Interpretering Bayesian Analysis

[kyzabee]

Would you be kind enough to scratch out the math, think ‘back of the napkin’, so we can get a better idea at how you arrived to -3? Also, what specific population are you pulling the autosomal data set from?

- Doc

Sure.

CH = Consequent Probability of the Hypothesis (our estimate of the probability of observing a lack of DNA evidence for the Book of Mormon, given an authentic Book of Mormon)

CH = Probability of observing no autosomal DNA evidence X Probability of observing no sex-linked DNA evidence

CH = .06 x .02 = .0012

CA = Consequent Probability of the Alternate Hypothesis (how likely it is that we would end up with no DNA evidence of a 6th century BC Middle-Eastern incursion if Lehi didn’t exist, which for our purposes is p = 1.)


Evidence Score = log10(CH/CA)

Evidence Score = log10(.0012/1)

Evidence Score = log10(.0012)

Evidence Score = -3 (rounded)

Here's the link to the study used by Southerton:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4209567/

[Philo Sofee]

I don't see your "work" here.

I was asked for the quick and dirty, so that's what I put together. Guess you'll just have to read the whole thing on Wednesday!

We just want to see how you are arriving at your numbers. There is no quick and dirty here, just demonstration of your use of Bayes. I am looking forward to seeing what you have. Please give us a link so we can see it, and then lets all hop back here to analyze it. Because as we work through things, Peterson over there probably will want to control things more and here we are far more free and easy to work through things in disagreement and agreement, analysis and learning. THANKS MAN!

[kyzabee]

I was asked for the quick and dirty, so that's what I put together. Guess you'll just have to read the whole thing on Wednesday!

We just want to see how you are arriving at your numbers. There is no quick and dirty here, just demonstration of your use of Bayes. I am looking forward to seeing what you have. Please give us a link so we can see it, and then lets all hop back here to analyze it. Because as we work through things, Peterson over there probably will want to control things more and here we are far more free and easy to work through things in disagreement and agreement, analysis and learning. THANKS MAN!

From the study cited above:

"Power to detect admixture (p<0.01) when present was 94%"

This corresponds to a likelihood of missing a real migration at 1 - .94 or .06, which is where the .06 comes from. The .02 comes from the strongest of the Bayes factors employed by the Dales, as indicated above.

The reason I didn't try to combine information from the other authors you listed is because this study had hard data to point to and they didn't.

[Philo Sofee]

Kyzabee
I treat Mesoamerica as the best current fit for the data, being agnostic to the various Mesoamerican models.

I do hope you understand that you must treat ALL geographical models with the same rigor, not just one. The background is an analysis of ALL geographical models, not just one of them. The ratio is going to be between various different geographical models. You need to compare and see the strengths and weaknesses based on the evidences of every model out there on where the Book of Mormon might have occurred. Once you get the probability of Mesoamerican model, then you need to do the same with another one and put those two into ratio (showing your evidences, your probabilities of each one, etc.) and see which one is the more probable and why, and then compare the next model with the same treatment.
We also are interested in seeing your overall probability on the background of what the probability is that there are so many differing geography models given the putative revelatory nature of the Book of Mormon itself. How likely is it that no real geography even exists given the claims of the Book of Mormon? How probable is it that this is the state of affairs we actually see given the Book of Mormon is true? How probable is it if it is written by Joseph Smith instead? And what is the liklihood ratio between that as well?
Just treating one model is to barely begin the use of all that we know up to this date about the Book of Mormon. At least I hope I am misreading you that you are only using one model instead of gathering the data of all of them, their evidences - pros and cons - and the likelihood ratios between all of them for an overall probability assessment.
This is how I understand Bayes needs to be used. ALL evidences pro and con, and all background pro and con for every model, of which there are at least 5 that I am aware of. All of that is in our background knowledge up to today and has to be calculated. We are hoping you can show us not only the numbers, but what evidences and backgrounds you use to justify what numbers you have, i.e., why did you give one model a mere 60% probability compared to another one of 75% as an example off the top of my head. What makes one model a higher probability than another? Which factors of evidences persuades you compared to other evidences which didn't, and what research did you use to arrive at your conclusions? etc., etc. The only reason I am bringing this up is I have not seen any of this in any of your studies so far at all. I am not at all clear on HOW you are using Bayes, let alone whether, in fact, you even are. We need to see your reasons why something persuades you or leaves you cold in other words. All that work has to be shown. Part of the reason for using Bayes is to JUSTIFY your reasons. If you don't show your reasoning, Bayes isn't being effective for anyone. Does that make sense?
Looking forward to seeing your material.

