Магистратура
2022/2023
Теория вероятностей и математическая статистика
Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Статус:
Курс по выбору (Науки о данных (Data Science))
Направление:
01.04.02. Прикладная математика и информатика
Где читается:
Факультет компьютерных наук
Когда читается:
1-й курс, 1 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Федянин Денис Николаевич
Прогр. обучения:
Науки о данных
Язык:
английский
Кредиты:
3
Контактные часы:
28
Course Syllabus
Abstract
The overwhelming majority of courses on data-mining and artificial intelligence implies a strong background in probability and statistics. The goal of this course is to provide those students who are not so keen on the subject matter with its fundamentals.
Learning Objectives
- To introduce the theoretical foundations of Probability theory.
- To introduce the theoretical foundations of Mathematical statistics.
- To provide the students with practical skills of modelling real-world in the framework of probability and statistics.
Expected Learning Outcomes
- Solve simple problems using linear and normal linear regression.
- Understand basic statistical models.
- Understand Empirical distribution function, method of moments, maximum likelihood principle.
- Understand fundamental concepts chi-squared test.
- Understand fundamental concepts of statistical hypothesis for the normal distribution.
- Understand fundamental concepts of statistical hypothesis.
- Understand fundamental concepts, advantages and limitations of Linear regression and Normal linear regression.
- Understand fundamental concepts, advantages and limitations of non-parametric statistics.
- Understand problems of statistics.
Course Contents
- Problems of Statistics. Parameter estimators. Basic statistical models. Distributions and sample statistics. Estimators. Unbiased estimators. Unbiased estimators for expectation and variance. Consistency. Efficiency and mean-squared error. Kramer-Rao inequality.
- Empirical distribution function. Empirical parameters. Method of moments. Maximum likelihood principle. Likelihood and loglikelihood.
- Multivariate normal distribution. Student and Fisher distributions. Normal sample.
- Testing statistical hypothesis. Null hypothesis. Test statistics. Type I and type II errors. Significant level. Critical region and critical values.
- Statistical hypothesis for the normal distribution. The one-sample t-test. Comparing two samples. Tests for variance.
- Chi-squared test. For known parameters. For unknown parameters.
- Non-parametric statistics. Sign test. Two-sided sign test. Wilcoxon sign-rank test.
- Tests for power-law distributions. Hill test. Ibragimov’s corrections for confident intervals. Data-collapse approach. Clauset-Shalizi-Newman test.
- Linear regression. Normal linear regression.
Interim Assessment
- 2022/2023 1st module0.2 * Обзорный доклад по статье (Article Review) + 0.3 * Домашние задания + 0.2 * Экзамен + 0.3 * Тесты
Bibliography
Recommended Core Bibliography
- Dekking F. M. et al. A Modern Introduction to Probability and Statistics: Understanding why and how. – Springer Science & Business Media, 2005. – 488 pp.
Recommended Additional Bibliography
- Wasserman, L. All of nonparametric statistics. – Springer Science & Business Media, 2006. – 270 pp.