The Interpreter; Bayes Theorem; Nephites and Mayans

[_Res Ipsa]

You're welcome, but I wasn't trying to tell you how to calculate the correct odds, I was pointing out that your understanding of gad's line was incorrect.

Not to be a stickler about the language, but the "and" is not ambiguous, it means the two things occur together, so i was just noting that your language:

"Given D, the probability of S is 1."

was not a correct statement.

Thanks, Lemmie. Please be a stickler about the language. I appreciate your willingness to correct my fumblings.

[_Res Ipsa]

I don't know if Gadianton's question about how the Dales got their 50 was trying to get at something else, but I think Res Ipsa probably has the Dales' methodology, except perhaps for the issue of false positives and false negatives.

I couldn’t find anything in the paper that explained how the Dales accounted for false positives and negatives. I’m guessing that false positives won’t occur because they assume Coe is always right. But I couldn’t find anything about false negatives.

[_Res Ipsa]

Could one example be:

Likelihood Book of Mormon is “true” given Joseph Smith incorrectly put horses in Mesoamerica in Mayan Times: .98
Likelihood Book of Mormon is fiction given Joseph Smith incorrectly put horses in Mesoamerica in Mayan Times: .02

Ok, it’s 49, but you get the drift.

Do you think the authors actually did this calculation?

Your phrasing of how this works isn't quite right. It's more like:

Likelihood Book of Mormon would mention horses (in the way it does) presuming the book is fictional: 0.098
Likelihood Book of Mormon would mention horses (in the way it does) presuming the book is historical: 0.002

0.098/0.002 = 49, but you get my drift.

I divided both numbers by 10 to emphasize that they don't have to add to one, and that neither one needs to be likely.

Thanks!! That really helps. I was struggling with the wording.

[_Res Ipsa]

(Everyone but Ipsa: every time you break out the probability theory to prove your point, Chino Blanco takes it over to Interpreter, the dales assume they get it and smile smugly when it's doubtful that they do get it, and pat themselves on the back, and then Allen Wyatt smiles knowingly about how anti-Mormons distort the truth. If there is any chance that any apologist is going to be struck with a knowledge of their own guilt, it's by breaking this down to a forth grade level)

That is a problem, since Res Ipsa incorrectly stated the Dales' likelihood ratio above. The hypothesis that the Book of Mormon is true should be in the denominator of his example, not the numerator.

ETA: i see analytics already commented on this, and made the correction.

I take comfort in the fact that the Dean’s comment was directed to everyone but me.

[_Water Dog]

Gadianton, I'm traveling atm, will respond when I can. Though looks like maybe your question was answered already. This thing is a mess. I'm resisting spending more than a few minutes reading the paper, but may just have to sit down and slog through it. A more more formal "this is exactly what they did and exactly why it's bs" response with examples of what a credible methodology would have looked like may be warranted. My "at a glance" hot take is that their math is probably fine in the sense the arithmetic checks out. The problem is with the application. Bad logic. Bayes is just some math based logic. The output is limited to the context of your inputs. hence my example we could use Bayes to analyse Star Trek universe. The results of our analysis could be perfect, but the input is fiction so it can't tell us anything about the real world. As far as I can tell from my quick look, this whole effort is bupkus, regardless of anything else that follows, because there's no mathematical or otherwise objectively justifiable logic for their inputs. That's not something you can poke holes in by going into the math itself. You'd have to go one by one through each input and argue against their made up numbers. Which seems pointless. I'll read the other comments to catch up.

[_Lemmie]

I've noted my concerns with the likelihood ratios used, so I wanted to address the independence issue.

It seems glaringly obvious that testing the 131 true statements from The Maya and the 18 non-true statements also noted by the author of The Maya does not constitute 147 independent tests, but apparently it is not obvious to the Dales' or to the stats person Wyatt had peer-review their paper. For that reason, I want to lay out a little more specifically the issue.

The Dales are clearly following a medical diagnostic testing model, so I looked for whether researchers in the medical field comment on using this model for multiple, possibly independent tests.

There are many such statements, but here is a particularly clear one from a U of Illinois medical school course covering medical testing:

A convenience of likelihood ratios and the odds formulation of Bayes theorem is that you can do things like this:

Posterior Odds = Prior Odds * LR for finding 1 * LR for finding 2 * ...

