= 27d567bc2d48d9f40e9ccc20ea370b15)
jsteinhardt comments on Rationality Quotes September 2013 - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (456)
Yeah. The problem is that most scientists seem to still be taught from textbooks that use a Popperian paradigm, or at least Popperian language, and they aren't necessarily taught probability theory very thoroughly, they're used to publishing papers that use p-value science even though they kinda know it's wrong, etc.
So maybe if we had an extended discussion about philosophy of science, they'd retract their Popperian statements and reformulate them to say something kinda related but less wrong. Maybe they're just sloppy with their philosophy of science when talking about subjects they don't put much credence in.
This does make it difficult to measure the degree to which, as Eliezer puts it, "the world is mad." Maybe the world looks mad when you take scientists' dinner party statements at face value, but looks less mad when you watch them try to solve problems they care about. On the other hand, even when looking at work they seem to care about, it often doesn't look like scientists know the basics of philosophy of science. Then again, maybe it's just an incentives problem. E.g. maybe the scientist's field basically requires you to publish with p-values, even if the scientists themselves are secretly Bayesians.
For what it's worth, I understand well the arguments in favor of Bayes, yet I don't think that scientific results should be published in a Bayesian manner. This is not to say that I don't think that frequentist statistics is frequently and grossly mis-used by many scientists, but I don't think Bayes is the solution to this. In fact, many of the problems with how statistics is used, such as implicitly performing many multiple comparisons without controlling for this, would be just as large of problems with Bayesian statistics.
Either the evidence is strong enough to overwhelm any reasonable prior, in which case frequentist statistics wlil detect the result just fine; or else the evidence is not so strong, in which case you are reduced to arguing about priors, which seems bad if the goal is to create a societal construct that reliable uncovers useful new truths.
No, the multiple comparisons problem, like optional stopping, and other selection effects that alter error probabilities are a much greater problem in Bayesian statistics because they regard error probabilities and the sampling distributions on which they are based as irrelevant to inference, once the data are in hand. That is a consequence of the likelihood principle (which follows from inference by Bayes theorem). I find it interesting that this blog takes a great interest in human biases, but guess what methodology is relied upon to provide evidence of those biases? Frequentist methods.
Deborah, what do you think of jsteinhardt's Beyond Bayesians and Frequentists?
But why not share likelihood ratios instead of posteriors, and then choose whether or not you also want to argue very much (in your scientific paper) about the priors?
What do you think "p<0.05" means?
(Your point is well taken but...)
Approximately it means "I have a financial or prestige incentive to find a relationship and I work in a field that doesn't take its science seriously".
Or, for instance in the case of particle physics, it means the probability you are just looking at background. You are painting with an overly broad brush. Sure, p-values are overused, but there are situations where the p-value IS the right thing to look at.
Well, technically, the probability that you will end up with a result given that you are just looking at background. I.e. the probability that after the experiment you will end up looking at background thinking it is not background*, assuming it is all background.
It's really awkward to describe that in English, though, and I just assume that this is what you mean (while Bayesianists assume that you are conflating the two).
Note that the 'brush' I am using is essentially painting the picture "0.05 is for sissies", not a rejection of p-values (which I may do elsewhere but with less contempt). The physics reference was to illustrate the contrast of standards between fields and why physics papers can be trusted more than medical papers.
That's what multiple testing correction is for.
With the thresholds from physics, we'd still be figuring out if penicillin really, actually kills certain bacteria (somewhat hyperbolic, 5 sigma ~ 1 in 3.5 million).
0.05 is a practical tradeoff, for supposed Bayesians, it is still much too strict, not too lax.
I for one think that 0.05 is way too lax (other than for the purposes of seeing whenever it is worth it to conduct a bigger study and other such value-of-information related uses) and 0.05 results require rather carefully constructed meta-study to interpret correctly. Because a selection factor of 20 is well within the range attainable by dodgy practices that are almost impossible to prevent, and even in the absence of the dodgy practices, selection due to you being more likely to hear of something interesting.
