NSCPHD1125 State space models and particle methods
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.
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.
- Category
- Hours
- Exam
- 10
- Laboratory
- 5
- Lectures
- 20
- Preparation
- 18
- Project work
- 15
- Total
- 68
Please register at: anders@math.ku.dk
- Credit
- 2,5 ECTS
- Type of assessment
- Continuous assessmentThe 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.
- Aid
- 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.
Course information
- Language
- English
- Course code
- NSCPHD1125
- Credit
- 2,5 ECTS
- Level
- Ph.D.
- Duration
- Placement
- Spring
- Schedule
- The course will be held 13-17. April 2015.
- Study board
- Natural Sciences PhD Committee
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Susanne Ditlevsen (susanne@math.ku.dk)
Lecturers
Professor Omiros Papaspiliopoulos, Universitat Pompeu Fabra,
Barcelona
Professor Nicolas Chopin, ENSAE, Paris