Syllabus
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.
Annotation
The aim of the course is to introduce basic statistical methods frequently used in analysis of experimental data in high energy physics. We focus mainly on practical aspects and application of the methods covered in the course.
For each topic an example code will be provided based on ROOT, RooFit, and RooStat and HistFitter tools.