SubjectsSubjects(version: 941)
Course, academic year 2022/2023
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Data Analysis and Modeling in Astronomy - NAST036
Title: Analýza dat a modelování v astronomii
Guaranteed by: Astronomical Institute of Charles University (32-AUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2012
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Note: enabled for web enrollment
Guarantor: doc. Mgr. Josef Ďurech, Ph.D.
Classification: Physics > Astronomy and Astrophysics
Annotation -
Last update: T_AUUK (16.05.2012)
Students will learn methods of statistical analysis of experimental data, fitting of theoretical models, estimation of parameters, how to estimate uncertainties of model parameters, Monte Carlo modeling, and testing of hypothesis. Another important topic is searching for periods in time series of observed data. The lecture is focused on practical applications in Astronomy and Astrophysics.
Course completion requirements -
Last update: prof. RNDr. David Vokrouhlický, DrSc. (13.06.2019)

Oral examination.

Literature -
Last update: T_AUUK (17.05.2012)

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

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

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

Requirements to the exam -
Last update: doc. Mgr. Josef Ďurech, Ph.D. (20.06.2019)

according to syllabus

Syllabus -
Last update: doc. Mgr. Josef Ďurech, Ph.D. (28.04.2020)

Random values, discrete and continuous probability distributions, probability density, statistical description of data, moments of the probability distribution.

Statistical tests, testing hypotheses, t-test, F-test, Chi^2 test, Kolmogorov-Smirnov test.

Linear correlation, correlation coefficient, principal component analysis.

Modeling of data and estimation of the parameters of the model, method of maximum likelihood, least square method, central limit theorem, robust methods, linear models, non-linear models, estimation of errors of parameters, Monte Carlo methods, bootstrap, Markov Chain Monte Carlo.

Methods for determining minimum of a n-dimensional function: simplex, Powell method, conjugate gradient method, Levenberg-Marquardt method, genetic algorithms.

Analysis of the time series, methods for determining periods: power spectrum, autocorrelation, Nyquist frequency, phase dispersion minimization, sampling, false periods.

Bayesian analysis - Bayes theorem, posterior probability density, examples.

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