I can only imagine considering it too strict if I were unaware of those issues or their importance (Bayesianism or not)
This goes much more so for weaker forms of information, such as "Here's a plausible looking speculation I came up with". To get anywhere with that kind of stuff one would need to somehow account for the preference towards specific lines of speculation.
edit: plus, effective cures in medicine are the ones supported by very very strong evidence, on par with particle physics (e.g. the same penicillin killing bacteria, you have really big sample sizes when you are dealing with bacteria). The weak stuff - antidepressants for which we don't know if they lower or raise the risk of the suicide, and are uncertain whenever the effect is an artefact from using in any way whatsoever a depression score that includes weight loss and insomnia as symptoms when testing a drug that causes weight gain and sleepiness.
I think it is mostly because priors for finding a strongly effective drug are very low, so when large p-values are involved, you can only find low effect, near-placebo drugs.
edit2: Other issue is that many studies are plagued by at least some un-blinding that can modulate the placebo effect. So, I think a threshold on the strength of the effect (not just p-value) is also necessary - things that are within the potential systematic error margin from the placebo effect may mostly be a result of systematic error.
edit3: By the way, note that for a study of same size, stronger effect will result in much lower p-value, and so a higher standard on p-values does not interfere with detection of strong effects much. When you are testing an antibiotic... well, the chance probability of one bacterium dying in some short timespan may be 0.1, and with antibiotic at a fairly high concentration, 99.99999... . Needless to say, a dozen bacteria put you far beyond the standards from the particle physics, and a whole poisoned petri dish makes point moot, with all the unconfidence coming from the possibility of killing the bacteria in some other way.
No, it isn't. In an environment where the incentive to find a positive result in huge and there are all sorts of flexibilities in what particular results to report and which studies to abandon entirely, 0.05 leaves far too many false positives. I really does begin to look like this. I don't advocate using the standards from physics but p=0.01 would be preferable.
Mind you, there is no particularly good reason why there is an arbitrary p value to equate with 'significance' anyhow.
Well, I would find it really awkward for a Bayesian to condone a modus operandi such as "The p-value of 0.15 indicates it is much more likely that there is a correlation than that the result is due to chance, however for all intents and purposes the scientific community will treat the correlation as non-existent, since we're not sufficiently certain of it (even though it likely exists)".
Similar to having choice of two roads to go down, one of which leads into the forbidden forest. Then saying "while I have decent evidence which way goes where, because I'm not yet really certain, I'll just toss a coin." How many false choices would you make in life, using an approach like that? Neglecting your duty to update, so to speak. A p-value of 0.15 is important evidence. A p-value of 0.05 is even more important evidence. It should not be disregarded, regardless of the perverse incentives in publishing and the false binary choice (if (p<=0.05) correlation=true, else correlation=false). However, for the medical community, a p-value of 0.15 might as well be 0.45, for practical purposes. Not published = not published.
This is especially pertinent given that many important chance discoveries may only barely reach significance initially, not because their effect size is so small, but because in medicine sample sizes often are, with the accompanying low power of discovering new effects. When you're just a grad student with samples from e.g. 10 patients (no economic incentive yet, not yet a large trial), unless you've found magical ambrosia, p-values may tend to be "insignificant", even of potentially significant breakthrough drugs .
Better to check out a few false candidates too many than to falsely dismiss important new discoveries. Falsely claiming a promising new substance to have no significant effect due to p-value shenanigans is much worse than not having tested it in the first place, since the "this avenue was fruitless" conclusion can steer research in the wrong direction (information spreads around somewhat even when unpublished, "group abc had no luck with testing substances xyz").
IOW, I'm more concerned with false negatives (may never get discovered as such, lost chance) than with false positives (get discovered later on -- in larger follow-up trials -- as being false positives). A sliding p-value scale may make sense, with initial screening tests having a lax barrier signifying a "should be investigated further", with a stricter standard for the follow-up investigations.
