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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?

#11

Post by gaur »

njohnson41 wrote: post #2

Good article. I'm only a bit disappointed that the author seems not to realize that Bayes' theorem is just a simple consequence of probability theory, and should be attractive not because "maybe the brain is Bayesian", but because it is based on sound set-theoretic and analytic principles. If Bayes' theorem is false, so is probability theory, and so is nearly everything we know about probability. Edit: Here is a good…

I guess a hard-line frequentist (if such a person exists) would counter that you can't assign probabilities to hypotheses or fixed parameters. Then Bayes's theorem (and every other statement about probability) is true only when applied to statements about how often a certain event will occur.

But of course, most people do assign probabilities to hypotheses and fixed parameters, even if only informally. Bayesian probability theory is an attempt to formalize that kind of intuitive reasoning.

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

#12

Post by GavinB »

This headline does not reflect the article and is needlessly inflammatory. This article is an explanation of Bayes theorem and overall very positive of it. The "used wrongly" quote is just stating that it's not immune to biases and error. Pretty much any tool "used wrongly" can cause errors.

(In case it's changed, the headline currently reads "Bayes theorem used wrongly, can promote superstition and pseudoscience")

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

#13

Post by lmm »

njohnson41 wrote: post #2

Good article. I'm only a bit disappointed that the author seems not to realize that Bayes' theorem is just a simple consequence of probability theory, and should be attractive not because "maybe the brain is Bayesian", but because it is based on sound set-theoretic and analytic principles. If Bayes' theorem is false, so is probability theory, and so is nearly everything we know about probability. Edit: Here is a good…

All probabilistic tools are accurate in theory, otherwise we wouldn't use them. Bayes' theorem is no different from e.g. the t-test in that regard. The question of whether it's worth using Bayes explicitly rather than other tools is and should be a question of whether we find it aligns with our understanding and helps us think more clearly.

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

#14

Post by Laaw »

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 out" is only good advice when the person you're saying it to realizes they're putting garbage in.

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

#15

Post by flurie »

cwyers wrote: post #5

> 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…

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

#16

Post by PaulHoule »

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 of the idea of a parameter estimator so we had a bunch of ad-hoc ways to fit power law coefficients that gave different answers and no way to judge goodness of fit that was thought out at all.

One postdoc in my lab suffered through a difficult job market before finally, after a decade of anxiety and uncertainty, got a tenure track position and eventually wrote a paper on how to fit power law curves... in a statistics journal.

And this was in a good department with people in which I was proud of both the teaching and research going on.

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

#17

Post by astine »

I've had people seriously claim to me that using Bayes theorem to evaluate beliefs that one deals with in ones everyday life using evidence that one comes across in everyday life was likely a good idea and would reduce bias. I wish I'd had the presence of mind to point out that that did nothing to eliminate the selection bias of one's own experience. No mathematical formula can draw meaning out of weak or flawed evidence.

Trying to do so is like trying to 'enhance' a blurry photo so that you can see details in the photo that didn't exist.

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

#18

Post by Anderkent »

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…

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'

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

#20

Post by hyperpape »

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 false positive, and 9801 will receive a correct negative. What are the odds that someone who has a positive test has cancer?"

It turns out that doctors and other professionals whose core professional competency doesn't concern probability do terribly when presented with percentages and Bayes theorem, but can handle natural frequencies quite well (here's one quick summary: http://opinionator.blogs.nytimes.com/2010/04/25/chances-are/...).

As is obvious, this isn't an argument that Bayes' theorem is wrong--it's a theorem after all. It's an argument about which types of reasoning people can be easily taught.

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