The Interpreter; Bayes Theorem; Nephites and Mayans

[_Analytics]

Analytics, I was just about to post this howler when I saw your entry:

We believe that facts with a 2% likelihood (one in 50 chance) are essentially impossible to guess correctly, given any amount of knowledge or study reasonably available to the writer of the Book of Mormon.

How can anyone with even a rudimentary knowledge of probability make this kind of statement? Pop quiz: If I start making guesses, each of which have a 2% chance of being correct, how many guesses must I make before there is a 50% chance that I've guessed one correctly? And the Dales characterize this as impossible? And this got past a statistician who peer reviewed the work?

That is hilarious!

I keep coming back to how Dr. Coe has said believing the Book of Mormon is Mayan is wishful thinking. The real value of this article is a case study in wishful thinking, confirmation bias, and other cognitive biases that caused an otherwise intelligent group of authors and peer reviewers to think this paper merited publication in a journal.

[_Lemmie]

Speaking of the likelihood ratios and calculations, keep in mind that the authors just took an ordinal ranking (like "good, better, best," or "3rd place, second place, first place," or, in the Dale's case, "positive," "supportive," and "strong,") and simply assigned cardinal values for the likelihood ratios of 2, 10, 50 (and the inverse, 1/2, 1/10, 1/50.) ("cardinal" meaning 2 is twice as big as 1, etc. Not just in some order, like "ordinal.")

(Not to mention that they also co-opted a scale where they changed "hardly worth mentioning" into "positive.")

The problem is exacerbated when they then accept these numbers AS those cardinal values for purposes of their conclusion about the likelihood of a historical Book of Mormon.

The result is that mathematically a 1/50 LR carries TWENTY-FIVE times as much weight as the LR of 1/2. In other words, they defined a "strong" correspondence as being 25 times the value of a "positive" correspondence. It is a completely arbitrary assessment. The Dales claim they are using the Kass paper's results to justify these LR values. No, they are not:

...and so these categories are not a calibration of the Bayes factor, but rather a rough descriptive statement about standards of evidence in scientific investigation.

in my opinion, the Dales did no calculations, but rather simply assigned values to various conclusions to manipulate the result.

[_Lemmie]

How can anyone with even a rudimentary knowledge of probability make this kind of statement? Pop quiz: If I start making guesses, each of which have a 2% chance of being correct, how many guesses must I make before there is a 50% chance that I've guessed correctly? And the Dales characterize this as impossible? And this got past a statistician who peer reviewed the work?

Someone should create a GoFundMe to send them a copy of Freakonomics.

At least.

[_Res Ipsa]

How can anyone with even a rudimentary knowledge of probability make this kind of statement? Pop quiz: If I start making guesses, each of which have a 2% chance of being correct, how many guesses must I make before there is a 50% chance that I've guessed correctly? And the Dales characterize this as impossible? And this got past a statistician who peer reviewed the work?

Someone should create a GoFundMe to send them a copy of Freakonomics.

No kidding!

[_Lemmie]

It's been difficult to decipher the authors' intent as their comments and even various parts of the paper don't seem to agree.

To illustrate, I've pulled out a few parts. Every single comment below is either from the paper or from their comments. Really.

>>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.

>>although there are more than 149 statements of fact in the Book of Mormon, we could only test these 149 statements because the remaining statements were not addressed by The Maya.

>>But we did compare all of the relevant claims from both books.

>> we not only included the facts summarized in Coe’s scholarly work The Maya but we also included fact claims from his non-scholarly pronouncements... and in his 1973 Dialogue article.

>>Again, it is only rational and honest to compare statements of fact which are dealt with by [the Book of Mormon and The Maya].

>>We did not limit ourselves to 131 pieces of evidence, nor did we define them as true.

>>On the contrary, the [131] statements in The Maya are the ones assumed to be true.

>>at no point was any B assumed or defined as true.

>>To repeat, for purposes of our Bayesian statistical analysis, we accept the universe of facts summarized by Dr. Coe in The Maya as essentially true.

