The Interpreter; Bayes Theorem; Nephites and Mayans

[Guest]

(Sorry for the brevity, it's a busy week, so I will expand on why I think the authors made this error in anoer post, plus additional math errors, but here is the bare bones analysis, which in my opinion renders their analysis completely meaningless. -L)

The biggest problem I see with the math regards the author's use of a likelihood ratio, which they define and calculate as follows:

This likelihood ratio is the strength of each individual statement of fact as a piece of evidence. It is calculated as the probability that the statement is true if whoever wrote the Book of Mormon was guessing divided by the probability that the statement is true if instead the Book of Mormon is fact-based and essentially historical.

Therefore the ratio can be written as:

P(B|A) / P(B|~A),

Where A is defined in the paper as the hypothesis that the Book of Mormon is fictional; ~A is the hypothesis that the Book of Mormon is not fictional.

First, the Bayes factor specifically accounts for the possibility that the evidence may have occurred under the other hypotheses. This is accomplished in the denominator of the Bayes factor.

No, it doesn't. Note that B is defined as the pieces of evidence, or, as the authors put it,

each individual statement of fact.

Note that the authors are asking if, under certain circumstances, about

...the probability that the statement is true...

But B is defined as a statement of fact, therefore

P(B) = 1,

by their own definition.

Therefore P(B|A) is also = 1, as is P(B|~A). This is because if B is true with a probability of 1, then it is true under all conditions, including whatever hypothesis under which it is being considered.

Therefore any likelihood ratio is 1/1, regardless of which piece of evidence is considered. Results of 2, 10, 50, .5, .1, and .02 are simply not possible.

1 to the power of 131 is still 1 (using their incorrectly applied definition of independent events), and thus the posterior odds, calculated as the likelihood ratio times the a priori odds, DO NOT CHANGE.

By their own calculations, the authors should therefore conclude that the incredibly overwhelming odds are still in favor of the Book of Mormon being fictional.

In the end, meaningless coincidences and parallels are not evidence that should change posterior odds. (This error seems to come from the authors seeing that likelihood ratios are used in medical testing, where there can be both false positives and false negatives, thus allowing the evidence to be "false," or untrue. The error was to translate that to a definition of evidence that they define as true, a priori.)

[_DrW]

Lemmie,

Thanks. So many problems, so little time.

Your comment and explanation of the author's really fundamental misunderstanding of Bayes Theorem should also go to the Interpreter comments section, along with some indication of your background, expertise, and credentials.

Everyone here knew there was trouble coming when the authors cited Wikipedia as a source for Bayes Theorem.

Again, if they had just stopped and thought about what they had done, and perhaps asked themselves if this were such a sure thing, why no one else had come up with this kind of (apparently) ironclad demonstration before. A little critical thinking goes a long way in a faith-based environment.

In any case, well done, Lemmie, Physics Guy and Symmachus.

[_MrStakhanovite]

But B is defined as a statement of fact, therefore

P(B) = 1,

by their own definition.

All this amounts to is taking issue with the semantic content of the English word "fact" and insisting that it maps onto a value of 1.

That isn't an error in operation and would be a trivial fix.

[_DrW]

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.

A very well done NOVA documentary from 2016 entitled, "Great Human Odyssey:
How early humans migrated out of Africa and populated the world" (including insights from historians, anthropologists, archaeologists and geneticists) is a science based narrative of human expansion out of Africa. It is well worth watching - especially because it rules out the possibility of blue water transoceanic crossings as a contributor of human genetic material in the New World.

It spends plenty of time on the genetic and archeological evidence regarding the first migration of homo sapiens into the Americas via Beringia. The acquisition of genetic markers absolutely unique to Amerindians gained on this particular odyssey, during the hold-up period, are explained.

If interested, you should be able to enter the title with the word NOVA into your local PBS TV station website and some kind of link for streaming.

[_Lemmie]

But B is defined as a statement of fact, therefore

P(B) = 1,

by their own definition.

All this amounts to is taking issue with the semantic content of the English word "fact" and insisting that it maps onto a value of 1.

That isn't an error in operation and would be a trivial fix.

