The Interpreter; Bayes Theorem; Nephites and Mayans

[_honorentheos]

Hi Lemmie, I'm curious if you have thoughts on the issue brought up in the last couple of comments between me and Brant? In particular, that the Book of Mormon can be used to support contradictory positions in relation to specific points taken from Coe but the papers methodology determined the correlation warranted their lowest probability Smith was guessing. It seems this shows rather conclusively the paper failed to use Bayes theorem properly wouldn't it? My understanding of Bayes is it is intended for working with conflicting positions to work out the probability of competing hypothesis being true. When the evidence in the Book of Mormon forces a supporter to present qualifying statements saying there are alternative interpretations available to justify the paper placing a item as a hit inspite of conflicting evidence being present and justifiably read in the Book of Mormon yet the authors assigned it as so detailed, specific and unusual it is unlike due to guesswork, it seems the act of doing so is essentially conceding the paper failed at it's stated purpose.

[_honorentheos]

This may have come up earlier in the thread and I missed it. But there is a sort of lost 116 pages version of this paper on Dr. Bruce Dale's blog that provides some insight into the thinking and approach followed for the Interpreter paper -

http://www.ohthatcleverkidjosephsmith.com/?p=414

[_Physics Guy]

Academic debate is usually respectful, because papers that get published in journals are usually not completely stupid. They might be wrong, even totally wrong, but if they are it's usually not for any really obvious reason. You can point out subtle flaws, or push the authors to walk their conclusion back a little bit. That won't work here because this paper is so childishly wrong.

What's the chance that an apple would fall to the ground if you dropped it? Well, the apple is made of at least a thousand little chunks of apple. At any moment each one of them could move in any direction. There are a lot of different directions in three-dimensional space, so the chance of each piece of apple moving straight down at any particular time is clearly very small. But let's be generous and say it's no smaller than 2%. Then what's the chance that all the pieces of apple fall straight down? Why, it's 0.02 to the power of at least a thousand!

That number is smaller than one divided by the number of electrons in the visible universe. Smaller than you could shake a stick at. Really small.

So never mind the Book of Mormon. The conclusion to which these authors' methodology leads is that apples can't fall.

Treating correlated data as independent is not a peccadillo pointed out by quibbling pedants. It's idiotic.

[_Lemmie]

This may have come up earlier in the thread and I missed it. But there is a sort of lost 116 pages version of this paper on Dr. Bruce Dale's blog that provides some insight into the thinking and approach followed for the Interpreter paper -

http://www.ohthatcleverkidjosephsmith.com/?p=414

from the blog entry:

OK, someone might point out here that I am “cherry-picking” the data, that is, I am only selecting data that agree with my point of view.

Fair enough. That is true. It is also exactly what the critics of Joseph Smith and the Book of Mormon have always done. They never, ever consider any of the contrary evidence; the evidence that Joseph Smith was indeed a true prophet. Not once have I seen any of his critics do that.

Wow. That explains so much.

And this:

Now, anyone can assign any likelihoods they want to these events that I have listed above.

At least he admits it here.

This:

4.Finally, there are a lot of so-called “experts” and detractors out there who claim the Book of Mormon is a fraud. Dr. Michael Coe, whom I discussed in Posts 13 and 15, is one of them. These experts usually cite one or two pieces of “evidence” that they claim disprove the Book of Mormon, or Joseph Smith or The Church of Jesus Christ of Latter-day Saints. But they never, ever cite any of the reams of physical, literary, social or other evidence supporting the Book of Mormon, Joseph or the Church.

Jenkins discussed that. And what "reams" of evidence?

Next:

I am trying to provide evidence for the defense. I feel no need to advocate for the prosecution, although I expect someday to summarize some of the evidence for the prosecution and evaluate it as I have done here for the defense using Bayesian likelihoods.

Some of it?

