The Interpreter; Bayes Theorem; Nephites and Mayans

[_Res Ipsa]

Dr. W,

Do we know whether CB has the chops to address any responses on technical issues? I don’t know the guy.

Also, lots of significant points have been made in this thread, but they aren’t organized. What would you think of starting a new thread in Celestial intended to organize and present these issues? The OP in the thread would end up being an organized rebuttal to the paper. It could start as a simple outline and then be fleshed out based on posts as they are made.

Res Ipsa,

So far, Mr. Blanco has done largely cut and paste. He has not clearly demonstrated that he personally has much more to contribute in this area than a desire to point out the absurdity of the entire enterprise.

Your idea of generating a condensed (perhaps nearly bullet point) version of the main take-home lessons from this thread in the Celestial forum sounds great. The issue for me, as it is for all of us, is time - especially during the work week.

Perhaps you could carve out a few general areas and seek volunteers. It seems to me that there are three main areas of comment/expertise needed.

First, of course, is Bayesian inference methodology and math. The natural pick for this would be Lemmie. She has already provided several excellent tutorials. It should not be too difficult to pull these together into a consolidated post, and use the information she has already provided to respond to some of the exchanges over in the Interpreter comments section on methodology. Analytics has also made some good comments here. Honorehtheos had already joined the fray over at the Interpreter.

Secondly would be a discussion of the inappropriateness (silliness) of the conclusions and claimed outcomes from the perspective of one who backs up and looks at a data space larger than the Book of Mormon, Coe, and (I believe, two other books). Several folks here have made great comments in this area, including Dr. Southerton, Dr. PG, Analytics, Water Dog, Exiled, etc. There are several P=0 aspects of the Book of Mormon outside the scope of the study that simply and clearly nullify the overarching conclusion of the authors. To ignore them and claim that the Book of Mormon is indeed historical, is the height of intellectual (and in this case academic) dishonesty.

Third might be someone who is, or had been, a Book of Mormon scholar of sorts, who has read Coe, and can reasonably criticize the Dale & Dale set-up and their choice and relative strength of positive and negative factors for the analysis. Pulling examples from some of the comments already in the Interpreter comment section, and giving attribution, might be especially effective. This one is more subjective, but Dale & Dale have done a terrible job and there are a few folks over on the Interpreter comment section who are taking them to task now. Grindael comes to mind.

Again, this is just a view from my foxhole. Don't see much of a chance for an highly ordered and organized approach and effort. The Dale & Dale nonsense is just not that important.

However, you are absolutely correct that buried in this thread is the, knowledge, information and insight sufficient to make a strong, rigorous, and authoritative rebuttal.

If you are anything like our attorneys, you have a knack for the organization and presentation of facts and evidence from disparate sources in a clear and coherent manner. Lemmie is a professional instructor at the university level.

If you want to do this, I can pitch in some over the weekend. I suggest that you start the thread, mainly because you are seen as (and clearly are) more reasoned and ecuimenical than a lot of us (especially me).

Anyway, I say you should just start, indicate where help is needed, and let folks pitch in. If no single person is overly burdened, and enough folks participate, it could become a classic thread and be something the board can be proud of. All that is needed are a few seed particles onto which information can collect and condense.

Thanks! That was very helpful. I've stuck a very rudimentary outline up in Celestial and will fill it in with details as I can. Anyone who wants to can chime in or correct my mistakes.

[_Res Ipsa]

Let me explain it with an example that shows what is going on, logically, behind the scenes (I don't know if the Dales understand the logic, but this is what they ought to be thinking if they understand anything more than the mechanics):

Notation:

H: the theory that the book is historical
F: the theory that the book is fictional
V: volcanoes being mentioned in the Book of Mormon
L(V|H): the likelihood of volcanos being mentioned in the book, presuming the book is historical
L(V|F): the likelihood of volcanos being mentioned in the book, presuming the book is fictional

Step 1: Assuming the Book of Mormon were fictional, what is the likelihood "Volcanoes" ended up in the book as it is?

L(V|F) = 0.00001

Step 2: Assuming the Book were historical, what is the likelihood "volcanoes" ended up in the book as it is?

L(V|H) = 0.0005

Likelihood = L(V|F) / L(V|H) = 0.02

In words, it is 50-times more likely (1/0.02 = 50) that a true book would get a "hit" on volcanoes than a false book would.
__________________________

Note that the underlying likelihood functions are actually quite small. Lots of true books don't mention volcanos. Likewise, lots of false books don't mention volcanos. But after you divide one likelihood by another, you get a likelihood ratio that might be of a more manageable magnitude.

In practice, coming up with the probability that a true book happens to mention volcanos is very difficult, just as coming up with the probability that a false book happens to mention volcanos. As a simplifying heuristic, they skipped straight to the ratio and decided that if something is mentioned in both the Book of Mormon and in The Maya, then the likelihood ratio must be between .02 and .5, depending upon how unlikely they subjectively think it would be for a guesser to guess the hit.

That is what they are attempting to do. Beyond the fact that they are treating correlated details as independent and assigning wildly biased ratios to various details, they are skipping a ton of information. For example, they should also include in their calculations something like this:

~J: Jade not being mentioned in the Book of Mormon, but being a big part of Mayan culture per The Maya.

