Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Maximal Internal Containing Interval

Description

This lecture covers the concept of the maximal internal containing interval, focusing on finding the interval containing a given set of points. It discusses the properties and solutions related to this concept, emphasizing the well-defined nature of the interval. The lecture also explores different scenarios and mathematical expressions to determine the maximal internal containing interval.

Official source

Related concepts (13)

Interval estimation

In statistics, interval estimation is the use of sample data to estimate an interval of possible values of a parameter of interest. This is in contrast to point estimation, which gives a single value. The most prevalent forms of interval estimation are confidence intervals (a frequentist method) and credible intervals (a Bayesian method); less common forms include likelihood intervals and fiducial intervals.

Credible interval

In Bayesian statistics, a credible interval is an interval within which an unobserved parameter value falls with a particular probability. It is an interval in the domain of a posterior probability distribution or a predictive distribution. The generalisation to multivariate problems is the credible region. Credible intervals are analogous to confidence intervals and confidence regions in frequentist statistics, although they differ on a philosophical basis: Bayesian intervals treat their bounds as fixed and the estimated parameter as a random variable, whereas frequentist confidence intervals treat their bounds as random variables and the parameter as a fixed value.

Maximal ideal

In mathematics, more specifically in ring theory, a maximal ideal is an ideal that is maximal (with respect to set inclusion) amongst all proper ideals. In other words, I is a maximal ideal of a ring R if there are no other ideals contained between I and R. Maximal ideals are important because the quotients of rings by maximal ideals are simple rings, and in the special case of unital commutative rings they are also fields.

Prediction interval

In statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which a future observation will fall, with a certain probability, given what has already been observed. Prediction intervals are often used in regression analysis.

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.

Related lectures (32)

Confidence Interval for Bernoulli Model Score

Explains how to calculate the confidence interval for the score parameter in the Bernoulli model.

Statistical Inference: Approximate Critical Values and Confidence Intervals

Covers the construction of confidence intervals and approximate critical values in statistical inference.

Optimality in Statistical Inference

Delves into the duality between confidence intervals and hypothesis tests, emphasizing the importance of precision and accuracy in estimation.

Confidence Intervals: Student, Asymptotic Wald

Covers confidence intervals for Gaussian means, Student distribution, and Wald confidence intervals for maximum likelihood estimators.

Confidence Intervals: Gaussian Estimation