The Interpreter; Bayes Theorem; Nephites and Mayans

[_Lemmie]

Apparently, they did include specific criticisms that Coe raised in his Dialogue paper as part of the analysis.

Yes, from the comments section, they clarified:

We did not limit ourselves to 131 pieces of evidence, nor did we define them as true. After searching all B we found 149 (not 131 as you repeatedly and mistakenly claim) statements of fact, B, about which there were corresponding statements of fact in The Maya. Of those 149 statements of fact in B for which corresponding statements of fact in The Maya existed we found that 131 of them agreed and 18 did not.

The issues i have are

1) that they ambiguously define a statement of fact as something that can be untrue,

2) that they now say that the 18 untrue "statements of fact" are in The Maya when at other times they define those 18 as being additional statements discussed elsewhere by Coe, and

3) that they say they "search[ed] all B," which they now apparently define as the full Book of Mormon text.

Nowhere in the paper do i recall them stating that they searched the full Book of Mormon to get their 131 +18 statements, but now, in the comments section, they say they did. It's interesting that they assert it now, in response to my comment posted over there by chino blanco. they say:

Your core criticism here seems to be “For example, elements B could be every statement in the Book of Mormon, both those known as factual, those known as nonfactual, those not known if they are either, etc. Every element needs to be part of the experiment.”

And follow that with:

The elements B are every statement of fact in the Book of Mormon text itself about the physical, political, geographical, religious, military, technological, and cultural environment. Every element B is part of the study, we did not exclude any portion of the Book of Mormon text from scrutiny.

https://www.mormoninterpreter.com/josep ... -the-maya/

Except that they are only considering those elements that were ALSO facts from The Maya (131) and ALSO non-facts Dr. Coe happened to comment on (18). Restricting the data set like that is absurd, especially since from it they conclude that the probability that the Book of Mormon is fictional is smaller than the mass of a neutrino.

[_I have a question]

This should have been a very simple and straightforward hit-piece on Dr Coe:
1. Dr Coe said the Book of Mormon doesn't reflect Mayan culture.
2. The Dales want to show it does.
3. The Dales draw parallels between the contents of Coes book 'The Maya' and the 'Book of Mormon'.
4. Ergo Dr Coe is wrong and has in fact been hoist by his own petard, so to speak.

Job done.

The whole nonsense about using Bayes Theorem to demonstrate just how unlikely it was that one of the other many explanations for Mayan culture appearing in the Book of Mormon, that of Joseph "guessing" content, has completely destroyed what might otherwise have been an interesting anthropological paper and discussion about 131 parallels between The Maya and The Book of Mormon.

Why the head of Interpreter Peer Review, Alan Wyatt, didn't knock this back and get them to pare it back to the 4 steps I've outlined above is a complete mystery. He must have foreseen that the math was going to get slaughtered. It's like he wanted the Dales and/or Interpreter to look stupid, and was prepared to make his competence look questionable to do so. That or he was asleep at the wheel.

[_Analytics]

One question, Analytics: Shouldn't V be something like: Book of Mormon correctly places volcanoes in Mesoamerica?

The way I frame it, the numerator represents the evidence in its totality the way it actually is. So V is more like, "the Book of Mormon describes volcanos the way it describes it."

The point is that if they describe volcanoes in a way that is really like how a Nephite would have described it, that is worth a lot of credit. But if they describe it in a way that is anachronistic or otherwise problematic, that deserves a lot less credit.

[_DrW]

This should have been a very simple and straightforward hit-piece on Dr Coe:
1. Dr Coe said the Book of Mormon doesn't reflect Mayan culture.
2. The Dales want to show it does.
3. The Dales draw parallels between the contents of Coes book 'The Maya' and the 'Book of Mormon'.
4. Ergo Dr Coe is wrong and has in fact been hoist by his own petard, so to speak.

Job done.

The whole nonsense about using Bayes Theorem to demonstrate just how unlikely it was that one of the other many explanations for Mayan culture appearing in the Book of Mormon, that of Joseph "guessing" content, has completely destroyed what might otherwise have been an interesting anthropological paper and discussion about 131 parallels between The Maya and The Book of Mormon.

Why the head of Interpreter Peer Review, Alan Wyatt, didn't knock this back and get them to pare it back to the 4 steps I've outlined above is a complete mystery. He must have foreseen that the math was going to get slaughtered. It's like he wanted the Dales and/or Interpreter to look stupid, and was prepared to make his competence look questionable to do so. That or he was asleep at the wheel.

As has been stated upthread, the Dales apparently elected to go for a pseudo-Bayesian Gish Gallop in an attempt to mask the weakness of their argument. As a consequence, unfortunately, their argument went from weak to absurd, as has been duly noted in the Interpreter comments section.

As to Wyatt's role, it looks to me as though he is in way over his head. The Interpreter must be really desperate for content. And besides, who would have thought that the article would become of interest to non-LDS readers with sufficient expertise to call it what it is?

[_Gadianton]

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?

