Probabilistic Modelling (Master’s Program: Computational Biomedicine)
Entry requirements: basic knowledge in field of probability theory and mathematical statistics
Language of the course: English
- to improve backgrounds in probability theory
- to develop skills in probabilistic modelling and statistic assessment
- 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, seminars, practical classes.
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.