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- Bayes'_rule abstract "In probability theory and applications, Bayes' rule relates the odds of event to event , before (prior to) and after (posterior to) conditioning on another event . The odds on to event is simply the ratio of the probabilities of the two events. The prior odds is the ratio of the unconditional or prior probabilities, the posterior odds is the ratio of conditional or posterior probabilities given the event . The relationship is expressed in terms of the likelihood ratio or Bayes factor, . By definition, this is the ratio of the conditional probabilities of the event given that is the case or that is the case, respectively. The rule simply states: posterior odds equals prior odds times Bayes factor (Gelman et al., 2005, Chapter 1). When arbitrarily many events are of interest, not just two, the rule can be rephrased as posterior is proportional to prior times likelihood, where the proportionality symbol means that the left hand side is proportional to (i.e., equals a constant times) the right hand side as varies, for fixed or given (Lee, 2012; Bertsch McGrayne, 2012). In this form it goes back to Laplace (1774) and to Cournot (1843); see Fienberg (2005).Bayes' rule is an equivalent way to formulate Bayes' theorem. If we know the odds for and against we also know the probabilities of . It may be preferred to Bayes' theorem in practice for a number of reasons.Bayes' rule is widely used in statistics, science and engineering, for instance in model selection, probabilistic expert systems based on Bayes networks, statistical proof in legal proceedings, email spam filters, and so on (Rosenthal, 2005; Bertsch McGrayne, 2012). As an elementary fact from the calculus of probability, Bayes' rule tells us how unconditional and conditional probabilities are related whether we work with a frequentist interpretation of probability or a Bayesian interpretation of probability. Under the Bayesian interpretation it is frequently applied in the situation where and are competing hypotheses, and is some observed evidence. The rule shows how one's judgement on whether or is true should be updated on observing the evidence (Gelman et al., 2003).".
- Bayes'_rule wikiPageExternalLink BayesRuleBookMain.html.
- Bayes'_rule wikiPageExternalLink 9781439880326.
- Bayes'_rule wikiPageExternalLink itila.
- Bayes'_rule wikiPageID "49785".
- Bayes'_rule wikiPageRevisionID "606596425".
- Bayes'_rule hasPhotoCollection Bayes'_rule.
- Bayes'_rule subject Category:Bayesian_inference.
- Bayes'_rule subject Category:Model_selection.
- Bayes'_rule subject Category:Statistical_ratios.
- Bayes'_rule type Abstraction100002137.
- Bayes'_rule type MagnitudeRelation113815152.
- Bayes'_rule type Ratio113819207.
- Bayes'_rule type Relation100031921.
- Bayes'_rule type StatisticalRatios.
- Bayes'_rule comment "In probability theory and applications, Bayes' rule relates the odds of event to event , before (prior to) and after (posterior to) conditioning on another event . The odds on to event is simply the ratio of the probabilities of the two events. The prior odds is the ratio of the unconditional or prior probabilities, the posterior odds is the ratio of conditional or posterior probabilities given the event . The relationship is expressed in terms of the likelihood ratio or Bayes factor, .".
- Bayes'_rule label "Bayes' rule".
- Bayes'_rule label "Regola di Bayes".
- Bayes'_rule sameAs Regola_di_Bayes.
- Bayes'_rule sameAs m.0h6761n.
- Bayes'_rule sameAs Q1754809.
- Bayes'_rule sameAs Q1754809.
- Bayes'_rule sameAs Bayes'_rule.
- Bayes'_rule wasDerivedFrom Bayes'_rule?oldid=606596425.
- Bayes'_rule isPrimaryTopicOf Bayes'_rule.