[Billy Shears]

Hi Kyler,

Thank you for your willingness to engage these issues here.

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...

I would like to make a quick clarification on this point. I chose the is-the-coin-weighted problem to illustrate Bayesian reasoning for two reasons:

1- it illustrates Bayesian reasoning in a simple case
2- it includes the drama of dealing with small probabilities

From beginning to end, your series is about small probabilities. What small probabilities imply and how they should be interpreted is the issue.

In general, I think the distributions for quantifying the unlikeliness of the Book of Mormon that you've presented are a fresh and novel way of looking at the problem. But when such an analysis indicates that a naturalistic Book of Mormon is unlikely, I have to ask myself compared to what?

It seems to me you handled this issue appropriately in Episode 2. When evaluated in isolation, the pattern of inconsistencies in the first vision accounts are unlikely if the event really happened, but those same inconsistencies are also unlikely if the whole thing was made up. By appropriately estimating and comparing both of those things, we have a chance of looking at the unlikeness of past events without committing postdiction.

Illustrating the issue in another way, imagine somebody reading the paper backwards. If they first read the statistics you plugged into the formula, what would they infer your argument is?

On Episode 1 they might guess you are saying, “A statistically significant sample of books written in the 19th century English are 250 pages long, plus-or-minus 100 pages. A statistically significant sample of books written in 5th century reformed Egyptian are 850 pages long, plus-or-minus 25 pages. The page length is an outlier for a book written in the 19th century, but fits like a glove for a book written in the 5th century. How did Joseph know this? Amazing!”

On Episode 3 they might guess you are saying, “The probability of somebody dictating a fake book in 65 days is 0.00001, but the probability of translating an authentic book in that length of time is exactly 100%! How did Joseph know before hand that the process needed to take exactly 65 days? Amazing!”

[Philo Sofee]

We just want to see how you are arriving at your numbers. There is no quick and dirty here, just demonstration of your use of Bayes. I am looking forward to seeing what you have. Please give us a link so we can see it, and then lets all hop back here to analyze it. Because as we work through things, Peterson over there probably will want to control things more and here we are far more free and easy to work through things in disagreement and agreement, analysis and learning. THANKS MAN!

From the study cited above:

"Power to detect admixture (p<0.01) when present was 94%"

This corresponds to a likelihood of missing a real migration at 1 - .94 or .06, which is where the .06 comes from. The .02 comes from the strongest of the Bayes factors employed by the Dales, as indicated above.

The reason I didn't try to combine information from the other authors you listed is because this study had hard data to point to and they didn't.

OK, that's just one study however, and only from one author. Why use Southerton instead of say Perego? For a valid probability you need comparisons of many many more studies don't you? I am assuming you are attempting to arrive at a more accurate probability yes?

And there needn't be hard data to utilize Bayes Theorem from an epistemic view. We can calculate, based on our own views of evidences and how well various studies use the evidence and backgrounds to see whether we agree or disagree with them and to what extent. For instance, Southerton I find very valuable, indeed! But Perego I also find very valuable and he is at loggerheads with Southerton. What is it that is going to help me accept Perego more than Southerton? We can put that epistemic probability to numbers to show our degree of acceptance or disagreement with any authors on any subjects. We just have to show which evidences and backgrounds were are bringing in to illustrate why we either accept or reject some study on a subject. That is what I am asking.
Hard data, is, of course, always a great thing, but sometimes we don't have hard data, but we don't get to ignore the probabilities anyway. We have to figure out where we stand and why we stand there, ready to adjust, when new data arrives (and it always does).
If all you are going to do is one study and one model the Mesoamerican model for the Book of Mormon, you are going to need serious updating almost immediately, because no one single data point can establish probabilities. Does that make sense?
Anyway, I will quit buggin you so you can present your data and analysis.

