Probabilistic Modelling (Master’s Program: Big Data)

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

Credits: 6

Course: Core

Language of the course: English

Objectives

  • to improve backgrounds in probability theory
  • to develop skills in probabilistic modelling and statistic assessment

Contents

-        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. Univariate stochastic process. Multivariate stochastic process. (Exact extreme distribution. Assymtotical extreme distributions. Fisher-Tipet theorem. Pickands-Balkema-de Haan Theorem. Block maxima method. Peak over threshold method. Joint maxima distributions. Extremes of stochastic processes.)

-        Forecasting backgrounds. Probabilistic forecasting models. Data assimilation. Forecast quality estimation. Model calibration. Ensemble forecasts.

Format

Lectures, seminars, practical classes.

Assessment

Grading: 30% participation in class discussions and/or individual presentation on a topic of interest, 60% results of practical tasks; 10% results of tests.

Additional opportunity to improve scores during the exam.