Bayesian information criterion and Occam's razor

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Difference between Bayesian information criterion and Occam's razor

Bayesian information criterion vs. Occam's razor

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. Occam's razor (also Ockham's razor or Ocham's razor; Latin: lex parsimoniae "law of parsimony") is the problem-solving principle that, the simplest explanation tends to be the right one.

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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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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Cambridge University Press

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

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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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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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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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