# MAT-61706 Bayesian Filtering and Smoothing, 5 cr

Robert Piche

#### Opetus

 Toteutuskerta Periodi Vastuuhenkilö Suoritusvaatimukset 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.

#### Osaamistavoitteet

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

#### Sisältö

 Sisältö Ydinsisältö Täydentävä tietämys Erityistietämys 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

#### Oppimateriaali

 Tyyppi Nimi Tekijä ISBN URL Lisätiedot Tenttimateriaali Book Bayesian Filtering and Smoothing Simo Särkkä 9781107619289 PDF is freely available. Yes

#### Esitietovaatimukset

 Opintojakso P/S Selite MAT-02506 Probability Calculus Mandatory MAT-61806 Optimisation and Statistical Data Analysis Advisable

Tietoa esitietovaatimuksista
Prerequisite knowledge: matrix algebra, probability, Matlab programming

#### Vastaavuudet

Opintojakso ei vastaan mitään toista opintojaksoa

 Päivittäjä: Piche Robert, 24.05.2019