Кто читает:: Кафедра прикладной математики и информатики (Нижний Новгород) (Факультет информатики, математики и компьютерных наук (Нижний Новгород))

Статус:: Курс обязательный

Когда читается:: 4-й курс, 1, 2 модуль

Преподаватель

Колданов Петр Александрович

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Abstract

This course examines multiple hypothesis testing procedures that allow you to answer several interrelated questions based on available observations or data, while monitoring some indicators of quality and the procedure used.

Learning Objectives

Recall the classical results of testing statistical hypotheses.Memorize the basic concepts of the theory of constructing multiple hypothesis testing procedures; apply the test obtained in the lecture to solve the problem on the basis of dispersion analysis; memorize the method of unification and intersection; study the concept of a hierarchical family; apply the LSD procedure in practice; study the closure principle of constructing multiple hypothesis testing procedures; apply the Hill procedure in practice; study the principle of partitioning for constructing procedures that control the probability of at least one false statement (FWER). Examine procedures that control the proportion of false claims (FDR). To apply the Hochberg procedure in practice; to study the procedures for choosing one of many hypotheses; to study what errors of the 1st and 2nd kind and risk and loss functions are; to count in practice the number of errors of the 1st and 2nd kind and the risk of the procedure; to study the Bayesian approach to multiple hypothesis testing. To put into practice the Bayesian approach to multiple hypothesis testing.

Expected Learning Outcomes

To apply classical approaches to hypothesis testing against alternatives in practice.
Recall classical approaches to testing hypotheses against alternatives.
To put into practice the test obtained in the lecture to solve the problem of variance analysis
Memorize the basic concepts of the theory of constructing multiple hypothesis testing procedures
Put the LSD procedure into practice
To study the concept of a hierarchical family
Memorize the method of union and intersection
Put the Hill procedure into practice.
To study the principle of closure of the construction of multiple hypothesis testing procedures.
To put into practice the maximum procedure of multiple hypothesis testing.
To study the optimal multiple hypothesis testing procedure controlling FWER.
To put the Hochberg procedure into practice.
To study the principle of partitioning to build procedures that control the probability of at least one false statement (FWER).
Examine procedures that control the proportion of false claims (FDR).
Calculate in practice the number of errors of the 1st and 2nd kind and the risk of the procedure.
To study what errors of the 1st and 2nd kind and functions of risk and loss are.
To study the procedures for choosing one of the many hypotheses.
To put Bayesian approach to multiple hypothesis testing into practice.
To study the Bayesian approach to multiple hypothesis testing.

Course Contents

The principle of closure.
Optimal maximal procedure for multiple hypothesis testing.
The union-intersection method. A hierarchical family.
An introduction to multiple hypothesis testing.
The two-solution rule. The Neiman-Pearson approach.
The principle of partitioning for constructing procedures that control the probability of at least one false statement (FWER). Procedures that control the proportion of false claims (FDR).
Procedures for selecting one of many hypotheses. The function of risk and loss. The Wald-Lehman theory.
The Bayesian approach to multiple hypothesis testing.

Assessment Elements

Control work 1
Control work 2
Control work 3
Exam

Interim Assessment

2025/2026 2nd module
0.5* mark for practice+ 0.5* mark for theory

Bibliography

Recommended Core Bibliography

Basics of modern mathematical statistics : exercises and solutions, , 2014
Graphical models with R, Hojsgaard, S., 2012
Introduction to mathematical statistics and its applications, Larsen, R. J., 2014
Introduction to mathematical statistics, Hogg, R. V., 2014
Mathematical statistics with applications in R, Ramachandran, K. M., 2015
Mathematical statistics with applications, Wackerly, D. D., 2008
Probability theory and statistical inference : econometric modeling with observational data, Spanos, A., 2000
Probability theory and statistical inference : econometric modeling with observational data, Spanos, A., 2004
Теория вероятностей и математическая статистика, Колданов, А. П., 2023
Теория вероятностей и математическая статистика, учебник, 243 с., Колданов, А. П., Колданов, П. А., 2023

Recommended Additional Bibliography

Advances in inequalities from probability theory and statistics, Barnett, N. S., 2008

Authors

Koldanov Petr Aleksandrovich

Бакалаврская программа «Прикладная математика и информатика»

Контакты

Introduction to multiple hypothesis testing procedures