Lets discuss Bayesian Statistics

[Bricker]

@steronz

As an outside observer, I think it would have been better if Bricker had jumped off the bandwagon as soon as he realized it was the wrong one, and then just admitted that he was on the wrong bandwagon instead of defending his rationale for getting on the wrong bandwagon in the first place.

Better? Ok, maybe.

But I have, perhaps naively, felt this message board was a place where it was possible to draw such distinctions and have them understood.

[Evil_Economist]

@steronz

If I’m understanding this correctly, let’s say you’re a junior detective assigned to a case. The initial case meeting starts out with you, your boss, and a half dozen other detectives in a room with a file sitting on an empty table. The chief detective opens it up and reads the entire contents of the file: “A woman claims she was raped.”

You pipe up and say, “There’s an 8 percent chance she’s lying,” and everyone nods wisely and applauds your contribution.

You all somehow solve that case and are assigned another one. You walk into the same room, and the chief opens the case file on the empty table. This time he reads, “A female stripper claims she was raped at a frat party.”

You pipe up and say, “If we didn’t know half of that information, there’d be an 8% chance she was lying.”

Just wanted to say that I love this post.

[steronz]

@Bricker

But I have, perhaps naively, felt this message board was a place where it was possible to draw such distinctions and have them understood.

And it is – I think this thread is a shining example of how the distinction has been drawn, and is clearly understood by all, even a dummy like me. (Fighting ignorance only took 6 years!)

Context is everything, I guess. I’m not going to fault people too much for not identifying the fine line you were walking in the name of fighting ignorance when you were posting in a thread that was about a non-theoretical case of a highly charged nature. It’d be nice if everyone had acknowledged your narrow, insignificant point and moved on, but… meh.

[Evil_Economist]

@Terr

I kinda see what you’re saying…

@Left Hand of Dorkness

I see what you’re saying, and an analogy might help.

I’ve got a random number generator that will generate a number between one and a million. It’s attached to a door. If it generates 1,000,000, the computer will rotate rooms such that there’s a brand new Ferrari behind the door. Otherwise, it rotates rooms such that there’s a hungry tiger behind the door. Got it? One in a million times=good; the rest of the time=bad.

But things aren’t so bad! I’ve got another number generator that will generate a number between 1 and 100. If it generates 1-99, it displays a sign telling you what’s behind the door; if it generates 100, it’ll display a sign telling you the exact opposite of the truth.

You look at the door. It says, “Ferrari!”

Do you open it?

I wouldn’t. Because the chance that the first random number generator rolled 1,000,000 is much lower than the chance that the second one rolled 100.

I think the probability here works exactly the same as it does in the 1-in-a-million people with AIDS, 1-in-100 people get bad test results example.

The way to explain it better, just say that there is no Ferrari. Only hungry tigers. If you know THAT, and the sign says “Ferrari” - don’t open the door.

Actually, this is a very good way to understand the concept.

If we know than there are never Ferraris behind the door, then we know the sign is lying. On the other hand, if we know that it’s always a Ferrari behind the door, then we know the sign is telling the truth. So our belief in the sign goes from 0% to 100% depending on the percentage of time that there’s a Ferrari behind the door.

If there’s a very small, but non-zero, chance of a Ferrari behind the door, then our belief in the sign should be greater than 0 but less than 100%. And as it becomes more likely that there’s a Ferrari behind the door, our belief in the sign should increase, going to 100% as the percentage of Ferraris behind the door goes to 100%.

[Evil_Economist]

@Maeglin

This error isn’t due to Bayesian inference but to the mistaken assumption that human behavior is ergodic. You rightly point out that it’s not. The behavior of individual people over time does not tend to converge to the population average when incentives and circumstances differ. Statistical inference, whether Bayesian or frequentist, is very limited when behavior is really non-ergodic.

I’m not familiar with the concept of ergodicity; I need to do some reading before I can comment on its applicability here.

[Deegeea]

@ultrafilter

If you’re flipping a fair coin 100 times, you’d expect to see 75 or more heads about once every 350,000 attempts. I’d be skeptical that your coin is fair.

This is the exact circumstance I am in with regards to a game I play online. Odds that are stated to be 50/50 are in fact coming out reliably 75/25. I posted about this in the bugs section of the site. The programmer checked over her code and could not find an error that would lead to this happening.

Most players, and apparently the programmer, concluded that it means this is all coincidence, and those 50/50 chances keep coming up around 75/25 (sometimes 70/30 or 80/20 or the like) by sheer random chance. Which is possible. But not, I aver, plausible. There has to be a bug.

[Maeglin]

@Evil_Economist

I’m not familiar with the concept of ergodicity; I need to do some reading before I can comment on its applicability here.

Trust me, it’s applicable. You put your finger right on it in your initial posing of the question.

An ergodic process is one for which the average over time of one actor eventually converges with the true population average. For human beings committing murder, this is absolutely not the case. It may well be that the true average of black men committing murder is x%, but it is probably not the case that over the course of his life, the probability of Barack Obama committing murder will converge with the true average.

Fine, one might say, you just need to control for more variables. It’s not enough to say that Obama is black man, we now need to calculate the murder rate of black men who went to Harvard and became president. Now our sample size is gone and we cannot make any inferences at all.

[monstro]

@Bricker

Perhaps, and maybe it was foolish of me to continue to insist on a concession that had zero practical applicability to the man discussion, but at the same time it seemed to me – and still does-- that on a website supposedly devoted to fighting ignorance, we can in fact say what is true and at the same time acknowledge that we’re talking about something true only in a vacuum.

I get the danger in, say, a newspaper article,of making a similar statement. But in the context of The STRAIGHT Dope, I am sorry, but we should be able to handle the distinction.