L(~J|H) = 0.90
L(~J|F) = 0.99

Likelihood ratio: 1.1

In words, the Book of Mormon doesn't mention Jade, yet Jade was there. Using the numbers I made up, it 1.1 times as likely that a false book wouldn't mention jade as a true book. Thus, the Book of Mormon failing to mention Jade is a nudge towards the book not fitting.

Several details like this missing from a true book is to be expected. But if hundreds and thousands are missing (as is the case), they add up and paint a picture that the Book of Mormon doesn't fit into the historical context. All of the misses that are captured this way cancel out the few hits that are arrived at by luck.

Thanks, Analytics. That is just what I was looking for.

Your last point is what I would put under my outline as a bias against "misses" resulting from the requirement that any comparison must be made of something that is mentioned in both books. That requirement does not affect "hits", as by definition a hit is mention in both books. But it eliminates many significant "misses" in which only one source mentions the subject. Jade is a perfect example.

[_Res Ipsa]

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

[Guest]

Maybe it is just wording, but this doesn't sound right to me. I'll reword and please tell me if it is what you intended.

S=Person has symptom
D=Person has disease

Given D, the probability of S is 1.
Given S, the likelihood that the person has the disease is .02

No, that's incorrect, this is about whether the symptom, or test, accurately predict the disease. so this:
"Given D, the probability of S is 1."

does not capture that the symptom or test could be a false positive (which is similar to the same mistake the authors are making).

So if the test is positive, you can determine:

P(test is positive, given disease), [true positive]
P(test is positive, given no disease), [false positive]

If the test is negative, you can determine:

P(test is negative, given disease), [false negative]
P(test is negative , given no disease), [true negative]

[_Analytics]

Thanks, Analytics. That is just what I was looking for.

Your last point is what I would put under my outline as a bias against "misses" resulting from the requirement that any comparison must be made of something that is mentioned in both books. That requirement does not affect "hits", as by definition a hit is mention in both books. But it eliminates many significant "misses" in which only one source mentions the subject. Jade is a perfect example.

You are welcome!

The other piece of "misses" of course is a lot less subtle. If the Book of Mormon mentions something that is missing from The Maya and is in fact implausible, then it is a catastrophic miss.

As a mathematical example:

C: 19th Century Protestant Christianity permeating Book of Mormon culture for 1,000 years

L(C|H) = 0.000000001
L(C|F) = 0.001

Likelihood ratio: 1,000,000

Not only is 19th Century Protestant Christianity existing in ancient America and not leaving even a hit of a trace extraordinarily anachronistic, the proposition that any religion could persist without evolving for 1,000 years is completely unrealistic. Mormonism has evolved dramatically even over the last 50 years. But the religion of the Book of Mormon didn't change for 1,000 years? No way.

Of course if we were doing this fairly, we would realize that this likelihood ratio is very highly correlated with other such things (e.g. the very high likelihood ratio of Joseph Smith in Isaiah), so it would be improper to multiply them together as if they were independent.

[_Res Ipsa]

Again, thanks. Is the lack of independence fatal, or is there a proper way to analyze the probability of non-independent events?

[_Philo Sofee]

Analytics
Not only is 19th Century Protestant Christianity existing in ancient America and not leaving even a hit of a trace extraordinarily anachronistic, the proposition that any religion could persist without evolving for 1,000 years is completely unrealistic. Mormonism has evolved dramatically even over the last 50 years. But the religion of the Book of Mormon didn't change for 1,000 years? No way.

A very profound point. I had not thought of this in this manner, and its significance is magnitudinally significant.

[_Water Dog]

Again, thanks. Is the lack of independence fatal, or is there a proper way to analyze the probability of non-independent events?

Yes, this is achieved through conditional probabilities, P(B|A). Like, what is the probability of going to jail if you robbed a bank. Determining dependency is actually one of he purposes of Bayes, and is one of the first things that needs to be done before trying to setup an inference problem because the problem cannot be setup properly without first determining interdependence between the inputs.

https://en.wikipedia.org/wiki/Bayesian_network

[_Res Ipsa]

Again, thanks. Is the lack of independence fatal, or is there a proper way to analyze the probability of non-independent events?

Yes, this is achieved through conditional probabilities, P(B|A). Like, what is the probability of going to jail if you robbed a bank. Determining dependency is actually one of he purposes of Bayes, and is one of the first things that needs to be done before trying to setup an inference problem because the problem cannot be setup properly without first determining interdependence between the inputs.

https://en.wikipedia.org/wiki/Bayesian_network

Thanks, WD.

[_Res Ipsa]

Again, thanks. Is the lack of independence fatal, or is there a proper way to analyze the probability of non-independent events?

Yes, this is achieved through conditional probabilities, P(B|A). Like, what is the probability of going to jail if you robbed a bank. Determining dependency is actually one of he purposes of Bayes, and is one of the first things that needs to be done before trying to setup an inference problem because the problem cannot be setup properly without first determining interdependence between the inputs.

https://en.wikipedia.org/wiki/Bayesian_network

Thanks, WD.