“plugging in the known value of Q(T | awake, room 1),”
But that is not known! That’s the value I am contesting your derivation of. You have asserted that it is 0.5 supposedly due to Bayes law but I am telling you that the math does not work out that way. If you want to convince me that Bayes law forces Q(T|awake, room 1) to be 0.5, then you need to write out that application of Bayes law and derive the number 0.5, not simply plug it in.
tgb
Karma: 1,873
You say: “being in room 1 is equally consistent with
Here it is with plugging in an unknown t instead of assuming a value of Q(T|awake):
Q(T| awake, room 1) = Q(room 1 | T, awake) Q (T | awake) / Q(room 1 | awake)
If Q(T|awake) = t, then Q(H | awake) = 1-t and Q(room 1| T, awake) = 0.5 etc. give that Q(room 1 | awake) = t /2 + (1-t) = 1 - t/2
So:
Q(T| awake, room 1) = (1/2) (t) / (1-t/2) = t/(2 - t)
For this to equal your value of 0.5, you must be assuming that t := Q(T|awake) = 2⁄3. I suspect you heuristically did “room 1 is ‘equally consistent’ with T and H meaning the the likelihoods are equal and so their posteriors are equal”. However, the likelihoods are not the same: room 1 is more consistent with H than with T in the sense of likelihoods and Bayes rule uses this. If you still think I’m wrong, please write out exactly the computation you’re claiming, which you haven’t yet done.
The problem is that we don’t know what P(T | awake) is (the P(A|C) factor in your notation). That’s the whole question at hand. You are implicitly assuming some value for it in this step.
Isn’t your application of Bayes’s rule wrong?
P(T | awake, room 1) = P(room 1 | T, awake) P (T | awake) / P(room 1 | awake)
The second and third factors on the RHS are exactly the values under contention.
Your estimate isn’t actually very good at estimating the population standard deviation (it substantially overestimates it), but it is good for estimating confidence intervals. That’s because confidence intervals also require you to account for the variance of the estimate of the mean, which is large when you only have two samples.
Simulating it out:
import numpy as np
x = np.random.normal(size=(100_000, 2))
diff = np.max(x, axis=1) - np.min(x, axis=1)
std_est = diff * 1.3
print(np.mean(std_est))
print(np.median(std_est))
This shows it over estimates (mean: 1.46, median 1.23, while the true standard deviation is 1). Using max—min gives a better estimator by both mean (1.13) and median (0.96). You are right that both the corrected sample standard deviation (max—min / sqrt(2)) and uncorrected sample standard deviation (max—min / 2) are quite biased downwards from the true standard deviation.
That being said, all of these are incredibly noisy estimators: the max-min estimator is only good for being within about 5x of the true value.
I used the oldest version available in the Wayback machine so presumably it was how it was published, but it does include an “update” note as if it’s undergone at least one revision. It’s not impossible that the wayback machine is missing the earliest version. I still think that “copy and paste into a janky content management system interface” is probably the cause of whatever bad formatting it had rather than outright malice, but it may have been worse then than we see now (they state that formatting was changed though it’s not clear when).
This is definitely a leading hypothesis but I think it’s also the case that going to the experts directly will lead you more astray in psychology than in some other fields because the quality of the work there has been lower. It makes sense that journalism is low quality if the experts are also low quality, though of course we would hope that journalists would be able to improve upon what they’re given (by e.g. consulting multiple experts). I guess one of my points is: if you don’t believe the traditional press media, who do you believe? I’m not convinced there’s an answer that improves upon the media (Wikipedia?). In fact, a fair number of the articles you might be thinking of could be authored by psychologists: at least my local paper often includes articles written by local researchers, physicians, etc. on the topics in their field, under the Opinion heading.
Not sure what articles would count as pop philosophy, though.For what it’s worth, circadian biology is quite open to popification. Eliezer Yudkowsky has written about finding the right timing to take melatonin for his sleep timing disorder. And practically all of us struggle with jet lag, daylight savings time changes (this part even being quite politicized!), or work schedules.
The clear reason to pay for news is that you can buy higher quality news than what your social media shows you. But I did definitely carve out politically sensitive areas in my discussion for a reason.
> They even changed font to random sizes to have it appear unhingedThis caught my eye, but appears to be false: https://web.archive.org/web/20170805210606/https://gizmodo.com/exclusive-heres-the-full-10-page-anti-diversity-screed-1797564320 Has some weird formatting, presumably from copying it in from a Google doc, and presumably also why it lost the figures and URLs. The formatting doesn’t look unhinged at all, just a bit awkward, though their summarizing the changes as removing “several” hyperlinks is terrible (it looks more like a couple dozen links in the original to me). Though, I would not have ever thought of Gizmodo as a being high tier journalism in the first place.
Good suggestion, though I don’t know how to systematically assess that. I can’t even think of what topics would be most likely to have this come up in.
Thanks for this example. I definitely see ridiculous headlines like that from less reputable places. Do you also have examples from the type of news media I’m talking about like WSJ? For example, searching “Washington Post AI robotics” I get headlines:
“Humanoid robots were sci-fi. Suddenly they’re everywhere” about companies investing in and demoing humanoid robots, which seems to be true.
