MAT-61806 Optimisation and Statistical Data Analysis, 5 cr

Additional information

Acceptable for postgraduate studies if grade is at least 3.
Suitable for postgraduate studies.

Person responsible

Robert Piche

Lessons

Implementation Period Person responsible Requirements
MAT-61806 2019-01 3 - 4 Mostafa Mansour
Robert Piche
The grade is based on a set of tests in the EXAM system. Bonus points are given for active participation in the weekly exercise sessions.

Learning Outcomes

After completing the course, the student has knowledge of problems, solution methods, and software for optimisation and statistical data analysis, and is able to use software to model and solve practical problems.

Content

Content Core content Complementary knowledge Specialist knowledge
1. Computer arithmetic: floating point numbers; FP arithmetic     
2. Linear programming: LP problems in production planning, transportation allocation, and diet planning; solving them with Matlab LINPROG  ill-posed LP problems   
3. Curve fitting: least squares fit of a line and of a polynomial; data linearisation transformations  robust curve fitting using linear programming   
4. Nonlinear least squares: problems in positioning, curve fitting, and feedback controller design; solution with Matlab LSQNONLIN  Gauss-Newton method; ill-conditioned problems   
5. Nonlinear optimisation: unconstrained problems and solution with FMINUNC; Lagrange multipliers; solution with FMINCON  quadratic cost with linear equality constraints   
6. Multiobjective optimisation: Pareto optimality; weighted sum method; goal attainment with FGOALATTAIN   Feedback controller design as a multiobjective optimisation problem.    
7. Visualising data: histogram, CDF, medians, quantiles, box plots, data graphics do's and don'ts   kernel smoothing with KSDENSITY   
8. Inference on categories: frequency diagram, Bayes formula, Bayesian nets, AISPACE software     
9. Inference on probability-of-success: binomial sampling model; posterior distribution and predictive distribution; using prior information; sequential learning  Monte Carlo method for inference on parameter difference   
10. Inference on an average: Gaussian sampling model; posterior distribution & predictive distribution; using prior information; sequential learning  normal QQ plot   
11. Multiple linear regression: fitting a line; posterior distribution & predictive distribution; sequential learning  fitting a polynomial; assessing the goodness of fit   
12. Filtering: state space model, Kalman filter, steady-state KF, target tracking  Bayes filter; channel estimation   

Prerequisites

Course Mandatory/Advisable Description
MAT-01566 Mathematics 5 Mandatory    
MAT-02106 Multivariable Calculus Mandatory    

Additional information about prerequisites
In addition to the mandatory prerequisites courses, the student should be competent in basic matrix analysis and basic Matlab programming..



Correspondence of content

Course Corresponds course  Description 
MAT-61806 Optimisation and Statistical Data Analysis, 5 cr ASE-4046 Optimisation and Data Analysis, 5 cr  

Updated by: Piche Robert, 11.04.2019