wow, thank you so much for this, made the concept so much clearer to me 
@Bips: Glad it helped!
[…] An Intuitive Explanation of Bayes’ Theorem – Eliezer Yudkowsky (shorter version here) […]
This post is filled with jargon, and I’m surprised people can tolerate it.
Nicely explained; this really helped me study for my stat final. Thanks!
Thanks so much for this simple breakdown!
“A Bayesian is someone who, vaguely expecting a horse, and glimpsing the tail of a donkey, concludes he has probably seen a mule.” - John Hussman
Not really helpful, but rather funny.
[…] is a really good guide to Bayes’ Theorem for […]
[…] An Intuitive (and Short) Explanation of Bayes' Theorem | BetterExplained Reply With Quote + Reply to Thread « Previous Thread | […]
@MH: Awesome, glad it helped.
Here are two contradictory statements in your article regarding False positives. I quote:
Pr(X|~A) = Chance of a positive test (X) given that you didn’t have cancer (~A). This is a false positive, 9.6% in our case.
The chances of a false positive = chance you don’t have cancer * chance test caught it anyway = 99% * 9.6% = 0.09504
These two interpretations of false positives are often mixed in various texts.
One is Pr(X|~A) and the other is Pr(X∩~A)
[…] An Intuitive (and Short) Explanation of Bayes' Theorem | BetterExplained Bayes' theorem was the subject of a detailed article. The essay is good, but over 15000 words long — here's the condensed version for Bayesian newcomers like myself: Tests are not the event. W… […]
You might want to look at this if you want to understand Bayes’ theorem in less than 2.5 minutes: http://www.youtube.com/watch?v=D8VZqxcu0I0
[…] If you are interested in reading a bit more, perhaps the best introduction to Bayes’ theorem is the Wikipedia introductory example – I strongly recommend you check it out. For a more thorough introduction I recommend reading the excellent post “An intuitive and short explanation of Bayes’ Theorem”. […]
[…] the likelihood of an event, based on a prior estimate and new information. His work is called Bayes Theorem, and it’s a simple equation. To solve it you need three […]
[…] Sounds like a false positive… An Intuitive (and Short) Explanation of Bayes' Theorem | BetterExplained Reply With Quote « Previous Thread | Next Thread […]
[…] Questions using Bayes Theorem then become just exercises in plugging percentages to these formulae. Often using a table can be a good idea. There are good examples of doing it that way here. […]
Do you know of “The theory that would not die,” Sharon Bertsch McGrayne’s history of the Bayes controversy? It is history at its best including breaking the Enigma Code during the Second World War, plus lots of other applications. The book was published by Yale University Press in 2011.
@Geoff: Glad it helped! I’m planning on doing a follow-up to Bayes since it’s used so much in spam filtering and other machine learning.