Example of using of BAYES' formula

# Example of using of BAYES' formula - Example of using of...

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03/12/09 Bayes’ formula (see Handout_ 5 …) P(B i )*P(A|B i ) P(B i )*P(A|B i ) P(B i )*P(A|B i ) P(B i | A ) = --------------------- = ------------------------ = ------------------- (5.9) P(A) k k Σ P(B i )*P(A|B i ) Σ P(A∩B i ) i =1 i =1 In a special case, when there are only two mutually exclusive complementary hypotheses _ B 1 = B and B 2 = B associated with the occurrence of event A , the formula (5.9) takes the forms: _ _ P(B| A ) = P(B)*P(A|B)/P(A) = P(B)*P(A|B) / [P(B)*P(A|B) + P(B)*P(A|B)] (5.9a) _ _ _ _ _ _ _ P(B| A ) = P(B)*P(A|B)/P(A) = P(B)*P(A|B) / [P(B)*P(A|B) + P(B)*P(A|B)] (5.9b) Using Tree Diagrams for Solving Bayes’ Theorem Problems (see homework #3) P(A|B 1 ) P(B 1 ) /--------------- A P( A ∩B 1 ) = P(B 1 )*P(A|B 1 ) ------------ B 1 * ……………. Branches for conditional probabilities of other events / \---------------- Ā, C, D… that may be associated with the set of / hypotheses { B i } / P(A|B 2 ) / P(B 2 ) /-------------- A P( A ∩B 2 ) = P(B 2 )*P(A|B 2 ) / ------------ B 2 * …………… / \--------------- * …………………………. .. \ A set of branches that initiate from a single \ …………………………… point (*) have a total probability of 1. \ \ …………………………… \ \ P(A|B k ) \ P(B k ) /-------------- A P( A ∩B k ) = P(B k )*P(A|B k ) --------- B k * …………. . \--------------- 1. Start a tree diagram with branches representing hypotheses B 1 , B 2 , …, B k associated with the occurrence of an event A . Label each branch with its corresponding probability P(B i ) . 2.

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Example of using of BAYES' formula - Example of using of...

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