Lecturer: Frank van der Meulen
prof in mathematical statistics
Vrije Universiteit Amsterdam
Department of Mathematics
Email: f.h.van.der.meulen@vu.nl
Course description
This MSc-level course introduces students 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 Nicolas Chopin and Omiros 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.
Learning objectives
By the end of the course, students will be able to:
- 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.