(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)

Res Ipsa, thank you so much, I owe you beer. This is exactly what I wrote down initially. I feel at least a little less alien now. But wow, what a balancing act you picked for them, eh? No, I don't think they did that calculation. I would put my bank account on it. Perhaps if they did the calculation, they can put their notes up for any one of the 150 or so data points to serve as an example? (with the reasoning of how they arrived at both the top and the bottom)

For this post, I'm just going to talk numbers, not concepts, even though the concepts are what matters and not the numbers. You picked the numbers you did for a reason, either consciously or subconsciously, because somehow, you and I came up with the very exact same thing as our first guess. But we both can do basic math, at least you can, sometimes I'm not sure about me. and I'm sorry, but but in what classroom will you get credit for a simple math problem if the answer is 50 and you put 49? How about this, do you think they could have picked something that actually came up to 50?

How about .5 / .01? Do you think the dales could have come up with that in their calculation?

I think that you picked .02 and .98 because they add up to 1, and dividing one into the other comes to 49, which is pretty close to what they got. I'm pretty sure that's why it was my first guess.

Now what does .02 mean? Well, whatever that .02 means, couldn't it be .03? If so and if that means we've still got to add to 1, then the top is .97. .97/.03 = 32, that's way off. or what about .01? that's 99, even worse. For any of us who guessed first by picking the two numbers that add up to 1 that can be divided to most closely approximate 50, we must have missed something important.

Now let's talk conceptually about what the top and bottom numbers could possibly mean in the Dale's interpretation in these scenarios:

.5/.01 . Since this is exactly 50, explain what the top and bottom could mean given what the Dales actually wrote in the paragraph? (or please pick any of their paragraphs with a 50) What would .99/.01 mean? and finally, what would .98/.02 mean?

I hate to pull a DCP here, but I will be leaving soon for a long trip, and I can't risk even looking at the board again until I've at least arrived at my destination.

[_I have a question]

From the comments:

Brandon Shumway
on May 6, 2019 at 11:01 pm said:
I am somewhat familiar with the statistical methods used here. I am a physician with a specialty of preventive medicine where we often deal with complex statistical models. While Bayesian statistics are quite useful when large amounts of data are available to give accurate assessments of probability, it is quite another thing to attempt to apply this to assumptions about the probability of a 19th century author describing a particular aspect of an ancient culture by chance. This is far outside the realm of engineering and it would be wise to acknowledge the differences between the nature of your work and the nature of what you are trying to do here.

You seem to assume that I did not carefully read appendix A. It is this appendix that is actually the source of my concerns about the lack of credibility in your conclusions. Since you asked for a specific example take any one of the correlations here:

“Active interchange of ideas and things among the elite.” You are assuming that this correlation alone would be very unlikely to guess about. You arbitrarily assign 0.02 based on your subjective assessment of the strength of that correlation. Now this might be true if you took 50 fictional books written about that time period and the Book of Mormon was the only one where 2 or more cultures exchanged ideas with each other but I find that strains credulity. Don’t you? Not just that, but that if each of those authors had to guess at whether civilizations exchanged ideas that all of them would say no except Joseph. I would argue that while this is certainly a positive correlation that it would be much more likely for an author of any time period to have some form of intercultural exchange as a part of a fictional narrative. This assessment would then lead to a value closer to 1 being assigned rather than the 0.02 which you assign. This fatally illogical reasoning is present throughout most of the points you discuss and again none of them have any credible data to support the quantification which you provide so it is a completely subjective assessment.

Even if all of the 131 correlations are very likely to be guessed by any author of the time period (they are not, but for sake of understanding the statistical flaws you are committing bear with me) and we give them a rating of 0.9. Stacking up that many chances that a person might guess something wrong even though it would be a perfectly logical thing to guess might lead you to believe that the Book of Mormon only had a chance of about 1 in a million of occurring (0.9^131 if you care to check). Do you see how this multiplicative reasoning will always lead you to faulty conclusions? This is exponentially true when you are dealing with 131 subjective guesses based on 0 data.

The problem with all of this is that people like me really want the Book of Mormon to be historically true. This would be very helpful in resolving some of the doubts which I am experiencing related to other issues. I want to believe that you are right but unfortunately my education allows me to see right through the statistical nightmare that this paper is. I have actually sat down with my own priors and understanding of various evidence for and against the Book of Mormon and attempted something not dissimilar from this paper. I quickly realized that when dealing with historical evidence which is inherently subjective, it is incredibly complex to do this type of calculation. When each answer holds uncertainty, that uncertainty is expanded in a multiplicative fashion and an honest assessment may always include 1 in the confidence interval. There are better tools for arriving at this type of truth.

The reason that I engage is to hopefully prevent poorly done apologetic messages from doing harm. If you feel I have misunderstood the statistical analysis that is your right to do so. If you truly believe that your assessment is so accurate then I encourage you to attempt submission to an actual statistics journal. In science, peer review is king. I seriously doubt that this would pass any sort of professional scrutiny if my amateurish eyes can see so many gaps in the methodology. If you were to retract the statistical portion of this paper and present just the 131 correlations which you found it might be better received.