And finally:

So I hope this particular post and my other posts will serve in some ways to “inoculate” church members against the intellectual dishonesty of cherry-picking, strengthen their faith, and help honest investigators see some of the breadth and depth of evidence that Joseph Smith was indeed a prophet…so that they can know for themselves that these things are true.

So, inoculate against the intellectual dishonesty of cherry-picking by posting an article in The Mormon Interpreter that is based on 1) cherry-picked, dependent data that is improperly presented as independent, fully representative data, and 2) improper use of probabilities that come from medical testing models with properties that his models do not have.

Thanks for finding that, honor, it gives an interesting perspective to how this article developed.

[_Water Dog]

What's the chance that an apple would fall to the ground if you dropped it? Well, the apple is made of at least a thousand little chunks of apple. At any moment each one of them could move in any direction. There are a lot of different directions in three-dimensional space, so the chance of each piece of apple moving straight down at any particular time is clearly very small. But let's be generous and say it's no smaller than 2%. Then what's the chance that all the pieces of apple fall straight down? Why, it's 0.02 to the power of at least a thousand!

That number is smaller than one divided by the number of electrons in the visible universe. Smaller than you could shake a stick at. Really small.

So never mind the Book of Mormon. The conclusion to which these authors' methodology leads is that apples can't fall.

Perfect comparison.

This may have come up earlier in the thread and I missed it. But there is a sort of lost 116 pages version of this paper on Dr. Bruce Dale's blog that provides some insight into the thinking and approach followed for the Interpreter paper -

http://www.ohthatcleverkidjosephsmith.com/?p=414

Great find. This really settles it I think. My original post reads as if it was written directly in response to this blog. Ironically, he even later uses the example of the odds that someone who received a positive cancer result actually has cancer.

The bottom line is these are newbs that don't know what they're doing. They drew off a knowledge of medical screening which was beginner level in terms of Bayes, without understanding the underlying math and concepts. They then attempted to shoehorn the Book of Mormon into the same setup/model, which is an out of context misapplication. Garbage in, garbage out.

A lot in here to unpack.

Dale's thinking is extremely binary. In Dale's mind, there are only two possibilities, Book of Mormon is true, or Joseph was a total con liar. It's a lot more complex than that. True in the sense of being god-inspired 100% literal historical revelation describing real peoples/events? Or true in the sense of containing spiritual truths? Can the book be partially true in terms of historicity, whether intentional or a consequence of Bible influence? He frames a very analog kind of issue that falls in a spectrum of many possibilities and hypothesis as a binary.

And then he takes this a step further. If the book is not "true," according to the Dales, that means Joseph was guessing in the same sense of rolling a dice or shaking a magic eight ball. As if Joseph sat down and asked, "what type of government should I give the Lehites Magic 8 Ball? Centralized or de-centralized? And then one by one he came up with a bullet list of societal features and had the Magic 8 Ball randomly decide them for him. If you read the blog, this is literally what he says.

One of the clearest illustrations of statistics is given by rolling dice. The population here is the values (1 through 6) on the six sides of the die. Since a die has six possible values, then there is a one in six chance (16.66666…% of the time) that the value “1” will turn up when the die is cast, ditto for each of the other values 2 through 6. If you have two dice, then each die is independent of each the other die and there is still only a one in six chance that any given value will turn up for that die when it is rolled.

Here is the key point: probabilities of individual events must be multiplied to estimate the probability of all the individual events occurring together or as a result of the same cause. The probability of each individual die coming up with a “1” is 16.666% (out to as many “6s” as you want).

But the probability of rolling “snake eyes” or both dice coming up with a “1” on the same roll (simultaneously) is not 16.6% but 16.6% (0.0166) times 16.6% (0.0166) or about 0.02756 or approximately 2.76% of the time. So roughly three times out of a hundred times that you roll two dice at the same time you will get snake eyes.

I invite you to perform that experiment. You can test this assertion and verify it for yourself.

