*** Welcome to piglix ***

Bayes factor


In statistics, the use of Bayes factors is a Bayesian alternative to classical hypothesis testing.Bayesian model comparison is a method of model selection based on Bayes factors. The models under consideration are statistical models. The aim of the Bayes factor is to quantify the support for a model over another, regardless of whether these models are correct. The technical definition of "support" in the context of Bayesian inference is described below.

Simply put, the Bayes factor is a ratio of the likelihood probability of two competing hypotheses, usually a null and an alternative.

The posterior probability Pr(M|D) of a model M given data D is given by Bayes' theorem:

The key data-dependent term Pr(D|M) is a likelihood, and represents the probability that some data are produced under the assumption of this model, M; evaluating it correctly is the key to Bayesian model comparison.

Given a model selection problem in which we have to choose between two models, on the basis of observed data D, the plausibility of the two different models M1 and M2, parametrised by model parameter vectors and is assessed by the Bayes factor K given by


...
Wikipedia

...