The Interpreter; Bayes Theorem; Nephites and Mayans

[_canpakes]

My understanding is he wasn't an outlier at all... everybody regarded the indians as tribal??

This.

I wonder why the authors of this paper went out of their way to ignore the more obvious reason for Smith’s word choice?

[_Gadianton]

Now back to basketball

But that you just get to observer, here you get to bring down the glass. I might have to ferry points made from the article over here and pretend I'm impressed, just provoke you into responding.

Controls are used to compare results of a hypothesis applied to known variables, to see the difference between those results and the results of applying the hypothesis to unknown variables, right?

I can't remember. It's been several long days of building tools to analyze the contents of a database, in between cleaning out my landscape rocks. I'm exhausted. But, I liked this quote, because it reminds me of what I've been doing these last few days, and I'm sure there's a lesson here. The biggest problem with a job like that is there's no explicit target, and so finding ways to calibrate the tools is really important.

[_Gadianton]

Then, once they had hammered out such a good list of questions for comparing societies in general, they could have applied it to the special case of the Book of Mormon society and the Mayans. If these authors had done this, then it seems to me that their Bayesian result would have been meaningful. Am I right about that, as being what it would take to do this analysis right?

I like your suggestion to really get specific and find flaws. It sounds like flaws abound from what everyone's saying, but it's all too easy to dismiss it on grounds that obviously the Book of Mormon is fiction, rather than honing on on where the mistakes occur. well, i haven't had a chance to look at it yet, but I will and then come back to your post.

[_Meadowchik]

Congratulations to the historicists! They've got a real win with this one, and we can now rest easy with the mathematically certain knowledge the Book of Mormon is historical, and all that follows from that proposition true.

Of course, Bayes's theorem, according to some of its fervent practitioners who are also historians, has shown that Jesus is not historical but rather a mythical figure like Hercules. So the problem these geniuses now have is: how to make sense of a mythical Jesus in a historical Book of Mormon. That's a tough one.


via Imgflip Meme Generator

The Columbia scholar who used Bayes to examine the probability of Jesus is who I asked about this, out of the blue. And he responded!

But it was short. He is not familiar enough with Mormonism to give an opinion.

And there we have it. Again and again. Unattached experts are very rarely interested in the unsubstantiated book of magic provenance. I'd guess that the MI article is not solid enough to capture interest.

[_moksha]

While the article did not specifically touch on the following scenario, I will offer it for your consideration:

Start of the Cambrian Era

A pond of chemicals has formed on the Pre-Cambrian earth. Protein molecules form. Protein molecules combine. Enough protein molecules combine to form the Book of Mormon.

Scientists from the Interpreter laugh at the statistical probability of this occurring, thereby proving the Book of Mormon is true.

[_Physics Guy]

Something that might be the most basic error in this paper was raised by JarMan at the other board. He pointed out that most of the features scored as "hit" common features to Maya and Book of Mormon societies are in fact common features of most ancient societies. This means that Smith might have gotten all his hits in one fell swoop by just deciding to make his Book of Mormon societies be like whatever he knew about other ancient societies. Even if he was not widely read in ancient history he would have known quite a bit about ancient societies from the Bible.

Because of this possibility it is wrong to multiply all those probabilities together as if every little feature of Book of Mormon/Mayan society would have been an independent guess on Smith's part. There might really only have been one guess, when Smith decided to make his Book of Mormon peoples live much the way people seemed to live in the Bible.

Most importantly, this is not just a minor technical issue that could never do much to change the paper's conclusion of incredibly low probability for a Joseph Smith guess. On the contrary this is a huge issue which really can demolish that low probability with a single blow, because it destroys the validity of multiplying many probabilities together. That's the problem with low Bayesian probabilities reached by multiplying many probabilities: the multiplication is the leverage that makes the probabilities come out so tiny, and so anything which invalidates the multiplication can destroy the seemingly unassailable result just as easily as it was created. Live by the sword, die by the sword.

[_Physics Guy]

Another candidate for the basic problem is normalization. Bayes's theorem says that the probability of a hypothesis given the data is the probability of the data given the hypothesis, times the prior probability of the hypothesis ... and then divided by the prior probability of the data. Since there is often no easy way to determine the prior probability of the data, this factor is often given scant attention, but it is logically necessary.

In cases where one is comparing hypotheses that are mutually exclusive and collectively exhaustive (i.e. they cover all possible explanations for the data), one can compute the prior probability in a way that is at least self-consistent by simply summing the probabilities of the data under each hypothesis, weighted by the prior probabilities of the hypotheses. This amounts to using the prior data probability as a normalization factor to ensure that the probabilities of all the hypotheses sum to one.

