# MAT-61806 Optimisation and Statistical Data Analysis, 5 cr

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