The Interpreter; Bayes Theorem; Nephites and Mayans

[_Lemmie]

This would be like the flesh eating virus example. Its pointless. the denominator shouldn't be 1, but what else could it be? If the denominator is say, .8, then that means there's a 20% chance that Coe is wrong about volcanoes, and dales assume hes right. I think this is the sort of point Lemmie was making. Lowering to .8 would also decrease our confidence in the Book of Mormon.

Yes, you have my point. the LR is a ratio of 2 probabilities, and probabilities can only be zero to one.

the denominator HAS to be less than 1, for a ratio to be 2, 10, or 50.

in your medical example, a denominator of less than 1 is normal, it's the probability you have the symptom, given you don't have the disease. A false positive.

But in the Dale's paper, the denominator is

P(B | ~A)

in my last post, i showed how, if B is true then P=1, and if B is false P = 0.

So, a true positive has probability = 1, and no chance for a false positive with a probability greater than 0, under assumptions of paper.

all positive LRs should be infinitely large, thus obviating the paper's conclusion.

(Without even addressing the independence issue, and multiplying LRs.)

[_Water Dog]

This would be like the flesh eating virus example. Its pointless. the denominator shouldn't be 1, but what else could it be? If the denominator is say, .8, then that means there's a 20% chance that Coe is wrong about volcanoes, and dales assume hes right. I think this is the sort of point Lemmie was making. Lowering to .8 would also decrease our confidence in the Book of Mormon.

Yes, you have my point. the LR is a ratio of 2 probabilities, and probabilities can only be zero to one.

the denominator HAS to be less than 1, for a ratio to be 2, 10, or 50.

in your medical example, a denominator of less than 1 is normal, it's the probability you have the symptom, given you don't have the disease. A false positive.

But in the Dale's paper, the denominator is

P(B | ~A)

in my last post, i showed how, if B is true then P=1, and if B is false P = 0.

So, a true positive has probability = 1, and no chance for a false positive with a probability greater than 0, under assumptions of paper.

all positive LRs should be infinitely large, thus obviating the paper's conclusion.

(Without even addressing the independence issue, and multiplying LRs.)

Exactly.

(A = patient)

prob A has symptom and disease true 1
prob A has symptom and disease false .02, then LR = 50

everyone in stage 5 lung cancer has coughed up blood. a few people cough up blood but don't have cancer.

Here's a classic example problem taught to students in introductory classes, if helpful to the discussion.

Let's say, statistically, 0.5% of a population has cancer. Easy peasy. You count the number of people who have cancer, you divide by the total population. A medical test to detect cancer is 90% accurate. If someone goes to the doctor and tests positive for cancer, what is the likelihood that they actually have cancer? A classic problem, and often used to help students understand concepts that maybe aren't intuitive at face value.

==>

P(cancer|population) = 0.005

P(positive|cancer) = 0.9

P(~cancer|population) = 1- P(cancer|population) = 0.995

P(positive|~cancer) = 1- P(positive|cancer) = 0.1

==> P(cancer|positive) = [P(positive|cancer)*P(cancer)]/[(P(positive|cancer)*P(cancer)) + (P(positive|~cancer)*P(~cancer))]

==> P(cancer|positive) = [0.9*0.005]/[(0.9*0.005) + (0.1*0.995)] ~= 0.04

So, you get a positive cancer test result, you only have a 4% chance of actually having cancer. And this is not a staged example to skew the results. 90% accuracy in a single test is pretty good. I'm not in the medical field, but in plenty of other fields people wish they had that kind of accuracy.

Dean Robbers,

I think there are several fundamental errors that combine to be fatal. The one Lemmie showed the math on is one of them. It is critical because the effects of hits and misses are not symmetrical. One piece of negative evidence can be fatal to a hypothesis, even in the face of many pieces of evidence that appear to confirm it. The Dales prevent that from happening by artificially constraining the lower bound of the likelihood ratios.

While I do see where you are coming from, I have to say, if they can't show the math behind how they constructed a single one of their LRs, which is very easy math, then I think this is bigger than all of the other problems.

I know, it's a bit like saying, suppose you're shot with a shotgun but at the same time a piano falls on your head and you're hit by a freight train, it's tough to call cause of death.

One could still be coherent and make the mistake Carrier proposes, but failing to rise to the level of coherency will always win.

I agree and this is precisely the point I was making several pages back. It's garbage in, garbage out. They haven't done the work necessary to determine their inputs. They haven't done the work to even determine the relevance of their inputs and whether they ought to be included as inputs in the first place. It's literally made up garbage. Multiplied together, or put into Baysean drag as Simon hilariously described it, and the magical result is Book of Mormon is true.

[_Water Dog]

I just realized I'm getting copied on the MI comments. Is Mr. Blanco the guy from reddit? Chino Blanco?

[_Water Dog]

I just realized I'm getting copied on the MI comments. Is Mr. Blanco the guy from reddit? Chino Blanco?

I think so.

https://www.reddit.com/r/Mormon/comment ... _bayesian/

[_Res Ipsa]

So, I want to make sure I understand this. So please, correct me where I will inevitably get something wrong.

We have some data in the form of sentences from Coe's book and sentences from the Book of Mormon. We are going to test different hypotheses for how we can explain the data, so use of likelihood ratios is appropriate. What we should do is list out the various hypothesis and a likelihood value between 0 and 1. And because we are talking about likelihood ratios, the likelihood value for the hypotheses don't have to total to one.

So, we have to generate hypotheses and assign likelihood values.

Smith accurately translated from a bona fide ancient mesoamerica record.
Smith extrapolated from knowledge of history and culture
Smith guessed and got lucky
The Book of Mormon is not a bona fide ancient record

Maybe this could be collapsed into my first and last hypotheses.

Then through what is to me statistical magic (unless we only use two hypotheses -- I can follow that much), we end up with, not the probability of the Book of Mormon being true, but which of our hypotheses is most likely compared to the others.

Is that, roughly, what the Dales purport to be doing should look like?

[_Physics Guy]

Regarding Lemmie's last point: I've been assuming that the Dales are effectively invoking an error model, such that for them the Book of Mormon could count as authentic Mayan history without necessarily agreeing completely with Coe's book. I assumed that this was because they allowed a chance (of at least 2%) that Coe's book was wrong. According to the surprising statement by them that Lemmie quoted, however, they have disavowed this. They say instead that they set the chance of Coe being wrong at flat zero.

Could they perhaps still be allowing an authentic Book of Mormon to disagree with Coe, by supposing that an authentic Book of Mormon might not necessarily be perfectly accurate? Real ancient records aren't necessarily perfect, after all. So the Dales might be allowing a minimum 2% chance that a real Nephi or Moroni or whoever might have messed up any single given feature of Mayan society.

As I've said, I find it absurd to set a floor for this chance at 2%. I think there must be some features of a society which far fewer than 2% of genuine chroniclers could ever get wrong. Moreover it would be bizarre to allow at least a 2% chance that contemporary historians (i.e. Moroni et al.) could have gotten things wrong about their own ancient society, while giving Coe no chance of error at all in looking back from 1965.

Nevertheless there might be at least a bit of wiggle room for the Dales to justify non-zero denominators. Just not denominators that are never smaller than 0.02.

[_Res Ipsa]

Regarding Lemmie's last point: I've been assuming that the Dales are effectively invoking an error model, such that for them the Book of Mormon could count as authentic Mayan history without necessarily agreeing completely with Coe's book. I assumed that this was because they allowed a chance (of at least 2%) that Coe's book was wrong. According to the surprising statement by them that Lemmie quoted, however, they have disavowed this. They say instead that they set the chance of Coe being wrong at flat zero.

Could they perhaps still be allowing an authentic Book of Mormon to disagree with Coe, by supposing that an authentic Book of Mormon might not necessarily be perfectly accurate? Real ancient records aren't necessarily perfect, after all. So the Dales might be allowing a minimum 2% chance that a real Nephi or Moroni or whoever might have messed up any single given feature of Mayan society.

As I've said, I find it absurd to set a floor for this chance at 2%. I think there must be some features of a society which far fewer than 2% of genuine chroniclers could ever get wrong. Moreover it would be bizarre to allow at least a 2% chance that contemporary historians (i.e. Moroni et al.) could have gotten things wrong about their own ancient society, while giving Coe no chance of error at all in looking back from 1965.

Nevertheless there might be at least a bit of wiggle room for the Dales to justify non-zero denominators. Just not denominators that are never smaller than 0.02.

I don't see anywhere in the analysis a value for a false negative (Book of Mormon true but states incorrect fact). I think they are using Coe's book as the measure of the true facts about the Maya -- a proxy for what we know about the Maya.

ETA: I guess one could say that the wiggle room is in the limits on the likelihood factors themselves.

[Guest]

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.

[_Analytics]

So, I want to make sure I understand this. So please, correct me where I will inevitably get something wrong.

We have some data in the form of sentences from Coe's book and sentences from the Book of Mormon. We are going to test different hypotheses for how we can explain the data, so use of likelihood ratios is appropriate. What we should do is list out the various hypothesis and a likelihood value between 0 and 1....

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.

[_Res Ipsa]

(A = patient)

prob A has symptom and disease true 1
prob A has symptom and disease false .02, then LR = 50

everyone in stage 5 lung cancer has coughed up blood. a few people cough up blood but don't have cancer.

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

prob horses guessed in mesoamerica and Book of Mormon is false 1
prob horses guessed in mesoamerica and Book of Mormon is true .02 LR = 50

don't agree? then how do YOU suggest they got 50? This appears to be an outright contradiction. To get a 50 LR, you have to make contradictory assumptions about the possibility Coe is wrong.

H: Joseph Smith incorrectly said there were horses in Mesoamerica America
W: Book of Mormon is fiction.

Given H, the probability of W is 1
Given W, the likelihood of H is .02

I don't see a problem, as the competing hypotheses don't say anything about the accuracy of Coe's book.