Syllabus
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.
Annotation
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.