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

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

#111

Post by TeMPOraL » Tue, Jan 05, 2016, 7:25 PM UTC

jacobolus wrote: post #109

woodchuck64 wrote: post #60

Earlier quoted context omitted.

> 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. I assume you're saying LessWrong folks are more prone to miscalculating priors than most. Could you give some examples of this?

The LessWrong folks aren’t obviously better or worse at calculating priors than anyone else. The “problem” is that their hobby is spending their free time considering outlandish scenarios, inventing arbitrary assumptions related to such scenarios, drawing questionable conclusions, and then convincing themselves that because they used logic and math, their analysis must be correct. Plenty of other folks who spend time…

Oh come on. That's how you're supposed to use math. To aid your thinking. Without it, and considering "outlandish scenarios", we would not have any scientific progress.

Also, this is one strange thing - any time someone asks us (the STEM crowd), "what will I ever use math for in my life?", the default answer seems to be, "it's about having more tools for thinking, and greater clarity of thought; it'll make you smarter". But then, some of us turn around and refuse to acknowledge that people who actually learn math and try to apply it may be getting those promised results. Whether it's LW people, programmers, engineers or scientists, the moment it matters, the default conclusion is that math gives nothing.

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

#112

Post by tzs » Tue, Jan 05, 2016, 7:27 PM UTC

Referring to an appearance of Bayes' theorem on Sheldon's whiteboard:

> Bayes’ theorem has become so popular that it even made a guest appearance on the hit CBS show Big Bang Theory

That's not a sign that it has become popular, any more than the appearance of the standard human pedigree notation used by genetic counselors on the same whiteboard indicates that standard human pedigree notation has become popular among the general public. It's simply a sign that BBT takes care to make the whiteboards generally scientifically sensible.

They have a UCLA physicist [1] consultant who works with the producers, writers, prop people, set decorators and others to try to make things scientifically accurate.

In this particular episode, both Bayes' theorem and the genetic information are there because Sheldon was trying to figure out his chances of surviving until technology reaches the point that he can transfer his mind to an AI and what he would have to do to improve those chances. So both those things were on the whiteboard because they are things that would be perfectly reasonable to find on the whiteboard of someone doing that.

They consulting physicist had a blog [2] where he covered most episodes and talked about the whiteboards and other scientific content. Here is the entry for the aforementioned episode [3].

[1] http://bigbangtheory.wikia.com/wiki/David_Saltzberg

[2] https://thebigblogtheory.wordpress.com

[3] https://thebigblogtheory.wordpress.com/2010/09/30/s04e02-the...

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

#113

Post by jacobolus » Tue, Jan 05, 2016, 7:31 PM UTC

TeMPOraL wrote: post #111

jacobolus wrote: post #109

Earlier quoted context omitted.

The LessWrong folks aren’t obviously better or worse at calculating priors than anyone else. The “problem” is that their hobby is spending their free time considering outlandish scenarios, inventing arbitrary assumptions related to such scenarios, drawing questionable conclusions, and then convincing themselves that because they used logic and math, their analysis must be correct. Plenty of other folks who spend time…

Oh come on. That's how you're supposed to use math. To aid your thinking. Without it, and considering "outlandish scenarios", we would not have any scientific progress. Also, this is one strange thing - any time someone asks us (the STEM crowd), "what will I ever use math for in my life?", the default answer seems to be, "it's about having more tools for thinking, and greater clarity of thought; it'll make you smarte…

What? Who said “math gives nothing”? I spend most of my day building things out of math. I think math and scientific inquiry are basically the most important tools invented/popularized in the past 1000 years.

The lapse here is not math, but rather spending lots of attention on abstract thought disconnected from any kind of reality check. Of course, there’s nothing inherently wrong with speculating sans evidence about the future, it’s generally a harmless hobby. In the best case it makes for fun SF novels. Convincing yourself, still without direct evidence, that your speculation reflects truth implies that something has gone off the rails in the reasoning process, however.

Using statistical analysis to understand real causal relationships in areas we have real data about is damn hard, and even plenty of people who are highly trained as statisticians screw up all the time. Academic fields like comparative politics (to take an example I spent a fair amount of time studying) are rife with poor conclusions drawn from bad analysis. The LessWrong folks are hardly unique in applying logic poorly. But they do tend to tackle more speculative questions and convince themselves more firmly of their conclusions (at least, such is my impression as an outsider).

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

#114

Post by Houshalter » Tue, Jan 05, 2016, 7:32 PM UTC

The fundamental insight of bayesian reasoning is that prior probabilities can matter a lot in some situations, even when the evidence seems fairly strong.

Look at scientific papers. Usually there is something called a p-value attached to it, which is usually around 0.05. This means there is only a 5% chance that the same result could have been produced by random chance.

How strong is that evidence, really? What if you started with a prior probability of 1 in 1,000 that it's actually true. That is, before you saw the paper, you would estimate there's only a 0.001% chance it's true. Out of 1,000 similar studies, 49 will be false and yet return a <0.05 p value. Only 1 will publish actually true results.

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

#115

Post by stuartaxelowen » Tue, Jan 05, 2016, 7:36 PM UTC

Retric wrote: post #110

XFrequentist wrote: post #35

Earlier quoted context omitted.

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…

Bayesian seems great when you first see it. It should be obvious how to apply it for something like a card game. The problem is how long would it take you to realize a deck of cards was missing the 4 of diamonds? What if the card was lost 1/2 way though the game? How about on the prior hand? In the end it's stuck at one level of recursion and all facts are fuzzy.

