Statistical theory

In statistics, a likelihood ratio test is a statistical test used to compare the goodness of fit of two models, one of which (the null model) is a special case of the other (the alternative model).

In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (a "false positive"), while a type II error is incorrectly retaining a false null hypothesis (a "false negative").

In statistics, the bias (or bias function) of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated.

Probability has a dual aspect: on the one hand the likelihood of hypotheses given the evidence for them, and on the other hand the behavior of stochastic processes such as the throwing of dice or coins.

Uncertainty is a situation which involves imperfect and/or unknown information.

Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component.

In statistics, interval estimation is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter, in contrast to point estimation, which is a single number.

Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset.

In probability theory and information theory, the Kullback–Leibler divergence, also called discrimination information (the name preferred by Kullback), information divergence, information gain, relative entropy, KLIC, KL divergence, is a measure of the difference between two probability distributions P and Q.

An a priori probability is a probability that is derived purely by deductive reasoning.

In statistics, a pivotal quantity or pivot is a function of observations and unobservable parameters whose probability distribution does not depend on the unknown parameters (also referred to as nuisance parameters).

The general linear model is a statistical linear model.

In robust statistics, Peirce's criterion is a rule for eliminating outliers from data sets, which was devised by Benjamin Peirce.

(For a broader coverage related to this topic, see Spline (mathematics).) The smoothing spline is a method of fitting a smooth curve to a set of noisy observations using a spline function.

In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter".

Given a set of N bivariate sample pairs (Xi, Yi), i = 1, .

Mathematical statistics is the application of mathematics to statistics, which was originally conceived as the science of the state — the collection and analysis of facts about a country: its economy, land, military, population, and so forth.

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean, and it informally measures how far a set of (random) numbers are spread out from their mean.

In information theory, systems are modeled by a transmitter, channel, and receiver.

In statistics, a likelihood function (often simply the likelihood) is a function of the parameters of a statistical model given data.

In signal processing, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval.

In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "theoretical value".

In the design of experiments, optimal designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion.

Benford's law, also called the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data.

In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables.