Question About Bayesian Analysis

I stated this before in the Pit thread: when you have to invent an outlandish scenario that is impossible to attach any kind of number to (whether that be statistical odds or prevalence), your argument immediately jumps the shark. Perhaps you could communicate your point in a less cartoonish way?

I’d be disinclined to believe my uncle’s story about Alec Baldwin and Gorbechev because I can’t imagine why a former head of state would be cutting a movie star’s hair in the middle of the street. Let alone imagine why Baldwin would be letting a bunch of monkeys lick his balls in broad day-light. The story just sounds implausible, given what we know about human dignity and the habits of well-known personages.

But there is nothing implausible at all about a white guy raping a black woman (or a Meeper tickling a Fleeper). I could imagine someone finding the story about Baldwin and Gorbechev incredible either in an absolute sense or a relative sense, but I fail to understand why anyone would see w-o-b rape in the same way.

As Noel wisely pointed out, what is the point of coming up with any kind of estimate of credibility when its inherently going to be arbitary? If you compute an estimate based on race you’ll get one number. But if you look at educational level, income, occupation, religion, or any other factor–either singly or in combination–you could get a completely different one. In the US, unfortunately, we are so stuck on race that that’s the first thing that is often seized upon. But 9.9 times out of 10, there’s a lot more going on besides race.

And in real life, there is not enough randomness to for this type of analyis, either. Not all black women are going have the same risk of being raped, and some forms of rape are going to be more likely than others, depending on the situation and the people involved. To see this only in terms of “math” is crazy because humans are not predictable enough.

The thread that spawned this and four others of various degrees, were based on a simple premise…“All things being equal”, can you use statistics to prove whether or not an individual who is in the lower end of the statistically pool is less credibility than one who’s in the majority.

The problem with these “chose one” hypotheticals, is that is usually pits a reasonable occurance against things like Dead Presidents that walk, Ninjas, monkies that write Hamlet or nickels that always land on their edges and then you’re asked to chose, usually with either a gun to your head or offers of millions of dollars, which is more credible.

I simply do not understand why at least from what I’ve seen, no one can answer the original question when asked in a hypothetical that resembles the original question; as it was originally asked, without having to further modify it.

You have two uncles, both of whom are equally honest and trustworthy.
Uncle Jack has brown hair and is in the majority says he saw an tiger waking down the street
Uncle Joe who has red hair(minority) says he saw a tiger walking down the street.

That’s it.

Why would Uncle Joe who’s as credible as Uncle Jack be less credible, just because he has red hair and as a group has less contact with ‘stuff’ than the majority?

I agree. There is no way to assign credibility to the REPORT of an event using statistics regarding the frequency of that event. The event and the report of the event are two different things.

So you would be equally willing to accept the report of a giraffe running down the street, as you would the report of Mikhail Gorbachev giving Alec Baldwin a haircut in the middle of the street while five monkeys were licking his balls?

If the credibility of the report is independent of the event being reported, then any report has to be treated with the same amount of skepticism (if coming from an equally-trustworthy source).

But the fact of the matter is, we do not treat all reports with the same amount of skepticism. Which means that the probability of the event being reported affects how much credibility we assign to the report of that event.

We mostly agree on this.

I haven’t read the other thread(s) on this, so I’m not sure how they were trying to use the math. I was just responding to the issues raised by some people in this thread who claimed that the probability of the event being reported bears no relation to the credibility of reports of that event (i.e. how willing we should be to accept it as truth)

Interestingly, Merriam-Webster defines incredible as:
too extraordinary and improbable to be believed <making incredible claims>”

So, the definition takes into account only the probability of the event being reported, and says nothing about the trustworthiness of the source of the report.

Maybe the title of a modern art piece at MOMA:
“Mikhail Gorbachev giving Alec Baldwin a haircut in the middle of the street while five monkeys are licking his testicles.”
:slight_smile:

Isn’t that how our justice system is supposed to work, when a crime of a plausible nature is reported?

Before you create another far-flung scenario involving zoo animals, Polerius, perhaps you could state your thoughts on the real hypothetical under debate.

Janice, a white woman, says she was raped by a white man.

Marie, a black woman, says she was raped by a white man.

Which woman’s claim is the most believable (credible)?

Of course, a further real world point, which I’m sure we’ve been taking for granted just to give the pro-statistical inferencers even the chance of saying something, is that “race” is not a binary division. The black/white divide does not cover the universe of possibility, and is not an “all or nothing” marker of separation. Even the concept of race, let alone separation of people into race-labelled “bins” is highly problematic. By what definition of racial difference were the alleged rapist and victim separated? By what definition were the reporting rate differences generated? What happens when you use a different definition?

The premise is that both events are plausible, but one occurs less frequently than the other. We’ve even demonstrated plenty of events in which you apply less credibility than you would to an even more unlikely event. Your hypotheticals wouldn’t be considered plausible by most people, which is what I believe holmes was objecting to.

The two events in question are much closer to hitting a color and hitting a number on a roulette spin. Both are perfectly plausible, both happen all of the time, yet the odds of one are quite a bit greater than the odds of the other. We stated that someone claiming to hit on a number is no less credible than the person claiming to hit on the color, all else being equal.

These are all very good points.

Can we at least stay away from absolute statements like the one from RaftPeople:
“There is no way to assign credibility to the REPORT of an event using statistics regarding the frequency of that event.”

Can we agree on the following:

  1. At the extremes (e.g. someone stating that they hit 10 numbers in a row in roullette), the probability of the event does start to affect how willing we are to accept the report of the event as true.

  2. Away from the extremes (in the “plausible” range), we are willing to bunch all events as, in some sense, equally-plausible, and therefore treat all reports of such events as equally-credible.

Please refer to DMC’s post for my response, it basically sums up my view.

On a side note, I haven’t seen a response countering my point regarding the Bayesian analysis flaw which assumes both meepers and fleepers should be included in the same pool to draw down the 3333 false reoprts, which implies an equal distribution of reports which is really an arbitrary decision. I know I’m locked in on this, but am I the only one that sees that flaw? Or did I miss it being spelled out on a previous post?

I thought we were interested in the math regarding the situation and not “how willing we are to accept the report.”

That’s why I used the abslute statement. When viewed from a mathematical point of view, I think that is is correct.

It is only a problem when we introduce our “willingness”, or if we introduce other information like the fallible nature of our brains when reporting events. If we are including the fallible nature of our brains then we’ve opened the door for other information too.

Sure, events in which the likelihood of it ever happening approaches zero, I agree that we can assign lower values of credibility (or lack thereof). What if we work with the following slightly modified version of his statement: “There is no way to assign credibility to the REPORT of a plausible event using statistics regarding frequency of that event.” I’m guessing that RaftPeople wouldn’t have too much objection to that modification, and it might even have been what his original intent was. In the other thread, the hypotheticals were getting more and more stupid by the minute, even though we stressed the word plausible over and over again, so after a while you give up even using the word.

But you gotta admit, if magellan had just added that the pet bald eagle had corn kerneled shit, you would have been sold on his argument. I personally had a moment of weakness when he dropped the gravity-defying nickel into the debate. I was like…wow, he’s almost getting through to me.

But then I woke up.

I made the same objection in the other thread. psychloan’s most important assumption is that we know how the claims distribute across populations. But the givens provided don’t allow us to make that kind of assumption. The false assuation rate of 25% applies to total claims. It says nothing about people.

It makes a lot more sense to see false claims as rate tied to true claims, since the type of interactions that make attacks possible (proximity, intimate relationships, etc.) also are the sowing grounds for false accusations. In other words, lying about an attack is just as much of a crime as causing an attack, and so you’d expect that the intangible barriers that prevent Fleepers from being tickled proportionately by Meepers, also prevents Fleepers from lying proportionately about Meepers. ::shrug::

Yes, you could use any distribution you wish. In that sense it is arbitrary, but if you actually want to use the results you try to use a distribution that is as close to the truth as possible. Of course that’s not so easy for real world problems. He just chose an equal distribution as a way to express the assumption of two “equally honest” populations. In reality that’s of course not exactly true, perhaps not even close. As I see it he was just trying to make a very simple and limited point. “Equally honest” populations (interpreted as equal distribution of false positives) do not necessarily result in equally credible (using this specific sense of “credible”) reports, it also depends on the distribution of true positives.

(Disclaimer: I don’t claim that either the numbers or the assumptions on distributions reflect reality especially well or that you should base any decision on real world cases on this simplistic model)

Not only that, but the studies that do exist, as wildly variable as they might be, all measure false rape claims as related to rape claims in general, not to the general population.