This is the huge and basic problem with this paper, and I would make sure to emphasise it clearly, rather than cloud it with wrangling over individual historical details.
I hear ya, but those details can be so much fun in showing how critical analysis from different points of view helps us understand how desperate the Mormons are to save their book which was doomed the moment it came out of the hat.
The math part is so far out there that I can't comprehend it.
The authors of this paper couldn't really follow their own math. It's not hard as math goes, but you do have to understand the logic of probability to see why anything like what they are trying to do could be meaningful. And then you have to understand a bit more about correlation in order to see why the stuff in this paper is nonsense. The authors clearly don't actually get those things, although they may think that they do.
They were probably counting on most of their readers not understanding their math, either. They don't adequately explain why their procedures are supposed to make sense, so it seems they weren't even trying to bring readers to understand a logical case, but were only hoping to give the impression that a wonderfully unassailable case had been made. In fairness, they probably weren't doing this cynically. The way they themselves apply rules without understanding makes me wonder whether they even know that it is possible to understand Bayesian inference, rather than simply accepting it as revelation.
If I remember correctly, the Dales' only statistics background is practical experience in analysing medical x-rays. In any case their background seems not to have given them any actual understanding of how Bayesian inference works. They just follow rules they've picked up, without understanding the principles well enough to see why those rules do not work at all in this unfamiliar kind of problem. They're like a couple of auto mechanics confidently building a rocket to Mars, thinking that all they need is to put in enough cylinders.
And I'm afraid I suspect it's not quite coincidental that this is a Mormon work. Plenty of non-Mormons can be confused about math, or suffer Dunning-Kruger delusions of competence. The most basic fault in this paper, however, is the authors' willingness to believe that some mathematical magic can turn their crude probability judgements into virtual proof that the Book of Mormon is authentic. Even inexpert statisticians would mostly pause at that kind of miracle, I think, and worry that it might be too good to be true. It seems to me that among the few who don't worry at all, when straw is seemingly spun into gold, there may be some overrepresentation of people who already believe in miraculous sources of knowledge like seer stones, visions, and the emotional "witness" of the Holy Spirit.
I will admit that I had fun going over the paper point by point, but it sounds like I could make a much better paper by attacking their approach to probability and only then going over individual points to see how they stack up. Now that I've had my fun, let me see if I can actually say something meaningful.
If I'm understanding correlation correctly, then one thing that Dale and Dale don't account for is that certain probabilities aren't independent. For example, all other things being equal, a book might have a 50% chance of having a king in it, and a book might have a 50% chance of having squabbling nobility in it, but the odds of having a king and having squabbling nobility in it are not 50% x 50%, because the two are linked. You have to ask what the odds of having squabbling nobility are if you already have a king in the book, and once you've got that probability settled, then you multiply the two together. To use another example, a book might have a very low probability of having thrones in it, but a book with a king in it might have a very high probability of also having a throne in it, perhaps as high as 90% or even higher, so even though thrones are generally statistically rare, their presence in a book that already has kings only slightly lowers the possibility of the book having both. Dale and Dale don't account for this at all.
Another mistake that they make is not having any justification for the weights they assign things. For example, if a point is (by their estimation) specific but not detailed or unusual, they assign it the weight of 2. Why 2? Why not 1.5 or 1.1? Why is getting this detail right enough justification to double the estimated likelihood that the book is fiction? Do they have any data justifying this strength? This especially applies to the points that they consider to be the strongest evidences for or against the Book of Mormon: they limit their analysis to giving only a strength of 50 to these things. Critics of the Book of Mormon would say that the presence of an anachronism counts for much more than just 50 to 1 odds. Dale and Dale give no justification for their assigning a relatively low strength to these things.
Also, I think I can say that they don't understand the competing hypotheses of the Book of Mormon origins, or that they're misrepresenting them. Consider all the details that could have come from the Bible. (Dale and Dale acknowledge this possibility in nine specific details, but I will argue that there are many more.) Joseph Smith's critics point to all of these details and say that these are evidence that Smith was copying the Bible. Dale and Dale say that these details are ones that match up with details in Coe's The Maya, so they count all of these in favor of the hypothesis that Smith was accurately describing the Maya. Even if all the details do match up with the Maya, do they really count for anything since they also match up with the Bible? If they could have come from either source, then you have to weigh the probabilities of one source against another. Dale and Dale don't do that. They act as if the only competing hypothesis was Smith coming up with details blindly, like a monkey hitting keys on a typewriter. If that was what was going on, then it would be miraculous if Smith got anything right, but the competing hypothesis is that Smith was not a complete idiot and that he had coherent materials to draw inspiration from. To apply this to a specific detail, consider slings. What are the odds that someone copying from the Bible would write about slings? That's the possibility that Dale and Dale should be considering, and they really don't seem to be doing so.
