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Bayesian Reasoning Product Rule: • P(A &B) = P(A|B) * P(B) Bayesian Reasoning Product Rule: • P(A &B) = P(A|B) * P(B) Shorthand for P(A=true & B=true) = P(A=true | B=true) * P(B=true) Bayesian Reasoning Product Rule: • P(A &B) = P(A|B) * P(B) = P(B|A) * P(A) Bayesian Reasoning Product Rule: • P(A &B) = P(A|B) * P(B) = P(B|A) * P(A) • P(A|B) = P(A & B) / P(B) Bayesian Reasoning Product Rules: • 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) Rev. Thomas Bayes (1702-1761) Bayesian Reasoning [C]onsider a 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]onsider a 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.) 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 College http://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html#explainaway P(B & C) → P(S) P(S & C) → P(B) http://www.cdc.gov/nchs/data/hus/2010/022.pdf 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) … quod bonum est tenete