andrew_gelman_stats andrew_gelman_stats-2012 andrew_gelman_stats-2012-1182 knowledge-graph by maker-knowledge-mining
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Introduction: Ryan Ickert writes: I was wondering if you’d seen this post , by a particle physicist with some degree of influence. Dr. Dorigo works at CERN and Fermilab. The penultimate paragraph is: From the above expression, the Frequentist researcher concludes that the tracker is indeed biased, and rejects the null hypothesis H0, since there is a less-than-2% probability (P’<α) that a result as the one observed could arise by chance! A Frequentist thus draws, strongly, the opposite conclusion than a Bayesian from the same set of data. How to solve the riddle? He goes on to not solve the riddle. Perhaps you can? Surely with the large sample size they have (n=10^6), the precision on the frequentist p-value is pretty good, is it not? My reply: The first comment on the site (by Anonymous [who, just to be clear, is not me; I have no idea who wrote that comment], 22 Feb 2012, 21:27pm) pretty much nails it: In setting up the Bayesian model, Dorigo assumed a silly distribution on th
sentIndex sentText sentNum sentScore
1 Ryan Ickert writes: I was wondering if you’d seen this post , by a particle physicist with some degree of influence. [sent-1, score-0.35]
2 The penultimate paragraph is: From the above expression, the Frequentist researcher concludes that the tracker is indeed biased, and rejects the null hypothesis H0, since there is a less-than-2% probability (P’<α) that a result as the one observed could arise by chance! [sent-4, score-0.423]
3 Surely with the large sample size they have (n=10^6), the precision on the frequentist p-value is pretty good, is it not? [sent-9, score-0.188]
4 My reply: The first comment on the site (by Anonymous [who, just to be clear, is not me; I have no idea who wrote that comment], 22 Feb 2012, 21:27pm) pretty much nails it: In setting up the Bayesian model, Dorigo assumed a silly distribution on the underlying parameter. [sent-10, score-0.419]
5 All sorts of silly models can work in some settings, but when a model gives nonsensical results—in this case, stating with near-certainty that a parameter equals zero, when the data clearly reject that hypothesis—then, it’s time to go back and figure out what in the model went wrong. [sent-11, score-0.551]
6 Our models are approximations that work reasonably well in some settings but not in others. [sent-13, score-0.19]
7 Dorigo also writes: A Bayesian researcher will need a prior probability density function (PDF) to make a statistical inference: a function describing the pre-experiment degree of belief on the value of R. [sent-16, score-0.597]
8 First, in general there is nothing more subjective about a prior distribution than about a data model: both are based on assumptions. [sent-19, score-0.373]
9 Second, if you have information, then it’s not “the lesser evil” to include it. [sent-20, score-0.159]
10 They said it was ok, but one wrote: There is a lot of poop being thrown these days between bayesians and frequentists. [sent-28, score-0.176]
11 I am not sure why; that fight seems so 2003 to me. [sent-29, score-0.072]
12 One thing I like about Bayesian methods is how they force you to put your assumptions out there, potentially to be criticized. [sent-33, score-0.166]
13 But I understand that others prefer a mode of inference that makes minimal assumptions. [sent-34, score-0.282]
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Introduction: Ryan Ickert writes: I was wondering if you’d seen this post , by a particle physicist with some degree of influence. Dr. Dorigo works at CERN and Fermilab. The penultimate paragraph is: From the above expression, the Frequentist researcher concludes that the tracker is indeed biased, and rejects the null hypothesis H0, since there is a less-than-2% probability (P’<α) that a result as the one observed could arise by chance! A Frequentist thus draws, strongly, the opposite conclusion than a Bayesian from the same set of data. How to solve the riddle? He goes on to not solve the riddle. Perhaps you can? Surely with the large sample size they have (n=10^6), the precision on the frequentist p-value is pretty good, is it not? My reply: The first comment on the site (by Anonymous [who, just to be clear, is not me; I have no idea who wrote that comment], 22 Feb 2012, 21:27pm) pretty much nails it: In setting up the Bayesian model, Dorigo assumed a silly distribution on th
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Introduction: Robert Bell pointed me to this post by Brad De Long on Bayesian statistics, and then I also noticed this from Noah Smith, who wrote: My impression is that although the Bayesian/Frequentist debate is interesting and intellectually fun, there’s really not much “there” there… despite being so-hip-right-now, Bayesian is not the Statistical Jesus. I’m happy to see the discussion going in this direction. Twenty-five years ago or so, when I got into this biz, there were some serious anti-Bayesian attitudes floating around in mainstream statistics. Discussions in the journals sometimes devolved into debates of the form, “Bayesians: knaves or fools?”. You’d get all sorts of free-floating skepticism about any prior distribution at all, even while people were accepting without question (and doing theory on) logistic regressions, proportional hazards models, and all sorts of strong strong models. (In the subfield of survey sampling, various prominent researchers would refuse to mode
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Introduction: Ryan Ickert writes: I was wondering if you’d seen this post , by a particle physicist with some degree of influence. Dr. Dorigo works at CERN and Fermilab. The penultimate paragraph is: From the above expression, the Frequentist researcher concludes that the tracker is indeed biased, and rejects the null hypothesis H0, since there is a less-than-2% probability (P’<α) that a result as the one observed could arise by chance! A Frequentist thus draws, strongly, the opposite conclusion than a Bayesian from the same set of data. How to solve the riddle? He goes on to not solve the riddle. Perhaps you can? Surely with the large sample size they have (n=10^6), the precision on the frequentist p-value is pretty good, is it not? My reply: The first comment on the site (by Anonymous [who, just to be clear, is not me; I have no idea who wrote that comment], 22 Feb 2012, 21:27pm) pretty much nails it: In setting up the Bayesian model, Dorigo assumed a silly distribution on th
Introduction: X writes : This paper discusses the dual interpretation of the Jeffreys– Lindley’s paradox associated with Bayesian posterior probabilities and Bayes factors, both as a differentiation between frequentist and Bayesian statistics and as a pointer to the difficulty of using improper priors while testing. We stress the considerable impact of this paradox on the foundations of both classical and Bayesian statistics. I like this paper in that he is transforming what is often seen as a philosophical argument into a technical issue, in this case a question of priors. Certain conventional priors (the so-called spike and slab) have poor statistical properties in settings such as model comparison (in addition to not making sense as prior distributions of any realistic state of knowledge). This reminds me of the way that we nowadays think about hierarchical models. In the old days there was much thoughtful debate about exchangeability and the so-called Stein paradox that partial pooling
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