>>[in Kass] the Bayes factor ...that is judged “not worth more than a bare mention”... [in our] paper, we call [it]…. “supportive” …

I separated out these three, two by the author, the last by Wyatt:

>>We prefer a more rational, more intellectually honest conclusion: The Book of Mormon is a real historical record. It is authentic.

>>Thus the Book of Mormon is not fiction–it is authentic, factual and set in ancient Mesoamerica to a very high degree of probability.

>>Those who try to assert that this paper is some sort of “apologetic work” that seeks to scientifically prove the historicity of the Book of Mormon or to somehow prove the truth of the Book of Mormon are missing the mark—this article attempts no such thing.

And finally, from the authors:

>>Did you actually read our article? It appears from your response that you did not.

[_Res Ipsa]

Lemmie, the authors keep referring to supportive, positive and strong as Bayesian terms. That seems misleading to me. Doing the Bayesian analysis requires no such descriptive terms, right?

[_Dr Exiled]

Hat's off to everyone here who helped in finding how the Dales went astray, the source of their bias and wishful thinking. It was a great takedown to witness.

DCP, do you still believe that this paper could be revolutionary as you claimed on Sic et Non when it first came out? What do you think the likelihood is now given the thrashing upthread? Each entry by our learned colleagues moved that probability ever closer to zero and now it is zero.

[_Lemmie]

Lemmie, the authors keep referring to supportive, positive and strong as Bayesian terms. That seems misleading to me. Doing the Bayesian analysis requires no such descriptive terms, right?

See my post on page 14, I discuss that:

viewtopic.php?p=1180601#p1180601

Main point:

So the categories describe the data; this does NOT justify the Dales' paper arbitrarily assigning their particular data a value equal to their approximate midpoints of the categories. The dales did no calculations, but rather simply assigned values to questions to manipulate the result

and from the Kass paper:

these categories are not a calibration of the Bayes factor, but rather a rough descriptive statement about standards of evidence in scientific investigation.

[_Everybody Wang Chung]

Thanks to everyone for making this understandable to math challenged people like me.

I just read the comments over at the Interpreter and I'm amazed at how the Dales feel everyone else is wrong and that the critics just don't understand their methodology.

Incredible. Folks, you just can't make this stuff up.

[_Gadianton]

Res, your 1/50 insight was hilarious, I had read that but it didn't connect...nice

--

other random thoughts. Lemmie quoted dales:

Note: only statements of fact which are dealt with by both books can be rationally admitted to the analysis; on statements of fact where one or the other book is silent, we cannot factually assume either agreement or disagreement. There is no rational scientific basis for doing so.

Presumably the Maya, for whatever reason, named several kinds of animals that weren't in mesoamerica. I imagine the reasons why are varied, including merely to communicate with a north american audience. But in describing the plants and animals of a region, there's no reason to talk about all the plants and animals that don't live in the regions, and so it's kind of unfortunate that the Book of Mormon took so many unnecessary hits.

it's also possible the Maya is silent on some of these animals, and they broke scientific rationality by taking statements from the Coe Dialogue article L mentioned.

the idea that it's scientifically irrational to take hits when one has no reason to expect the comparison text would reflect misses is totally irrational.

--

also note that while Wyatt and dales tried, at least in one spot, to make the comparisons really about the book to deflect from their stupendous odds conclusion. The project seemed to be: okay, Coe has these anti-writings, these are the misses; but lets go to Coe's ordinary work and find the hits he won't talk about. The problem is, they clearly don't disagree with any of Coe's statements they read as hits, and so they are fully supporting their original 10 ^ 152 number as valid, if not underestimated. Also, they dispute nearly all the misses, and merely give Coe the benefit of the doubt. So in actuality, if a better book of Mesoamerica had been written, say by John Sorenson, then that 10 ^ 152 number really becomes a lower bound for odds that may require insights from number theory to even communicate.