It's stuck in the reality you define - you can add the last hand, all cards seen so far, and the color of people's jackets to the model if you so please.

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

#116

Post by SandroG » Tue, Jan 05, 2016, 7:40 PM UTC

Bayes in action: The author of this article had a set of prior beliefs about the Bayes's Theorem, which evolved after he reviewed more evidence.

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

#117

Post by TeMPOraL » Tue, Jan 05, 2016, 7:44 PM UTC

RodericDay wrote: post #78

TeMPOraL wrote: post #62

Earlier quoted context omitted.

I'm not that huge advocate of LW. I used to frequent the site, I read the Sequences and generally liked what I saw. RE parts you quoted. Of course they look bad, because they've been ripped out from context. Race: http://lesswrong.com/lw/kk/why_are_individual_iq_differences... This is an article asking, to quote: "But why is it that the rest of the world seems to think that individual genetic differences are okay, wh…

I guess I just disagree with you that they're taken out of context? 1. Bond posits Yudkowski thinks that racism is mostly due to genetic difference, and not about the deliberate, mostly political disenfranchisement of minorities. You say this is a wrong because his appraisal of the situation as being caused by genetic disparities is benevolent, and that he wants to work to "fix" it. These aren't in contradiction- to…

The racism and feminism points Bond makes sound to me like typical social justice warrior bullshit - no matter what you do, you're a misogynist racist. Disagreeing with the modern trend of mindless outrage paints you as an enemy. So does ignoring the topic. So let me skip it, because I do disagree with Bond very seriously about that part of the text, and I don't want to start another SJW subthread here.

> Nothing here seems to be a counter, you're just basically saying "it's politically incorrect so it's probably right".

No; I'm saying that just because he's politically incorrect, doesn't mean he's wrong. And it most definitely does not mean Bond gets to assume all the bad things he did about the author. Eliezer is just toying with an idea based on some observations. Personally, I find his idea intriguing and worth considering, given that time and again I've learned that when the general population seems to believe something counterintuitive and self-serving, like "those rich people are stupid and evil", they're usually wrong.

> The whole point is that these kind of people find these questions ("is rape really bad?") really intriguing rather than obvious.

I think we disagree on the interpretation. Many stories raise weird questions about morality; that's the reason we have literature. Please find me a place on LW where people, and Eliezer in particular, were seriously advocating for rape. Also it's worth noting that the rape angle was just a passing remark in the story, a way to shake the audience a little bit - and otherwise in no way relevant to the plot.

> I think you're too uncharitable to critical writers like Bond (it took me a while to acquire a taste for this vicious kind of writing), underestimating their and their audiences' understanding. As a result, you think this context adds way more than it does.

Maybe I am, but it's because I've been a member of groups that were on the receiving end of such writings, and spent a lot of time debunking them point-by-point to concerned friends and colleagues who stumbled upon them. It's painful, and you realize just how helpless you are against people who argue dishonestly.

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

#118

Post by iraphael » Tue, Jan 05, 2016, 7:48 PM UTC

darawk wrote: post #89

> If you get tested again, you can reduce your uncertainty I've always been bothered by statements like this about medical tests. This assumes that false positives are statistically independent. But isn't it more likely in general that false positives would be highly correlated in individuals, test administrators, or labs? E.g. If the same person takes the same test from the same doctor and sends it to the same lab,…

I think the idea is that, if you retake the test, your system will be in a different state (our organism's biochemistry fluctuates naturally). So if something in your system caused a false positive, there's a chance it won't be there when you retake the test and you will get a true negative.

Basically, you're thinking of your blood composition as stateless, when it may also be counted as an "external factor".

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

#119

Post by irotatori » Tue, Jan 05, 2016, 7:49 PM UTC

TeMPOraL wrote: post #38

XFrequentist wrote: post #35

Earlier quoted context omitted.

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.

A fascinating illustration of this being the phenomenon of Roko's basilisk.

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

#120

Post by ikeboy » Tue, Jan 05, 2016, 7:49 PM UTC

RodericDay wrote: post #57

TeMPOraL wrote: post #45

Earlier quoted context omitted.

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 th…

I know you're a huge advocate for Lesswrong, but not "everybody" or "anyone" has quotes ripe for picking like Yudkowsky. Stephen Bond is not just throwing some opinion out there, he's backing it up with first-hand sources: Yudkowsky on his simplified views of why race gets brought up: > "Race adds extra controversy to everything; in that sense, it's obvious what difference skin colour makes politically". > "Group inj…

> "Group injustice has no existence apart from injustice to individuals. It's individuals who have brains to experience suffering. It's individuals who deserve, and often don't get, a fair chance at life. [...] Skin colour has nothing to do with it, nothing at all."

Those parentheses obscure a significant point. The full paragraph is

>So, in defiance of this psychological difference, and in defiance of politics, let me point out that a group injustice has no existence apart from injustice to individuals. It's individuals who have brains to experience suffering. It's individuals who deserve, and often don't get, a fair chance at life. If God has not given intelligence in equal measure to all his children, God stands convicted of a crime against humanity, period. Skin colour has nothing to do with it, nothing at all.

He's claiming that skin color has nothing to do with the (according to him) injustice of different people having different intelligences. He's not claiming that skin color has nothing to do with why people don't get a fair chance at life. "Skin colour has nothing to do with it" is making a moral claim, not an empirical one.