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Course, academic year 2018/2019
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Statistical methods in high energy physics - NJSF143
Title in English: Statistické metody ve fyzice vysokých energií
Guaranteed by: Institute of Particle and Nuclear Physics (32-UCJF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: Mgr. Daniel Scheirich, Ph.D.
Mgr. Oldřich Kepka, Ph.D.
Annotation -
Last update: T_UCJF (27.03.2014)
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. Part of the lecture is an exercise session where implementation and usage examples are demonstrated using Root, RooFit, and RooStat tools. The course is suited mainly for students of the doctoral programme or second- year students of the master's programme.
Course completion requirements -
Last update: Mgr. Daniel Scheirich, Ph.D. (19.02.2018)

Written exam. The first written exam will be held during the last lecture.

Syllabus -
Last update: T_UCJF (27.03.2014)

brief introduction to mathematical statistics: probability, probability density function, cumulative probability function, moments, MC method, error propagation, correlation, characteristic function, examples of common probability density functions

Maximum likelihood parameter estimates: 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, examples in Root a RooFit

Confidence intervals of parameter estimators: classical confidence intervals, examples for gaussian, poisson and binomial distributions, confidence intervals for M.L. estimators, multi-dimensional confidence intervals, confidence intervals near parameter space boundary, Bayesian approach

Statistical tests: hypothesis, test statistics, confidence level, Fisher discriminant, non-linear discriminant (neural networks, boosted decision trees, ...), signal-background separation, goodness of fit, implementation in ROOT framework

Limit setting: local p a p0 values, significance, global significance (look-elsewhere effect), CLs method, profiling, frequentist vs. bayesian approach, examples of implementation in RooFit and RooStat

Unfolding: impact of a detector resolution on data, migration matrix, migration matrix inversion and problems of this method, regularization, variance and bias of the unfolded distributions, unfolding techniques, Root examples

Systematic uncertainties: common systematic uncertainties (energy and momentum scale, uncertainty in efficiency and resolution), systematic uncertainty propagation, toy MC, bootstrap method

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