One would think so, right?!! But the authors are very clear, the only things they are willing to admit into evidence and consider are the "facts" actually in the book, The Maya, that they can compare to items in the Book of Mormon:

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.

Even though elsewhere they deplore others who limit evidence like this:

It is a common error (deliberate or otherwise) to consider only a few pieces of evidence when examining the truth or falsity of a given hypothesis. In the extreme, this practice is called cherry-picking. In cherry-picking, evidence against one’s existing hypothesis is deliberately excluded from consideration. This practice is, of course, dishonest....

These practices of cherry-picking... cannot be allowed in scientific enquiry. They are neither rational nor honest. We must consider all relevant evidence if we hope to make honest, rational decisions.

[_Lemmie]

Regarding Mr Stak's point about re-stating how to map the information without limiting it to being a fact; even with that fix, another large problem arises.

Suppose B is now just a statement, possible factual, but not required to be. In that case, the probability of the evidence being factual and matching a fact in The Maya given the Book of Mormon is NOT fiction but is factual, is, defined as:

P(B|~A)

Note that the probability that an element B from the Book of Mormon, assuming that the Book of Mormon is not fiction, that matches a fact in The Mayan, is 1 Meaning yes, if the Book of Mormon is true, then statements from it that match facts from the Mayan are, with certainty, facts.

This means that the denominator of the likelihood ratio is 1.

The authors allow for ratios of 2, 10, and 50, to show support for the hypothesis that the Book of Mormon is fictional. However, with a denominator of 1, the numerator would have to be greater than 1, which is not possible, since the numerator is also a probability, ranging from 0 to 1, inclusive.

This means that there is no way that this model, even with the correction in terminology that B may or may not be a fact, can give any weight greater than one to a guess in the Book of Mormon that matches a fact in the other book, meaning it is not possible for the model to produce any likelihood ratios that support the hypothesis that the Book of Mormon is fiction.

If the element B is not a fact, then the following probability is meaningless:

P(B|~A)

At best it is equal to zero, meaning likelihood ratios cannot be calculated because the ratio is undefined (due to being divided by zero). If the probability is anything greater than zero, not only would it require finding a non-fact in the Maya book (which the authors ruled out), but it also implies that the Book of Mormon introduced a non-fact, in other words, fiction, which collapses the hypothesis back to A, the Book of Mormon is fictional.

[_Res Ipsa]

Ok, I’ve now read the whole paper, and I have a very basic question: does it actually use Bayesian analysis at all? I don’t see the authors ever use Bayes’ theorem in examining any of their pieces of data. When they describe the use of BayesIan analysis in medicine, they fail to even mention the most significant aspect of it’s use: taking account of the fake positives and negatives of the test. That indicates to me that the author’s don’t even understand how to properly use Bayes’ Theorem to evaluate evidence. They act as if all there is to Bayes is the use of prior probability. They don’t do the heavy lifting of working through the equation to rigorously determine the actual strength of each piece of evidence.

[_Lemmie]

Ok, I’ve now read the whole paper, and I have a very basic question: does it actually use Bayesian analysis at all? I don’t see the authors ever use Bayes’ theorem in examining any of their pieces of data. When they describe the use of BayesIan analysis in medicine, they fail to even mention the most significant aspect of it’s use: taking account of the fake positives and negatives of the test. That indicates to me that the author’s don’t even understand how to properly use Bayes’ Theorem to evaluate evidence. They act as if all there is to Bayes is the use of prior probability. They don’t do the heavy lifting of working through the equation to rigorously determine the actual strength of each piece of evidence.

They are taking a shortcut and using the idea of a Bayesian factor called a likelihood ratio, such that posterior odds = likeliehood ratio x prior odds.

It's a technique that doesn't fit their model at all, and they don't seem to understand its mathematical limitations. Not to mention their very, very wrong use of the concept of independent events.

[_Lemmie]

A comment from SeN:

Oh, and speaking of the peer-reviewed pages of Interpreter, I find it incredibly convenient that Lemmie (in that same thread) can dismiss, out of hand, my assurance that the pages are, indeed, peer-reviewed.

I know they are because as editor of the journal I personally look at each and every review and monitor the entire process. Critics are quick to disparage our peer review simply because they don't believe that anything we publish could reasonably pass peer review.

