MAT-61706 Bayesian Filtering and Smoothing, 5 cr
Additional information
Suitable for postgraduate studies.
Person responsible
Robert Piche
Lessons
| Implementation | Period | Person responsible | Requirements |
| MAT-61706 2019-01 | 3 - 4 |
Mostafa Mansour Robert Piche |
Solving weekly homework problems, participation in the weekly exercise sessions, and successful completion of the take-home final exam. |
Learning Outcomes
After completing the course, the student can apply modern algorithms of Bayesian filtering and smoothing. Student is capable of (grade (3/5)) 1. using the basic concepts and formulas of probability and Bayesian statistical inference. 2. presenting a model-based time-series estimation problem in a state-space form and understanding its statistical assumptions and limitations. 3. implementing the Kalman filter and the most common approximations of the nonlinear Bayesian filter and smoother. 4. understanding the approximations and limitations of different non-linear filters. 5. implementing computations and interpret results for estimating static parameters of the state space model. Grade (1/5): goal 4 and at least two other goals achieved
Content
| Content | Core content | Complementary knowledge | Specialist knowledge |
| 1. | Multivariate probability basics and the multivariate Gaussian distribution. | Chebyshev inequality | Laws of total expectation and total variance |
| 2. | Kalman filter | Stationary Kalman filter, information filter, treatment of missing measurement | discretisations of stochastic differential equation; Joseph formula |
| 3. | EKF, UKF, bootstrap particle filter | EKF2, GHKF, importance sampling, SIR | stratified resampling, RB particle filter |
| 4. | Bayesian fixed-interval filtering, RTS smoother | RTS extensions; particle smoother | fixed-lag smoothing; fixed-point smoothing |
| 5. | State-space model parameter estimation using MCMC | State space model parameter estimation using EM |
Study material
| Type | Name | Author | ISBN | URL | Additional information | Examination material |
| Book | Bayesian Filtering and Smoothing | Simo Särkkä | 9781107619289 | PDF is freely available. | Yes |
Prerequisites
| Course | Mandatory/Advisable | Description |
| MAT-02506 Probability Calculus | Mandatory | |
| MAT-61806 Optimisation and Statistical Data Analysis | Advisable |
Additional information about prerequisites
Prerequisite knowledge: matrix algebra, probability, Matlab programming
Correspondence of content
There is no equivalence with any other courses