Going on further, if we want to roll three dice at the same time, what will be the probability of rolling three “1s”? By the formula, it is 0.166 x 0.166 x 0.166 equals 0.00457 or about 5 times in a thousand. (That’s a lot of dice rolling to test the assertion, or you can just take my word for it. :)). If we roll four dice together, what is the probability of rolling four “1”s simultaneously? It is 0.000761, or about 8 times in ten thousand rolls of the four dice.

So he sets the stage with dice rolling. Then he shoehorns Joseph Smith into this.

OK, enough of quoting myself. The “population” here is the specific testable facts, statements and claims in the revelations and other divine guidance given to Joseph Smith, in other words, when Joseph was acting as a prophet.

Why those times? Because Joseph never claimed to be infallible. He never claimed to be more than a mortal man. And he never, ever claimed to be perfect in his statements as a fallible human being. So it is no use to test those statements, although many detractors of Joseph do exactly that. The detractors spend no effort on studying the revelations given to Joseph to test that revealed evidence, which is abundant and specific.

So, Joseph did say that there was no error in the revelations he had taught. These revelations include the Book of Mormon, the Doctrine and Covenants and The Pearl of Great Price. Thus we can test Joseph’s prophetic credentials statistically based on the revelations he received. If he really was a prophet, then those supposed statements of fact given to him by revelation are true. If Joseph was just a man, then all those statements of fact are just guesses. If they are guesses, then some guesses will be right, and some will be wrong.

Now, in the real world, we usually don’t experience the kind of mathematically well-defined probabilities that rolling dice offers to us. Instead, we usually deal with “odds” or “probabilities”, many of which are somewhat subjective. By “subjective”, I mean that the individual must decide for himself/herself what constitutes strong evidence, what evidence is positive but not especially strong, and what evidence is just barely worth mentioning.

The above quote is where things start to get interesting. Dale just admitted his paper is SUBJECTIVE. He is not relying on objectively-derived LRs based on some math or data or even a stated rationale. He then goes on to explain where his ratios come from.

In the Bayesian approach, we write the likelihood ratio (the likelihood that Joseph Smith was a false prophet) as:

P(D|H)/P(D|~H)

Where D is the data to be entered in the ratio. Also, H is the hypothesis being tested, that Joseph Smith was false prophet and therefore a liar, because he claimed to be a prophet. On the other hand, ~H is the converse hypothesis, in other words, the hypothesis that Joseph was a true prophet and that he gained his knowledge from God.

We can assign a likelihood ratio or “Bayes factor” to each statement of fact associated with the revelations given to Joseph. This likelihood ratio is the probability that the statement is true given the assumption that he was just guessing divided by the probability that the statement is true given the assumption that he was a prophet. This likelihood ratio therefore represents the strength of the evidence, in this case the evidence against Joseph being a prophet.

Here is a good introduction to Bayes’ theorem, which underlies the analysis that I am going to present in this blog.

https://en.wikipedia.org/wiki/Bayes%27_ ... 80.99_rule

Once we have decided on the likelihood of guessing correctly about each specific fact, we then multiply the likelihoods of guessing right about each of these specific facts. The number obtained by multiplying all of those individual likelihoods together is the strength of the total body of evidence that Joseph was a really good guesser instead of a prophet. This number is also the likelihood that he was a liar and fraud, because Joseph was not a prophet as he claimed to be.

Now, here is a key point about Bayesian analysis. It is important to understand that this Bayes factor or likelihood ratio, or the strength of the new evidence, tells us how much we should change our prior beliefs based on the new evidence. In Bayesian analysis, our prior beliefs about a particular hypothesis or idea are called the “skeptical prior odds”. The change in the prior beliefs as a result of the new evidence are called the “posterior odds”.

