Probabilistic Methods of Data Analysis

Entry requirements: Basics of probability theory and mathematical statistics

Credits: 6

Course: Core

Language of the course: Russian

Objectives

  • To develop skills in probabilistic modelling and multivariate statistical analysis
  • To deepen the knowledge of probability theory

Contents

– Probabilistic methods for one-dimensional random variable. Basic concepts of distribution law, distribution function, distribution density (and their properties). Estimation methods of distribution parameters. Probabilistic interval, confidence interval, tolerance interval.
– Probabilistic methods for multidimensional random variable. Regression analysis. Correlation analysis. Principal component analysis. Multidimensional interval estimations of distribution parameters, and regression.
– Probabilistic models for one-dimensional and multidimensional random processes, and fields. Random function and its connection to time processes and fields. Stationary state definition in narrow and road sense. Ergodic processes. Periodically correlated random processes. Gaussian processes. Markov processes. Dynamic system model. Regression models for random processes. Correlation analysis of random processes. Autoregression model. Wold's model. Rice model. Autoregressive-moving average model. Trend modelling. Auto- and cross-spectral
analysis. Fourier transform Wiener-Khinchin theorem.

Format

Practical sessions

Assessment

Attendance is mandatory. Students should complete all the assignments. The final grade is based on the student performance throughout the course.