Editing Talk:1132: Frequentists vs. Bayesians
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Something should be added about the prior probability of the sun going nova, as that is the primary substantive point. "The neutrino detector is evidence that the Sun has exploded. It's showing an observation which is 35 times more likely to appear if the Sun has exploded than if it hasn't (likelihood ratio of 35:1). The Bayesian just doesn't think that's strong enough evidence to overcome the prior odds, i.e., after multiplying the prior odds by 35 they still aren't very high." - http://lesswrong.com/r/discussion/lw/fe5/xkcd_frequentist_vs_bayesians/ [[Special:Contributions/209.65.52.92|209.65.52.92]] 23:51, 9 November 2012 (UTC) | Something should be added about the prior probability of the sun going nova, as that is the primary substantive point. "The neutrino detector is evidence that the Sun has exploded. It's showing an observation which is 35 times more likely to appear if the Sun has exploded than if it hasn't (likelihood ratio of 35:1). The Bayesian just doesn't think that's strong enough evidence to overcome the prior odds, i.e., after multiplying the prior odds by 35 they still aren't very high." - http://lesswrong.com/r/discussion/lw/fe5/xkcd_frequentist_vs_bayesians/ [[Special:Contributions/209.65.52.92|209.65.52.92]] 23:51, 9 November 2012 (UTC) | ||
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Here's what I get for the application of Bayes' Theorem: | Here's what I get for the application of Bayes' Theorem: | ||
− | : P(N|Y) = P(Y|N) * P(N) / P(Y): = P(Y|N) * P(N) / [P(Y|N) * P(N) + P(Y|~N) * P(~N)] | + | : P(N|Y) = P(Y|N) * P(N) / P(Y) |
+ | : = P(Y|N) * P(N) / [P(Y|N) * P(N) + P(Y|~N) * P(~N)] | ||
: = 35/36 * P(N) / [35/36 * P(N) + 1/36 * (1 - P(N))] | : = 35/36 * P(N) / [35/36 * P(N) + 1/36 * (1 - P(N))] | ||
: = 35 * P(N) / [35 * P(N) - P(N) + 1] | : = 35 * P(N) / [35 * P(N) - P(N) + 1] | ||
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:Yes, you would be able to ask. While neutrinos move almost at speed of light, the plasma of the explosion is significally slower, [http://en.wikipedia.org/wiki/Supernova 10% of speed of light tops]. You will have more that hour to ask. (Note that technically, sun can't go [http://en.wikipedia.org/wiki/Nova nova], because nova is white dwarf with external source of hydrogen. It can (and will), however, go supernova, which I assume is what Randall means.) -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 09:19, 12 November 2012 (UTC) | :Yes, you would be able to ask. While neutrinos move almost at speed of light, the plasma of the explosion is significally slower, [http://en.wikipedia.org/wiki/Supernova 10% of speed of light tops]. You will have more that hour to ask. (Note that technically, sun can't go [http://en.wikipedia.org/wiki/Nova nova], because nova is white dwarf with external source of hydrogen. It can (and will), however, go supernova, which I assume is what Randall means.) -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 09:19, 12 November 2012 (UTC) | ||
− | :: | + | :: Nor can the sun go supernova, as it has insufficient mass. It will slowly become hotter, rendering Earth uninhabitable in a few billion years. In about 5 billion years it will puff up into a red giant, swallowing the inner planets. After that, it will gradually blow off its lighter gasses, eventually leaving behind the core, a white dwarf. {{unsigned|50.0.38.245}} |
− | ::: | + | :::I left your comment here so I can set you straight on something. '''''DO NOT EVER''''' edit any editor's comments on a discussion page. You can reply to their comment, but you do not edit another person's words. You do that again, you get the banhammer. [[User:Lcarsos|lcarsos]] ([[User talk:Lcarsos|talk]]) 17:38, 13 November 2012 (UTC) |
I think the explanation is wrong or otherwise lacking in its explanation: The P-value is not the entire problem with the frequentist's viewpoint (or alternatively, the problem with the p-value hasn't been explained). The Frequentist has looked strictly at a two case scenario: Either the machine rolls 6-6 and is lying, or it doesn't rolls 6-6 and it is telling the truth. Therefore, there is a 35/36 probability (97.22%) that the machine is telling the truth and therefore the sun has exploded. The Bayesian is factoring in outside facts and information to improve the accuracy of the probability model. He says "Either the machine rolls 6-6 (a 1/36 probability, or 2.77%) or the sun has exploded (an aparently far less likely scenario). Given