[Gadianton]

Interestingly enough, the trajectory of evidence over time is a useful piece of evidence in itself, and I'll

This episode was supposed to be about conclusions, but the point of this has always been that there aren’t any—that there’s always room for further investigation, that conclusions are necessarily tentative, and that answers will never be final. The question we should ask ourselves now isn’t, “is the Book of Mormon authentic?” We could instead ask two other questions: “is there enough evidence for me to hope”, and “do I have enough hope to exercise faith”. be discussing it in Episode 15

You can assume prior odds of 10 ^ -40 that a coin is fair, and then flip the coin over and over and watch it crawl up (the trajectory), and keep fake drama going after thirteen flips that we still have a long way to go to win. If you were on the receiving end of that kind of demonstration and the topic was anything but something you have a life investment in, you'd smile and walk away, figuring you're being put on. That's one way Bayes can be used to prime the unsuspecting for a scam. If you were us, you'd be laughing also. A frequentist wouldn't start with the prior, and so beating insurmountable odds can't be part of the ruse, and in addition, you'd have to flip the coin until you have a proper distribution.

The analogy to the coin flip and what you and the Dales are doing, is in the fake, ridiculous prior, and watching the evidence slowly beat the fake odds. The dis-analogy is that while both go up impressively to the eye of the gullible, one will eventually end in a distribution, where we're uncertain about the other. I mean, if you take a proposition we all agree is false due to really low odds, but give a prior far lower than that, we could sit back and watch it win for a short time and declare victory.

Think about "there's always room for investigation" and "conclusions are always tentative" in the coin flip analogy. In terms of Hume's bare principle of induction, sure, but realistically, if you're coming away from your study with odds billions and trillions to one that the Book of Mormon in ancient, and still leaving open the serious possibility that evidence could overturn it, then statistics is useless, or you've done something wrong.

In your world, every piece of evidence produces astronomical odds one way or another. From what I understand, Carrier's project didn't have this kind of volatility. One day, I read about DNA evidence, and I'm assured 100,000: 1 that the Book of Mormon isn't ancient. I'm a hardened skeptic. The next day, I read about page length, and that exactly offsets yesterday's criticism. The following day, I read about the first vision, and now I'm 100,000: 1 in favor. And then, we're dealing in evidence presenting in orders of magnitude according to you, and so we can be quadrillions to one in favor of the Book of Mormon when the big earthquake comes, the '9', that wipes a lot or maybe all of it away.

This might be a profile of security for a Dogecoin trader, but few others.

[huckelberry]

It may be obvious enough that people have not bothered to remark but there is another important problem here. These either or choices block out or hide other possibilities that may be more likely,

1 Joseph may be the author but may be using a variety of sources for inspiration. He is clearly skilled at making paraphrases of scripture. He may be riffing off of other authors giving the appearance of multiple voices.

2The first vision could be a spiritual type experience Joseph had like many other people. He may have developed his ideas of what it meant and adjusted his memory as a result. With time an experience like other peoples became bigger, more authoritative, more concrete. It may be taken into consideration that Mr Finney, a contemporary evangelist preacher had Jesus appear to him also. Perhaps Jesus really did or perhaps that was Mr Finneys interpretation of his personal faith experience.

3 Automatic writing or fraudulent dictation? More likely it was the development and creation of stories Joseph thought were inspired. Or perhaps there were stories that he thought were exciting and caused him to feel inspired. In either case you have story creation by the natural means of imagination that is employed by countless numbers of story tellers.

Sounds like you may not have read the essays. I'd suggest giving them a try.

kyzbee, this is a rather thin reply. I have read some stuff about these questions. What essays are you referring to? What am I missing?

[kyzabee]

And there needn't be hard data to utilize Bayes Theorem from an epistemic view.

But if there is hard data, we should probably prefer it to epistemic theorizing.

[kyzabee]

Sounds like you may not have read the essays. I'd suggest giving them a try.

kyzbee, this is a rather thin reply. I have read some stuff about these questions. What essays are you referring to? What am I missing?

The point of the thread, I'm pretty sure:

https://interpreterfoundation.org/estim ... vidence-0/