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 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

Updated by: Piche Robert, 24.05.2019