This approach to data is frequently used in medical tests. I thank my son, Brian Marshall Dale, Ph. D. in biomedical engineering, for this specific example. Brian pointed me toward Bayesian statistics and provided a number of helpful editorial suggestions for this post.

http://doingbayesiandataanalysis.blogsp ... is_27.html

For example, if a disease is somewhat rare then an individual might have “skeptical prior odds” of 1:1000 for them having the disease. If the test has a likelihood ratio of 100 (a good medical test for screening) then our posterior odds would be 1:1000 x 100 = 1:10 for them having the disease. The individual piece of evidence changed our minds substantially (from 1:1000 to 1:10) but because we were initially quite skeptical (1:1000) that the person had the disease, we still think it is more likely that they do not have the disease (1:10). A doctor would then call for a more definitive (and more expensive or invasive) test to give additional information and we would continue to update our new odds as we received new information.

The subject of this blog is the prophetic status of Joseph Smith. If we choose, we can start with an extremely “skeptical prior odds” that Joseph was a prophet. We choose to allow only a 1:1,000,000,000 (one in a billion) chance that he is a prophet. Thus we start with odds of 1,000,000,000:1 (a billion to one) that he is just guessing. This means that even before we look at the evidence, we are very confident that he is not a prophet, and the statement of facts he made are just guesses. We would require supporting evidence with a likelihood of 0.000000001 (one billionth) in order to change our beliefs to the point where we would consider “even odds” (1:1) that he is a prophet, and evidence even stronger than that to consider it likely or be confident that he is a prophet.

So here is another illustration of the approach I am suggesting to test the prophetic claims of Joseph Smith.

An acquaintance of mine claims to have really good astronomical equipment and data. Using his equipment and data, he says that I will be able to observe the first rays of dawn from a particular window in my house at 5:10 a.m. on my 67th birthday, Tuesday June 13, 2017. He furthermore tells me that the moon (in its crescent phase) will disappear below the northwestern horizon that same morning at 3:25 a.m. as observed from that very same window.

So, I want to test this fellow’s claims. I am somewhat skeptical of his claims and decide to assign skeptical prior odds of 1000 to 1. In other words, I think it is about 1000 times more likely that he does not have the equipment and data that he claims to have, or stated another way, the odds of him having this equipment and data are 0.001 or one in a thousand.

But I want to test his claim. He might be telling the truth. Does he have a good astronomical equipment and data or not?

I get up really early on June 13, 2017 and go to that particular window. Sure enough, I see the tip of the crescent moon disappear in the northwest right at 3:25 a.m., according to my wall clock, which happens to be a very accurate atomic clock. I am impressed, so I decide to wait up and test his next prediction. I go to the same window at 5:05 a.m. Again, just as he predicted, I see the first edge of the arc of the sun appear just a few minutes later, as near as I can tell, right at 5:10 a.m.

So, I have two choices. Either this guy is a very good guesser, or he does have access to good astronomical equipment and data.

How good a guesser?

Well, this is not exactly the same as rolling dice where the odds are well known. The odds are up to me to decide. For my own reasons, I can decide that the odds of guessing correctly that the moon would disappear at a certain place on the horizon at a particular time as seen from a particular point would be about 1 in 1000. Since the sun is bigger, and many people (at least us early risers), have a better general idea of when the sun comes up than when the moon sets, I give him a 1 in 100 chance of guessing the correct time of sunrise, as seen from the particular place on a particular day.

If I just consider the first event, the setting of the moon, then Bayesian analysis requires me to multiply the probability that he could correctly guess the time of moon set (1000 to one) times my skeptical prior of one in a thousand (0.001). The result is 1:1 or even odds. I am impressed but not yet convinced.

But he also correctly predicted the time of sunrise, which I thought was 100 to one against. So I must multiply the odds of both correct predictions (1000 to one and 100 to one) times my skeptical prior of 1 in a thousand. The result is 100:1. For me, this is really strong evidence. I am now convinced of his claim to have good astronomic equipment and data.

Now, let’s apply this approach to a just a few of the statements of fact in the revelations given to Joseph Smith. Since I really, really don’t want to believe a false prophet, I decide to make the test a very severe one. On the other hand, there have been prophets before, and Joseph might also be a prophet, so I have to keep that possibility open.

