Probabilistic Modelling

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, seminars, practical classes.

Assessment

60% results of practical tasks, 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.