andrew_gelman_stats andrew_gelman_stats-2013 andrew_gelman_stats-2013-1695 knowledge-graph by maker-knowledge-mining
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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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1 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. [sent-6, score-0.599]
2 (In the subfield of survey sampling, various prominent researchers would refuse to model the data at all while having no problem treating nominal sampling problems as if they were real (despite this sort of evidence to the contrary). [sent-7, score-0.357]
3 Those were the dark days, when even to do Bayesian inference (outside of some small set of fenced-in topics such as genetics that had very clear prior distributions) made you suspect in some quarters. [sent-9, score-0.386]
4 Bayesian methods are not only accepted, they’re thriving to the extent that in many cases the strongest argument against Bayes is that it’s not universally wonderful (a point with which I agree; see yesterday’s discussion ). [sent-12, score-0.373]
5 The field really has moved forward, and indeed one reason why I don’t think Bayesian methods are always so necessary is that non-Bayesian methods use similar ideas. [sent-21, score-0.35]
6 Take-home message for economists One thing I’d like economists to get out of this discussion is: statistical ideas matter. [sent-23, score-0.289]
7 A lot of the best statistical methods out there—however labeled—work by combining lots of information and modeling the resulting variation. [sent-31, score-0.389]
8 Instead, hypothesis testing typically means that you do what’s necessary to get statistical significance, then you make a very strong claim that might make no sense at all. [sent-37, score-0.621]
9 Or, conversely, you slice the data up into little pieces so that no single piece is statistically significant, and then act as if the effect you’re studying is zero. [sent-39, score-0.325]
10 The sad story of conventional hypothesis testing is that it is all to quick to run with a statistically significant result even if it’s coming from noise. [sent-40, score-0.368]
11 Smith elaborates and makes another mistake, writing: If I have a strong prior, and crappy data, in Bayesian I know exactly what to do; I stick with my priors. [sent-42, score-0.344]
12 In Frequentist, nobody tells me what to do, but what I’ll probably do is weaken my prior based on the fact that I couldn’t find strong support for it. [sent-43, score-0.452]
13 Third, if you have weak data and your prior is informative, this does not imply that your prior should be weakened! [sent-51, score-0.828]
14 If my prior reading of the literature suggests that a parameter theta should be between -0. [sent-52, score-0.383]
15 I very much respect the idea of data reduction and summarizing the information from any particular study without prejudice, but if I have to make a decision or a scientific inference, then I see no reason to rely on whatever small dataset happens to be in my viewer right now. [sent-55, score-0.636]
16 No matter how kosher the data summary was (and, actually, in that case the published analysis had problems even as a classical data summary), the punchline of the paper was a generalization about the population—an inference. [sent-60, score-0.485]
17 Still, there’s a lot more information in the mass of polls than in any single survey. [sent-64, score-0.305]
18 So, to the extent that “Bayesian” is associated with using additional information rather than relying on a single dataset, I see why Nate is happy to associate himself with that label. [sent-65, score-0.299]
19 To put it another way: to the non-Bayesian, a Bayesian is someone who pollutes clean data with a subjective prior distribution. [sent-66, score-0.593]
20 Again, I see that this can be a useful principle for creating data summaries (each polling organization can report its own numbers based on its own data) but it doesn’t make a lot of sense to me if the goal is decision making or scientific inference. [sent-68, score-0.612]
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