1 / 17

Understanding Bayesian Reasoning and Product Rules

Learn how to apply Bayesian Reasoning and Product Rules to calculate probabilities confidently. Includes examples and explanations to master this essential statistical concept.

andres
Download Presentation

Understanding Bayesian Reasoning and Product Rules

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Product Rule: Bayesian Reasoning • P(A &B) = P(A|B) * P(B)

  2. 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)

  3. Product Rule: Bayesian Reasoning • P(A &B) = P(A|B) * P(B) = P(B|A) * P(A)

  4. 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)

  5. 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)

  6. [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

  7. [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

  8. 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

  9. Berkson’s Paradox(“Explaining Away”,Selection Bias) Brainy Sporty College http://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html#explainaway

  10. 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

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

  12. 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)

  13. 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)

  14. … quod bonumesttenete

More Related