Interpretering Bayesian Analysis

[Analytics]

*a dramatic puff of smoke appears*

Hi all! Kyler here. Not sure who's been doing the demonology, but it appears I've been summoned.

I love a dramatic entrance. Welcome!

Can we agree in principle that the thing I'm trying to do is reasonable and potentially useful?

I’ll state for the record that in the past I’ve defended Richard Carrier for using a Bayesian framework to evaluate the historicity of Jesus. Consistency forces me to say that in principle, there is nothing wrong with you or the Dales taking the same approach for evaluating the historicity of the Book of Mormon. And it seems to me that unlike the Dales, you actually understand the statistics.

I’ll leave it to others to debate whether the specific probabilities you are plugging into the formulas are appropriate, but I do want to make one comment about something you said here.

Billy's laid out a lot here, but I'll try to take it a piece at a time.

"Say I have a coin."

I'd quibble pretty strongly with your particular example, as something like a chi-square or Fisher's Exact test would be much more appropriate than just comparing the raw probability of achieving that specific string, and it would avoid the drama of dealing with small probabilities, but Billy's general point is accurate here. This is in principle what I'm trying to do--to estimate the probability of observing a piece of evidence under the two (or sometimes three) competing hypotheses.

It's worth noting here that the more appropriate test would be comparing p = .43 (chisq(1) = .60) with p = .60 (chisq(1) = .27). . .

In my field (actuarial science) we continuously repeat clichés like, “All models are wrong. Some are useful.” A few weeks ago Kerry Shirts mentioned the Beta distribution, and since this is related to that, I’ll flesh out a third approach that like all models will also be wrong, but hopefully will also be useful in this context.

Billy looked at the likelihood of getting a specific series of test results with p = 0.5 and p = 0.55. You could take that approach one step further and calculate the likelihood of getting those results with every value of p between 0 and 1. The result would be a likelihood function. You could then shake your hand and do some calculus magic to find the value of p that maximizes the likelihood function. That would be the maximum likelihood estimator of p.

Creating and evaluating a likelihood function is somewhat tedious, but it turns out there is a probability distribution that has almost exactly the same shape as the likelihood function. That is the Beta distribution with parameters Beta(18,12) (the numbers of heads and tails that were rolled). From that, we can easily see that we can be 90% certain that the true probability of flipping a head is between 45% and 74%. That confirms what everybody else has seen—this just isn’t enough data to tell us what p is with a high degree of precision.

But anyway, welcome to the board.

[kyzabee]

"I would hope you have listened to Mormon Expression’s podcast on how to build a trans-oceanic vessel."

I haven't, though I worked off of Zelph on the Shelf's treatment, which I assume was similar. My guess is that Mormon Expressions similarly glossed over the wide variety of ways ancient societies engaged in trans-oceanic travel.

This suggests to me you haven’t read the relevant section of the Book of Mormon, if you’re comparing it to what we know about ancient seafaring peoples.

The Book of Mormon is very specific about building bellows, mining ore, smelting ore, and crafting tools, just as a means to begin to construct the ship. All which was accomplished in a matter of months by a couple men.

I am glad that your instinct on this one is to go with the “Nephi didn’t do anything particularly miraculous” apologetic approach rather than “God can make anything happen no matter how impossible.” At least we can discuss the details and compare them to actual ancient societies to see if they do indeed match up.

The critics generally assume that he had to be working with iron, which would've been true if he had to put together a renaissance sailing vessel. But if all he's doing is putting together a set of woodworking tools, then copper would've done the job, and the smelting requirements are something he could've put together without too much trouble, with copper desposits apparently available at the Bountiful site.

https://www.epiceras-ancientegypt.com/a ... tools.html

That would get even easier if Lehi's family had experience with metalsmithing, which the book itself hints at:

https://clearldsdoctrine.neocities.org/ ... salem.html

The only thing miraculous I allow here is Nephi receiving instruction on how to build and sail it. I figure if God's allowed to do anything, he's allowed to talk to people.

[Dr Moore]

I would wager the participants on this board could identify 500 or more relevant points of evidence that merit consideration, if “all of the evidence” is on the table. Negative and positive.

L. Ron was definitely huge. But in what way is he unexpected? I expect that his religious movement falls pretty well as expected on the distribution of other religious movements, and his books on the distribution of other fictional works. As you say, it's not enough for me to argue that the book's unique, I have to argue that it's different from what we would've had good reason to expect

Why was Joseph Smith, in his time and with his experiences, talents and curiosities not expected?

[Dr Moore]

Also, Dr. R, in another thread here I offered to give you DNA and chiasmus “for free” because as a proxy for requesting logical arguments for independence, that one is so logically obvious as to be a straw man for my critique.

