Methods and models for multivariate data analysis
Entry requirements: Basic knowledge in field of probability theory and mathematical statistics.
Language of the course: English
Students will improve backgrounds in probability theory and develop skills in probabilistic modelling and statistic assessment.
Main topics of the discipline:
- Probabilistic models for random variables. Univariate random variable. CDF and PDF. Probability distribution parameters estimation. Probabilistic interval. Confidence interval;Probabilistic models for random variables. Multivariate random variable. Regression and correlation analysis. Principal component analysis. Multidimentional interval estimates;
- Probabilistic models for stochastic processes. Univariate stochastic process. Multivariate stochastic process. Temporal stochastic process and random fields. Gaussian stochastic processes. Stationarity and non-stationarity. Ergodic processes. Markov processes. Dynamic system model. Regression models for stochastic processes. Correlation analysis of stochastic processes. ARMA model. Trend model. Spectrum analysis. Furier transformation. Wiener-Khinchin theorem;
- Extreme values theory. Univariate random variable. Multivariate random variable. Exact extreme distribution. Assymtotical extreme distributions. Fisher-Tipet theorem. Pickands-Balkema-de Haan Theorem. Block maxima method. Peak over threshold method. Joint maxima distributions.
Lectures and lab sessions
60% results of lab works, 30% participation in class discussions and/or individual presentation on a topic of interest, 10% results of tests.
Additional opportunity to improve scores during the exam.