## F7270 Mathematical methods for numerical data analysis

Faculty of Science
Spring 2020
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
Teacher(s)
Mgr. Filip Münz, PhD. (lecturer)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
Mgr. Filip Münz, PhD. (seminar tutor)
Guaranteed by
prof. Mgr. Dominik Munzar, Dr.
Department of Condensed Matter Physics - Physics Section - Faculty of Science
Contact Person: Mgr. Filip Münz, PhD.
Supplier department: Department of Condensed Matter Physics - Physics Section - Faculty of Science
Timetable of Seminar Groups
F7270/01: No timetable has been entered into IS.
Prerequisites
Knowledge of mathematics, physics and experimental physics on the bachelor curriculum level.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The goal of this course is to explain basic procedures in the probability theory and mathematical statistics, especially in application to experimental data treatment and stating and testing of the hypotheses.
Learning outcomes
Student are able upon finishing this course to:
- describe a random variable (RV) with several characteristics;
- give properties of a combination of RVs (average, maximum);
- name several discrete and continuous distributions of RVs, roughly characterize them and bring them into the context of experimental practice;
- specify basic properties of a good statistic estimate;
- use a maximum likelihood method for an estimate of a specific parameter;
- apply a linear model to a chosen problem;
- conduct a hypothesis test of a match between experimental and theoretical distribution
Syllabus
• Probability, random variables. Random vector, statistical dependence. Central limit theorem. Multidimensional normal distribution. Standard probability distributions and their relationships. Statistical estimates, maximum likelihood, least squares. Position of an unknown symmetrical distribution. Linear model for multiple unknowns. Nonlinear model, numerical minimization. Statistical tests, Pearson and Kolmogorov method.
Literature
recommended literature
• Statistical methods in experimental physics. Edited by Frederick E. James. 2nd ed. Hackensack, N.J.: World Scientific, 2006. xviii, 345. ISBN 9789812705273. info
• MARTIN, B. R. Statistics for physical sciences : an introduction. 1st ed. Boston: Academic Press, 2012. x, 302. ISBN 9780123877604. info
• HUMLÍČEK, Josef. Statistické zpracování výsledků měření. 1. vyd. Brno: Rektorát UJEP, 1984. 101 s. info
• EADIE, W. T. Statističeskije metody v eksperimental'noj fizike : Statistical methods in experimental physics (Orig.) : Statistical methods in experimental physics (Orig.). Moskva: Atomizdat, 1976. 334 s. info
• BARLOW, Roger. Statistics : a guide to the use of statistical methods in the physical sciences. Chichester: John Wiley & Sons, 1989. xv, 204. ISBN 0471922943. info
• COWAN, Glen. Statistical data analysis. Oxford: Clarendon Press, 1998. xi, 197 s. ISBN 0-19-850155-2. info
• ANDĚL, Jiří. Základy matematické statistiky. 2., opr. vyd. Praha: Matfyzpress, 2007. 358 s. ISBN 9788073780012. info
not specified
• BRANDT, Siegmund. Data analysis : statistical and computational methods for scientists and engineers. Translated by Glen Cowan. 3rd ed. New York: Springer-Verlag, 1998. xxxiv, 652. ISBN 0387984984. info
Teaching methods
lectures, seminars, data analysis as a homework
Assessment methods
Final project evaluating computer-generated data: estimates, identification of outliers, testing data distribution, evaluation of indirect measurements, statistical dependence of retrieved parameters.
Language of instruction
Czech
Follow-Up Courses