[kyzabee]

"Creating and evaluating a likelihood function is somewhat tedious, but it turns out there is a probability distribution that has almost exactly the same shape as the likelihood function. That is the Beta distribution with parameters Beta(18,12) (the numbers of heads and tails that were rolled). From that, we can easily see that we can be 90% certain that the true probability of flipping a head is between 45% and 74%."

And this is where my psych-oriented stats begin to fail me, as I don't have enough training to fit these sort of custom distributions, and why you'll see me using a lot of chi-squares and t-tests and z-scores. If you ever see a spot where you think a different model would be appropriate I'd be happy for your insight.

[kyzabee]

I would wager the participants on this board could identify 500 or more relevant points of evidence that merit consideration, if “all of the evidence” is on the table. Negative and positive.

L. Ron was definitely huge. But in what way is he unexpected? I expect that his religious movement falls pretty well as expected on the distribution of other religious movements, and his books on the distribution of other fictional works. As you say, it's not enough for me to argue that the book's unique, I have to argue that it's different from what we would've had good reason to expect

Why was Joseph Smith, in his time and with his experiences, talents and curiosities not expected?

Joseph Smith himself isn't, but the book definitely is. And, as I just argued in part, I find what the witnesses claimed to see and their subsequent failure to recant to be unexpected, particularly in the face of what I see as overwhelming motivation to do so. Critics have obviously worked hard to find explanations for these unexpected features, but the fact that they've had to do so itself admits their unexpected nature.

And I obviously tend to find those explanations wanting, and this project is essentially me instantiating those observations in numerical form.

[kyzabee]

Also, Dr. R, in another thread here I offered to give you DNA and chiasmus “for free” because as a proxy for requesting logical arguments for independence, that one is so logically obvious as to be a straw man for my critique.

That one's just one example, but its an illustrative one, and the others don't really get any better. I'd also have to do things like:

Chiasmus and internal geographic consistency
Political incorrectness and book length
Transoceanic voyages and the Book of Mormon Onomomasticon
Prophetic imperfections and Uto-Aztecan language correspondences

and so on and so forth, 231 times in total, not counting all the internal independence assumptions I use within each episode (which would put the number of required orthogonality demonstrations into the thousands).

[Meadowchik]

Critics have obviously worked hard to find explanations for these unexpected features, but the fact that they've had to do so itself admits their unexpected nature.

And I obviously tend to find those explanations wanting, and this project is essentially me instantiating those observations in numerical form.

Why are they unexpected? I think the surprise some may feel results from misunderstanding the culture of the time. Spiritualism was everywhere. Spiritual experiences were unpredictable and often inscrutable. But recanting? And the implication of intentional deception?

From our point of view, the credibility of the current church hangs on them. But from their point of view, their credibility hung on their trustworthiness.

I think that in their time, it was much more understandable to have an inscrutable even contradictory spiritual experience than to be a liar.

[Gadianton]

I am glad that your instinct on this one is to go with the “Nephi didn’t do anything particularly miraculous” apologetic approach rather than “God can make anything happen no matter how impossible.

I don't think it's that easy to escape "God can do anything" once it's brought to the table. If God can do anything, then he's the alt hypothesis for absolutely every event big or small. If we have a history of allowing God to only be the explanation for the things we can't explain, then forget about Bayes, what we've really got is good old "God of the Gaps" on our hands. If a horse has 10:1 odds for winning a race and the horse wins, nothing at all precludes a God with a theoretical probability of 100% of making the horse win from making the horse win, in fact, he's the most likely explanation.

Other versions of God-of-the-Gaps are found in aliens or reality as a simulation. Aliens could also explain Joseph Smith and the Book of Mormon. Moroni could be an alien. In fact, on my mission, we found a self-published book in a library one day that was written by a local (to that small country) who used the Book of Mormon as a data point for his Ancient Aliens hypothesis.

How are we going to decide between Moroni as an alien and Moroni as an angel from God? Simple. Alien technology might be superb, but God is by definition, the most powerful being to-be-thought, therefore God is the most likely explanation. It's like parsimony in reverse.

[Doctor CamNC4Me]

I would wager the participants on this board could identify 500 or more relevant points of evidence that merit consideration, if “all of the evidence” is on the table. Negative and positive.

L. Ron was definitely huge. But in what way is he unexpected? I expect that his religious movement falls pretty well as expected on the distribution of other religious movements, and his books on the distribution of other fictional works. As you say, it's not enough for me to argue that the book's unique, I have to argue that it's different from what we would've had good reason to expect

Why was Joseph Smith, in his time and with his experiences, talents and curiosities not expected?

That's a good question. About the same time this happened, the Seventh Day Adventists came on the scene with visions, revelations, and whatnot. They have ~19M claimed members worldwide. Are they statistically true, too?

- Doc