student gives one or two talks. At the start of the course there are lectures.

Method of Assessment

Depending on the number of students, the grade will consist of the average of the grades for presentation and an oral examination. There will be a minimum attendance requirement in order to get a grade for this course. The exact requirement will be determined at the beginning of the seminar. Due to the nature of the seminar, there will not be a resit.

Literature

"An Introduction to Sequential Monte Carlo Methods"(Springer) by Chopin and Papaspiliopoulos

Target Audience

If the number of participating students is too low to have a presentation every week, we might change some sessions into discussions of material that has to be read in advance.

Entry Requirements

Solid understanding of probability theory and statistics at bachelor level mathematics.