But I am really skeptical, so my skeptical prior will be a billion to one. In other words, I decide ahead of time that the likelihood that Joseph was a false prophet was a billion to one. Said another way, the likelihood that he was true prophet was one in a billion. So it is going to take a lot of evidence to convince me that he was a true prophet.

To make my analysis, I decide to assign one of three different likelihood ratios to each testable fact that I consider. I will use 2 (0.50) for evidence that is “not worth more than a bare mention”, 10 (0.10) for “positive” evidence, and 50 (0.02) for “strong” evidence for (or against) H, the hypothesis that Joseph was a liar (or a true prophet). These values are typically used in the literature on Bayesian statistics.

If familiar with Bayes you'll recognize some of the language he's using here. Strong evidence. Barely worth a mention, etc. This is straight from Harrold Jeffreys well known scale for interpreting K, the bayes factor a.k.a. LR/likelihood ratio.

https://en.wikipedia.org/wiki/Bayes_factor

What Dale did is subjectively concoct a list of "evidence." He then subjectively assigned a list of K/LR values to each item in the list depending on whether he, subjectively, considered it "strong" or "weak" etc. And then he multiplied all that shiz together and got a very big faith promoting number. That's it. So, that being the case, the MI paper tells us nothing about the objective world. It tells us the subjective results of what's going on in Dale's brain and nothing more. So what he's come up with is a methodology for how other people can delude themselves into subjectively believing things which are objectively idiotic. 1) Create a list of stuff you think is cool. 2) Assign arbitrary K values to them based on scale of nerdiness. 3) Multiply together. 4) If number is greater than 50/50, keep paying money to the Mormon church. 5) If number is <50/50, evaluate social costs, return to #1 and add more cool things to list to get the number you want. 6) Repeat. 7) Bayes proves church is true!

[_Lemmie]

Hi Lemmie, I'm curious if you have thoughts on the issue brought up in the last couple of comments between me and Brant? In particular, that the Book of Mormon can be used to support contradictory positions in relation to specific points taken from Coe but the papers methodology determined the correlation warranted their lowest probability Smith was guessing. It seems this shows rather conclusively the paper failed to use Bayes theorem properly wouldn't it? My understanding of Bayes is it is intended for working with conflicting positions to work out the probability of competing hypothesis being true. When the evidence in the Book of Mormon forces a supporter to present qualifying statements saying there are alternative interpretations available to justify the paper placing a item as a hit inspite of conflicting evidence being present and justifiably read in the Book of Mormon yet the authors assigned it as so detailed, specific and unusual it is unlike due to guesswork, it seems the act of doing so is essentially conceding the paper failed at it's stated purpose.

Sorry I didn't see this sooner, i have read yours but let me look back at his posts before answering.

[_Water Dog]

So I hope this particular post and my other posts will serve in some ways to “inoculate” church members against the intellectual dishonesty of cherry-picking, strengthen their faith, and help honest investigators see some of the breadth and depth of evidence that Joseph Smith was indeed a prophet…so that they can know for themselves that these things are true.

So, inoculate against the intellectual dishonesty of cherry-picking by posting an article in The Mormon Interpreter that is based on 1) cherry-picked, dependent data that is improperly presented as independent, fully representative data, and 2) improper use of probabilities that come from medical testing models with properties that his models do not have.

Thanks for finding that, honor, it gives an interesting perspective to how this article developed.

Quite a thing. in my opinion, this blog is really sad to read. Yes, he comes across as somewhat prickly and self righteous. And I agree with DrW that he's abusing his credentials in a reckless way that potentially harms others. That being said, the man is just human. He is scared. He is being driven by a lot of fear, which ultimately leads back to love for his family. He's insecure and really a child in a lot of ways. And he's a total hypocrite. He is literally does the very thing he's speaking against. SMH.

