Interpretering Bayesian Analysis

[Dr Moore]

Also, to level set, here's the order of magnitude of confidence we have in quantum mechanics. It is widely cited as the most accurate model of reality that has been created by man:

Quantum physics is probably the most precise scientific discipline ever devised by humankind. It can predict certain properties with extreme accuracy, to 10 decimal places, which later experiments confirm exactly.

https://phys.org/news/2019-04-common-my ... ysics.html

Somehow, you will prove that the Book of Mormon is at least 30 orders of magnitude more likely to be true than our theories of quantum mechanics. Can you begin to see how ridiculous this all is?

Anything is possible if you count all of the “sixes” you can find, giving them 1 in 100 odds, and ignore most of the “ones through fives.”

[kyzabee]

Also, to level set, here's the order of magnitude of confidence we have in quantum mechanics. It is widely cited as the most accurate model of reality that has been created by man:

Quantum physics is probably the most precise scientific discipline ever devised by humankind. It can predict certain properties with extreme accuracy, to 10 decimal places, which later experiments confirm exactly.

https://phys.org/news/2019-04-common-my ... ysics.html

Somehow, you will prove that the Book of Mormon is at least 30 orders of magnitude more likely to be true than our theories of quantum mechanics. Can you begin to see how ridiculous this all is?

There's a difference between the precision of certain predictions (which is really a limitation of the instruments we use for physics measurement), and estimating the likelihood of given events.

But I'll set that difference aside for the moment, and suggest to you that the truth of quantum mechanics wasn't established by a single experiment where the probability of error was on the scale of 10 orders of magnitude. It was established by dozens of such experiments by independent laboratories. The probability that those all of those experiments were flukes has gone way beyond 10^-10, and is likely in the 10^-1000 range, if not more.

But even with that amount of certainty involved, all it would take is a single observation (measured with certainty by independent researchers) that quantum mechanics can't explain in order to send physics theorists back to the drawing board. The same is true here. It doesn't really matter that I end up with greater than 40 orders of magnitude pointing toward authenticity. A solid enough piece of evidence against it could arrive tomorrow and overturn my result completely.

I got the estimate that I did because I saw a number of items that were extremely unexpected under the assumption that the book was a modern fraud, and I didn't see enough on the other side to effectively counter it. That's all that number means. It doesn't mean that I think I only have a 1 in 10^40 chance of being wrong about the Book of Mormon. The odds that I'm wrong outweigh my 1 in 10^40 estimate. The odds that I'm hallucinating you right now probably outweight it. But that's how I weigh the current state of the evidence. When the evidence changes, and the arguments change, I intend that my beliefs will change with them.

[Doctor CamNC4Me]

Well, yes. To break this down in the simplest manner I can, I don’t see why you can’t identify a ‘hit’ off the top of your head, and then simply reproduce the analysis in a post. At that point you and the folks here can discuss each step and its reasoning with regard to your finding. For example:

1. ‘Cat’ is a hit for the Book of Mormon.

2. Here’s my reasoning.

3. Here’s the math. x+y+z = cat is a hit

4. Discuss x, y, z, reasoning, and result

- Doc

We can do that for the DNA analysis right now, as it ended up being relatively simple on the math side.

The lack of Lehite DNA represents evidence against an authentic Book of Mormon with an evidence score of -3 (decreasing the probability of an authentic Book of Mormon by 3 orders of magnitude).

In terms of how likely we would be to observe that lack of DNA if the book was a fraud, I used p = 1. I have a line that if the book were fraudulent, we'd be as likely to expect Lehite DNA in the Americas as Hobbit DNA in Wales.

In terms of how likely we'd be to observe the lack of DNA if the book were authentic, I split it up into separate estimates for Autosomal and Sex-Linked DNA, which I treated as independent.

For autosomal DNA, I took a look at a study used by Simon Southerton tracking historical migrations worldwide. The simulation data for that study found that 6% of real migrations would've been missed. Despite Lehi's genetic contribution likely having a much smaller proportion of DNA than average, and was at a greater time depth than average (both of which would've made it easier to miss), I used p = .06 as the estimate for the likelihood of not observing Lehi's DNA if his migration was real.

In terms of sex-linked DNA, as faithful, critical, and neutral scholars all seemed to agree that the sex-linked DNA could've been lost to time due to genetic drift and population bottlenecks, and as there are quite a few examples of this occurring in real life, it didn't seem appropriate to use an astronomically low estimate. I made an attempt at modeling it myself using python, and learned some interesting things, but none of my attempts appeared to give me anything realistic. I ended up assigning the lowest Bayes factor as used by the Dales (and secular scholars), which was p = .02 (note that the Dales' own analysis gave DNA as a whole a p = .5).

