the theory that would not die how Bayes' rule cracked the enigma code, hunted down Russian submarines, and emerged triumphant from two centuries of controversy McGrayne, S. B., Yale University Press, 2011
You are sitting in front of a doctor and she says …
4 million – HIV- 1,400 – HIV+ Test has a 1% error rate If don’t have HIV then 1% of time it says you have it If you do have HIV then 1% of time it says you don’t have it You have been told that you have a positive test (and you don’t use intravenous drugs recreationally or partake of risky sexual practices) What is the probability that you actually have an HIV infection?
P(Data|Hyp) Data HypAC A99% 1% C 1%99% P(Hyp) A 99.9% C 0.1% Reference A C Read
Reference A C A 99.9% C 0.1% A -> A 98.9% A->C 0.999% C -> C 0.099% 10 -3 % A->C 0.999% C -> C 0.099% Read C A->C 91% C -> C 9% A->C -> A C->C->A A->C->C 0.91% C->C->C 8.9% A->C->C 9.25% C->C->C 90.75% A->C->C 0.91%
Bayesian Statistics Simple mathematical basis Long period before it was used widely conceptual problems computationally difficult (Hyp can get very large) Technique useful for many otherwise intractable problems