Finally, to make another comparison to monkeys with typewriters, I think that Dale and Dale are poorly counting certain details against Smith in relation to how they're counting hits. Consider their "hit" of City of Laman (Lamanai) "occupied from earliest times". They give credit to Smith for getting this name right, which is fair. But what about all the other names that Smith made which have no parallel in the Maya? Where is Zarahemla? Where are Jacobugath and Manti? Should we count all of these at hits against the Book of Mormon, since they have no apparent parallels? I think it's at least worth considering the possibility that Smith was just making up names, and among so many names being made up, the odds were actually pretty good that he would eventually get one of them right. Dale and Dale are content to give Smith credit for a hit and just ignore the misses.
Thank you all for the feedback you've provided so far. Am I on the right track with what I'm saying now?
This response to Billy Spears by Bruce Dale is just cringe-inducing:
...The Bayesian method my son Brian and I applied in our Interpreter paper may indeed be the best choice among set of bad options. It may be the cleanest dirty shirt in the laundry. But before it was published, that paper went through one of the most rigorous and demanding reviews that I have ever experienced in 40 plus years of writing 300 plus research papers and 60 plus patents...
Putting one's professional work on the line to defend the silliness of the playground peer review offered by the Interpreter? That was still as embarrassing to read as it was originally.
The authors of this paper couldn't really follow their own math. It's not hard as math goes, but you do have to understand the logic of probability to see why anything like what they are trying to do could be meaningful. And then you have to understand a bit more about correlation in order to see why the stuff in this paper is nonsense. The authors clearly don't actually get those things, although they may think that they do.
They were probably counting on most of their readers not understanding their math, either. They don't adequately explain why their procedures are supposed to make sense, so it seems they weren't even trying to bring readers to understand a logical case, but were only hoping to give the impression that a wonderfully unassailable case had been made. In fairness, they probably weren't doing this cynically. The way they themselves apply rules without understanding makes me wonder whether they even know that it is possible to understand Bayesian inference, rather than simply accepting it as revelation.
If I remember correctly, the Dales' only statistics background is practical experience in analysing medical x-rays. In any case their background seems not to have given them any actual understanding of how Bayesian inference works. They just follow rules they've picked up, without understanding the principles well enough to see why those rules do not work at all in this unfamiliar kind of problem....
I agree, with one small exception. It seems they knew enough to realize the "rules" they inappropriately applied could also be manipulated:
This conversation reminded me: when the Dales first posted their article, I looked back into the Intepreter's history to see if any other articles used Bayesian approaches. There was one, and in the comment section, Bruce Dale, who at the time was developing his article, made this very telling comment:
Bruce on November 9, 2013 at 9:23 pm
There is another (but still equivalent) form of Bayes rule that might make this point more clearly and less controversially than the form in the blog above:
odds(H|E)/odds(H) = prob(E|H)/prob(E|H*)
We don’t need to guess individual values for any of the quantities here to show how Bayes’ rule can help us in thinking about The Late War and Book of Mormon authorship and influence questions.
This equation says that the ratio of (posterior odds of H to prior odds of H) is equal to the ratio of the [probability of a true positive (sensitivity) to the probability of a false positive (specificity)]. If a true positive is much more likely than a false positive, the posterior odds increases relative to the prior odds. If a true positive is about as likely as a false positive, the posterior odds stays about the same as the prior odds.
This is important in the Late War situation because there is not much information about how sensitive and specific the Johnsons’ procedures are. In my opinion, sensitivity is decreased and specificity is increased by at least two features of the Johnsons’ study:
1. the massive search model tends to produce false positives.
2. the dependence of weights on a randomly selected corpus (from books of many genres between 1500 and 1830) tends to affect sensitivity and specificity in unpredictable ways; I can conceive of ways in which sensitivity is decreased and specificity is increased.....
Note that a "true positive" would correlate to items in the Book of Mormon that he argues match the items in the Maya book. A "false positive" would correlate to his very small list of items mentioned in the Book of Mormon that Coe mentioned are not Mayan.