Doing the math, you can multiply .06 by .02 to make p = .0012, which, when taking the log10 of that value (after dividing by our probability value for the hypothesis of fraud of 1), gives us an evidence score of -3.

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

[Philo Sofee]

Well, yes. To break this down in the simplest manner I can, I don’t see why you can’t identify a ‘hit’ off the top of your head, and then simply reproduce the analysis in a post. At that point you and the folks here can discuss each step and its reasoning with regard to your finding. For example:

1. ‘Cat’ is a hit for the Book of Mormon.

2. Here’s my reasoning.

3. Here’s the math. x+y+z = cat is a hit

4. Discuss x, y, z, reasoning, and result

- Doc

We can do that for the DNA analysis right now, as it ended up being relatively simple on the math side.

The lack of Lehite DNA represents evidence against an authentic Book of Mormon with an evidence score of -3 (decreasing the probability of an authentic Book of Mormon by 3 orders of magnitude).

In terms of how likely we would be to observe that lack of DNA if the book was a fraud, I used p = 1. I have a line that if the book were fraudulent, we'd be as likely to expect Lehite DNA in the Americas as Hobbit DNA in Wales.

In terms of how likely we'd be to observe the lack of DNA if the book were authentic, I split it up into separate estimates for Autosomal and Sex-Linked DNA, which I treated as independent.

For autosomal DNA, I took a look at a study used by Simon Southerton tracking historical migrations worldwide. The simulation data for that study found that 6% of real migrations would've been missed. Despite Lehi's genetic contribution likely having a much smaller proportion of DNA than average, and was at a greater time depth than average (both of which would've made it easier to miss), I used p = .06 as the estimate for the likelihood of not observing Lehi's DNA if his migration was real.

In terms of sex-linked DNA, as faithful, critical, and neutral scholars all seemed to agree that the sex-linked DNA could've been lost to time due to genetic drift and population bottlenecks, and as there are quite a few examples of this occurring in real life, it didn't seem appropriate to use an astronomically low estimate. I made an attempt at modeling it myself using python, and learned some interesting things, but none of my attempts appeared to give me anything realistic. I ended up assigning the lowest Bayes factor as used by the Dales (and secular scholars), which was p = .02 (note that the Dales' own analysis gave DNA as a whole a p = .5).

Doing the math, you can multiply .06 by .02 to make p = .0012, which, when taking the log10 of that value (after dividing by our probability value for the hypothesis of fraud of 1), gives us an evidence score of -3.

I don't see your "work" here. Tell us how and why you get the numbers you do, and what they are based on... why no comparison of Southerton's materials to what FAIR has posted? or anything from FARMS? We need to see HOW you arrive at the numbers, not just giving us the numbers. I'm not at all clear how you are even trying to use Bayes here. I see no comparisons at all. No sources and what you think their numbers are in comparison to the ones you have here. We need to see the actual path you trod to get to here. Did you look at Ugo Perego's materials, and if so, what numbers have you arrived in relation to other work on DNA and the Lamanites? Anything of Tom Murphy? Scott Woodward? David G. Stewart, Jr.? Daniel C. Peterson? Matt Roper? Brent Metcalfe? Dan Vogel? Rod Meldrum? John Butler? Brant Gardner? What numbers of his led you to compare to Southerton in order to arrive here where you are at? Any of the other scholars who are non-Mormon who have had a say in this?

[huckelberry]

What Kyler Is Doing: Problem 1
The first fundamental problem is that on every episode, he changes his hypothesis to suite the evidence he is looking for. On the first one, the hypotheses were:

H0: Joseph Smith was author
H1: Ancient collection of authors

On the second episode:

H0: The first vision story was fraudulent
H1: The first vision story is based on an actual event

On the third:

H0: The Book of Mormon was either automatic writing or fraudulent dictation
H1: The Book of Mormon dictation was created by “authentic dictation”

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.

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.

[huckelberry]

"1) How much of the negative evidence do you intend to treat?"

All the major classes of evidence that I could think of I tried to work into the analysis, generally focusing on those that seemed to have gained traction in the internet age. I'm bound to have missed a bunch (Treasure Digging didn't make the list, for instance, as I realized when Billy brought it up this week, though that probabiy isn't independent with my analysis on prophetic imperfections), and I'm happy to take feedback on missing ones you feel would have some weight to them. Here's the full list of negative posts, in case you're curious:

2 - First Vision
4 - DNA
6 - Political Incorrectness
8 - Transoceanic Voyages
10 - King James Plagiarism/Errors
12 - Late War/View of the Hebrews Plagiarism
14 - Archaeological Anachronisms (collated a bunch of anachronisms here)
16 - Thematic Anachronisms (also another collation)
18 - Prophetic Imperfections
20 - Place-Name Plagiarism (i.e. Holley's map)
22 - Book of Abraham (collation)

