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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?

#141

Post by danieltillett »

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…

The reason why doctors and other professionals find it difficult to understand is because they are paid for treating people. As Upton Sinclair observed “It is difficult to get a man to understand something, when his salary depends on his not understanding it.”

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

#142

Post by [deleted] »

TeMPOraL wrote: post #36
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…

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?

[deleted]

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

#143

Post by arcanus »

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?

This does happen. I've had paper reviewers request results with an appropriately selected uninformative prior: https://en.wikipedia.org/wiki/Jeffreys_prior

Typically, if you are practitioner in the field, it is not too difficult to identify instances where the result is highly dependent on the choice of prior.

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

#144

Post by XFrequentist »

jsprogrammer wrote: post #93
Fomite wrote: post #42

Earlier quoted context omitted.

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…

Bayesian analysis comes directly from the probability axioms, which are 'frequentist'.

Huh? You mean the Kolmogorov axioms? In what sense are these 'frequentist'?

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

#145

Post by XFrequentist »

1812Overture wrote: post #133
1024core wrote: post #84

Earlier quoted context omitted.

> 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."

This made me chuckle.

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

#146

Post by unimpressive »

Apocryphon wrote: post #135
woodchuck64 wrote: post #131

Earlier quoted context omitted.

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

https://en.wikipedia.org/wiki/Pascals_wager

I don't think it would be fair to malign philosophers because they come up with outlandish scary scenarios that scare people with OCD sometimes. It's not like LW gives Roko significant air time or serious treatment (EY freaking out and deleting it was partially principle of the thing, partially the fear that somebody might follow this road of thought to come up with something more terrifying and he doesn't want to take the community there, etc) somebody doing this is generally taken as a sign of serious crankery.

(FWIW, I agree with the top parent post that the hyping of Bayes Theorem is one of the LW foibles. At least the presentation of it.)

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

#147

Post by cobaltblue »

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…

IQ is held in high esteem because research around g is very good and comprehensive, perhaps the crown jewel of psychology. Additionally most people's knowledge of the Flynn effect is out of date -- recent studies (here's one: http://www.sciencedirect.com/science/article/pii/S0160289615... in fact here's a boatload of references http://www.iapsych.com/iqmr/fe/MasterFlynnEffectreferencelis...) show a rise, leveling off, and then an overall fall from the beginning in performance over the last 40 years rather than the continuous rise (or at least non-decreasing) behavior most people would probably bet on from their layman understanding of the effect. (Additionally ethnic gaps have remained despite controls for everything and it is this unfortunate reality that I think is the reason for so much dismissal of IQ...)

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

#148

Post by woodchuck64 »

Apocryphon wrote: post #135
woodchuck64 wrote: post #131

Earlier quoted context omitted.

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

This is still working backwards: a thought experiment that increases your chances of being tortured by a future AI? Surely outlandish! But why? Which premises are truly outlandish, arbitrary, etc? What I see given the premises is no more than what Yudkowsky's already said: ".. a Friendly AI torturing people who didn't help it exist has probability ~0, nor did I ever say otherwise."

(However, I agree that to be genuinely distressed by the thought experiment possibility suggests more is going on psychologically than a rational assessment of unknowns, but this seems to be a minority of the community)

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

#149

Post by marcosdumay »

hyperpape wrote: post #83
vinchuco wrote: post #51

Earlier quoted context omitted.

Except when https://en.m.wikipedia.org/wiki/Simpson%27s_paradox

It's a lovely phenomenon, but what are you trying to say?

Maybe that the natural frequency "normatized" for some people may be completely different from the actual frequency that apply to them, because the people that researched the frequency did their grouping badly.

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

#150

Post by neaden »

sharkbot wrote: post #73
IanCal wrote: post #31

Earlier quoted context omitted.

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?

This comes to mind: https://en.wikipedia.org/wiki/Aumann's_agreement_theorem Essentially, two genuine Bayesian rationalists (with some hand wavy preconditions) cannot agree to disagree; ie, they will eventually converge onto the same understanding of an event.

This isn't true though, the problem is there are generally more then 2 possible explanations. For instance let's imagine both of us are using an experimental telescope to observe if some event occurs. We are then looking at four possible scenarios. The telescope could work/not work correctly and the event could happen/not happen. You are confident that the telescope works correctly and also confident that the event will not occur so you give high prior probability to the first and a low to the second. I on the other hand think the telescope is rubbish and the event will almost certainly occur and do the opposite. We sit down and wait and do not observe the event. You then come to the conclusion that the event did not occur and the telescope works correctly, while I come to the reverse conclusion.
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