1132: Frequentists vs. Bayesians

2012-11-29T15:26:15Z

198.84.184.180: /* Explanation */

{{comic
| number = 1132
| date = November 9, 2012
| title = Frequentists vs. Bayesians
| image = frequentists_vs_bayesians.png
| imagesize =
| titletext = 'Detector! What would the Bayesian statistician say if I asked him whether the--'<br>[roll] 'I AM A NEUTRINO DETECTOR, NOT A LABYRINTH GUARD. SERIOUSLY, DID YOUR BRAIN FALL OUT?'<br>[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 {{w|Bayes Theorem|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 and the last two frames suggest that "frequentist" interpretation of statistics is somehow wrong, which is not actually the case. The Bayesian interpretation and the frequentist interpretation are not mutually exclusive and neither is wrong. It's the misuse of P values that causes the character in the panel labeled "Frequentist Statistician" to conclude that the sun has exploded, not the use of frequentist statistics. (In particular, P-values are usually used only for numerical values that are known to fall along a specific distribution – in this case, it is used to determine the significance of a discrete event, which is wrong.)

The final panel is a tongue-in-cheek reference to the absurdity of the premise. If the sun did explode, he won't need to pay out the bet because the Earth and everyone on it would be destroyed. But if it didn't explode, then he'll win $50. It also likely refers to a well-publicized bet that Nate Silver tried to make with Joe Scarborough regarding the outcome of the election:

[[File:Nate Silver Tweet.png|.@JoeNBC: If you think it's a toss-up, let's bet. If Obama wins, you donate $1,000 to the American Red Cross. If Romney wins, I do. Deal?|right]]

The title text refers to a classic series of logic puzzles known as {{w|Knights_and_Knaves#Question_3|Knights and Knaves}}, 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. Two such guards were featured in the 1986 Jim Henson movie ''Labyrinth'', which is referenced in the text.

==Transcript==
:Did the sun just explode? (It's night, so we're not sure)

:[Two statisticians stand alongside an adorable little computer that is suspiciously similar to K-9 that speaks in Westminster typeface]
:Frequentist Statistician: This neutrino detector measures whether the sun has gone nova.
:Bayesian Statistician: Then, it rolls two dice. If they both come up as six, it lies to us. Otherwise, it tells the truth.
:Frequentist Statistician:: Let's try. [to the detector] Detector! Has the sun gone nova?
:Detector: ''roll'' YES.

:Frequentist Statistician:
:Frequentist Statistician: The probability of this result happening by chance is 1/36=0.027. Since p<0.05, I conclude that the sun has exploded.

:Bayesian Statistician:
:Bayesian Statistician: Bet you $50 it hasn't.

{{comic discussion}}
[[Category:Comics featuring Cueball]]
[[Category:Math]]
[[Category:Statistics]]
[[Category:Physics]]

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1132: Frequentists vs. Bayesians