This paper is nonsense, turns Bayes on its head. I'm sure the math is sound. From my very quick review the level of math they're getting into is nothing more than introductory level. It's a classic case of garbage in, garbage out. They are misapplying the science. Math can be applied to anything. We can count the number of Klingons in Star Trek and generate some stats. Doesn't mean anything.
For example, the probability values assigned to "events" is arbitrary. Take the first event in their list.
Fundamental level of political organization is the independent city-state
Coe’s standard: “Sylvanus Morley had thought that there was once a single great political entity, which he called the ‘Old Empire,’ but once the full significance of Emblem Glyphs had been recognized, it was clear that there had never been any such thing. In its stead, Mayanists proposed a more Balkanized model, in which each ‘city state’ was essentially independent of all the others; the political power of even large entities like Tikal would have been confined to a relatively small area, the distance from the capital to the polity’s borders seldom exceeding a day’s march” (p. 274).
Book of Mormon correspondence: Throughout the Book of Mormon itself there is never a reference to “Nephite nation” or to a “Lamanite nation.” Interestingly, the word nation is used in reference to the Jaredites (Ether 1:43), a very different people culturally than the Lehites. The Book of Mormon uses this phrase: “nations, kindreds, tongues and people.” The Nephites and Lamanites were clearly kindreds. In contrast, the word nation is used frequently in terms of the “nations of the Gentiles.” The noncanonical Guide to the Scriptures has eight references to “Nephite nation,” showing how deeply engrained this idea of nationhood is in modern readers. But the Book of Mormon never puts those two words together for Nephite/Lamanite societies. The nation-state is not a political structure found anywhere in the Book of Mormon. Instead, the Book of Mormon peoples were organized politically in city-states. Often one city-state would dominate a group of other city-states. This dominance is the subject of the next correspondence
Analysis of correspondence: The correspondence is specific and detailed. There is not a single reference in the text of the Book of Mormon to “Nephite nation” or “Lamanite nation.” It is also unusual. Joseph Smith was growing up in the new nation of America, with a great deal of pride and self-identity as an independent nation. How did he avoid identifying the Lamanite or Nephite peoples as “nations”? But he did avoid it. What a lucky “guess” — over and over again during the course of the Book of Mormon history.
Likelihood = 0.02
Seriously, what the hell are they talking about? How did they come up with 2%? What does this value represent? It's completely made up. They are arbitrarily asserting that because the Book of Mormon doesn't use the word "nation" that there is a 2% chance Joseph Smith could have by-chance been right about a decentralized tribal system? How do they calculate this 2%?
This is not how Bayes works. Whatever logic is applied to a hypothesis has to be equally applied against it, which is to say you have to test an indefinite number of other hypothesis in exactly the same manner and then compare and contrast and see how things shake out, if there are "more likely" or "similarly likely" events.
Taking this example of the political organization. What are all the possible explanations for why the word "nation" doesn't appear in reference to the Lamanites/Nephites? On what basis should we expect to see the word nation, yet it's auspiciously absent? How would we go about determining this? I'm not sure. Because there are simply too many variables to account for. Essentially what we'd need is a sample of a thousand or so men from the early 19th century. Have them all sit down and write a short story on a fictitious ancient American civilizations. How many of those people, based on common knowledge of the day, would have described them as "nations" or otherwise described a political structure that is at odds with current understanding? Since we can't really do that, what's the next best thing? I suppose someone would have to drum up a list of anything written about indians/ancient americans in the early 19th century. Classify it as centralized or decentralized. But even that wouldn't tell us the "likelihood" of Joseph doing it the way he did it, or the likelihood of his description not "matching" with the Mayans or some other ancient american civilization. But at least it would tell us if Joseph was an outlier compared to his peers. My understanding is he wasn't an outlier at all... everybody regarded the indians as tribal??
We could come up with all sorts of conjecture accounting for why Joseph didn't use the word "nation," none of which leads to the conclusion that Joseph only had a 2% chance of doing it the way he did it, absent honest to god inspiration.
There's a lot more that could be said about all this. Another example, you cannot compound probabilities for independent events. Every time you roll the dice, you are starting from scratch. As the article starts out by pointing out, there is a (1/6)^2=~2.8% chance of rolling a snake eyes. But that's NOT the same thing as rolling a dice once, and then rolling it a second time. It doesn't matter if you rolled a 1 on your last turn. On this new turn, you are starting from scratch, and you have a 1/6=~16% chance of rolling a 1. There is no mystical woo woo hidden in the ether somewhere connecting the results of your first turn with your second turn. And yet, that's exactly what this paper does. It links "events" which have no connection whatsoever in order to arrive at compounded probabilities of their occurrence.
There really isn't anything worth talking about here. The paper is idiotic.