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##### Bayesian Reasoning

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**Product Rule:**Bayesian Reasoning • P(A &B) = P(A|B) * P(B)**Product Rule:**Bayesian Reasoning • P(A &B) = P(A|B) * P(B) Shorthand for P(A=true & B=true) = P(A=true | B=true) * P(B=true)**Product Rule:**Bayesian Reasoning • P(A &B) = P(A|B) * P(B) = P(B|A) * P(A)**Product Rule:**Bayesian Reasoning • P(A &B) = P(A|B) * P(B) = P(B|A) * P(A) • P(A|B) = P(A &B) / P(B)**Rev. Thomas Bayes**(1702-1761) Product Rules: Bayesian Reasoning • P(A|B) = P(A &B) / P(B) • P(A &B) = P(A|B) * P(B) = P(B|A) * P(A) Bayes’ Rule: • P(A|B) = P(A &B) / P(B) • = P(B|A) * P(A) / P(B)**[C]onsidera situation in which painstaking survey work has**previously established that in the general population only 1% of subjects abuse a certain dangerous drug. Suppose that a person is randomly selected from [the] population for a drug test and the test yields a positive result. Suppose that the test has a 99% hit rate and a 5% false alarm rate. [How certain are we that the person is abusing the drug?] Bayesian Reasoning**[C]onsidera situation in which painstaking survey work has**previously established that in the general population only 1% of subjects abuse a certain dangerous drug. Suppose that a person is randomly selected from [the] population for a drug test and the test yields a positive result. Suppose that the test has a 99% hit rate and a 5% false alarm rate. [How certain are we that the person is abusing the drug?] Bayesian Reasoning**Online commentators cited my mother as an example of why no**parent should hire a nanny. (In fact, parents and other family members are responsible for nearly eighty percent of cases involving shaken-baby syndrome.) Bayesian Reasoning**Berkson’s Paradox(“Explaining Away”,Selection Bias)**Brainy Sporty College http://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html#explainaway**Berkson’s Paradox(“Explaining Away”,Selection Bias)**Brainy Sporty P(B & C) → P(S) College P(S & C) → P(B) http://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html#explainaway**Thou shalt not answer questionnaires**Or quizzes upon World-Affairs, Nor with compliance Take any test. Thou shalt not sit With statisticians nor commit A social science. - W.H. Auden (1907-1973)**The separation of state and church must be complemented by**the separation of state and science, that most recent, most aggressive, and most dogmatic religious institution. - Paul Feyerabend (1924-1994)