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- Chain_rule_(probability) abstract "In probability theory, the chain rule permits the calculation of any member of the joint distribution of a set of random variables using only conditional probabilities. The rule is useful in the study of Bayesian networks, which describe a probability distribution in terms of conditional probabilities.Consider an indexed set of sets . To find the value of this member of the joint distribution, we can apply the definition of conditional probability to obtain:Repeating this process with each final term creates the product:With four variables, the chain rule produces this product of conditional probabilities:This rule is illustrated in the following example. Urn 1 has 1 black ball and 2 white balls and Urn 2 has 1 black ball and 3 white balls. Suppose we pick an urn at random and then select a ball from that urn. Let event A be choosing the first urn: P(A) = P(~A) = 1/2. Let event B be the chance we choose a white ball. The chance of choosing a white ball, given that we've chosen the first urn, is P(B|A) = 2/3. Event A, B would be their intersection: choosing the first urn and a white ball from it. The probability can be found by the chain rule for probability:.".
- Chain_rule_(probability) wikiPageExternalLink the_chain_rule_of_probability.
- Chain_rule_(probability) wikiPageID "24380013".
- Chain_rule_(probability) wikiPageRevisionID "603249450".
- Chain_rule_(probability) hasPhotoCollection Chain_rule_(probability).
- Chain_rule_(probability) subject Category:Probability_theory.
- Chain_rule_(probability) comment "In probability theory, the chain rule permits the calculation of any member of the joint distribution of a set of random variables using only conditional probabilities. The rule is useful in the study of Bayesian networks, which describe a probability distribution in terms of conditional probabilities.Consider an indexed set of sets .".
- Chain_rule_(probability) label "Chain rule (probability)".
- Chain_rule_(probability) sameAs m.07scj_c.
- Chain_rule_(probability) sameAs Q17004731.
- Chain_rule_(probability) sameAs Q17004731.
- Chain_rule_(probability) wasDerivedFrom Chain_rule_(probability)?oldid=603249450.
- Chain_rule_(probability) isPrimaryTopicOf Chain_rule_(probability).