Lecture

Statistical Inference: Approximate Critical Values and Confidence Intervals

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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 covers the theoretical background for statistical inference, focusing on the construction of confidence intervals and the use of approximate critical values. The instructor explains the concept of pivots and approximate pivots, illustrating their application in various statistical scenarios. Key topics include Wald tests, Slutsky's theorem, interpretation of confidence intervals, and the importance of understanding the probabilistic nature of intervals. Through examples and theoretical explanations, students will gain insights into the construction and interpretation of confidence intervals in statistical inference.

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

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics, Statistical hypothesis testing

Related concepts (32)

Statistical assumption

Statistics, like all mathematical disciplines, does not infer valid conclusions from nothing. Inferring interesting conclusions about real statistical populations almost always requires some background assumptions. Those assumptions must be made carefully, because incorrect assumptions can generate wildly inaccurate conclusions. Here are some examples of statistical assumptions: Independence of observations from each other (this assumption is an especially common error). Independence of observational error from potential confounding effects.

Probability

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin.

Statistics

Statistics (from German: Statistik, () "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal".

Probability theory

Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space.

Confidence interval

In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used. The confidence level, degree of confidence or confidence coefficient represents the long-run proportion of CIs (at the given confidence level) that theoretically contain the true value of the parameter; this is tantamount to the nominal coverage probability.

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Estimators and Confidence Intervals

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Interval Estimation

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Confidence Intervals: Definition and Estimation

Explains confidence intervals, parameter estimation methods, and the central limit theorem in statistical inference.

Estimation and Confidence Intervals

Explores bias, variance, and confidence intervals in parameter estimation using examples and distributions.

Confidence Intervals and Hypothesis Testing

Explores confidence intervals, hypothesis testing, and decision-making using test statistics and p-values.

Related concepts (32)

Statistical assumption