Notice he says "I can conceive of ways in which sensitivity is decreased and specificity is increased....."
And also the reverse, such as, having 130+ items in the numerator, and less than 20 in the denominator, and then assuming independence so elements in both can be multiplied.
I am simplifying the process a little, but I really think that Bruce Dale originally began this analysis because he was sure he had came up with a sneaky way to skew the results in his favor. I think he just didn't count on getting caught in such blatant manipulation.
You’ll notice Rasmussen’s entire analysis also relies on this gimmick, as Physics Guy explained in discussing KR’s strategy. It’s about as dishonest a way to use stats as one can come up with. But the Interpreter says all the works under discussion here passed their “rigorous” peer review with flying colors. No one wants to verify that, however. No surprise there.
Ty on November 6, 2013 at 10:27 pm
Good article. The audience at mormoninterpreter is too broad to publish a lot of math, but I love and use Bayesian statistics. Is there a version I can read to see the math behind the inference?
Reply
Bruce
Bruce on November 6, 2013 at 10:51 pm
Ty,
Thanks for the comment. Surprisingly there isn’t much more to it than Bayes’ rule as shown in the article. I arrived at the conditional probabilities subjectively based on the reasons I noted, as well as experience in genomics where massive searches for base pair sequences involved in various conditions are plagued by false matches.
This is a very telling comment, combined with Bruce's previous comments. In his medical experience, false positives are a plague, which I take to mean he assumes they are meaningless.
In his medical experience, maybe they are, but in the Book of Mormon experiment he is setting up, "false positives" are the only evidence the authors allow to show the Book of Mormon doesn't match Mayan history.
His starting assumption that false positives are something that "plagued" their research, as well as his previous statement that massive searches and randomized data selection tend to increase false positives tells me that the Dales had a very specific outcome in mind when they limited their study to an uneven comparison with one book, and cherry-picked rather than randomized for data selection.
Their goal was to falsely skew the data toward true positives, which boosted their hypothesis. Throwing in the independence element further skewed the results into the realm of the utterly ridiculous.
There's definitely something funny in the Dales' attitudes to this work of theirs, because it really shouldn't be hard for anyone who can do both basic logic and basic arithmetic to notice that their procedure has to be ridiculous—and yet they don't seem to notice. Maybe they really were being disingenuous and consciously deceiving "for the Lord". At least as far as I can, I want to assume instead that they're just naïve about how reason works, and seriously expect magic tricks to deliver truth. I mean, even their invocation of peer review is another instance of appeal to authority. I wonder whether they've ever really understood anything, because it seems as though all they know is accepting conclusions from authority.
The Dales only allow a handful of different probability values; if I remember rightly, the smallest one in their set is 0.02. The excuse they offer for this bizarre rule is a set of qualitative descriptions of different probability levels, which they found in a book they cite.
In that book, a probability of 0.02 is described as "very unlikely," or something, while a probability of 0.25 (or something) is something like "somewhat unlikely", and so on. That's quite fine, but by no means at all does it mean what the Dales take it to mean. Instead of recognising it as a handy rule of thumb for roughly translating probabilities into qualitative terms, they take it as an exact translation between qualitative impressions and probabilities. So they think it is valid in reverse, such that anything and everything which strikes them subjectively as "very unlikely" is to be assigned a probability of exactly 0.02, and so on. This is so obviously silly that it's hard to believe anyone would think this way, but so the Dales seem to think.
As Iodo_the_bear recognises, that floor value of 0.02 on all probabilities has deadly effects when it's combined with the Dales' thoughtless approach to correlation.
Really dealing properly with general kinds of correlation can be tricky, but you can get the main effects that appear in this paper just by thinking of grouping, just as Iodo_the_bear notes. Do you count thrones and crowns and sceptres and castles and succession by primogeniture and power struggles with nobles and divine right and a title of "king" as separate issues, or do you group them into one item as monarchy? This can be a subtle business that punishes carelessness with massive errors even if you don't have an arbitrarily imposed floor value of 0.02 in your probabilities, but if you do have that floor, then this grouping issue is utterly lethal.
Each of those eight issues is separately pretty unlikely, out of all the social conventions there could be. So if you count them all separately and treat them as uncorrelated, as the Dales do, you get a total probability for all of them of (0.02)^8, or a likelihood factor of 50^8. If instead you lump them as one factor, that probability for all of them rockets up to (0.02)^1, just because that probability floor value doesn't let you adjust the likelihood down any lower.
