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Last update: KFNTJC/MFF.CUNI.CZ (16.04.2008)
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Last update: prof. Mgr. Jakub Čížek, Ph.D. (06.10.2017)
Student obtains basic knowledge about methods of statistical analysis of experimental data within the Bayesian approach, Bayes theorem, fitting of theoretical models, estimation of parameters, methods how to estimate uncertainties, Monte Carlo modeling, and testing of hypothesis. The lecture is focused on practical applications in analysis of data obtained in physical experiments. |
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Last update: prof. Mgr. Jakub Čížek, Ph.D. (10.06.2019)
oral exam |
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Last update: prof. Mgr. Jakub Čížek, Ph.D. (10.06.2019)
D.S. Silva, "Data Analysis A Bayesian Tutorial" (Claredon Press, Oxford, 1998). 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). |
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Last update: prof. Mgr. Jakub Čížek, Ph.D. (10.06.2019)
lecture |
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Last update: prof. Mgr. Jakub Čížek, Ph.D. (10.06.2019)
Oral exam covers topics presented in lectures during semester. |
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Last update: prof. Mgr. Jakub Čížek, Ph.D. (06.10.2017)
A summary of basic concepts of mathematical statistics: the probability measure, random variables, probability distribution functions, convergence of random variables, conditional and marginal probabilities, random samples, the expectation value, the variance, the covariance matrix, the coefficient of linear correlation, higher moments, the characteristic functions and their use, transformation of random variables, the convolution.
The Bayes theorem, the Tchebycheff inequality and the Central Limit theorem.
A survey and properties of the most relevant statistical distributions for the needs of processing the data from physical measurements. Mutual relations between some of these distributions.
Statistics for estimating parameters and their main characteristics (consistency, unbiasedness and sufficiency). Selected methods for constructing these statistics. Fisher's statistical information and the Rao-Cramér inequality.
Parameter estimation by the method of the least squares (the linear model and a sub-model, testing their validity). Gauss-Markov theorem. Properties of residuals of the fit, bands of reliability. The chi-square test. Smoothing the experimentally assessed functions with the aid of the regression polynomial. The use of Forsythe polynomials for suppression of numerical instabilities. Selected iteration methods for finding the least square in case of non-linear models.
The maximum likelihood method and its use for parameter estimation.
Simulation of random processes by the Monte Carlo Method. Deterministic generators of random numbers. Basic methods for generating random samples (the method of the inverse distribution functions, the method of von Neumann, methods generating discrete random quantities). The use of the Monte Carlo Method for a design of an experiment and evaluation of experimental data.
The Bayesian use of Bayes theorem (the prior and posterior probability densities, the procedure for estimating unknown parameters). Illustrating examples of the use of the Bayesian approach. |