|
|
|
||
Last update: doc. Mgr. Milan Krtička, Ph.D. (20.09.2019)
|
|
||
Last update: doc. Mgr. Milan Krtička, Ph.D. (20.09.2019)
Final grade will be based on a combination of the written exam and homework. |
|
||
Last update: doc. Mgr. Milan Krtička, Ph.D. (06.10.2020)
Brief introduction to mathematical statistics: probability, probability density function, cumulative probability function, moments, MC method, error propagation, correlation, examples of common probability density functions
Parameter estimation: Classical definition of interval estimates, example for normal and binomial distribution. Maximum likelihood method: definition, variance of M.L. estimates (analytical method, MC method, RCF bound, graphical method), multi-parameter estimates, likelihood contours and their interpretation, binned M.L. method, relation with the least square method, M.L. for weighted data, extended likelihood, constrained likelihood, profile likelihood
Statistical tests: hypothesis, test statistics, confidence level, profile likelihood test, discovery and limit setting for new physics models, p a p0 values, significance, CLs method. Goodness of fit test.
Multivariate techniques for signal and background separation: Fisher discriminant, non-linear discriminants (neural networks, boosted decision trees, ...).
Unfolding: impact of a detector resolution on data, migration matrix, migration matrix inversion and problems of this method, regularisation, variance and bias of the unfolded distributions, unfolding techniques
More details on http://ipnp.cz/?page_id=4280. |