Interpretering Bayesian Analysis

[Doctor CamNC4Me]

I'd suggest the Cassius faculty stick with one issue and run it through the Bayesian analysis with Dr. Rasmussen. It's important to not let the sacred timeline branch, otherwise there'll be too many Kangs in the kitchen.

- Doc

[kyzabee]

5) Would you please explain why rare = true? I get that rare = rare, but how do you justify rare equals true?

It's essentially the same logic used in all significance testing. If you get a statistical result that's far enough from the null hypothesis, eventually you conclude that the rarity of the result isn't a fluke, and that whatever hypothesis you're testing should be preferred.

One of the main innovations with Bayes is that there's a recognition that the null hypothesis often isn't good enough, and that some hypotheses need to handicapped beyond the assumption of no effect. In that case you need to specify both (or multiple) hypotheses, dividing up the probability space appropriately, and then see if the statistical result can clear your custom bar.

So rare doesn't equal true, but enough rare will eventually lead me to place my bets on a different horse.

I also kind of like the diffusion analogy I used when talking with Billy. Since we can come up with whatever number of hypotheses we feel like, there's a universe of potential explanations out there to explain any given piece of evidence. Bayesian analyses essentially push our belief away from all the hypotheses where the evidence is less likely to be observed to ones where it's more likely to be observed. With enough evidence and enough statistical diffusion pressure we should eventually land on the explanation that fits the best. That's an idealized model, though, and in reality we have to pick our hypotheses and see how they work out. In this case, that would be the broad hypotheses of authenticity and fraud (with the hypotheses becoming more detailed as needed to fit the context of a given analysis). If a piece of evidence is expected under authenticity and not expected under fraud, then authenticity gets stronger and fraud gets weaker, and it works the same way the other direction.

[kyzabee]

I'd suggest the Cassius faculty stick with one issue and run it through the Bayesian analysis with Dr. Rasmussen. It's important to not let the sacred timeline branch, otherwise there'll be too many Kangs in the kitchen.

- Doc

"If you think my methods are questionable, just wait until you meet my variants."

[kyzabee]

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.

That's an interesting assumption, and it sounds plausible enough in its way. I've wondered similar things myself. It's why I see their failure to recant individually as a possible (though minority) outcome. But these people were still human. They had large beefs with Joseph and they knew very clearly that they would have instant notoriety and a huge following if they blew Joseph's game open. They also weren't alone. Multiplying the odds of one person failing to recant across the available witnesses steepens the curve quite quickly. It's not a critical strike, but I see it as a definite glancing blow against the hypothesis of fraud.

Again, as with all these content-oriented thoughts I'm happy to continue the discussion when the analysis crosses that bridge.

[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.



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

The claims of visions and revelations themselves aren't unexpected. To have them result in something like the Book of Mormon is another story.

That about does it for me for this morning. I may pop in later this evening. Cheers!

[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.

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).

My point is that all of these have a Bayesian component that lives in the mind and experiences of Joseph. Until you can uncorrelate him from himself, it’s pointless.

[Dr Moore]

The claims of visions and revelations themselves aren't unexpected. To have them result in something like the Book of Mormon is another story.

Again, this premises assumes something about Joseph and so do each of your Bayesian conditionals. It’s a process problem, start to finish.

[Gadianton]

He needs to choose what, specifically, he is testing. He then needs to rigorously stick to that. He can’t test these various things and update a “posterior probability” of something that is meaningful.

Thanks for dropping in Billy, I mentioned I'd hold off to thoroughly consider your comments before responding.

My first observation regards point 1. I totally agree, the "evidence" -- at least the stuff so far -- has nothing to do with the Book of Mormon being ancient. The exercise is pointless on its face. However, I do believe there is a method to the madness. Kyler's origin story -- If I'm not mistaken -- begins with recognizing one of the (many, many) flaws in the Dales' Guesser paper. He recognized the independence problem. In order to justify multiplying an arbitrarily long string of numbers together to either get to arrive at a big number or to overcome 10 ^ - 158,494 million he's got to make each piece of evidence independent, and what better way to accomplish that than to be sure they actually have nothing to do with each other? Surely, Joseph Smith's first vision story isn't dependent on Chiasmus? (Dr. Moore still has a rejoinder: even then they might be correlated, but let's give it the benefit of the doubt for a moment for the sake of showing the motivation, which was understandable)

[Gadianton]

Kyler,

I don't want to overwhelm you as there are so many directions to come at this from and several folks interested in what you're doing, and so I'm going to restrict myself to one question for you today.

You've fundamentally followed the path of the Dales, of multiplying a string of improbabilities in order to get to numbers so big (or small) they are rarely talked about in the real world. That alone should be a red flag that you're doing something wrong. But if that's not a red flag, consider the following thought experiment:

KR is born a few decades prior to his actual birth, and discovering critics and apologists in the seventies. He learns about Bayes and goes down the same path of assessing the evidence of the Book of Mormon. He decides before the fact that 10 ^ -42 is the number to beat. However, because it's the seventies, Chiasmus haven't been discovered yet (I don't think) nor has Uto-Aztecan origins by renowned philologist, Brian Stubbs, and neither has the 15th century text been discovered and so the KR of this timeline only has 20 pieces of evidence. Suppose today's KR beats the 10 ^ -42 odds but not by enough to impress absolute certainty upon the critic. That implies that our alt KR would miss by quadrillions to one or worse. Would alt KR admit defeat --- would alt KR admit the Book of Mormon most likely is not ancient, and critics have very good reason to disbelieve it, or would he look for 3 more pieces of evidence?

I will give you a day to think about this (even if it won't take you that long to think about it) and follow up with a second, similar thought experiment.

[Dr Exiled]

I'm afraid the desire to believe will affect this exercise given how fuzzy subjective beliefs can be. DNA evidence or the lack thereof hasn't shaken the faith derived from emotional experience, so emotion will probably play out here and infect the whole thing. Can a contrary conclusion to God being involved with the Book of Mormon ever be reached? What are the odds of this given the group pressure to support the faithful conclusion? Perhaps the desired outcome of this exercise is having a mathematical overlay to the worn out bias argument?

Incidentally, given where DNA science is today, what are the odds the witnesses were at least delusional if not fraudulent or a mixture of the two? They probably had an emotionally charged experience given the build up and each probably had a different experience. However Joseph Smith was there to control the interpretation of the experience after the fact and demanded to control the wording of whatever they experienced. Publishing the Joseph Smith version sealed the witnesses to that version and denying it subsequently would have had the high cost of admitting to being deluded or worse. Who wants to be labeled as a crazy or a fraudulent actor?