It probably is too lax. I'd settle for 0.01, but 0.005 or 0.001 would be better for most applications (i.e - where you can get it). We have have the whole range of numbers between 1 in 25 and 1 in 3.5 million to choose from, and I'd like to see an actual argument before concluding that the number we picked mostly from historical accident was actually right all along. Still, a big part of the problem is the 'p-value' itself, not the number coming after it. Apart from the statistical issues, it's far too often mistaken for something else, as RobbBB has pointed out elsewhere in this thread.
No, it's the probability that you'd see a result that extreme (or more extreme) conditioned on just looking at background. Frequentists can't evaluate unconditional probabilities, and 'probability that I see noise given that I see X' (if that's what you had in mind) is quite different from 'probability that I see X given that I see noise'.
(Incidentally, the fact that this kind of conflation is so common is one of the strongest arguments against defaulting to p-values.)
Keep in mind that he and other physicists do not generally consider "probability that it is noise, given an observation X" to even be a statement about the world (it's a statement about one's personal beliefs, after all, one's confidence in the engineering of an experimental apparatus, and so on and so forth), so they are perhaps conflating much less than it would appear under very literal reading. This is why I like the idea of using the word "plausibility" to describe beliefs, and "probability" to describe things such as the probability of an event rigorously calculated using a specific model.
edit: note by the way that physicists can consider a very strong result - e.g. those superluminal neutrinos - extremely implausible on the basis of a prior - and correctly conclude that there is most likely a problem with their machinery, on the basis of ratio between the likelihood of seeing that via noise to likelihood of seeing that via hardware fault. How's that even possible without actually performing Bayesian inference?
edit2: also note that there is a fundamental difference as with plausibilities you will have to be careful to avoid vicious cycles in the collective reasoning. Plausibility, as needed for combining it with other plausibilities, is not a real number, it is a real number with attached description of how exactly it was made, so that evidence would not be double-counted. The number itself is of little use to communication for this reason.
It's about the probability that there is an effect which will cause this deviation from background to become more and more supported by additional data rather than simply regress to the mean (or with your wording, the other way around). That seems fairly based-in-the-world to me.
The actual reality either has this effect, or it does not. You can quantify your uncertainty with a number, that would require you to assign some a-priori probability, which you'll have to choose arbitrarily.
You can contrast this to a die roll which scrambles initial phase space, mapping (approximately but very close to) 1/6 of any physically small region of it to each number on the die, the 1/6 being an objective property of how symmetrical dies bounce.
The p-value is "the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true." It is often misinterpreted, e.g. by 68 out of 70 academic psychologists studied by Oakes (1986, pp. 79-82).
The p-value is not the same as the Bayes factor:
I wasn't saying it was the same, my point is that reporting the data on which one can update in Bayesian manner is the norm. (As is updating, e.g. if the null hypothesis is really plausible, at p<0.05 nobody's really going to believe you anyway)
With regards to the Bayes factor. The issue is that there is a whole continuum of alternate hypotheses. There's no single factor between those that you can report on which could be used for combining evidence in favour of quantitatively different alternative "most supported" hypotheses. The case of the null hypothesis (vs all possible other hypotheses) is special in that regard, and so that is what a number is reported for.
With regards to the case of the ratio between evidence for two point hypotheses, as discussed in the article you link: Neyman-Pearson lemma is quite old.
With regards to the cause of experiment termination, you have to account somewhere for the fact that termination of the experiment has the potential to cherry pick and thus bias the resulting data (if that is what he's talking about, because its not clear to me what is his point and it seems to me that he misunderstood the issue).
Furthermore, the relevant mathematics probably originates from the particle physics, where it serves a different role: a threshold on the p-value is here to quantify the worst-case likelihood that your experimental apparatus will be sending people on the wild goose chase. It has more to do with the value of the experiment than probabilities, given that priors for hypotheses in physics would require a well defined hypotheses space (which is absent). And given that the work on the production of stronger evidence is a more effective way to spend your time there than any debating of the priors. And given that the p-value related issues in any case can be utterly dwarfed by systematic errors and problems with the experimental set up, something the probability of which changes after the publication as other physicists do or do not point towards potential problems in the set up.
