1132: Frequentists vs. Bayesians

Explain xkcd: It's 'cause you're dumb.
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The title text refers to a classic series of logic puzzles (and the movie Labyrinth), where there are two guards in front of two exit doors, one of which is real and the other leads to death. One guard is a liar and the other tells the truth. The visitor doesn't know which is which, and is allowed to ask one question to one guard. The solution is to ask either guard what the other one would say is the real exit, then choose the opposite.
 
The title text refers to a classic series of logic puzzles (and the movie Labyrinth), where there are two guards in front of two exit doors, one of which is real and the other leads to death. One guard is a liar and the other tells the truth. The visitor doesn't know which is which, and is allowed to ask one question to one guard. The solution is to ask either guard what the other one would say is the real exit, then choose the opposite.
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It is always a good bet that the sun hasn't gone nova, if you can get anyone to take it.  When you lose, there will not be time to collect.

Revision as of 15:23, 9 November 2012

Frequentists vs. Bayesians
'Detector! What would the Bayesian statistician say if I asked him whether the--'[roll] 'I AM A NEUTRINO DETECTOR, NOT A LABYRINTH GUARD. SERIOUSLY, DID YOUR BRAIN FALL OUT?'[roll] '... yes.'
Title text: 'Detector! What would the Bayesian statistician say if I asked him whether the--'
[roll] 'I AM A NEUTRINO DETECTOR, NOT A LABYRINTH GUARD. SERIOUSLY, DID YOUR BRAIN FALL OUT?'
[roll] '... yes.'

Explanation

This is another comic about the accuracy of presidential election predictions that used Bayesian statistical models, such as Nate Silver's 538 and Professor Sam Wang's PEC. Thomas Bayes studied conditional probability - the likelihood that one event is true when given information about some other related event. From Wikipedia: "Bayesian interpretation expresses how a subjective degree of belief should rationally change to account for evidence".

In the comic, the likelihood that the detector is lying is much higher than the likelihood of the Sun exploding. Therefore, one should conclude that a single "yes" result is probably a false positive. The bit about "p < 0.05" comes from a naive interpretation of modern scientific research standards (known as the P value), where a result is presumed to be valid if there is less than a 5% chance that it came from random chance. There is a 1/36 chance of rolling two sixes on 2d6.

The title text refers to a classic series of logic puzzles (and the movie Labyrinth), where there are two guards in front of two exit doors, one of which is real and the other leads to death. One guard is a liar and the other tells the truth. The visitor doesn't know which is which, and is allowed to ask one question to one guard. The solution is to ask either guard what the other one would say is the real exit, then choose the opposite.

It is always a good bet that the sun hasn't gone nova, if you can get anyone to take it. When you lose, there will not be time to collect.

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