the comparison, the Bayesian believes it is MORE probable that the machine rolled 6-6 than the sun exploded, given the relative probabilities. If the latter is a 1 in a million chance (0.000001%), it is 2,777,777 times more likely that the machine rolled 6-6 than the sun exploded. | I think the explanation is wrong or otherwise lacking in its explanation: The P-value is not the entire problem with the frequentist's viewpoint (or alternatively, the problem with the p-value hasn't been explained). The Frequentist has looked strictly at a two case scenario: Either the machine rolls 6-6 and is lying, or it doesn't rolls 6-6 and it is telling the truth. Therefore, there is a 35/36 probability (97.22%) that the machine is telling the truth and therefore the sun has exploded. The Bayesian is factoring in outside facts and information to improve the accuracy of the probability model. He says "Either the machine rolls 6-6 (a 1/36 probability, or 2.77%) or the sun has exploded (an aparently far less likely scenario). Given the comparison, the Bayesian believes it is MORE probable that the machine rolled 6-6 than the sun exploded, given the relative probabilities. If the latter is a 1 in a million chance (0.000001%), it is 2,777,777 times more likely that the machine rolled 6-6 than the sun exploded. | ||
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Another source of explanation: http://stats.stackexchange.com/questions/43339/whats-wrong-with-xkcds-frequentists-vs-bayesians-comic --[[User:JakubNarebski|JakubNarebski]] ([[User talk:JakubNarebski|talk]]) 20:12, 12 November 2012 (UTC) | Another source of explanation: http://stats.stackexchange.com/questions/43339/whats-wrong-with-xkcds-frequentists-vs-bayesians-comic --[[User:JakubNarebski|JakubNarebski]] ([[User talk:JakubNarebski|talk]]) 20:12, 12 November 2012 (UTC) | ||
− | The P-value really has nothing to do with it. If I think that there is a 35/36 chance that the sun has exploded, then I should we willing to take any bet that the sun has exploded with better than 1:35 odds. For example, if someone bets me that the sun has exploded in which they will pay me $2 if the sun has exploded and I will pay them $35 if it hasn't, then based on my belief that the sun has exploded with 35/36 probability, then my expected value for this bet is 2*35/36 - 35 * 1/36 = 35/36 dollars and I will take this bet. Clearly I would also take a bet with 1:1 odds - my estimated expected value in the proposed bet in the comic would be 50*35/36 - 50 * 1/36 = $49 (approximately), and I would for sure take this bet. The Bayesian on the other hand has a much lower belief that the sun has exploded because he takes into account the prior probability of the sun exploding, so he would take the reverse side of the bet. The difference is that the Bayesian uses prior probabilities in computing his belief in an event, whereas frequentists do not believe that you can put prior probabilities on events in the real world. Also note that this comic has nothing to do with whether people would die if the sun went nova - the comic is titled "Frequentists vs Bayesians" and is about the difference between these two approaches. | + | The P-value really has nothing to do with it. If I think that there is a 35/36 chance that the sun has exploded, then I should we willing to take any bet that the sun has exploded with better than 1:35 odds. For example, if someone bets me that the sun has exploded in which they will pay me $2 if the sun has exploded and I will pay them $35 if it hasn't, then based on my belief that the sun has exploded with 35/36 probability, then my expected value for this bet is 2*35/36 - 35 * 1/36 = 35/36 dollars and I will take this bet. Clearly I would also take a bet with 1:1 odds - my estimated expected value in the proposed bet in the comic would be 50*35/36 - 50 * 1/36 = $49 (approximately), and I would for sure take this bet. The Bayesian on the other hand has a much lower belief that the sun has exploded because he takes into account the prior probability of the sun exploding, so he would take the reverse side of the bet. The difference is that the Bayesian uses prior probabilities in computing his belief in an event, whereas frequentists do not believe that you can put prior probabilities on events in the real world. Also note that this comic has nothing to do with whether people would die if the sun went nova - the comic is titled "Frequentists vs Bayesians" and is about the difference between these two approaches. |
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