**Bayesian**- CRM114, oft cited as a Bayesian filter, is not intended to use a Bayes filter in production, but includes the ″unigram″ feature for reference. (wikipedia.org)
- Bayesian email filters utilize Bayes' theorem. (wikipedia.org)
- In statistics, the use of Bayes factors is a Bayesian alternative to classical hypothesis testing. (wikipedia.org)
- Bayesian model comparison is a method of model selection based on Bayes factors. (wikipedia.org)
- For models where an explicit version of the likelihood is not available or too costly to evaluate numerically, approximate Bayesian computation can be used for model selection in a Bayesian framework, with the caveat that approximate-Bayesian estimates of Bayes factors are often biased. (wikipedia.org)
- Bayesian procedures, including Bayes factors, are coherent, so there is no need to draw such a distinction. (wikipedia.org)
- For decision-making, Bayesian statisticians might use a Bayes factor combined with a prior distribution and a loss function associated with making the wrong choice. (wikipedia.org)

**probability**- Naive Bayes classifiers work by correlating the use of tokens (typically words, or sometimes other things), with spam and non-spam e-mails and then using Bayes' theorem to calculate a probability that an email is or is not spam. (wikipedia.org)
- This contribution is called the posterior probability and is computed using Bayes' theorem. (wikipedia.org)
- The Bayes factor is a ratio of the likelihood probability of two competing hypotheses, usually a null and an alternative. (wikipedia.org)
- Professor Stephen Stigler, historian of statistical science, thinks that Bayes became interested in the subject while reviewing a work written in 1755 by Thomas Simpson, but George Alfred Barnard thinks he learned mathematics and probability from a book by Abraham de Moivre. (wikipedia.org)
- Bayes' solution to a problem of inverse probability was presented in "An Essay towards solving a Problem in the Doctrine of Chances" which was read to the Royal Society in 1763 after Bayes' death. (wikipedia.org)

**displaystyle**- Bayes' theorem can be applied to a pair of competing models M 1 {\displaystyle M_{1}} and M 2 {\displaystyle M_{2}} for data D {\displaystyle D} , one of which may be true (though which one is unknown) but which both cannot be true simultaneously. (wikipedia.org)
- The remaining Bayes factor P ( D ∣ M 2 ) / P ( D ∣ M 1 ) {\displaystyle P(D\mid M_{2})/P(D\mid M_{1})} is not so easy to evaluate, since in general it requires marginalizing nuisance parameters. (wikipedia.org)
- When the two models are equally probable a priori, so that Pr ( M 1 ) = Pr ( M 2 ) {\displaystyle \Pr(M_{1})=\Pr(M_{2})} , the Bayes factor is equal to the ratio of posterior probabilities of M1 and M2. (wikipedia.org)

**statistical**- Naive Bayes classifiers are a popular statistical technique of e-mail filtering. (wikipedia.org)
- If instead of the Bayes factor integral, the likelihood corresponding to the maximum likelihood estimate of the parameter for each statistical model is used, then the test becomes a classical likelihood-ratio test. (wikipedia.org)

**assumptions**- In this second letter Selvin proposed a solution based on Bayes' theorem and explicitly outlined some assumptions concerning the moderator's behavior. (wikipedia.org)
- Both theories derive a best linear unbiased estimator, based on assumptions on covariances, make use of Gauss-Markov theorem to prove independence of the estimate and error, and make use of very similar formulae. (wikipedia.org)

**context**- An alternative table, widely cited, is provided by Kass and Raftery (1995): The use of Bayes factors or classical hypothesis testing takes place in the context of inference rather than decision-making under uncertainty. (wikipedia.org)

**factor**- The aim of the Bayes factor is to quantify the support for a model over another, regardless of whether these models are correct. (wikipedia.org)

**solution**- Bayes' "Essay" contains his solution to a similar problem posed by Abraham de Moivre, author of The Doctrine of Chances (1718). (wikipedia.org)

**case**- c. 1701 - 7 April 1761) was an English statistician, philosopher and Presbyterian minister who is known for having formulated a specific case of the theorem that bears his name: Bayes' theorem. (wikipedia.org)
- This essay contains a statement of a special case of Bayes' theorem. (wikipedia.org)

**includes**- However, an advantage of the use of Bayes factors is that it automatically, and quite naturally, includes a penalty for including too much model structure. (wikipedia.org)

**known**- c. 300 BC - Euclid's Elements expound geometry as a system of theorems following logically from axioms known with certainty. (wikipedia.org)