Interesting that they mention the medical case, when there's some psychological work around the idea that we should present these cases in terms of natural frequencies instead of Bayes' theorem. The natural frequencies approach is to say "if 10000 people take the test, 100 will have cancer. Of them, 99 will get an accurate positive test, and 1 will have a false negative test. Of the other 9900, 99 will receive a fals…
Bayes's Theorem: What's the Big Deal?
51–60 of 267 posts
Re: Bayes's Theorem: What's the Big Deal?
#52I'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?
First Qn: yes. But the rabbit is hiding in the 'enough'. Most commonly the poor uses of BT end up with a narratively argued prior + a single suite of evidence.
For a finite set of evidence (particularly chosen by someone with bias), bias + evidence can be arbitrarily far from the truth.
Re: Bayes's Theorem: What's the Big Deal?
#53I'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?
> That is to say, if you start with any prior, will enough additional pieces of evidence always let you converge on the truth?
Yes, with two caveats. First, you can't have assigned zero probability to the right answer. Which means that if you have a probability distribution over hypotheses, and the right answer wasn't one of the hypotheses in the distribution, you're doomed from the start. The Solomonoff prior is a mathematical construct that gets around this problem by including every hypothesis that can be expressed as a Turing machine, but it gets used more as a philosophical token than an actual computing tool because it's unfeasible to use directly. The second issue is that if you have a bad enough prior, "enough additional pieces of evidence" can be an arbitrarily large amount, and there may only be a limited amount of evidence available to collect. In particular, rerunning an experiment over and over can only provide a limited amount of evidence, because of the possibility that some systematic error affects every instance of the experiment.
Re: Bayes's Theorem: What's the Big Deal?
#54> In many cases, estimating the prior is just guesswork, allowing subjective factors to creep into your calculations. You might be guessing the probability of something that--unlike cancer—does not even exist, such as strings, multiverses, inflation or God. You might then cite dubious evidence to support your dubious belief. In this way, Bayes’ theorem can promote pseudoscience and superstition as well as reason. Oh…
> If nothing else, this provides inspiration for me to quit procrastinating on my "ASK ME ABOUT ROKO'S BASILISK" novelty t-shirt idea.
Can you tell us the story about that party when you got so drunk and started yelling in anger at a poor random dude? Except you weren't drunk at all and the dude behaved like an asshole, but nobody cares about the truth since you're a nerd and you look cute when you're sad that we're telling stories about your drinking problems.
That's basically what happened there. I wish people stopped with this Roko's Basilisk nonsense.
Re: Bayes's Theorem: What's the Big Deal?
#55Earlier quoted context omitted.
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.
I think GP's point is that in the case of interacting with an individual patient, the Bayesian conception of probability as a quantification of degree of belief is actually more intuitive than the frequentist conception of probability as a relative frequency of outcomes under repeated hypothetical experimentation.
Re: Bayes's Theorem: What's the Big Deal?
#56Earlier quoted context omitted.
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?
In my field (Epidemiology), when doing Bayesian analysis, it is very common to set one's priors to be a distribution. Sometimes the point estimate and spread of a previously conducted study or meta-analysis, sometimes merely a uniform distribution with upper and lower bounds ("It is extremely unlikely that the relative risk of disease for this exposure is below 0.01 or above 100...") It's been argued that frequentist…
How does that work? It doesn't sound like a well-defined distribution since the area under the curve needs to be 1.
Re: Bayes's Theorem: What's the Big Deal?
#57I 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…
I've seen this type of writing before. It's a kind of twisted pseudo-criticism you write against a group you dislike. You can compose stuff like this against any group. It sounds believable from the outside, especially if you start sceptical to begin with. But take a closer look - it's actually full of ad-hominems, cherry-picking facts and presenting them in worst light possible. I've been a part of several groups th…
I know you're a huge advocate for Lesswrong, but not "everybody" or "anyone" has quotes ripe for picking like Yudkowsky. Stephen Bond is not just throwing some opinion out there, he's backing it up with first-hand sources:
Yudkowsky on his simplified views of why race gets brought up:
> "Race adds extra controversy to everything; in that sense, it's obvious what difference skin colour makes politically".
> "Group injustice has no existence apart from injustice to individuals. It's individuals who have brains to experience suffering. It's individuals who deserve, and often don't get, a fair chance at life. [...] Skin colour has nothing to do with it, nothing at all."
Yudkowsky on our current societal structure, adulating the people who give him funding:
> One of the major surprises I received when I moved out of childhood into the real world, was the degree to which the world is stratified by genuine competence.
Yudkowsky writing short stories about a society where rape is legal, leaving himself ample room for plausible deniability, but putting it up "for debate":
>> "No, us. The ones who remembered the ancient world. Back then we still had our hands on a large share of the capital and tremendous influence in the grant committees. When our children legalized rape, we thought that the Future had gone wrong."
>> Akon's mouth hung open. "You were that prude?"
(https://web.archive.org/web/20131206200429/http://lesswrong....)
I think some well-meaning LessWrongers get caught in the crossfire, but I think the essay makes a very well grounded case for the blindspots "rationalists" have towards politics that suit the identity of people like Yudkowski.
Re: Bayes's Theorem: What's the Big Deal?
#58So can frequentism. Many investigators in parapsychology who were sincere and intelligent appear to have based their career on the incorrect use of frequentist statistics. And it's not just them. Ernerst Rutherford, who discovered the atomic nucleus, "If your experiment needs statistics, you ought to do a better experiment." In the 1990s I was a physics grad student and I think none of the professors had ever heard o…
I'm a little confused. Are you saying that a tenure track prof wrote a paper on how to evauluate fitted power law curves? Was it something else besides least squares? Because I can't possibly see this getting accepted to a statistics journal.
Fitting distributions is a little bit different than the usual model fitting scenario where least squares is appropriate. Sometimes people do things like construct a histogram and then do a least squares fit to the bin heights, but that procedure doesn't satisfy the usual assumptions that justify least squares (observations with independent, equal variance, Gaussian errors).
Cosma Shalizi has written some interesting posts on this subject, and also published papers in statistics journals:
Re: Bayes's Theorem: What's the Big Deal?
#59Earlier quoted context omitted.
FWIW, it seems to me that a major benefit of the Bayesian approach is to make bad reasoning (in the form of, say, an unreasonable prior) transparent and obvious. I've never heard it claimed that the Bayesian approach was robust to sophisticated idiocy (neither on LessWrong nor mainstream writing on Bayesian methods), except in the narrow techical sense that the posterior asymptotically approximates the likelihood giv…
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?
Re: Bayes's Theorem: What's the Big Deal?
#60I'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…
> 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.
I assume you're saying LessWrong folks are more prone to miscalculating priors than most. Could you give some examples of this?