But this only works when the likelihood ratios are conditionally independent.

This means that the likelihood ratio for a finding should not depend on the likelihood ratio for another finding.

http://araw.mede.uic.edu/~alansz/course ... week4.html

Back to the paper, note that the denominator of the likelihood ratios is

P(B| ~A) ,

Where B represents the statements the authors have collected from Dr. Coe's book: 131 statements that are true, that also show up in the Book of Mormon.

It also includes 18 statements that are false, from Dr. Coe's talks about in various speeches or articles.

Therefore, every likelihood ratio being calculated is based on probabilities about a statement B, and every statement B comes from a single author, in his discussion of the Mayan era, and how the Book of Mormon may or may not match the Mayan era.

Let me emphasize, all 147 statements B, in all 147 likelihood ratios, are coming from a single author, as he is discussing a single topic.

There is no way any reasonable person could conclude that all 147 statements are completely independent from each other, to justify multiplying all 147 LR by each other to change the odds. It is not rational.

Gadianton asked about the value 10^-32 and its likelihood in statistical research; in this case the Interpreter article reaches that value only by making the completely non-credible assumption that 147 statements, all from a single author, all about a single topic, constitute completely and totally independent statements. It is absurd.

[_Res Ipsa]

Lemmie, I’m trying to wrap my brain around your point about the denominators and independence. I could see it with the numerators but hadn’t thought about the denominators. Would you say the problem is broader than just using Coe’s book? Even if we just used the facts about the Mayan civilization, whatever they are, they’re not truly independent. For example, geography and climate influence available food, which affects culture, etc. Does this doom the exercise out of the gate, or is there an adjustment to the math that one could make to account for the lack of independence? WD showed me an example with two factors, but how would one do it with 147?

[_Lemmie]

Lemmie, I’m trying to wrap my brain around your point about the denominators and independence. I could see it with the numerators but hadn’t thought about the denominators. Would you say the problem is broader than just using Coe’s book? Even if we just used the facts about the Mayan civilization, whatever they are, they’re not truly independent. For example, geography and climate influence available food, which affects culture, etc.

Yes, absolutely, but it doesn't take more than one relationship to show that multiple things are not independent.

Does this doom the exercise out of the gate, or is there an adjustment to the math that one could make to account for the lack of independence? WD showed me an example with two factors, but how would one do it with 147?

maybe, let me try setting up an example. it's complicated by both numerator and denominator dependencies.

[_Res Ipsa]

The more I read and think about the paper, the more it strikes me how biased the methodology is against strong evidence that the Book of Mormon is fiction and in favor of weak evidence that the Book of Mormon is genuine history. I would identify the following as cases of this bias:

1. The arbitrary limit on Likelihood Ratios, which does not effect week evidence but dramatically reduces the effect of strong evidence.

2. The restriction to instances in which the element is addressed in both books, which does not effect evidence in favor of historicity but arbitrarily restricts the evidence in favor of fiction;

3. Failure to follow the paper’s stated methodology, resulting in overstating the strength of evidence in favor of historicity.

We’ve identifier other problems with the paper, but are there others that specifically bias the paper against strong evidence in favor of fiction?

[_Physics Guy]

Large as those effects are, I think the biggest problem with the paper is still an enormous bias in favor of weak evidence against fiction, treating all the "hits", however weak, as independent random guesses with moderately low probabilities.

Multiplying so many smallish probabilities together is what makes the final probability come out so low in the end, but it's ridiculously illogical. If the Book of Mormon is fake, it's still trying to portray an ancient society consistently, based on substantial knowledge of at least Biblical ancient societies. It's also trying to portray some kind of American geography (whether North or Meso). So there aren't just a few overlooked correlations among some of the hits: all those 100+ features are massively correlated, such that they really only represent a handful of independent decisions on the part of a fictional writer, at most.

If the Dales are allowed to get away with multiplying 10% a hundred times, then they can afford to laugh off every other criticism, even ones severe enough to boost their final chance of fraud by huge factors. The incredibly tiny product of a hundred small factors will still leave them with a chance so small there's little practical difference between it and zero.

What kicks the legs out from under them is demolishing that big multiplication. Their hits are highly correlated, so their probabilities are not independent. That's what cuts this paper down to the point where the remaining problems finish it off.