Interpretering Bayesian Analysis

[Gadianton]

Thanks for these insights, Billy.

Putting two of these together:

“You know, the most amazing thing happened to me tonight. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight

He says the probability of fiction being dictated in 65 days is 0.000000154. Okay. Whatever. As I emphasized earlier, reality is unlikely. But he then compares that to the probability of authentic scripture being dictated in 65 days. What is the probability authentic scripture is dictated in 65 days? According to Kyler, it is 100%.

The probability of that one license plate driving by is millions to 1. The probability of that one license plate driving by, should God will it, is 100%.

Therefore...

[Philo Sofee]

Welcome Billy Shears! What a treat! Gad, Symmachus, Lem Doc Cam, Dr. Moore, Dr. W, a host of others on Bayes, and now Shears. I am unworthy to be here, but thanks all for letting me hang around. Billy says it so much clearer than I have. It is nice to see I am at least in the ball park with my meager understanding...

[Lem]

Thanks for these insights, Billy.

Putting two of these together:

“You know, the most amazing thing happened to me tonight. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight

He says the probability of fiction being dictated in 65 days is 0.000000154. Okay. Whatever. As I emphasized earlier, reality is unlikely. But he then compares that to the probability of authentic scripture being dictated in 65 days. What is the probability authentic scripture is dictated in 65 days? According to Kyler, it is 100%.

The probability of that one license plate driving by is millions to 1. The probability of that one license plate driving by, should God will it, is 100%.

Therefore...

adding some context,

The probability of that one license plate driving by [before it happens] is millions to 1. The probability of that one license plate driving by [after it actually happened and after someone circled the bullseye and arbitrarily declared]... God will[ed] it, is 100%.

[Doctor CamNC4Me]

In response to Dave6 pointing out the good faith offers presented here Dr. Rasmussen states:

Kyler Ray Rasmussen > Daved6

I'm not sure why people feel the need to throw money around to get my attention. Whether anybody wants to donate to the Interpreter is their business, but a polite invitation will suffice. I'm reachable at bayesianbom-at-gmail.com.

I don’t want to donate to the Interpreter, but if anyone would like to extend him an invitation to participate here, where professional collaboration is being offered gratis, my offer to send him a thousand dollars or donate it to a charity of his choosing, if he meets the terms of my offer, still stands.

- Doc

[Dr Moore]

I tried the polite invitation.

It goes like this.

Legitimate critique …. “here’s why I’m right anyway, and you would agree if you were critiquing in good faith.”

[kyzabee]

*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.

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). Ultimately it's a very similar overall result when the two probabilities are compared. Either way, my analysis would correctly identify that this represents very weak evidence (with an evidence score of 0).

But lets pretend for a moment that we're comparing Billy's estimate of obtaining that piece of evidence under a given theory (1 in a billion or so), and my estimate (.43). Why did my analysis say the probability was high and Billy's say it was low? Because his particular method didn't account for sampling error, and mine did. My estimates were better, in that they took sample size into account. And therein lies the beauty of Bayesian analysis. It allowed Billy to clearly present and analyze his evidence and draw his conclusions, and it allow me to understand exactly what he did and then come along and do it better.

Because that's ultimately what I'm trying to do here, and where I think the strength of the approach lies: I'm trying to think through the problem of Book of Mormon authenticity as clearly as I can, taking into account as much evidence as possible, working as hard as I can to account for my own biases, and to make it as easy as possible for my inevitable errors to be corrected.

Billy even did that last bit for me on my first post. I said that the Book of Mormon was an outlier when compared to other 19th century fictional works, and though he largely agreed with that conclusion, he had two valid points to make: 1) that a better hypothesis was that Joseph was trying to write something similar to the Bible, and 2) that a normal distribution might not be the best distribution to use when calculating the probability of observing the Book of Mormon's page count. Though I didn't think either change would ultimately alter the outcome much, and told him why I thought so, we both immediately knew what we would need to do to resolve the dispute and potentially improve the estimate: collect more data on books "similar to the Bible", and test out some alternate distributions to see if they might be a better fit for the data.

What my post did in that case was act as a sounding rod. I know with my limited time and resources and intelligence that I can't perfectly understand how strong pieces of evidence are. But with what I do have I can make a somewhat educated guess. I can then test that guess with other smart people, including those who disagree with me. From there, I know what direction I can go to make that estimate better.

