Methods and models for multivariate data analysis

Entry requirements: Basic knowledge in field of probability theory and mathematical statistics.

Credits: 4

Semester: 2

Course: Core

Language of the course: English

Lecturer

Anna Kalyuzhnaya

Objectives

Students will improve backgrounds in probability theory and develop skills in probabilistic modelling and statistic assessment.

Contents

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.

Format

Lectures and lab sessions

Assessment

Examination.

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.