NSCPHD1125 State space models and particle methods

Volume 2014/2015

Subject area
The course is about sequential algorithms for statistical inference. There will be
particular emphasis on inference for state space models (e.g. hidden Markov models, change point models, and more general partially observed Markov processes).

Scientific content
In the course we will develop an accessible introduction to the Feynman-Kac formalization of such sequential algorithms, and we will demonstrate the strength
of this approach in deriving filtering/smoothing/prediction recursions and simulation algorithms. This machinery will be used to provide numerical methods for the estimation of hidden Markov models and linear-Gaussian state space models. We will then provide a rigorous description of importance sampling as a tool for obtaining Monte Carlo estimates of inferential quantities of interest. This Monte Carlo technique will be combined with the Feynman-Kac formalisation to yield the family of particle filtering methods, and more generally the family of Sequential Monte Carlo (SMC) methods. We will demonstrate the potential and limitations of SMC for statistical inference in a wide range of models and applications. The course will also discuss latest research developments in this field, including particle MCMC and SMC^2 methods. The material is largely based on a forthcoming book by Chopin and Papaspiliopoulos. 

Learning Outcome

Knowledge The student should know about sequential algorithms for statistical inference, in particular for state space models Skills The students should

-  be able to perform estimation in hidden Markov models and linear Gaussian state space models. -  be familiar with the theory of SMC methods. 

Competences The student should be able to generalize from the specific models introduced in the course to specific problems encountered further on.


Phd student in statistics or similar. Some familiarity with programming in R or similar is recommended.
A combination of lectures and exercises for five intensive days.
  • Category
  • Hours
  • Exam
  • 10
  • Laboratory
  • 5
  • Lectures
  • 20
  • Preparation
  • 18
  • Project work
  • 15
  • Total
  • 68
2,5 ECTS
Type of assessment
Continuous assessment
The course will contain a mandatory group project and each participant will be assigned to one project which is to be done during the course. The students will be arranged in groups of 4-5 people. The projects will be open ended - no correct answer will exist! The aim is to experiment creatively and learn the challenges and inner workings of state space models and particle methods under supervision. The students will present their work and results (blackboard/projector but no typed text expected). The assessment will not be strict, the point is to get the students trying things out as a research project.
All aids allowed
Marking scale
passed/not passed
Censorship form
No external censorship
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.