PhD Course on State Space Models and Particle Methods

Monday April 13th  - Friday April 17th, 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

The student should know about sequential algorithms for statistical inference,
in particular for state space models. The student should also be able to perform estimation in hidden Markov models and linear Gaussian state space models and be familiar with the theory of SMC methods. The student should be able to generalize from the specific models introduced in the course to specific problems encountered further on.

Teaching and learning methods

A combination of lectures and exercises for five intensive days

Credits and assesment

The work load of the course corresponds to 2.5 ECTS. 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.

Academic qualifications

PhD student in statistics or similar. Some familiarity with programming in R or similar is recommended. The course is primarily aimed at PhD students from Science but is open to others as well on a first-come, first-served basis. A list of participants will be available here.


Registration is now closed. Deadline for registration is April 1st, 2015 and participation is free of charge. Please register by filling in the form available here. It is recommended to sign up as soon as possible due to a restricted number of participants. Note that the registration is NOT completed until you recieve a confirmation email.  You will later receive a second email with information about whether or not you have been accepted to the course. 


Auditorium 10 at the HC Ørsted institute, Universitetsparken 5, 2100 Copenhagen Denmark. 


The course begins 9.15 Monday April 13th 2015 and finish 12.45 on Friday April 17th 2015.

Time Monday Tuesday Wednesday Thursday Friday
09.15 - 10.15 Session 1.1 Session 2.1 Session 3.1 Session 4.1 Session 5.1
10.30 - 11.30 Session 1.2 Session 2.1+2.2 Session 3.2 Session 4.2 Session 5.1
11.45 - 12.45 Session 1.3 Session 2.2 Session 3.3 Session 4.3 Session 5.2
13.00 - 14.15 Lunch Lunch Lunch Lunch
14.15 - 15.15 Session 1.4 Group work Group work Group work
15.15 - 16.15 Group work Group work Group work
16.15 - 18.00 Group work
19.00 - ?? Social dinner


Conference Dinner

The conference dinner will take place on Thursday 19.00 at Llama, Lille Kongensgade 14, 1074 København K


Unfortunately we do not have the possibility to give financial support.

Accommodation and Travel Information

Information about accomodation, arrival in Copenhagen, and travel between the airport, Maths Institute and hotels, as well as how to use the city's public transport system, is available here.


  • Anders Jensen (Contact person)
  • Susanne Ditlevsen
  • Omiros Papaspiliopoulos
  • Nicolas Chopin