121–130 of 267 posts
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Yup. Actually, a common theme on LessWrong was realizing that with better reasoning tools you're more able to bullshit yourself , and so you need to be extra-careful.
How do you be extra careful except by developing yet more powerful reasoning tools?
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It's true that when the question is formed in frequentist terms, the answer is much more intuitive. But is that how the problem occurs in real life? The doctor doesn't see ten thousand people take a test; they see a person take a test, and get either a positive or negative result. The traditional way of forming the problem seems closer to actual experience: 'your patient tested positive. you know how accurate the tes…
I'm not quite sure what you're saying. Doctors don't observe probabilities or enormous frequencies. Either way, there are good odds that this is information that someone is communicating to them, not the result of their personal experience.
Reality does not neatly format itself for easy plug-and-chug into your formulas. To appropriately respond to reality, you must be good at recognizing when there's a mapping to a well-tested formula, technique, or phenomenon.
Therefore, if you require problems to be phrased in a way such that that's already done, that means you're not good at that domain; blaming the phrasing of the problem is missing the point.
Indeed, 90% of the mental work lies in recognizing such isomorphisms, not in cranking through the algorithm once it's recognized, and this is a hard skill to teach. (Schools that teach how to attack word problems have to rely on crude word-match techniques to identify e.g. when you want to subtract vs add vs divide.)
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Bayesian seems great when you first see it. It should be obvious how to apply it for something like a card game. The problem is how long would it take you to realize a deck of cards was missing the 4 of diamonds? What if the card was lost 1/2 way though the game? How about on the prior hand? In the end it's stuck at one level of recursion and all facts are fuzzy.
It's stuck in the reality you define - you can add the last hand, all cards seen so far, and the color of people's jackets to the model if you so please.
I think Stephen Bond did some excellent takedowns of the identity politics that has arisen around Bayes' Theorem back in the day. I wonder where he's at these days. The Cult of Bayes' Theorem http://laurencetennant.com/bonds/cultofbayes.html > One of Yudkowsky's constant refrains, appropriating language from Frank Herbert's Dune, is "Politics is the Mind-killer". Under this rallying cry, Lesswrong insiders attempt to…
Other reactions include "I was raised in an actual cult, and the differences I see include that LW encourages debate and EY is frequently criticized."
Some commenters did agree with at least parts of the article, though. Even the ones that agreed said it seemed to be more "personal attacks" than "excellent takedowns", though.
I personally think it seems kind of... "smug", I think, is the word I want to use? "Smug" writing isn't necessarily wrong, but it generally seems to have other priorities than discovering the truth. I disagree that I'd eventually acquire a taste for this "vicious" kind of writing - I've read smug writing that I otherwise agree with, and it still makes me uncomfortable.
The current fashion for BT really bugs me. BT inverts conditional probabilities. If you can estimate P(E), P(H) and P(E|H) better than P(H|E) it will give you a better result. It is one of many probability identities. But someone it has become 'the one', as if, say P(H|E) = P(H&E)/P(E) isn't much use, but put two of those together: world changing. I've seen so much crap come out of this fad. My particular favourite i…
It's just an equation. Garbage inputs will yield garbage outputs. In the realm of theology, it is of no more use than Pascal's Wager as an expected value calculation. All the input values are made up, so the output value is equally fabricated.
If you're using it on real, verifiable statistics, such as verified spam in an e-mail corpus, you can use Bayes to make a classifier to automatically identify spam to a high degree of accuracy. But if you are estimating for any of the three numbers you need to know, the fourth that you calculate will also be suspect.
I've been saying this for years , and this is a large reason why I find the LessWrong folks to be almost entirely full of it. Their inability to come up with accurate priors is completely lost on many of the folks who follow this kind of thinking. A couple of comments are saying, "no duh" to this article, but those folks likely don't realize quite how many other people are falling into this trap. "Garbage in, garbage…
Do priors just start you off closer to the truth? That is to say, if you start with any prior, will enough additional pieces of evidence always let you converge on the truth? Does anyone commonly set their priors to be a distribution? Perhaps a range or actually a normal distribution to represent a prior with uncertainty?
Almost everyone does this, and the solution is a posterior probability distribution. Most uses of Bayesian techniques that I'm familiar with are based on Monte Carlo simulations, where priors are drawn from the specified prior distribution, processed in some fashion, and result in samples of the posterior distribution.
This is especially helpful when you don't view the problem as having a 'true' single answer with some 'uncertainty' but instead have actual variability in the system, which is described by the posterior distribution.
Thinking about it, I'm really not sure in what instance the prior wouldn't be a distribution. It is, by definition, a probability. I suppose you could have a singular value, where the pdf is a delta function, but what's the point of doing the Bayesian inversion or estimation then? If you have a single value with prior p(x) = 0 or 1, you should end up with the posterior p(x|d)=0 or 1.
So the simplest case is where the prior is a binary: Say p(x=yes) = 0.6, p(x=no)=0.4. Or something like that. It's not a continuous distribution but it's still a distribution. The sum/integral of all cases has to be 1.
> If you get tested again, you can reduce your uncertainty I've always been bothered by statements like this about medical tests. This assumes that false positives are statistically independent. But isn't it more likely in general that false positives would be highly correlated in individuals, test administrators, or labs? E.g. If the same person takes the same test from the same doctor and sends it to the same lab,…
That's a nitpick on a correct statement. Unless two tests are always perfectly correlated , you will reduce your uncertainty. They don't need to be independent.
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This is a general argument against statistics . Or math, in general. Yes, dressing your bullshit in math can make people believe you more, but it doesn't change the fact that you're lying. Are we supposed to stop using math for good because evil people are using it for evil?
No, it's an argument against using statistics without first considering the strength of your data.
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Oh come on. That's how you're supposed to use math. To aid your thinking. Without it, and considering "outlandish scenarios", we would not have any scientific progress. Also, this is one strange thing - any time someone asks us (the STEM crowd), "what will I ever use math for in my life?", the default answer seems to be, "it's about having more tools for thinking, and greater clarity of thought; it'll make you smarte…
What? Who said “math gives nothing”? I spend most of my day building things out of math. I think math and scientific inquiry are basically the most important tools invented/popularized in the past 1000 years. The lapse here is not math, but rather spending lots of attention on abstract thought disconnected from any kind of reality check. Of course, there’s nothing inherently wrong with speculating sans evidence about…
Which is why every so often you'll get things like a physicist spending a couple months studying economics in their free time and deciding that they can now unlock the secret to economics which has eluded economists.
This xkcd comic sums it up well:
A (very simple) example: I trade stocks. My starting point is that I think a stock has a 50% chance of rising next year. Then I want to do a Bayesian iteration with the stock's P/E ratio based on historical data for stocks with similar P/E ratios. Then I want to also incorporate the P/E ratio of the industry the stock is in. Obviously these two inputs are correlated and if you have enough correlated variables, the whole thing breaks down because the simple theorem only works if all the inputs are independent of each other.