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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?

#41

Post by such_a_casual »

So let me get this straight, statistics can be misused? I almost stopped reading as soon as I saw the image from the big bang theory. (That show presents nerds the way other people want to see them. Not the way nerds actually are.) It appears that the author of this article is just a journalist:

http://www.johnhorgan.org/

I don't see anything in there about him ever being a scientist, a statistician, or anyone who would actually use this theorem. In fact, he even went to school for journalism.

I really don't understand where this author is coming from when he says things like, "I conveniently decided that Bayes was a passing fad." Why should we care about his opinion on the matter? Is he reporting to us what Bay Theorem is and its significance, or is he giving us his uniformed opinion on the matter?

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

#42

Post by Fomite »

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?

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 analysis is essentially a Bayesian analysis with a prior distribution centered on zero with bounds from positive to negative infinity.

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

#43

Post by Fomite »

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?

I had a professor in graduate school who suggested exactly this - each study should conduct a meta-analysis of all previous studies on the subject, use that estimate as their prior, update, and publish for the next study...

The problem is, having tried it, this is much more difficult to do in practice.

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

#44

Post by hyperpape »

Anderkent wrote: post #28
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 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.

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

#45

Post by TeMPOraL »

RodericDay wrote: post #30

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…

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 that were targeted by such prose - first the religious group I grew up in, that is a minority in my country; then the school I went to. My university year used (a very lite version of) such criticism against another, so I've seen it from the other side as well. Hell, people write shit like this about HN!

It's hard to defend against such criticism. You'll get boggled down in refuting specific accusations, but this is something you can never win. The only winning move is to ignore it completely. Personally, I shun and shame people who write such stuff, regardless of whether I agree or disagree with their victims. Dishonesty is a poison that destroys societies.

TL;DR: this text is harmful, malicious bullshit. If it at least offended people with style, there would be something to save it.

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

#46

Post by sago »

lordCarbonFiber wrote: post #7
theseatoms wrote: post #3

> The potential for Bayes abuse begins with P(B), your initial estimate of the probability of your belief, often called the “prior.” tldr; priors matter

That was my thought as well. Garbage in = garbage out, that's pretty standard in most fields. I really didn't like how the author treated the theorem as if it's some sort of magic, aside from something everyone that's taken a college prob/stat class has derived from first principles.

The problem is that advocates do treat it as a magical thing. They extrapolate from the fact it is proven to the claim that all knowledge is Bayesian, to the implication that all Bayesian reasoning is knowledge.

This fashion is why, for example, BT has been used to both prove the resurrection of Jesus, and to prove that Jesus didn't exist: both to a very high probability.

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

#47

Post by TeMPOraL »

astine wrote: post #37
Anderkent wrote: post #18

Earlier quoted context omitted.

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 o…

Honesty is an ultimate issue here. If my reasoning is shoddy, but I plug it into some math apparatus, then it'll likely make my problems obviously wrong. If my reasoning is very inaccurate and the data uncertain, being precise about it can at least make the results salvageable. Scott Alexander argues for this position quite well in [0].

Humans can lie with statistics well. But they can lie with plain language even better.

[0] - http://slatestarcodex.com/2013/05/02/if-its-worth-doing-its-...

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

#48

Post by sago »

The current fashion for BT really bugs me.

BT inverts conditional probabilities. If you can estimate P(E), P(H) and P(E|H) better than P(H|E) it will give you a better result. It is one of many probability identities. But someone it has become 'the one', as if, say P(H|E) = P(H&E)/P(E) isn't much use, but put two of those together: world changing.

I've seen so much crap come out of this fad. My particular favourite is in theology. William Lane Craig has demonstrated that Jesus raised from the dead, to a high probability. Richard Carrier has shown that there was no historical Jesus. Funny how few people ever run BT and find it contradicts their views.

I think part of the problem comes from a lack of understanding of the difference between frequentist and bayesian interpretations of probability. I've yet to see these folks show BT working in anything but frequentist data. And then they'll switch and use it to demonstrate why their Bayesian situation is correct.

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

#49

Post by PaulHoule »

3pt14159 wrote: post #33
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.

It is far beyond least squares as it was and is practiced

There already was stuff in the stats literature in the 1990s that was much better but people in the physics community (such as myself) were not aware of that literature. On the other hand, stats people were not particular aware of the way power laws were occuring in physics.

I saw things that did not add up ten years earlier and Mark Newman did too but we were both so caught up in the rat race, consensus reality, collective delusion, whatever you call it that I left physics before I could address the problem and he suffered through years of bullshit before he could find the time to do something about it.

Watching Mark write great papers, write great book chapters and suffer from tremendous anxiety over his career was a big reason why I left.

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

#50

Post by Anderkent »

hyperpape wrote: post #44
Anderkent wrote: post #28

Earlier 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.

Doctors observe a result of the test, and know the basic probabilities (in the example, 99% test accuracy, 1% of population have the disease). The problem is that they [often] draw incorrect conclusions from those observations (99% test accuracy and you tested positive? well then you likely - 99% - have the disease, right?).

The question formed as 'your one patient tested positively' is more immediately relevant, I'd think. The correspondence with actual practice is obvious. The question formed as 'out of 10000 ...' could be remembered as a quirk of statistics, but not actually recalled when someone tests positively for cancer.

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