Therefore, there must not be meaningful peer review. (Seems like a variant of the ergo propter hoc fallacy.)

http://disq.us/p/21mkbt0

Actually, I have been very specific about why I don't think the Interpreter articles are peer-reviewed. (Assuming a standard definition of peer-review.)

Every paper I have read from the Interpreter that uses math or statistics has had extreme errors in use of techniques, testing methods, interpretation, etc. Not that peer-review would fix everything, but the errors I've observed would not get beyond an ordinary, typical, statistically-oriented peer review in an academic journal.

Allen Wyatt is very quick to make assumptions about my reasoning that are not true and that show he has not actually read my objections, but rather assumes all critics think the same way. There must be a name for that....

[_Analytics]

(Sorry for the brevity, it's a busy week, so I will expand on why I think the authors made this error in anoer post, plus additional math errors, but here is the bare bones analysis, which in my opinion renders their analysis completely meaningless. -L)

The biggest problem I see with the math regards the author's use of a likelihood ratio, which they define and calculate as follows:

This likelihood ratio is the strength of each individual statement of fact as a piece of evidence. It is calculated as the probability that the statement is true if whoever wrote the Book of Mormon was guessing divided by the probability that the statement is true if instead the Book of Mormon is fact-based and essentially historical.

Therefore the ratio can be written as:

P(B|A) / P(B|~A),

Where A is defined in the paper as the hypothesis that the Book of Mormon is fictional; ~A is the hypothesis that the Book of Mormon is not fictional.

First, the Bayes factor specifically accounts for the possibility that the evidence may have occurred under the other hypotheses. This is accomplished in the denominator of the Bayes factor.

No, it doesn't. Note that B is defined as the pieces of evidence, or, as the authors put it,

each individual statement of fact.

Note that the authors are asking if, under certain circumstances, about

...the probability that the statement is true...

But B is defined as a statement of fact, therefore

P(B) = 1,

by their own definition.

Therefore P(B|A) is also = 1, as is P(B|~A). This is because if B is true with a probability of 1, then it is true under all conditions, including whatever hypothesis under which it is being considered....

I'm not following you here at all.

If we give these authors the benefit of the doubt that they understand the basic math, "B" means the basket of evidence that we actually have. Thus, P(B|A) means, "What is the probability we'd see this basket of evidence if the book is historical?" Likewise, P(B|~A) means, "What is the probability we'd see this basket of evidence if the book isn't historical?"

What the authors are trying to do is look at each piece of evidence and compare the likelihood that a true book would happen to mention something in the book versus the likelihood that a false book would happen to mention something in the book. Picking up their points at random, point of evidence 1.9 is "some rulers live in luxury." The Book of Mormon mentions this. A hit! Their analysis is that a true book is twice as likely as a false book to mention that some of the rulers live in luxury. Therefore, the likelihood ratio is 0.5. Then, they go on to point of evidence 1.10, "elaborate thrones." The Book of Mormon mentions this. Another hit! They conclude that a true book is 10 times more likely than a false book to mention elaborate thrones. Therefore, the likelihood ratio is 0.1. Skipping down to point 2.19, "Cities and lands named after founder." The Book of Mormon does this. Another hit! A true book is twice as likely as a false book to name cities after a founder, so the likelihood is 0.5.

Five points:

1- Artificially limiting the ratios to between 100 and 0.1 is ludicrous. The probability of, say, the Isaiah chapters being an accurate translation of an authentic 600 B.C. manuscript are closer to 1 in a billion than to 1 in 100. Yet their methodology limits this to 1 in 100.

2- The evidence they select is arbitrary and incomplete: they didn't mention the Isaiah problem, for example, so they didn't even score 100 points on that to the critics--even though the point deserves way more than that.

3- How can you possibly conclude that a true book mentioning "excellent workmanship" (point 6.18) is 50 times more likely than a false book mentioning it? This is totally made up.

4- Their arbitrary approach to selecting and weighing evidence has no resemblance to Carrier's analysis.

5- Reading this whole thing would be a colossal waste of time. I can't even imagine somebody taking the time to write it.