Treating medieval European-style monarchy as a set of eight uncorrelated items wildly underestimates its probability, by ignoring correlations. Grouping all eight things into one item, on the other hand, may well wildly overestimate its probability, because of the arbitrary floor value of 0.02.
The point is not that the Dales' procedures will always wildly overstate or understate probabilities. It can go either way—and it can go by a lot, either way. The point is that grouping or splitting happens at the whim of the authors. So the authors can minimise the impact of adverse evidence as much as they want, by judicious grouping, and maximise the impact of favourable evidence as much as they want, by judicious splitting and ignoring correlations. Heck, they can simply fail to think of a bunch of adverse factors, while racking their brains until they come up with more favourable factors. The numbers of each kind of item are arbitrary, at the whim of the authors.
And because all of this is multiplicative, the biases absolutely do not just average away when many items are considered. Instead the biases amplify exponentially, so that the apparent conclusion can be absolutely anything the authors may choose. The only reason they don't find much higher odds still against the Book of Mormon being fake is that they decided that what they had was enough. If they had needed to make the odds even longer, they easily could have.
Or if they had wanted to "prove" that the Book of Mormon was fake, they could have made the odds come out just as long on the other side.
Thank you all again for the good feedback. I've prepared a new draft of the paper, and it's much shorter this time, but I think it gives better weight to what Dale and Dale get wrong.
---
Mixing Math with Humanities and Getting It Wrong: A Critique of a Statistical Analysis of Positive and Negative Correspondences between the Book of Mormon and The Maya
Introduction
Bruce E. Dale and Brian Dale wrote a paper, titled Joseph Smith: The World's Greatest Guesser, in which they critique Dr. Michael Coe's critique of the Book of Mormon. In his published article and interviews which Dale and Dale cite, Coe claims that the Book of Mormon is a grossly inaccurate description of ancient America, so the most likely explanation of its origins is that someone in the 19th century made it all up. Dale and Dale claim that the Book of Mormon gets so many details right about ancient America that the most likely explanation for it is that it is indeed an ancient document, since a modern document couldn't have been correct in so many particulars. They employ statistical analysis in their argument, claiming that the odds of getting so many things right is virtually impossible for a lucky guess. I am not an expert in statistical analysis, but I believe that I can show that their analysis is flawed and that they give far too much credit to the book for what it gets right and not enough discredit for what it gets wrong.
Before I get too far, I want to make clear my own claims. Like Coe, I argue that the Book of Mormon is a 19th-century document. I claim that it draws inspiration from sources in Joseph Smith's own environment, so that the details that it gets right are best explained as Smith drawing inspiration from elements around him that just luckily happen to match the details of ancient America, and that the details that it gets wrong also come from these same sources. I will call this hypothesis the 19th-century hypothesis, and I will refer to Dale and Dale's hypothesis as the ancient America hypothesis. I believe that a critical weakness in Dale and Dale's paper is that they did not give proper consideration to the 19th-century hypothesis. Their competing hypothesis seems to be that Joseph Smith was just blindly guessing about every detail he put in the Book of Mormon, as though he was drawing letters out of a hat. If Smith was indeed just blindly guessing, it would be impressive if he got any details right at all, but that's not what I accuse him of doing. My hypothesis (which is also the hypothesis or the conclusion of many other critics of Joseph Smith) is that Smith drew inspiration from the environment around him in making the Book of Mormon, including the practices of contemporary people and cultures, available literature, and widely known facts. (See Appendix A for details on which contemporary literature I consider to be most important.) To further elaborate on the differences between these hypotheses, the ancient America hypothesis requires the Book of Mormon to be miraculous in origin, since Smith had no conventional way of translating ancient records and since Smith himself claimed the origin of the plates and the translation process to be divine in nature, while the 19th-century hypothesis supposes the Book of Mormon to be human in origin, and full of stupid human mistakes.
