Bachelor
2025/2026
Foundations of Modern Probability
Type:
Elective course (Data Science and Business Analytics)
Delivered by:
Big Data and Information Retrieval School
Where:
Faculty of Computer Science
When:
3 year, 3, 4 module
Open to:
students of one campus
Language:
English
ECTS credits:
4
Contact hours:
68
Course Syllabus
Abstract
This course offers a rigorous exploration of the mathematical foundations of advanced statistical methods, designed for computer science students seeking to deepen their understanding of the theory behind key statistical tools. Students will develop expertise in techniques such as the method of moments, maximum likelihood estimation, Bayesian inference, and regression analysis, alongside a comprehensive study of confidence intervals and testing frameworks. Emphasis is placed on both theoretical rigor and practical relevance, preparing students to apply these methods to machine learning, optimization, and data science challenges.
Learning Objectives
- Develop a deep understanding of the theoretical principles underlying advanced statistical methods, including probability models, convergence, and estimation techniques
- Gain the skills to effectively use statistical tools such as hypothesis testing, regression analysis, and Bayesian inference in computational and data-driven applications.
Expected Learning Outcomes
- Students will be able to understand and apply the mathematical principles behind key statistical methods, including estimation and hypothesis testing.
- Students will be able to analyze and interpret different types of convergence for random variables and their implications in statistical modeling.
- Students will be able to construct and evaluate statistical models using techniques such as maximum likelihood estimation and the method of moments.
- Students will be able to design and implement confidence intervals and hypothesis tests for real-world data analysis scenarios.
- Students will be able to apply advanced statistical methods to machine learning, optimization, and data science challenges.
- Students will be able to critically assess the assumptions and limitations of statistical tools and adapt them for specific computational applications.
Course Contents
- Convergence of random variables
- Characteristic functions
- Limit Theorems
- Gaussian vectors
- Convergence of random vectors
- Empirical CDF
- Point estimators
- Comparison of estimators
- Maximum likelihood estimator
- Sufficient statistics
- Confidence intervals
- Bayesian estimators
- Linear regression model
- Hypothesis testing
Interim Assessment
- 2025/2026 4th module0 * Bonus activities + 0.5 * Exam + 0.25 * Final written test + 0.25 * Midterm
Bibliography
Recommended Core Bibliography
- Problems in probability, Shiryaev, A. N., 2012
- Введение в математическую статистику, Ивченко, Г. И., 2015
- Курс теории вероятностей и математической статистики, Севастьянов, Б. А., 2004
- Курс теории вероятностей, Чистяков, В. П., 2003
- Математическая статистика : учебник, Боровков, А. А., 2007
- Мера и интеграл, Толстов, Г. П., 1976
Recommended Additional Bibliography
- 9780429766749 - Blitzstein, Joseph K.; Hwang, Jessica - Introduction to Probability, Second Edition - 2019 - Chapman and Hall/CRC - http://search.ebscohost.com/login.aspx?direct=true&db=nlebk&AN=2024519 - nlebk - 2024519
- Matloff, N. S. (2020). Probability and Statistics for Data Science : Math + R + Data. Chapman and Hall/CRC.