Suppose I have two mutually exclusive and collectively exhaustive hypotheses: (A) the Book of Mormon is historically accurate, or else (B) it is not. If we say that (B) implies similarities between Nephites and Mayans must be just lucky guesses, and I find 20 genuinely independent similar features that would each be a 50/50 guess, then I get to count a (1/2)^20 factor in P(B). That's a little under 1 in a million. If there are also two genuinely independent factors that are blatantly different, then that's exactly what you'd expect under (B), so I only get a factor of about 1^2, leaving me still at one in a million.

Think it looks bad for (B)? We're not finished. So far our P(B) is unnormalized, because we have not yet divided it by the prior probability of the data. To determine that normalization factor we have to work out P(A).

Those 20 hits are only what you'd expect under (A), so we just get a factor of 1^20 from them, which is still one. But it would be extremely bizarre for an accurate historical account to somehow screw up even one major feature of Mayan society. So each of those two discrepancies brings P(A) down by a factor of, say, one in a thousand. So now P(A) is also around one in a million.

If the prior probabilities of A and B are equal then the total unnormalized probability so far is 1 in a million for A plus 1 in a million for B, making 2 in a million in total. Normalizing them both into true probabilities by dividing them both by this total leaves the final probabilities of both A and B at one-in-a-million divided by two-in-a-million: in other words, 50%. Those two discrepancies have balanced out the twenty hits.

This example has used arbitrarily made-up numbers, but it shows the point. When the un-normalized probabilities of all hypotheses are low, normalization can push the probabilities back up by huge factors. This is once again not a minor technical quibble that can hardly affect the strong conclusion, but a crucial issue that can utterly destroy the paper's conclusion, in spite of the large number of "hits" it considers.

[_Gadianton]

Something that might be the most basic error in this paper was raised by JarMan at the other board. He pointed out that most of the features scored as "hit" common features to Maya and Book of Mormon societies are in fact common features of most ancient societies.

I think this is getting warmer, although Lemmie did mention "coincidences", but she needs to get used to talking to the rest of us rather than other stats experts (I don't mean to include *you* in *us* PG but I do mean to include me) who don't immediately see exactly what she means. That's the word she used that stuck in my head yesterday, though.

I had two points on my mind when I woke up. The first was the laughable suggestion of using "Manuscript story" as a "control". It's like 20 pages of real text. In fact, the length of it has been used by apologists to discredit it as a source for the Book of Mormon. What this argument really is, is that the longer the book is, the more likely it is to be ancient.

The other point is similar if not the same. Bayes is intuitive for really simple contrived problems that take stats experts to think of, not the every-man who is the protagonist in the Bayes example. For instance, the every-man sees a party going on down the street and rolls over. He remembers hearing his neighbor talk about going to the party, and so gives it a prior probability that his neighbor is there. He thinks: let me see if his car is there. Then he spots his neighbor's car, and updates the prior. Now what if he didn't see his car? Have they really accounted for that? They accounted for not seeing his neighbor's bike, had his question had been about the bike, but that's not the same thing.

Now imagine this: you wake up bound and gagged and you hear dark voices talking outside your door about the long airplane flight and you suddenly come to believe you've been taken hostage and are in another country. Now, this isn't so easy. It could be five minutes if you get to a street and see license plates. But you could spend days or weeks without enough information, yet plenty of false positives to multiply together.

What Brant Gardner said that always stuck with me is that he quit looking for the Book of Mormon in Mesoamerica, and began looking for Mesoamerica in the Book of Mormon. To me what this says is he started looking where the opportunities for coincidences abound. To look for Mesoamerica in the Book of Mormon, you need rigorous controls. And that's what these guys did, except with about 50 pages of text as their control. They can rather, begin with archive.org.

[_DrW]

Physics Guy,

Thanks for taking the time to describe specific methodological failures with the Dale & Dale paper. You found two significant problems in the application of Bayes Theorem to the subject matter of the paper in question.

Others have found many more problems with the paper and especially its conclusions. These include passages in the Book of Mormon itself that completely negate its truth claims in the light of scientific findings, but I digress.

You, on the other hand, went further and provided clear professorial explanations as to the effects that these failures would have on the claimed outcome.

The paper is a hot mess from start (including the title) to finish. However, in looking at some of the comments and the authors responses, Dale Sr. seems to be defending the faulty application of Bayes with denials and bald appeals to the authority of the claimed peer reviewers, including his son as co-author.

One wonders if they actually took some time to step back (way back) and consider the wider implications of their hyper-optimistic and wholly unwarranted conclusion before pressing the SEND button. One wonders if the paid any attention the word 'scholarship' in the Interpreter mission statement.

This is a request to at least consider submitting a condensed version of your two explanatory posts to the comments section for the Interpreter article. Everyone concerned could learn from your work on this. The fact that you are not LDS (or former LDS), and your academic credentials, would give your comments and explanations swing weight.

[_Dr Exiled]

I think DNA is the key as Dr. W said early on. The probability of historicity no matter how desirous one is to believe is zero when facing the mountain of DNA evidence. So, the probability the interpreter article is flawed has to be 100% and this is just another failure in attempting to use science to prove historicity.