Statistical Methodology
When weighing evidence, it's important to consider how that evidence counts towards all the hypotheses being considered. If you have two competing hypotheses and your available evidence can count equally well towards both of them, then you don't have a reason to favor either hypothesis. It's not enough to say that the evidence fits well with one hypothesis; you have to be able to say that the evidence fits one hypothesis more neatly than it fits the other. With that in mind, let's reconsider some of the points of evidence that Dale and Dale cite in the Book of Mormon's favor:
Tribute being required of subjects. They assign a likelihood of Smith getting this right as 0.1
Limited number of important patrilineages. They assign this a 0.02
Sacrifice of children and others to gods. They assign this a 0.1
Close association of temples with sacred mountains/hills. They assign this a 0.02
Temple and other religious rituals involve bloodletting. They assign this a 0.5
Pantheistic religion and idols. They assign this a 0.1
Divination: consulting oracles for secular guidance and assistance. They assign this a 0.1
Stones and slings used as weapons for fighting. They assign this a 0.02
Periods of terrible drought separated by decades or centuries with resulting famines. They assign this a 0.1
The thing that all of these points have in common is that Dale and Dale admit that Smith could have gotten these details from the Bible. This is precisely what I accuse Smith of doing. In fact, critics like myself might point towards all of these points in a case against Smith! In spite of this possibility, Dale and Dale are still content to heavily weigh these points in Smith's favor. In the case of divination for instance, they weigh this in Smith's favor with a strength of 0.1. Dale and Dale's justification for assigning the divination detail a weight of 0.1 is that it is specific and detailed, but not unusual. They offer no data to support this. As far as I can tell, the only justification they offer for this classification is that it is "Bayesian". But is it? Bayesian analysis works perfectly well with other probabilities, so long as you apply the methods properly.
This lack of justification becomes really noticeable at the extremes. The lowest strength they give any correspondence is 0.5, meaning that by their estimation, getting it right doubles the likelihood that the Book of Mormon is an authentic record of ancient America. Is this justified? Dale and Dale note that some correspondences are too obvious to count for anything, such as "the fact that people eat food", so those are essentially given a strength of 1. Where are all the strengths between 1 and 0.5? Aren't there any correspondences with a strength of 0.6 or 0.7? Then, at the other extreme, the highest strength they give any correspondences is 0.02, either for or against the Book of Mormon. This creates a huge imbalance in favor of the ancient America hypothesis. Critics would say that since the Book of Mormon clearly says that there were domesticated horses at its specified time in ancient Mesoamerica and since there were no horses anywhere in the Americas during that time, this should weigh heavily against the ancient America hypothesis, perhaps with a strength of 0.000001 or more. Dale and Dale again offer no data in support of their relatively low estimation of any evidence against the ancient America hypothesis. Their only justification appears to be that 0.02 is considered "strong", and apparently nothing can be stronger than that.
There is at least one more flaw in their basic statistical methodology: they don't account for correlated probabilities. Every correspondence they mention is treated as statistically independent from all others. This becomes hard to justify when you look at some of the correspondences they mention. For instance, one of their correspondences is that royalty exists, and another is that there are elaborate thrones. Are these actually independent of each other? What are the odds of royalty without thrones? Dale and Dale are content to treat these separately. Dale and Dale appear to pile on with correspondences that should be correlated, adding "some rulers live in luxury" and "royal or elite marriages for political purposes" to the pile of evidence in favor of the ancient America hypothesis without stopping to consider how the odds of any one of these affects the odds of finding the others.
In short, their statistical methodology is filled with errors, and none of it can be taken seriously. I think that we are justified in dismissing the whole paper on these grounds. That said, I want to take some time to look at the correspondences they mention, as I think that examining these in greater details shows how eager Dale and Dale are to interpret evidence in favor of the ancient America hypothesis and how quick they are to dismiss evidence in favor of the 19th-century hypothesis.
Correspondences, Reconsidered
Biblical Correspondences
Dale and Dale mention the nine points listed above as correspondences that could have been inspired by reading the Bible. If a correspondence could come from a Biblical source, then they admit that the correspondence is not unusual, but that's the end of what they're willing to concede to the 19th-century hypothesis, but sometimes they don't even concede that. Consider the use of slings. They count as "specific, detailed and unusual" in favor of the ancient America hypothesis. They fail to consider that slings are repeatedly mentioned in the Bible as a favored weapon of war, and that the sling is the weapon of choice in the famous story of David and Goliath. We can thus argue that the mention of slings is not unusual to either hypothesis, and that it is specific and detailed in ways that both hypotheses can account for. It deserves no weight in favor of either.