In my opinion.

But we never talk about things in a vacuum, Bricker. Not even on the SD.

If I’m reading a newspaper article about white collar crime, and the journalist slips in a statistic about 30% of white collar criminals being from the highest tax bracket, then I’m not going to flip out. It’s not the most earth-shattering news in the world, but depending on what the article is about, it may be relevant.

But if I’m talking about a working class guy who is accused of embezzling money, and someone says something like, “Most embezzlers are rich! So this guy is likely innocent!”, then that person’s head is full of garbage. That is the type of ignorance I’ve been fighting. I don’t know what ignorance you’ve been battling, but that has been my position.

[Carmady]

@Bricker

Well, I still defend the position that as between you and Huerta88, he was calmly offering cites and supporting arguments, and you were simply gainsaying his position, so that I found him a more effective rhetor.

I would rethink that position. Huerta88’s math was wrong before you even posted in that thread. I’ll give an example with made up numbers.

Ab = allegation by a black woman that a white man raped her
Rb = the rape actually happened
Aw = allegation by a white woman that a white man raped her
Rw = the rape actually happened

Suppose:

P(Rb)= .01
P(A|Rb)= .9
P(A|Rb’)= .001
P(Rw) = .1
P(Aw|Rw)= .7
P(Aw|Rw’)= .01

Then P(Rb|Ab)= .901

And P(Rw|Aw)= .886

The probability of a black woman’s accusation being true would be slightly higher, even though white women were 10 times more likely to be raped by a white man.

That is, even if black women are much less likely to be raped by white men than white women are, if a randomly selected black woman is also less likely to falsely claim that a white man raped her, and/or if black women are more likely to report such a rape, then a greater percentage of accusations by black women may be true than by white women. It does seem reasonable that a greater percentage of white women would make such false claims, for the same reason that a greater percentage would actually be raped by white men; proximity, dating within the same race, etc.

Even in a vacuum his argument was incorrect.

Ignoring that the math was very wrong, the argument would have failed anyway because you can’t pick and choose which variables to look at after the fact. What I mean is, if you said “using this data about white on black rape, I will calculate the probability that the next accusation is true” that would make some sense. But it would be wrong to say “this accusation just happened, and as I look through the circumstances I notice it was a white on black crime… I choose to use that to make my calculations.”

[monstro]

I’ve been thinking, Bricker, and I’m going to admit to feeling a bit salty with you. And justifiably I think. I think you are intelligent enough to know good and well what you with the face had been arguing incessantly. You can accuse her of being a lot of things, but obtuse is not one.

Never once did you say that you disagreed with Huerta. You created a thread supporting him, in fact. A very “good ole boy” thread. Simultaneously, you called you with the face an idiot. Repeatedly. Even as poster after poster chimed in agreement with her and tried to school you, you never said, “You have given me something to chew over” or “You’ve got me all wrong! I agree with you about this, just not about that.” Rather, in all trainwreck threads you just bowed out after the kitchen got too hot, leaving the impression that your mind had never been changed.

So I’m finding this recent relevation from you about “vacuums” and whatnot puzzling. It comes across as a sneaky way to not own up to simply being mistaken, to being human and simply not understanding a complex subject. In other words, instead of saying “mea culpa”, you’re moving goalposts so that you with the face still looks wrong to those who don’t know any better.

It’s not a big deal, I know, but I think I’ve been harboring some harsh feelings about you as a direct result of those exchanges. And they came out in the other thread. Maybe I’ll be able to move on now that I’ve gotten this off of my chest.

[Left_Hand_of_Dorkness]

@monstro

So I’m finding this recent relevation from you about “vacuums” and whatnot puzzling. It comes across as a sneaky way to not own up to simply being mistaken, to being human and simply not understanding a complex subject. In other words, instead of saying “mea culpa”, you’re moving goalposts so that you with the face still looks wrong to those who don’t know any better.

FWIW, monstro, I feel almost exactly the same could be said about you and your sister. Bricker’s qualifications of his statements were pretty pedantic, but they were in the original thread, and it seemed to me as though she and you WERE being obtuse about what he was saying, and that you were, if not moving the goalposts, at least strawmanning him.

[monstro]

@Left_Hand_of_Dorkness

FWIW, monstro, I feel almost exactly the same could be said about you and your sister. Bricker’s qualifications of his statements were pretty pedantic, but they were in the original thread, and it seemed to me as though she and you WERE being obtuse about what he was saying, and that you were, if not moving the goalposts, at least strawmanning him.

I gave him plenty of opportunity to say, “I agree with you, but what I’m saying is…” At least I do not recall this happening. If you care to plunge into those threads and bring back an instance of him conceding anything, I’ll apologize. But I do not recall this occurring.

Rather, I recall him regaling us with ridiculous scenario after ridiculous scenario, never once answering the questions posed to him that would have gotten at the heart of his “real” argument. If we misunderstood him, it was because he was too busy calling people “idiots” to explain himself adequately.

But I’m going to leave this alone. I don’t want to give off the impression (any more than I already have) that I am obsessed with Bricker or this particular issue. I’m ready to forgive and forget. Finally.

[ExcitedIdiot]

@Terr

I disagree. Knowing that the person got a positive result on an imperfect test allows us to increase the likelihood to 99 in 100. The prevalence of HIV in the population has no influence, whatsoever, on the efficacy of the test. Whether it is one in a million, or one in a thousand, after the test it is still 99 in 100.

If a million people are tested, and the test is 99% accurate, we know there will be 10,000 false positives. God already told us there would be only one person(on average) with HIV in this group. That makes 10,001 tests that will come up positive, with only 1 person actually infected. Thus, 1 in 10,001.