The Interpreter; Bayes Theorem; Nephites and Mayans

[_Gadianton]

In other words the likelihood ratios for false statements in the Book of Mormon have a denominator close to zero, and to limit the corresponding ratios to 2, 10, and 50 is arbitrary and does not reflect their own set-up.

So bottom line, to use 3 ratios for support of the historical Book of Mormon and then simply assign the inverse of those ratios for non-historical Book of Mormon is WRONG. It assumes the denominators of both ratios are free to range from 0 to 1 and they are not.

This feels like familiar territory, and I'm trying to pin down what the new information is. I think maybe 1) the more rigorous way you now show that denominator must be zero (or close) on misses, and 2) while the denominators on hits are valid (even if (i think) meaningless), the picks of numerators could still end up with 2, 10, and 50; but not so with the misses, which are incoherent, instead, they just assumed an inverse of the ratio for hits, for misses.

What's the chance that the Dales started out just trying to refute Coe's statement (that the societies portrayed in the Book of Mormon are nothing like Mayan society), and then got carried away into making a Bayesian claim that the Book of Mormon is almost certainly true?

A few posts ago I essentially agreed with that. They were mad that Coe produced anti-mormon materials, and said, hey, let's go look at this neutral book "the maya" and see what he should have found in favor. Supposing they find hits, now there must be a way to compare the significance between the hits and misses, as normally apologists would just argue against the misses and say they aren't misses. They want to beat him at his own game. I can only speculate they really wanted Coe to be wrong in an embarrassing way, by showing if he'd been fair with his own model, then he'd have overwhelmingly concluded the Book of Mormon was true. But they, in my opinion, really created a lower bound for the lunacy of the Book of Mormon as objectively true, because they clearly believe a better book on Maya, either fewer mistakes or informed from future discoveries, would not contain the misses. So if we were to actually use their real confidence levels without giving all the benefits of the doubt, the 10 ^ 132 should be significantly higher.

[_Res Ipsa]

Just another problem: time. The Dales ignore the fact that the Mayan civilization changed over time, as did the civilizations in the Book of Mormon. The count any correspondence as a hit, regardless of time. So, for example, if Nephi asserts a fact shortly after the folks arrive in the world, the Dales will count a similar observation in The Maya as a hit, even if it occurred hundreds of years later. They make a stab at justifying this method in the paper, but their reasoning doesn’t hold water. For a hypothetical example: if the Book of Mormon stated that the Nephites had a certain technology 500 years before the Mayans developed it, that should be counted as a miss. The Dales would count it as a hit.

[_Lemmie]

In other words the likelihood ratios for false statements in the Book of Mormon have a denominator close to zero, and to limit the corresponding ratios to 2, 10, and 50 is arbitrary and does not reflect their own set-up.

So bottom line, to use 3 ratios for support of the historical Book of Mormon and then simply assign the inverse of those ratios for non-historical Book of Mormon is WRONG. It assumes the denominators of both ratios are free to range from 0 to 1 and they are not.

This feels like familiar territory, and I'm trying to pin down what the new information is. I think maybe 1) the more rigorous way you now show that denominator must be zero (or close) on misses, and 2) while the denominators on hits are valid (even if (i think) meaningless), the picks of numerators could still end up with 2, 10, and 50; but not so with the misses, which are incoherent, instead, they just assumed an inverse of the ratio for hits, for misses.

You are correct, i have referred to parts of it, but there is one piece of technical information I hesitated to add.

You had the sense something should sum to one, and you are correct, but it is not the top and bottom of a single likelihood ratio. It is the total statements B true and B not true under a given hypothesis, so that is the two denominators of the two different LR ratio set-ups (based on considering the 2x2 matrix that medical diagnostic tests used to determine LRs for false positives and false negatives).

In other words, it is equivalent to the denominator of the LR that supports Book of Mormon historical (LR < 1) and the denominator of the LR that supports Book of Mormon fictional (LR > 1) that must sum to one.

P(B true | Book of Mormon not fiction) + P(B not true | Book of Mormon not fiction) = 1

If the first term = almost 1, which the Dales defined as such, the second term MUST = almost 0, and therefore the smallest LR in support of fictional Book of Mormon MUST be a number approaching infinity ( because dividing by a number approaching zero), therefore, a single positive Llikelihood ratio is enough to overcome ALL 131 LRs less than one.