Consider other points, such as the presence of pantheistic religion and idols. The Old and New Testament are filled with condemnations of idolatry. What are the odds that someone copying from the Bible could have copied these sentiments? Dale and Dale do not consider this possibility, instead weighing this one as 0.1 in favor of the ancient America hypothesis, just because it is specific and detailed. To the close association of temples and sacred mountains, they give Smith a 0.02 likelihood of guessing it correctly. They seem to forget that mountains are repeatedly used as sacred places, such mount Sinai where Moses spoke with God, or the mount of transfiguration where Moses and Elijah appeared alongside the glorified Jesus. What makes this detail decidedly not in favor of the ancient America hypothesis is that the only correspondence with the Book of Mormon is in 2 Nephi 12:2-3, where the author is explicitly quoting Isaiah. This one fits perfectly with the 19th-century hypothesis, and Dale and Dale just ignore that fact.
There are other correspondences that could easily have come from the Bible. Dale and Dale point to "towers built, some very tall, possibly watchtowers" as specific and detailed evidence in favor of the ancient America hypothesis, forgetting that towers are mentioned dozens of times in the Bible, with watchmen on the tower also repeatedly being mentioned in these contexts. For another point to consider, they have the correspondence of "'seating' means accession to political power" listed as having a likelihood of 0.02, overlooking the fact that the Bible repeatedly speaks of sitting in judgment, or being given a seat as a symbol of authority (see Esther 3:1 and Revelation 13:2). What are the odds that someone copying the Bible would routinely use Biblical language? Dale and Dale do not consider this possibility.
Obvious Correspondences
There are some details that Dale and Dale cite in favor of the ancient America hypothesis which seem too obvious to mention. Consider the following:
Many cities exist (likelihood = 0.1)
Some rulers live in luxury (likelihood = 0.5)
Gifts to the king for political advantage (likelihood = 0.5)
Political factions organize around a member of the elite (likelihood = 0.1)
Tribute required of subjects (likelihood = 0.1)
There are captains serving kings (likelihood = 0.5)
Those of noble birth aspire to power (likelihood = 0.5)
Slavery practiced (likelihood = 0.1)
Strong class distinctions based on noble birth, wealth and specialized learning (likelihood = 0.1)
Menial workers, extreme inequality, ignorance and oppression (likelihood = 0.5)
Marketplaces exist (likelihood = 0.1)
Cities and lands named after founder (likelihood = 0.5)
There are many more like these. Are we actually justified in granting any of these a likelihood of less than 1? Couldn't anyone with common sense have come up with these? How stupid do Dale and Dale think Joseph Smith was?
There are also correspondences that are less obvious but which did have clear parallels in Joseph Smith's time and place. Dale and Dale assign the correspondence of "Foreigners/new rulers introduce/impose a new language/writing system on indigenous peoples" a likelihood of 0.02, saying that "European settlers in North America were not trying to impose a new language on the Native Americans, they were trying to take get rid of the Indians and take their lands". They are apparently ignorant of the sad history of American Indian boarding schools, in which European settlers made great effort to impose a new language and culture on the Native Americans.
False Correspondences
There are a few correspondences that Dale and Dale make which, in my opinion, are not actually justified by a close reading of the Book of Mormon. Consider the very first correspondence they list: "Fundamental level of political organization is the independent city-state". Their justification for this one is that "Throughout the Book of Mormon itself there is never a reference to 'Nephite nation' or to a 'Lamanite nation.'" They forget that the Book of Mormon does, in fact, use the word "nation" to describe the Nephites in Moroni 8:27. I think that it's also worth noting that the same verses uses "people of the Nephites" as equivalent to "nation", and the Book of Mormon frequently speaks about the "people of the Nephites" and the "people of the Lamanites". (See Alma 51:9 for an example of both.) If "people" is equivalent to "nation", as the Book of Mormon seems to treat it, then the Book of Mormon makes repeated references to nations instead of independent city-states.
Consider also this correspondence: "Candidates for high office had to possess hidden knowledge". For this one, they cite Enos 1:1 and Mosiah 1:2. Neither of these make reference to hidden knowledge. They both speak about people being taught in the language of their fathers. This is not presented as secret knowledge; in the context of the Book of Mormon, this is just part of receiving a good education. Consider 1 Nephi 1:1, in which we read: "I, Nephi, having been born of goodly parents, therefore I was taught somewhat in all the learning of my father". Being taught in the learning on your father is something that all good parents are supposed to do. On a similar bad note, Dale and Dale point to 1 Nephi 3:19 and the same Mosiah 1:2 in support of the correspondence of "Arcane sacred or prestige language". 1 Nephi 3:19 is referring to the language of the fathers as something to be preserved and shared, not something to be jealously guarded. There is no evidence in the Book of Mormon of an arcane sacred language, despite Dale and Dale's claims.