It's a bloodbath for the Dales, for Alan Wyatt and for Interpreter.
If this paper has been peer reviewed by someone supposedly with expertise in the statistical side of thing (as Wyatt Twerp claims), I'd suggest they get Interpreter to sign a non disclosure agreement, because if their name comes out they'll be ruined.

[_Analytics]

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.

[_Lemmie]

How about .5 / .01? Do you think the dales could have come up with that in their calculation?

I think that you picked .02 and .98 because they add up to 1, and dividing one into the other comes to 49, which is pretty close to what they got. I'm pretty sure that's why it was my first guess.

Now what does .02 mean? Well, whatever that .02 means, couldn't it be .03? If so and if that means we've still got to add to 1, then the top is .97. .97/.03 = 32, that's way off. or what about .01? that's 99, even worse. For any of us who guessed first by picking the two numbers that add up to 1 that can be divided to most closely approximate 50, we must have missed something important.

I'm not sure you are asking this so I apologize if it's not what you meant, but picking the numbers does NOT mean they have to sum to 1, but it does mean the ratio has to equal one of the 6 ratios they allow:

2, 10, or 50 for the positive LRs.

and the reciprocals:

1/2, 1/10, or 1/50 for the negative LRs.

The .02 you are asking about is the ratio 1 over 50. If you note that the LR is the ratio of 2 probabilities, which can only go 0 to 1, inclusive, then .02 = 1/50 can be represented by probability ratios such as:

0.02 / 1, or 0.01/0.5, or 0.001/0.05 etc.

The 2 probabilities don't have to sum to one because they are not related that way, but they each have to be between 0 and 1.

for the LR = 50, the inverse ratios work,

1 / 0.02, or .5 / .01, or 0.05 / 0.001.

I'm pretty sure they did not calculate any of those, but are just picking easy levels of numbers that correspond to the medical literature, as they said this in a comment:

We weight the evidence for the Book of Mormon as 0.02, 0.1 and 0.5 if that evidence is Bayesian “supportive”, “positive” or “strong” as described in our paper. These numerical values are chosen from the technical literature.

and also:

At the bottom of page 85 is the reference from which we took the numerical values of the three relative strengths of evidence that we use to weight evidence both for and against the Book of Mormon. (Robert E. Kass and Adrian E. Raftery, “Bayes Factors,” Journal of the American Statistical Association 90, no. 430 (1995): 777, doi:10.2307/2291091.)

I have to look further, but I think they are just picking the numbers because they are the numbers that best match a loglinear approximation model that quickly estimates approximate changes in probability when results of a new medical test are being considered. For example, see this article:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1495095/

Here is an explanation from it, for the ratios 2, 5, and 10:

Table 1 is easy to recall at the bedside by simply remembering 3 specific LRs—2, 5, and 10—and the first 3 multiples of 15 (i.e., 15, 30, and 45). An LR of 2 increases probability 15%, one of 5 increases it 30%, and one of 10 increases it 45%. For those LRs between 0 and 1, the clinician simply inverts 2, 5, and 10 (i.e., 1/2 = 0.5, 1/5 = 0.2, 1/10 = 0.1). Just as the LR of 2.0 increases probability 15%, its inverse, 0.5, decreases probability 15%. Similarly, an LR of 0.2 (the inverse of 5) decreases probability 30%, and a LR of 0.1 (the inverse of 10) decreases it 45%. These benchmark LRs can be used to approximate the remainder of Table 1.

[Guest]

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?

(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.

[_Physics Guy]

Cheers for Brandon Shumway, who describes himself as an amateur but has a better grasp of the issues than the Dales. If he has doubts about Mormonism and was hoping for a solid argument for Book of Mormon historicity, seeing the Interpreter editors continue to uphold this paper is probably not helping his doubts.

For me it can't shake a faith in Mormonism but it is shaking a sort of second-order faith. There are some beliefs I don't share but that I think are defensible and legitimate, and I like it when defenders of those beliefs put up their best case, so that when people decide for themselves what to believe, they'll decide for the right reasons, having seen all sides presented fairly, instead of falling for some fallacy. I feel bad if someone defends a legitimate belief with a lousy argument, whether I actually share the belief or not. Somebody might either accept the bad argument, and that seems bad to me even if I agree with the belief itself, or reject the belief without having seen its better arguments, and that seems bad to me even if I also reject the belief.

But then there are some beliefs that I just think are bad or stupid, and I can't help but feel it's for the best if the defenders of those beliefs make as big fools of themselves as possible, so that nobody even wastes time on that awful stuff.

I'm kind of struggling at the moment to keep Mormonism in the first category instead of the second. Unlike an actual faith crisis, this second-order crisis is not stressful for me. It's just a little weird. Watching what's happening with this paper, I'm in this sort of superposition state of sympathy and Schadenfreude.