| Course label : | Advanced statistical estimation |
|---|---|
| Teaching departement : | MIN / Applied Mathematics and General Computing |
| Teaching manager : | Mister AUGUSTIN MOUZE |
| Education language : | |
| Potential ects : | 0 |
| Results grid : | |
| Code and label (hp) : | SMD_SDI_ESA - Estimation statistique avancée |
Education team
Teachers : Mister AUGUSTIN MOUZE / Mister LOUIS FILSTROFF / Mister PHILIPPE VANHEEGHE
External contributors (business, research, secondary education): various temporary teachers
Summary
Statistical estimation may be considered to cope with the extraction of information from observations (physical measurements, data, ￜ) in the presence of random disturbances. This course is designed to strike a balance between a theoretical exposition and the practical aspects of the statistical estimation in order to build efficient estimation algorithms that may be implemented on a computer. The program of this course includes A review of probability for the statistical estimation. The mathematical definition of the estimation problem. To determine an optimal estimator, it is first necessary to get a model of the data considering their randomness. The question of assessing the estimator performances is studied. The classical estimation paradigm is discussed. Minimum Variance Unbiased Estimator, the Cramer-Rao lower bound, data linear models, best linear unbiased estimator. The concept of sufficient statistics, the exponential family of probability distributions, the Rao-Blackwell-Lehmann-Scheffe theorem. Then, the maximum likelihood estimation and the least square approach are investigated. In the previous part of the course the classical approach to statistical estimation is considered, in this approach the parameter to be estimated is assumed to be a deterministic but unknown constant. It is necessary now to tackle the problem of estimating a parameter which is represented by a random variable. This is the Bayesian approach of the statistical estimation. The principle of the Bayesian estimation paradigm is presented. The last part of this course is dedicated to the Expectation-Maximization (EM) algorithm.
Educational goals
Sustainable development goals
Knowledge control procedures
Continuous Assessment
Comments:
Online resources
Pedagogy
Sequencing / learning methods
| Number of hours - Lectures : | 10 |
|---|---|
| Number of hours - Tutorial : | 10 |
| Number of hours - Practical work : | 0 |
| Number of hours - Seminar : | 0 |
| Number of hours - Half-group seminar : | 0 |
| Number of student hours in TEA (Autonomous learning) : | 0 |
| Number of student hours in TNE (Non-supervised activities) : | 0 |
| Number of hours in CB (Fixed exams) : | 0 |
| Number of student hours in PER (Personal work) : | 0 |
| Number of hours - Projects : | 0 |