While I'm here, I can defend my specific estimates if you want me to, but I know those are going to be wrong to some extent or another. What I'm really here to defend is the utility of the Bayesian approach as a method for clear thinking. And as someone who has experienced faith crises and who has family on both sides of the fence, I was in sore need of clear thinking for a long time. After two years of trying out this approach, I can attest two things: 1) my working knowledge of both the critical and faithful scholarship has increased several times over, and 2) thinking clearly about that evidence has led me to approach the question of authenticity with a great deal more humility than it did previously. You'll see me conclude at the end of this not that the Book of Mormon must be authentic, but only that my read of the evidence gives me reason for hope.

I'll eventually comment further on Billy's thoughts, because I'm not quite sure he's quite captured the methodological details accurately, but I think I'll stop there for the moment. Can we agree in principle that the thing I'm trying to do is reasonable and potentially useful?

[Gadianton]

Kyler,

Dan Peterson forbids his commenters from posting here, so it took guts for you to register. Welcome to the forum.

[kyzabee]

"Dan Peterson forbids his commenters from posting here"

I've received no such injunction, and he even encouraged me a bit to engage with Dr. Moore. I'll be aligning with his wish to not link to this forum, though.

Also, thanks Gadianton! Glad to be here. I just hope to avoid the phallic representations of Joseph I ran into last time I peeked in.

[Philo Sofee]

kyzabee
Because that's ultimately what I'm trying to do here, and where I think the strength of the approach lies: I'm trying to think through the problem of Book of Mormon authenticity as clearly as I can, taking into account as much evidence as possible, working as hard as I can to account for my own biases, and to make it as easy as possible for my inevitable errors to be corrected.

Excellent, and welcome! We look forward to analyzing things with you. In the above case, quit worrying about Joseph Smith. Get onto the evidences and all the background knowledge of the Book of Mormon. And you can't ignore the former attempts of apologists to present authenticating evidences which have now been refuted either.

That is part of the background we now understand.
From my view as well, you cannot ignore that you honestly have no first ground for even supposing Nephites and Lamanites ever existed, since there literally are no artifacts of them which world scholars, archaeologists, historians agree that they were a real, living people. You have no choice but to also acknowledge Bill Hamblin's debate with Philip Jenkins and how Jenkins brought that out and Hamblin could not overcome the obvious fact. That also is now part of the background of the Book of Mormon which must be taken into account.
We also have the background knowledge that all the various geographical theories actually weakens the overall probability since they all share and compete with the probability space in the claim of the Book of Mormon being authentic in an actual geographical setting. So none of the various theories can be as high as the single contrasting theory that Joseph Smith himself invented it. The evidence for its reality in an actual geographical setting is going to have to be seriously strong in order to help it compete with the contrasting theory of Joseph Smith inventing it.
The DNA is gonna be a lulu as well since that too is also part of our background knowledge which must be acknowledged and calculated, as well a the various General Authorities teachings of who the Lamanites were, where they originated, etc. Also don't forget the Jaredites as supposed Olmecs! That too is part of our background knowledge which cannot be ignored. And also the background knowledge that no actual historians or archaeologists have agreed with Mormon scholars, and why they haven't. The LDS evidence does not appear to be all that solid to the world, and this also is part of our overall background knowledge which cannot be ignored, but must be thrown into the hopper of calculating the probabilities.
There is so much more, but this gives you a flavor of the idea of putting the two theories into a ratio.
Looking forward to the discussion of evidences and background knowledge and theories!

[Philo Sofee]

"Dan Peterson forbids his commenters from posting here"

I've received no such injunction, and he even encouraged me a bit to engage with Dr. Moore. I'll be aligning with his wish to not link to this forum, though.

Also, thanks Gadianton! Glad to be here. I just hope to avoid the phallic representations of Joseph I ran into last time I peeked in.

Just ignore those. We really do want to see how you arrive at your probabilities and how you use Bayes Theorem. I think you are in a very tall, difficult order myself. But if the evidences are strong enough and realistic enough it can be changed. This is exciting to see if you can show Bayes helps the Book of Mormon.
23 posts, I fear, are not even going to scratch the surface, but we shall see.