“Not ready for robots in homes? The maker of a friendly new humanoid thinks it might change your mind” about the product “Sprout” by Fauna Robotics, which seems okay unless Fauna is completely faking it
“Russia’s much-hyped humanoid robot face-plants onstage during debut” OK
“Opinion | The Chinese robots are coming” hard to assess but not particularly hyperbolic
“Robot smaller than grain of salt can ‘sense, think and act’” subtitled “With solar cells and its own propulsion system, the device is a step toward sending robots into the human body”. This seems closest to what you’re talking about. Here’s a press release for it: https://www.seas.upenn.edu/stories/penn-and-umich-create-worlds-smallest-programmable-autonomous-robots/ I’m sure this is an optimistic take on a research project but it seems fairly reasonable
(I realize now that “robotics” wasn’t really in your original statement, I guess I extrapolated that from your drone example.)
Is the Gell-Mann effect overrated?
Drug approvals have gone up in recent years: https://pmc.ncbi.nlm.nih.gov/articles/PMC10856271/ (figure 1). Of course most of those are not ones that you’ll encounter in day-to-day life. Meanwhile, some of the most commonly used over-the-counter drugs from previous decades have been pulled from the market or made harder to get (cold medicine particularly: phenylpropanolamine due to rare side effects in 2000, oral phenylephrine due to lack of effect last year, and pseudoephedrine restricted to behind the counter due to use in meth a decade ago or so).
I was going to say that you should still have the kid checked due to “secondary drowning”, but apparently that’s largely a myth: https://www.redcross.org/take-a-class/resources/articles/dry-or-delayed-secondary-drowning According to the Red Cross, there’s no record of anyone nearly drowning, completely returning to normal, and then dying afterwards. If the person had shown symptoms like confusion or coughing, they’d be at risk for later dying despite rescue, but not if they completely and quickly recovered after the incident.
I’m not as concerned about your points because there are a number of projects already doing something similar and (if you believe them) succeeding at it. Here’s a paper comparing some of them: https://www.biorxiv.org/content/10.1101/2025.02.11.637758v2.full
ML arguments can take more data as input. In particular, the genomic sequence is not a predictor used in LASSO regression models: the variants are just arbitrarily coded as 0,1, or 2 alternative allele count. The LASSO models have limited ability to pool information across variants or across data modes. ML models like this one can (in theory) predict effects of variants just based off their sequence on data like RNA-sequencing (which shows which genes are actively being transcribed). That information is effectively pooled across variants and ties genomic sequence to another data type (RNA-seq). If you include that information into a disease-effect prediction model, you might improve upon the LASSO regression model. There are a lot of papers claiming to do that now, for example the BRCA1 supervised experiment in the EVO-2 paper. Of course, a supervised disease-effect prediction layer could be LASSO itself and just include some additional features derived from the ML model.
This is a lovely little problem, so thank you for sharing it. I thought at first it would be [a different problem](https://www.wolfram.com/mathematica/new-in-9/markov-chains-and-queues/coin-flip-sequences.html) that’s similarly paradoxical.
Again, why wouldn’t you want to read things addressed to other sorts of audiences if you thought altering public opinion on that topic was important? Maybe you don’t care about altering public opinion but a large number of people here say they do care.
He’s influential and it’s worth knowing what his opinion is because it will become the opinion of many of his readers. Hes also representative of what a lot of other people are (independently) thinking.
What’s Scott Alexander qualified to comment on? Should we not care about the opinion of Joe Biden because he has no particular knowledge about AI? Sure, I’m doubt we learn anything from rebutting his arguments, but once upon a time LW cared about changing the public opinion on this matter and so should absolutely care about reading that public opinion.
Honestly, I embarrassed for us that this needs to be said.
But you don’t need grades to separate yourself academically. You take harder classes to do that. And incentivizing GPA again will only punish people for taking actual classes instead of sticking to easier ones they can get an A in.
Concretely, everyone in my math department that was there to actually get an econ job took the basic undergrad sequences and everyone looking to actually do math started with the honors (“throw you in the deep end until you can actually write a proof”) course and rapidly started taking graduate-level courses. The difference on their transcript was obvious but not necessarily on their GPA.
What system would turn that into a highly legible number akin to GPA? I’m not sure, some sort of ELO system?
Thank you for the explanation. We need some better notation for this: write I(x) to mean that I observed x (or will observe it). Write E(x) to mean that I know that there exists with certainty someone who observed x (or will observe it).
First, in general, we don’t expect P(I(x)) = P(E(x)). For example, P(I(room 1)|I(room 2)) = 0 but P(E(room 1) | I(room 2)) = 1.
You define “simple Bayes” to mean:
P(y | I(x)) = P(y | E(x)) for any y and x
I would argue that you really need to pick a totally different name for this property since it doesn’t have anything to do with Bayes’ law. (If anything, I would call it “nonstandard Bayes”.) And your definition of it in your article needs to be clearer: as stated, it’s just about I(x) without mentioning E(x).
This is also the same crux that the paradox has always revolved around: does finding out who you are give you information? I think that’s closer to the standard phrasing and makes it more clear what you’re being asked to give up or not. You’re not being asked to give up Bayes’ law: that’s always true.