Bayesian Reasoning

• P(A &B) = P(A|B) * P(B)

Product Rule:

Bayesian Reasoning

• P(A &B) = P(A|B) * P(B)

Product Rule:

Shorthand for P(A=true & B=true) = P(A=true | B=true) * P(B=true)

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(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(A &B) = P(A|B) * P(B)

= P(B|A) * P(A)

Product Rules:

Rev. Thomas Bayes (1702-1761)

• P(A|B) = P(A & B) / P(B) = P(B|A) * P(A) / P(B)

Bayes’ Rule:

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 ReasoningOnline commentators cited my mother as an example of why no parent should hire a nanny. (In fact, parents and other familymembers 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(S & C) → P(B)

P(B & C) → P(S)

http://www.cdc.gov/nchs/data/hus/2010/022.pdf

Thou shalt not answer questionnairesOr quizzes upon World-Affairs,Nor with complianceTake any test. Thou shalt not sitWith statisticians nor commitA 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