[_Dr Exiled]

Here's a possible title for a rebuttal article: Dr. Dale's Epic Fail: How an Engineer Used Bayesian Statistics to Delude Himself and Others about the Book of Mormon.

[_Water Dog]

So Gadianton, I'm not sure if your question got answered previously, but it would seem this blog answers it. The LRs are derived from Harrold Jeffrey's K table. But here's the thing. They are using it in reverse! The point of the K table is to make a judgement call on a mathematically derived likelihood ratio. Based on the table, compare the results of competing hypothesis, determining them to be "strong" or "weak" or "barely worth a mention" etc., relative to one another. They are doing the opposite. I cannot emphasize enough how completely and totally wrong this is. It is the mathematical equivalent of starting with the conclusion. They aren't starting with evidence and following it to a conclusion. They are feeding in a conclusion to describe the so-called evidence. They take these K labels and use it to invent LRs for historical bullet points. They subjectively look at the bullet point, like the word "nation" appearing in the Book of Mormon and decide for themselves that's "strong" or "weak" etc. Using the table that gives them a LR. Multiplied together. Add in an irrelevant "skepticism" factor to make it seem like they're being generous.

ROFL

[_Water Dog]

Here's a possible title for a rebuttal article: Dr. Dale's Epic Fail: How an Engineer Used Bayesian Statistics to Delude Himself and Others about the Book of Mormon.

You know, in principle his idea isn't bad. A random idea that could be fun would be to setup a crowd sourced Mormonism model that calculates the strength of different hypothesis. I'm thinking something like this. You let people enter pure data. Things that appear in the book, or other things related to Mormonism in general, and also historical facts sourced separate from sources like Coe. Then from that people can start creating a separate list of hypothesis or questions. Then from there coming up with probability calculations. Essentially crowd source a Bayes network that constantly adjusts based on the body of research. People can continuously add and update data if its accuracy is disputed. We break down data points based on objectivity or subjectivity. Like, does the Book of Mormon actually describe a decentralized government or not? Seems there are arguments in both directions. And then calculate different results depending on which things they want to compare. This would be a major undertaking but would be pretty interesting to see the results. Common sense suggests that the model would overwhelmingly show the church is not true.

Here's another idea. We could setup a website that is a kind of Quiz. Titled something like, "Do I believe in the Book of Mormon?" Then start asking questions.

1) Do you think the Book of Mormon has to be literal history in order to be a "true" book? Yes or no.

2) Do you think the Book of Mormon could contain pieces of accurate history even if the narrative if fictional? Yes or no.

Then start giving them different bullet points and have them score them.

3) The word "steel" appears in the Book of Mormon five separate times. Such as in 2 Nephi 5:15 which reads, "And I did teach my people to build buildings, and to work in all manner of wood, and of iron, and of copper, and of brass, and of steel, and of gold, and of silver, and of precious ores, which were in great abundance." How important do you think the presence of steel in ancient America is, as evidence in favor of the Book of Mormon? Irrelevant. Barely worth mentioning. Substantial. Strong. Very strong. The question could also include off to the side a quite from Guns, Germs, Steel about the significance of steel in terms of societal impact.

And then you just keep going down the list of things. But try to decouple and reduce the scope of each element as much as possible. You could have several questions related to just one thing, like horses. Horses vs. Tapir. Elephants. Curelom. Various plants. Trinitarian theology. Polygamy. Isaiah. KJV. Each type of metal mentioned. Yada yada.

Then at the end they hit the "score myself" button. How many TBMs are rattled with the results, "You are totally an atheist and don't at all believe in the Book of Mormon. Based on your answers, it is a trillion times more likely that you're a closet homosexual than the Book of Mormon is true."

What you then do is before scoring their results you ask them to state their belief level. Then this whole endeavor becomes a science experiment to assess cognitive dissonance. From our study, it turns out 80% of self-described "believing" Mormons actually secretly don't believe in the Book of Mormon at all but don't realize this about themselves because they are completely and totally ignorant about what is actually contained in this book.