Thirdly, let's look at the claimed correspondence of "multiple calendars kept", to which Dale and Dale assign a likelihood of 0.02. The standard from Coe that they cite refers to keeping years of different lengths. The verses they cite in the Book of Mormon don't speak of any such thing. 3 Nephi 1:1 is an instance of the author telling us how many years had passed away since a certain event had happened (specifically, since the reign of the judges began) while also telling us how many years have passed away since a more distant event happened. These events are actually part of the same calendar, not different calendars. 3 Nephi 2:7-8 is the author again telling us how many years have passed since a certain event, and noting that the Nephites have restarted their calendar. This does not match the multiple calendar system that Coe describes at all. In fact, these verses claim that the people of ancient America gave special attention to events in the years 600 BCE and 0 CE, when we find no evidence of them placing any special import on events at those times. How can we honestly count this as evidence in favor of the ancient America hypothesis?
Missing Negative Correspondences
There are a few instances where Dale and Dale list positive correspondences without noting possible negative correspondences with an obvious connection. One such correspondence is "City of Laman (Lamanai) 'occupied from earliest times'". They give Smith credit for naming an important city correctly, which is fair, but if Smith deserves credit for getting a city right, how much discredit does he deserve for getting cities wrong? We have Laman which we can point to as Lamanai, but where is Zarahemla? Where are Jacobugath and Manti? Zarahemla in particular is occupied from early times, and there is no name like it. Shouldn't we give Smith some discredit for naming cities that don't exist?
Then there is the way that Dale and Dale treat correspondence with Christianity. They list this one as "Strong Christian elements in Maya religion" and give it a likelihood of 0.02. Critics of the Book of Mormon may justly counter that the Christian elements within the Book of Mormon do not match the general tendencies of the Maya. Instead, the Book of Mormon describes a very specific Christianity, with many important resemblances to Pauline doctrine and 19th-century religious practices. Alexander Campbell, an early critic of the Book of Mormon, observed in his book Delusions that the Book of Mormon discusses "all the great controversies - infant baptism, ordination, the trinity, regeneration, repentance, justification, the fall of man, the atonement, transubstantiation, fasting, penance, church government, religious experience, the call to the ministry, the general resurrection, eternal punishment, who may baptize, and even the question of freemasonry, republican government, and the rights of man." How justified are Dale and Dale in pointing to the Christian tendencies that the Maya did have without noticing the specific tendencies that they didn't have?
There are also negative correspondences that Dale and Dale point out when reviewing View of the Hebrews as a control text which they strangely fail to apply to the Book of Mormon. Consider the following:
The ancestors of the American Indians observed the Law of Moses
Language of the native Americans appears to have been Hebrew
They have acknowledged one, and only one God
Indians called on the name of Jehovah
All of these can be found in the Book of Mormon. Why don't Dale and Dale count them against the ancient America hypothesis?
Before moving on, I also have to note one correspondence that Dale and Dale weighed as both positive and negative: the presence of refined gold. I would ask Dale and Dale to review their paper more carefully and make up their minds about how to count this one.
Poorly Weighted Negative Correspondences
Finally, we get to the negative correspondences which Dale and Dale do count against the ancient America hypothesis. The highest strength they grant any of these is 50. Let's consider if this low strength is justified.
Dale and Dale observe: "The Book of Mormon clearly states that there were horses among the Book of Mormon peoples and that the horses existed in both Lehite and Jaredite times" and then simply say that "Dr. Coe insists that they did not exist." Dr. Coe is not the only one saying so. The physical evidence indicates quite strongly that horses did not exist during the supposed time of the Lehites. We are entitled to ask what the actual odds are of a genuine historical record naming an animal that did not exist at the time. Could we put them at one in a million, or one in a billion? Dale and Dale are content to give the Book of Mormon an odds of 0.02 of getting this fact wrong while still being an authentic ancient record. This strikes me as absurd. We run into a similar problem with goats, cattle, and donkeys, which Dale and Dale again only assign a strength of 50.
