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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?

#31

Post by IanCal »

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…

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?

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

#32

Post by SFjulie1 »

http://elis.dvo.ru/~lab_11/bib/hershkowitz-nadal.pdf I found a thesis on the topic.

Seems the upper bound of estimation when using bayesian probability for estimating parameters with data gets overestimated when the size of the data grows.

It does not makes sense to me, can someone explain this to me as if I was an idiot?

PS one of the searcher in his lab used to say: if you try to find to hard a physical law, you might eventually find it.

(quote from the thesis below)

Most of the results concerning the behavior of the mutual information, observed for this particular family, are ‘‘universal,’’ in that they will be qualitatively the same for any problem that can be formulated as either a parameter estimation task or a neural coding task. .... Besides the asymptotic regime p large, N arbitrary, we have also considered the case of large N at any given value of a5p/N. In this regime we have both replica calculations and exact bounds, in particular, an upper bound for the class information and explicit upper and lower bounds for the mutual information obtained with the techniques of [7]. The results suggest that the replica symmetry ansatz give the correct solution. The lower bound is then quite good whereas the upper bound overestimate the mutual information by a factor that keeps increasing with the data size.

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

#33

Post by 3pt14159 »

PaulHoule wrote: post #16

So 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.

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

#34

Post by cronjobber »

Here's a proposal: Bayesian scientists shouldn't select their own prior. Instead publish how your results would update any prior, including the one picked by me, the reader.

I certainly haven't thought this through, but maybe this would make science more modular: combine the updates from M studies and calculate the new, combined update. Statisticians, does this work?

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

#35

Post by XFrequentist »

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…

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 given infinite data (provably true under some assumptions but irrelevant to the objections in the OP).

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

#36

Post by TeMPOraL »

astine wrote: post #10
stuartaxelowen wrote: post #4

Read through most of the article just for "people can abuse priors"? Come on. Anything, used wrongly, can promote superstition and pseudoscience.

I think you're missing the broader argument, which is using 'mathy' concepts to dress up poor reasoning. Obviously priors matter, but what matters most of all is how good/complete your evidence is. Using a mathematical formula to lend credence to weak evidence (through liberal use of assumptions) is a hallmark of pseudoscience. The same could be said of many of the abuses of statistics and Bayes theorem is merely one…

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?

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

#37

Post by astine »

Anderkent wrote: post #18
astine wrote: post #10

Earlier quoted context omitted.

I think you're missing the broader argument, which is using 'mathy' concepts to dress up poor reasoning. Obviously priors matter, but what matters most of all is how good/complete your evidence is. Using a mathematical formula to lend credence to weak evidence (through liberal use of assumptions) is a hallmark of pseudoscience. The same could be said of many of the abuses of statistics and Bayes theorem is merely one…

Is using mathy concepts to dress up poor reasoning worse than not using anything to back up your reasoning? At least you can point out exactly what's wrong with the mathy reasoning. A colleague of mine says 'Sometimes pulling numbers out of your arse and using them to make a decision is better than pulling a decision out of your arse'

"Is using mathy concepts to dress up poor reasoning worse than not using anything to back up your reasoning?"

I believe so. If your belief is baseless, or based on flimsy evidence or simple bias, it's best if that's obvious. Dressing up weak reasoning to seem stronger is a form of lying. It's what we call sophistry. A big part of the problem is that for a lot of people don't understand the math well enough to point out what's wrong with it or have a bias towards explanations that seem complex or sophisticated but really aren't.

It's true that sometimes we have to make a decision based on poor or no evidence but it should be clear that that is the case when that is the case. Dressing up the argument only obfuscates that.

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

#38

Post by TeMPOraL »

XFrequentist wrote: post #35
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…

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.

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

#39

Post by XFrequentist »

cronjobber wrote: post #34

Here's a proposal: Bayesian scientists shouldn't select their own prior. Instead publish how your results would update any prior, including the one picked by me, the reader. I certainly haven't thought this through, but maybe this would make science more modular: combine the updates from M studies and calculate the new, combined update. Statisticians, does this work?

Yes - Laplace originally proposed this, it's a good approach (and incidentally the basis for Bayesian meta-analysis). Google "skeptical prior" for more.

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

#40

Post by XFrequentist »

IanCal wrote: post #31
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…

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?

Yes and yes and yes!

ETA - caveat to the 2nd question: ... unless you've restricted your prior to exclude the truth.

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