Lecture

Optimal Testing Methods

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In course

MATH-240: Statistics

Ce cours donne une introduction au traitement mathématique de la théorie de l'inférence statistique en utilisant la notion de vraisemblance comme un thème central. ...

Description

This lecture by the instructor covers the fundamental concepts of optimal testing methods in statistics, focusing on the Neyman-Pearson framework. It discusses the decision-making process between two hypotheses based on test statistics and critical regions. The lecture explores the Neyman-Pearson lemma, optimal tests for specific models like the exponential family, and the concept of optimality in hypothesis testing. It also delves into the construction of test functions for different types of hypotheses, such as simple vs. simple, unilateral vs. bilateral, and the importance of minimizing error probabilities. The lecture concludes with the notion of optimality in tests and the significance of the likelihood ratio in statistical decision-making.

Instructors (2)

Victor Panaretos

Curriculum vitae Background & EducationPublications & PreprintsHonours & AwardsEditorial ActivitiesInvited Talks & Seminars Teaching & PhD PhD Students Ulysse Naepels, Nikitas Georgakis, Ho Yun Past EPFL PhD Students Andrea Kraus, Shahin Tavakoli, Mikael Kuusela, Yoav Zemel, Marie-Hélène Descary, Valentina Masarotto, Tomas Rubin, Tomas Masák, Laya Ghodrati, Kartik Waghmare, Leonardo Santoro Past EPFL PhD Students as codirector Matthieu Simeoni, Ophelia Miralles, Sonia Alouini, Timmy Rong Tian Tse, Krali M

Yoav Zemel

Official source

Related concepts (30)

Statistical hypothesis testing

A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see .

Likelihood function

In statistical inference, the likelihood function quantifies the plausibility of parameter values characterizing a statistical model in light of observed data. Its most typical usage is to compare possible parameter values (under a fixed set of observations and a particular model), where higher values of likelihood are preferred because they correspond to more probable parameter values.

Likelihood principle

In statistics, the likelihood principle is the proposition that, given a statistical model, all the evidence in a sample relevant to model parameters is contained in the likelihood function. A likelihood function arises from a probability density function considered as a function of its distributional parameterization argument.

Null hypothesis

In scientific research, the null hypothesis (often denoted H0) is the claim that no relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative relationship does not exist, hence the term "null". In addition to the null hypothesis, an alternative hypothesis is also developed, which claims that a relationship does exist between two variables.

Texas Instruments

Texas Instruments Incorporated (TI) is an American technology company headquartered in Dallas, Texas, that designs and manufactures semiconductors and various integrated circuits, which it sells to electronics designers and manufacturers globally. It is one of the top 10 semiconductor companies worldwide based on sales volume. The company's focus is on developing analog chips and embedded processors, which account for more than 80% of its revenue.

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