Bayes's Theorem: What's the Big Deal? • Hacker News Board

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

#21

Post by exelius » Tue, Jan 05, 2016, 4:26 PM UTC

Bayesian probability is catching on because the technology has finally caught up to the point where it's feasible. Thanks to the web and the proliferation of big data, we now have enough observations that Bayesian models can be trained (this was always the hard part). This doesn't mean we don't need smart people figuring out what things the model should and shouldn't look at; but it's at least possible to do today.

It also doesn't hurt that the Bayes theorem is at its heart a map-reduce problem. Where once Bayes' theorem was considered a cumbersome artifact for "brute forcing" probability, it's now likely faster than competing methods of statistical analysis.

We almost seem to be getting to the point in ad targeting where demographics are expressed in terms of a set of bayesian properties. You don't even care what the properties are; just that they're potentially more willing than average to use your product.

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

#22

Post by cwyers » Tue, Jan 05, 2016, 4:26 PM UTC

flurie wrote: post #15

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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The second one is actually mine, I didn't promote it because I was unhappy with the font.

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

#23

Post by NN88 » Tue, Jan 05, 2016, 4:27 PM UTC

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…

Rutherford should just be happy he discovered the last reasonably tangible piece of matter humanity will see for a long time, if ever.

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

#24

Post by mikeash » Tue, Jan 05, 2016, 4:29 PM UTC

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…

Just because a theorem is true doesn't mean you can't misuse it or that you don't need to do some work to map it to reality.

For example, the Banach-Tarski theorem is solid, but that doesn't mean you can start a business making golf balls by buying one and then endlessly replicating it.

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

#25

Post by mfoy_ » Tue, Jan 05, 2016, 4:29 PM UTC

GavinB wrote: post #12

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")

I think the title isn't quite so off. The article is trying to point out that people should be wary of using it wrongly.

Like other commentators have pointed out, the saying "garbage in garbage out" only helps when you stop to think whether or not you're putting garbage in.

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

#26

Post by Anderkent » Tue, Jan 05, 2016, 4:30 PM UTC

astine wrote: post #17

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 evid…

Even if you only get weak of flawed evidence, then you do what you can to make the best decisions given that evidence. No one tries to suggest you do actual bayesian calculations on everything you know, for the simplest reason that it's not computationally viable.

But if your beliefs directly contradict bayes then you're doing something wrong - there's an inconsistency that's likely worth investigating, unless the matter is really minor. It's a sanity check for your decision making, not a constructive algorithm for the best decision.

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

#27

Post by vezzy-fnord » Tue, Jan 05, 2016, 4:33 PM UTC

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…

Yudkowsky has been one of the most instrumental and highly regarded figures in promoting Bayesian epistemology, among other woo that engineers and programmers are oddly susceptible to. Nothing wrong with singling him out.

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

#28

Post by Anderkent » Tue, Jan 05, 2016, 4:33 PM UTC

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…

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 test is, and how common the disease is; how likely is it that the result is a false positive?'

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

#29

Post by vezzy-fnord » Tue, Jan 05, 2016, 4:36 PM UTC

If you have some time to spare, here's a great paper on a similar topic: the (mis)use of mathematics and in particular equilibrium methods in economics after Samuelson and Hicks ("What Went Wrong with Economics?", Peter J. Boettke, 1997): http://www.the-dissident.com/Boettke_CR.pdf

Pretty much every debate on economic policy between the left and right is full of fallacies emanating from this episode in history.

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

#30

Post by RodericDay » Tue, Jan 05, 2016, 4:39 PM UTC

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 purge discussions of any political opinions they disagree with. They strive to convince themselves and their followers that they are dealing in questions of pure, refined "rationality" with no political content. However, the version of "rationality" they preach is expressly politicised.