SubjectsSubjects(version: 849)
Course, academic year 2019/2020
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Statistical Methods of Experimental Data Processing - NMAF017
Title in English: Statistické metody zpracování experimentálních dat
Guaranteed by: Department of Low Temperature Physics (32-KFNT)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
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: doc. Ing. František Bečvář, DrSc.
prof. Mgr. Jakub Čížek, Ph.D.
Classification: Physics > Mathematics for Physicists
Annotation -
Last update: KFNTJC (04.05.2005)
Basic concepts in probability - random quantities, probability distributions, moments. Parameter estimation by the methods of maximum likelihood and least squares. Testing of hypotheses. Data processing - analysis of regression, interpolation and extrapolation of data, data reduction, decomposition of spectra.
Aim of the course -
Last update: KFNTJC/MFF.CUNI.CZ (16.04.2008)

Student obtains basic knowledge about methods of statistical analysis of experimental data,

distribution of random variable,fitting of theoretical models and dependencies,

estimation of parameters, Monte Carlo modeling, and testing of hypothesis.

Course completion requirements -
Last update: prof. Mgr. Jakub Čížek, Ph.D. (10.06.2019)

oral exam

Literature -
Last update: prof. Mgr. Jakub Čížek, Ph.D. (10.06.2019)

W.T. Eadie et al., "Statistical Methods in Experimental Physics" (North Holland, Amsterdam, 1971).

G. Cowan, "Statistical Data Analysis", (Oxford Science Publications, Clarendon Press, Oxford 1998).

R.J. Barlow, "Statistics. A Guide to the Use of Statistical Methods in the Physical Sciences", (John Wiley & Sons, Chichester 1989).

Teaching methods -
Last update: prof. Mgr. Jakub Čížek, Ph.D. (10.06.2019)

lecture

Requirements to the exam -
Last update: prof. Mgr. Jakub Čížek, Ph.D. (10.06.2019)

Oral exam covers topics presented in lectures during semester.

Syllabus -
Last update: T_KFNT (06.05.2003)
  • Basic concepts: probability and the probability measure, a random variable, probability density functions, a random sample, parametrization of probability densities.
  • Conditional and marginal probabilities. The Bayes theorem and its use.
  • The expectation value and variance of a random variable. Central and non-central moments. Covariance matrix of random variables. Statistical independence. The variance of a function of random variables. Transformations of random variables. The convolution and its properties.
  • Characteristic functions of random variables and their use.
  • A survey of the most relevant statistical distributions (the uniform, binomial, multinomial, Poisson, normal,chi.square, Student, Fisher, Cauchy, log-normal, etc.). Their properties and situations where we encounter them.
  • The Central Limit theorem and an example of it use.
  • Estimates of unknown parameters. Consictency and unbiasedness of estimates. Some methods for construction of statistics for estimating parameters. - Likelihood functions and the methd of meaximum likelihood.
  • The method opf least squares in its general formulation. The main properties of the weighted quadratic deviation. The Gauss-Markov theorem. The linear model: estimates of parameters, their covatiance matrix, smothing of empirically determined function values, determination of the band of reliability, the problem of numerical stability and its solutions.
  • Statistical hypotheses and their testing. The concept of testing statistic. Examples of testing.

 
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