A side note: there's a value of information issue here. I know that if I were to discuss Christian theology with you (not the atheism, but the fine points of the life of Jesus, that sort of thing, which I never really had time or inclination to look into), the expected value of information to you would be quite low. Because most of the time that I spent practising mathematics and such, you spent on the former. It would be especially the case if you entered some sort of very popular contest in any way requiring theological knowledge, and scored #10th of all time on a metric that someone else seen fit to chose in advance. The same goes for discussions of mathematics, but the other way around. This is also the case for any experts you are talking to. They're rather rational people, that's how they got to have impressive accomplishments, and a lot of practical rationality is about ignoring low expected value pursuits. Einsteins and Fermis of this world do not get to accomplish so much on so many different occasions without great innate abilities for that kind of thing. They also hold teaching positions and it is more productive for them to correct misconceptions in the eager students who are up to speed on the fundamental knowledge.
(with #10th I'm alluding to this result of mine ).
Mmm. I've read a lot of dumb papers where they show that their model beats a totally stupid model, rather than that their model beats the best model in the literature. In algorithm design fields, you generally need to publish a use case where your implementation of your new algorithm beats your implementation of the best other algorithms for that problem in the field (which is still gameable, because you implement both algorithms, but harder).
Thinking about the academic controversy I learned about most recently, it seems like if authors had to say "this evidence is n:1 support for our hypothesis over the hypothesis proposed in X" instead of "the evidence is n:1 support for our hypothesis over there being nothing going on" they would have a much harder time writing papers that don't advance the literature, and you might see more scientists being convinced of other hypotheses because they have to implement them personally.
In physics a new theory has to be supported over the other theories, for example. What you're talking about would have to be something that happens in sciences that primarily find weak effects in the noise and co-founders anyway, i.e. psychology, sociology, and the like.
I think you need to specifically mention what fields you are talking about, because not everyone knows that issues differ between fields.
With regards to malemployment debate you link, there's a possibility that many of the college graduates have not actually learned anything that they could utilize, in the first place, and consequently there exist nothing worth describing as 'malemployment'. Is that the alternate model you are thinking of?
Most of the examples I can think of come from those fields. There are a few papers in harder sciences which people in the field don't take seriously because they don't address the other prominent theories, but which people outside of the field think look serious because they're not aware that the paper ignores other theories.
I was thinking mostly that it looked like the two authors were talking past one another. Group A says "hey, there's heterogeneity in wages which is predicted by malemployment" whereas Group B says "but average wages are high, so there can't be malemployment," which ignores the heterogeneity. I do think that a signalling model of education (students have different levels of talent, and more talented students tend to go for more education, but education has little direct effect on talent) explains the heterogeneity and the wage differentials, and it would be nice to see both groups address that as well.
Once again, which education? Clearly, a training course for, say, a truck driver, is not signalling, but exactly what it says on the can: a training course for driving trucks. A language course, likewise so. Same goes for mathematics, hard sciences, and engineering disciplines. Which may perhaps be likened to necessity of training for a formula 1 driver, irrespective of the level of innate talent (within the human range of ability).
Now, if that was within the realm of actual science, something like this "signalling model of education" would be immediately invalidated by the truck driving example. No excuses. One can mend it into a "signalling model of some components of education in soft sciences". Where there's a big problem for "signalling" model: a PhD in those fields in particular is a poorer indicator of ability, innate and learned, than in technical fields (lower average IQs, etc), and signals very little.
edit: by the way, the innate 'talent' is not in any way exclusive of importance of learning; some recent research indicates that highly intelligent individuals retain neuroplasticity for longer time, which lets them acquire more skills. Which would by the way explain why child prodigies fairly often become very mediocre adults, especially whenever lack of learning is involved.