(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.)