It'll be interesting to see how people here feel about my treatment of the negative evidence. The goal was to try to treat it in a fairer and more complete fashion than critical treatments generally have for the positive evidence.
..........

how about,
1 Where are all of the native Americans in the book? North central and south America were all populated by many people long before the Book of Mormon time.
2 How come there is no trouble establishing political unity and independence with all those other people around?
3 Possession of steel and horses would be a great help in achieving survival as a group with all those other people. How could such critical items get lost?
4 and of course dna.
5 Where is the location? check out Shulems thread on where that book is really located.
6 the book is packed with 19th century Protestant revivalist themes and ideas.
7 The general point of view is from a 19th century American view, America's role , the role of natives. themes made common by things like view of the Hebrews. There is no plagiarism here, that idea is merely a distraction. It is a matter of what place in time is the narrative created from.

some of the main points that I see.

[Philo Sofee]

Good points Huckleberry. Now lest Kyzaboo feels pressured, I am hoping all of this is in the hopper already as it ought to be in order to give an accurate probability, which is why I have already noted to Kyzabee this is an ongoing discussion bound to take some time because I want to see how his probabilities of each thing (evidence, background theme) is utilized and what it is compared to, and how, and which item either raises or lowers the numbers as the comparisons continue until he has arrived at something rational. I hope to see how he sees each of the only few authors I mentioned and what their works and research did to either lower or raise the probabilities as he works through them and what it is about each of their work which he believes or disbelieves and shows us the strength of his beliefs and disbeliefs with numbers.

After all, that is the entire point. Show how each item raises or lowers the probability on the various hypotheses. So far, I grasp two of them in ratio. Joseph Smith received the Book of Mormon from God vs. Joseph Smith wrote it himself under his environmental influences.

[kyzabee]

What Kyler Is Doing: Problem 1
The first fundamental problem is that on every episode, he changes his hypothesis to suite the evidence he is looking for. On the first one, the hypotheses were:

H0: Joseph Smith was author
H1: Ancient collection of authors

On the second episode:

H0: The first vision story was fraudulent
H1: The first vision story is based on an actual event

On the third:

H0: The Book of Mormon was either automatic writing or fraudulent dictation
H1: The Book of Mormon dictation was created by “authentic dictation”

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.

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.

[kyzabee]

"1) How much of the negative evidence do you intend to treat?"

All the major classes of evidence that I could think of I tried to work into the analysis, generally focusing on those that seemed to have gained traction in the internet age. I'm bound to have missed a bunch (Treasure Digging didn't make the list, for instance, as I realized when Billy brought it up this week, though that probabiy isn't independent with my analysis on prophetic imperfections), and I'm happy to take feedback on missing ones you feel would have some weight to them. Here's the full list of negative posts, in case you're curious:

2 - First Vision
4 - DNA
6 - Political Incorrectness
8 - Transoceanic Voyages
10 - King James Plagiarism/Errors
12 - Late War/View of the Hebrews Plagiarism
14 - Archaeological Anachronisms (collated a bunch of anachronisms here)
16 - Thematic Anachronisms (also another collation)
18 - Prophetic Imperfections
20 - Place-Name Plagiarism (i.e. Holley's map)
22 - Book of Abraham (collation)

It'll be interesting to see how people here feel about my treatment of the negative evidence. The goal was to try to treat it in a fairer and more complete fashion than critical treatments generally have for the positive evidence.
..........

how about,
1 Where are all of the native Americans in the book? North central and south America were all populated by many people long before the Book of Mormon time.
2 How come there is no trouble establishing political unity and independence with all those other people around?
3 Possession of steel and horses would be a great help in achieving survival as a group with all those other people. How could such critical items get lost?
4 and of course dna.
5 Where is the location? check out Shulems thread on where that book is really located.
6 the book is packed with 19th century Protestant revivalist themes and ideas.
7 The general point of view is from a 19th century American view, America's role , the role of natives. themes made common by things like view of the Hebrews. There is no plagiarism here, that idea is merely a distraction. It is a matter of what place in time is the narrative created from.

some of the main points that I see.

1 From what I understand there's quite a bit of implied evidence for others in the book, from the change in skin color to the incursion of foreign cultures, to various statements of lineage being direct from Lehi (which wouldn't be necessary if everyone was).
2 There's plenty of evidence of that later on, and Nephi would've had good reason to downplay that in a narrative designed to establish his own political legitimacy.
3 This is incorporated into Episode 14.
4 See Episode 4.
5 There's several items pertinent to geography, including Episode 14, 15, and 17. I treat Mesoamerica as the best current fit for the data, being agnostic to the various Mesoamerican models.
6 This is incorporated into Episode 16.
7 Glad you agree there's no plagiarism, but you might be interested in Episode 12 anyway.

[kyzabee]

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!