Then there are technologies to consider. Dale and Dale concede that iron and steel probably did not exist in ancient America, despite the Book of Mormon saying that they did, and then have the nerve to say "to enable a rigorous test of the Book of Mormon, we grant this correspondence the maximum possible evidentiary weight" as if they actually granted it maximum possible weight. They do not consider the actual odds of these technologies somehow existing among the Nephites and then vanishing. Iron and steel production leave clear traces, not just of the actual metal used but of the methods used to make them. Where are the remains of the furnaces used and the charcoal burnt? These traces have been found across the world, in some cases as far back as the 14th century BCE. Where are all the traces in ancient America? Dale and Dale seem to think that there is a 0.02 probability that these technologies existed in ancient America but then disappeared, leaving only one trace in the Book of Mormon instead of thousands of artifacts.
There's also the use of plants to consider. Dale and Dale count the absence of wheat as a negative correspondence, but give it the low weight of 2. They justify this by saying that there is "no claim in the Book of Mormon that those peoples domesticated wheat". This is plainly stupid, as Mosiah 9:9 clearly states that the Nephites tilled the ground with seeds of wheat. It is also worth noting in 3 Nephi 18:18 that Jesus makes a clear reference to sifting wheat, indicating that the Nephites knew what wheat was and how to sift it. Dale and Dale further justify the low weight by saying: "Wheat may not have been widely grown, and therefore the evidence for wheat more difficult to detect centuries later." The trouble here is that wheat would live behind very clear traces in the fossil record. Wheat produces pollen, and pollen spreads like glitter, and it fossilizes well because of how durable it is. If wheat had existed anywhere, there would be traces of it, yet Dale and Dale seem to think it reasonable to assign a 0.02 likelihood to the possibility that it somehow disappeared. This also applies to barley, which was apparently important enough of a crop that Nephite currency was pegged to it (see Alma 11:7) but which has also disappeared. Dale and Dale expect us to believe that there's a 2% chance of this disappearance.
Perhaps the worst weighing comes in their consideration of the lack of Middle Eastern DNA in ancient America. Dale and Dale give this a meager weight of 2, indicating that they think that there's a 50% chance that this could have happened. This is quite wrong, for several reasons. One is that the presence of alternative sources of DNA is itself problematic for the Book of Mormon. Besides the Jaredites who went entirely extinct, the book never makes any mention of non-Middle Eastern sources of DNA in ancient America; the only sources ever given are the Lehites and the Mulekites, with all Book of Mormon characters tracing their ancestry to these sources, such as Ammoron tracing his ancestry to Zoram in Alma 54:23. Thus the presence of any DNA from outside the Middle East is problematic for the Book of Mormon's narrative, but the problem is much worse than the existence of non-Jewish DNA. The problem is that the non-Jewish DNA is all there is. All traces of Jewish DNA among Native Americans can be traced to migrations after Columbus. The Middle Eastern populations that should be there from Lehi and Mulek are simply absent. Simon Southerton goes into detail on this matter in The Sacred Curse: How Native American DNA Exposes Mormonism's Lamanite Myth. Dale and Dale cite Ugo Perego's work, but Southerton demonstrates that the factors cited by Perego, including the founder effect and population bottleneck, are insufficient to explain the total disappearance of ancient Middle Eastern DNA. Perego and others also claim that we might not know Lehite DNA if we found it, but the Book of Mormon makes it clear that Lehi, Ishmael, Mulek, and all of their contemporaries were Israelites, and we have know a considerable amount about their DNA because we have existing known populations to draw from. The "scientific issues" that Dale and Dale point to in order to explain the DNA's disappearance simply aren't good enough.
In other words, we have a series of negative correspondences that should command huge weight, but Dale and Dale give them only 50 or less, and then complement themselves for awarding these the "maximum possible weight". There isn't good justification for granting any of these objections such a low weight, and Dale and Dale did it over and over.
Summary
The paper strikes me as a disaster. It gives huge credit to the Book of Mormon for stating obvious facts about the human condition, it fails to properly consider the strength of a competing hypothesis for the book's origin, and it massively undervalues the strength of the evidence against the book, and then it calls all of this "Bayesian". This is no way to actually estimate the likelihood of any hypothesis about a book's origin. The most rational response to a paper like this is to dismiss it.
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I haven't found any responses to Dale and Dale's paper that have been published in any outlet like Dialogue or Sunstone. There have been some excellent objections in forums like this one and Mormon Dialogue, but no one has gone to the trouble of getting their objections formally published. I think it might be worth the bother to get something published, especially since Dale and Dale went to the trouble of publishing this one and a follow-up (subtitled "Still the World's Greatest Guesser").
