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Bayesian information criterion

Index Bayesian information criterion

In statistics, the Bayesian information criterion (BIC) or Schwarz criterion (also SBC, SBIC) is a criterion for model selection among a finite set of models; the model with the lowest BIC is preferred. [1]

36 relations: Academic Press, Akaike information criterion, Annals of Statistics, Annals of the Institute of Statistical Mathematics, Bayes factor, Bayesian inference, Big O notation, Biometrika, Cambridge University Press, Dependent and independent variables, Deviance (statistics), Deviance information criterion, F-test, Feature selection, Fisher information, Function (mathematics), Hannan–Quinn information criterion, Jensen–Shannon divergence, Journal of the American Statistical Association, Kullback–Leibler divergence, Laplace's method, Likelihood function, Likelihood-ratio test, Linear regression, Maximum likelihood estimation, Minimum description length, Minimum message length, Model selection, Monthly Notices of the Royal Astronomical Society, Normal distribution, Observation, Overfitting, Parameter, Statistics, Taylor series, World Scientific.

Academic Press

Academic Press is an academic book publisher.

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Akaike information criterion

The Akaike information criterion (AIC) is an estimator of the relative quality of statistical models for a given set of data.

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Annals of Statistics

The Annals of Statistics is a peer-reviewed statistics journal published by the Institute of Mathematical Statistics.

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Annals of the Institute of Statistical Mathematics

Annals of the Institute of Statistical Mathematics is a bimonthly peer-reviewed scientific journal covering statistics.

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Bayes factor

In statistics, the use of Bayes factors is a Bayesian alternative to classical hypothesis testing.

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Bayesian inference

Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available.

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Big O notation

Big O notation is a mathematical notation that describes the limiting behaviour of a function when the argument tends towards a particular value or infinity.

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Biometrika

Biometrika is a peer-reviewed scientific journal published by Oxford University Press for the Biometrika Trust.

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Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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Dependent and independent variables

In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.

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Deviance (statistics)

In statistics, deviance is a goodness-of-fit statistic for a statistical model; it is often used for statistical hypothesis testing.

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Deviance information criterion

The deviance information criterion (DIC) is a hierarchical modeling generalization of the Akaike information criterion (AIC) and the Bayesian information criterion (BIC).

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F-test

An F-test is any statistical test in which the test statistic has an ''F''-distribution under the null hypothesis.

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Feature selection

In machine learning and statistics, feature selection, also known as variable selection, attribute selection or variable subset selection, is the process of selecting a subset of relevant features (variables, predictors) for use in model construction.

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Fisher information

In mathematical statistics, the Fisher information (sometimes simply called information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Hannan–Quinn information criterion

In statistics, the Hannan–Quinn information criterion (HQC) is a criterion for model selection.

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Jensen–Shannon divergence

In probability theory and statistics, the Jensen–Shannon divergence is a method of measuring the similarity between two probability distributions.

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Journal of the American Statistical Association

The Journal of the American Statistical Association (JASA) is the primary journal published by the American Statistical Association, the main professional body for statisticians in the United States.

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Kullback–Leibler divergence

In mathematical statistics, the Kullback–Leibler divergence (also called relative entropy) is a measure of how one probability distribution diverges from a second, expected probability distribution.

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Laplace's method

In mathematics, Laplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form where ƒ(x) is some twice-differentiable function, M is a large number, and the endpoints a and b could possibly be infinite.

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Likelihood function

In frequentist inference, a likelihood function (often simply the likelihood) is a function of the parameters of a statistical model, given specific observed data.

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Likelihood-ratio test

In statistics, a likelihood ratio test (LR test) is a statistical test used for comparing the goodness of fit of two statistical models — a null model against an alternative model.

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Linear regression

In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables).

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Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of a statistical model, given observations.

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Minimum description length

The minimum description length (MDL) principle is a formalization of Occam's razor in which the best hypothesis (a model and its parameters) for a given set of data is the one that leads to the best compression of the data.

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Minimum message length

Minimum message length (MML) is a formal information theory restatement of Occam's Razor: even when models are equal in goodness of fit accuracy to the observed data, the one generating the shortest overall message is more likely to be correct (where the message consists of a statement of the model, followed by a statement of data encoded concisely using that model).

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Model selection

Model selection is the task of selecting a statistical model from a set of candidate models, given data.

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Monthly Notices of the Royal Astronomical Society

Monthly Notices of the Royal Astronomical Society (MNRAS) is a peer-reviewed scientific journal covering research in astronomy and astrophysics.

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Normal distribution

In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.

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Observation

Observation is the active acquisition of information from a primary source.

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Overfitting

In statistics, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit additional data or predict future observations reliably".

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Parameter

A parameter (from the Ancient Greek παρά, para: "beside", "subsidiary"; and μέτρον, metron: "measure"), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.

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Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

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Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

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World Scientific

World Scientific Publishing is an academic publisher of scientific, technical, and medical books and journals headquartered in Singapore.

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References

[1] https://en.wikipedia.org/wiki/Bayesian_information_criterion

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