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Bayes's Theorem: What's the Big Deal?

blogs.scientificamerican.com

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Re: Bayes's Theorem: What's the Big Deal?

#131

Post by woodchuck64 »

jacobolus wrote: post #109
woodchuck64 wrote: post #60

Earlier quoted context omitted.

> 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?

The LessWrong folks aren’t obviously better or worse at calculating priors than anyone else. The “problem” is that their hobby is spending their free time considering outlandish scenarios, inventing arbitrary assumptions related to such scenarios, drawing questionable conclusions, and then convincing themselves that because they used logic and math, their analysis must be correct. Plenty of other folks who spend time…

But these aren't examples so much as vague caricatures. The subject matter that LessWrong considers is certainly unusual, but that alone should not be enough to call it arbitrary, questionable or outlandish.

Re: Bayes's Theorem: What's the Big Deal?

#132

Post by TillE »

bigfudge wrote: post #128
astine wrote: post #81

Earlier quoted context omitted.

No, it's an argument against using statistics without first considering the strength of your data.

But being a good bayesian makes you do exactly this. The process of describing priors makes it obvious you need to do a sensitivity analysis to check how much the prior is influencing the conclusions...

> being a good bayesian

This is exactly what weirds people out about LessWrong folk. They talk about a tool as if it's a religion.

Re: Bayes's Theorem: What's the Big Deal?

#133

Post by 1812Overture »

1024core wrote: post #84
XFrequentist wrote: post #35

Earlier 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…

> I've never heard it claimed that the Bayesian approach was robust to sophisticated idiocy Alas, nothing is robust to sophisticated idiocy.

"If you make something idiot proof, someone will just make a better idiot."

Re: Bayes's Theorem: What's the Big Deal?

#134

Post by jsprogrammer »

jedberg wrote: post #103
darawk wrote: post #89

> 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,…

You could also look at it the other way: Using the same doctor and lab and procedure is the best way to eliminate a false positive, because if the cause was external, then the cause may not be repeated. But if you went to a new lab/doctor/whatever, you've now introduced new variables that could cause a false positive on top of whatever already caused it. Given that it could go either way, it makes sense to think of e…

Down mods for this?

More information allows for better reasoning. Repeating the same test and also doing a "more independent" test are the minimum next two things you should do given a positive result on a single test.

Re: Bayes's Theorem: What's the Big Deal?

#135

Post by Apocryphon »

woodchuck64 wrote: post #131
jacobolus wrote: post #109

Earlier quoted context omitted.

The LessWrong folks aren’t obviously better or worse at calculating priors than anyone else. The “problem” is that their hobby is spending their free time considering outlandish scenarios, inventing arbitrary assumptions related to such scenarios, drawing questionable conclusions, and then convincing themselves that because they used logic and math, their analysis must be correct. Plenty of other folks who spend time…

But these aren't examples so much as vague caricatures. The subject matter that LessWrong considers is certainly unusual, but that alone should not be enough to call it arbitrary, questionable or outlandish.

http://rationalwiki.org/wiki/Roko%27s_basilisk

Re: Bayes's Theorem: What's the Big Deal?

#136

Post by TeMPOraL »

TillE wrote: post #132
bigfudge wrote: post #128

Earlier quoted context omitted.

But being a good bayesian makes you do exactly this. The process of describing priors makes it obvious you need to do a sensitivity analysis to check how much the prior is influencing the conclusions...

> being a good bayesian This is exactly what weirds people out about LessWrong folk. They talk about a tool as if it's a religion.

It's a running joke there.

The people need to get over it. LW crowd is a group of people studying a pretty specific set of subjects, focused around a single website. It's typical for such a group to develop their own jargon and insider jokes, which may look weird from outside. It's normal.

Re: Bayes's Theorem: What's the Big Deal?

#137

Post by bduerst »

hyperpape wrote: post #20

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…

Doctors and professionals are probably not as concerned about Bayes because cancer isn't identically or independently distributed across the population.

Also, endocrinology diagnostic platforms usually don't have identical accuracy rates for positive and negative results, varying by test, machine, controls used, etc.

Re: Bayes's Theorem: What's the Big Deal?

#138

Post by danieltillett »

Chathamization wrote: post #95
TeMPOraL wrote: post #66

Earlier quoted context omitted.

You can't protect yourself in 100% - it would require developing more powerful reasoning tools in an infinite regression. But what you can do is to use introspection, and triple-check your reasoning when it seems to defy common sense or leads you to weird (awful) conclusions. That's why LW is so big on biases and heuristics by the way - you can treat them as a list of warning signs; if your reasoning seems to match s…

The problem with trying to rely on heuristics to avoid biases is people often ignore the biases in the heuristics of choice. To continue the example of LW, there are many people there who seem to think highly of IQ test, and who ignore the many issues with them (the Flynn effect an the effect of incentives being a couple examples of the flaws in IQ tests). Trying to remove biases is great. But there is a problem when…

The Flynn effect mystery is exactly the same as the mystery that in most countries the younger population is taller than the previous generation. The fact that the Flynn effect only occurs in the bottom half of the intelligence distrubtion is a bit of a clue as to what is the cause.

Re: Bayes's Theorem: What's the Big Deal?

#140

Post by arcanus »

Laaw wrote: post #14

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…

> Their inability to come up with accurate priors is completely lost on many of the folks who follow this kind of thinking.

Mis-specified/faulty priors are absolutely a possible pitfall of Bayes, but Jeffreys Priors are a means to circumvent this: https://en.wikipedia.org/wiki/Jeffreys_prior

Another thing not mentioned in the article is that Bayes DOES converge to the frequentist result in the limit of big data.

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