### Bayes` Rule Intro

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