Sorry, it is so technical, I'll try to demonstrate better in a future post. That's why it is so irritating to see the Dale's mis-use the math, they really don't know what they are doing. AT ALL. I cut them some slack before, but now they have asserted that the denominator allows for both hypotheses, AND they confirmed they are using the medical diagnosis format, therefore they have to conform to the theoretical constraints of the math.

But your instincts are correct that some probabilities must add to 1. Just not the top and bottom of the likelihood ratio.

[_DrW]

You are correct, i have referred to parts of it, but there is one piece of technical information I hesitated to add.

You had the sense something should sum to one, and you are correct, but it is not the top and bottom of a single likelihood ratio. It is the total statements B true and B not true under a given hypothesis, so that is the two denominators of the two different LR ratio set-ups (based on considering the 2x2 matrix that medical diagnostic tests used to determine LRs for false positives and false negatives).

In other words, it is equivalent to the denominator of the LR that supports Book of Mormon historical (LR < 1) and the denominator of the LR that supports Book of Mormon fictional (LR > 1) that must sum to one.

P(B true | Book of Mormon not fiction) + P(B not true | Book of Mormon not fiction) = 1

If the first term = almost 1, which the Dales defined as such, the second term MUST = almost 0, and therefore the smallest LR in support of fictional Book of Mormon MUST be a number approaching infinity ( because dividing by a number approaching zero), therefore, a single positive Llikelihood ratio is enough to overcome ALL 131 LRs less than one.

Sorry, it is so technical, I'll try to demonstrate better in a future post. That's why it is so irritating to see the Dale's mis-use the math, they really don't know what they are doing. AT ALL. I cut them some slack before, but now they have asserted that the denominator allows for both hypotheses, AND they confirmed they are using the medical diagnosis format, therefore they have to conform to the theoretical constraints of the math.

But your instincts are correct that some probabilities must add to 1. Just not the top and bottom of the likelihood ratio.

Hey Lemmie,

At some point, perhaps you could write and post a little online test covering Bayesian inference so folks who have diligently studied the posts on this thread would have an opportunity for some "continuing education credits". (No need to worry about open book - if one doesn't have this stuff down cold, no normal colleague or book I have seen is going to help much.)

You could challenge DCP to post the test on the Interpreter website, or over at SeN, so the Dales and interested faithful readers over there could take it.

To make it interesting, you could suggest that the Dales either "Pass the Test or Pull the Paper".

Just a thought in case you might be interested.

[_Gadianton]

You had the sense something should sum to one, and you are correct, but it is not the top and bottom of a single likelihood ratio.

Yeah, I resigned on that. BUT, just to be clear, none of the medical examples I came up with and posted summed to 1 and they all made perfect sense to me, my sense was that the weird assumption using coe book true as filter linked the top and bottom in a way they normally wouldn't be linked, but I came to believe that was not only wrong, but not possible.

It is the total statements B true and B not true under a given hypothesis, so that is the two denominators of the two different LR ratio set-ups (based on considering the 2x2 matrix that medical diagnostic tests used to determine LRs for false positives and false negatives).

Good to know and makes sense.

In other words, it is equivalent to the denominator of the LR that supports Book of Mormon historical (LR < 1) and the denominator of the LR that supports Book of Mormon fictional (LR > 1) that must sum to one.

P(B true | Book of Mormon not fiction) + P(B not true | Book of Mormon not fiction) = 1

If the first term = almost 1, which the Dales defined as such, the second term MUST = almost 0, and therefore the smallest LR in support of fictional Book of Mormon MUST be a number approaching infinity ( because dividing by a number approaching zero), therefore, a single positive Llikelihood ratio is enough to overcome ALL 131 LRs less than one.

Sorry, it is so technical, I'll try to demonstrate better in a future post.

Actually, of all your technical posts this is the clearest one. Maybe we're getting used to the ideas, but I think this is the starting point, as I remember stats, you start up by dividing up the probability space. Without that clear model, understanding how pieces interrelate is difficult. start with a venn diagram etc.. and go from there.

But your instincts are correct that some probabilities must add to 1. Just not the top and bottom of the likelihood ratio.

Thanks but unfortunately, just to be fair, my instincts were actually incorrect, lol, since the 'add to one' idea i was on about, was due to thinking a weird constraint erroneously made that the case. It may count in the apologist universe where we can count false positives but I prefer the real world.

This particular post tells me exactly what I need to google so very good explanation. a second thing you've made clear in this post that was never clear to me was that we can actually state the dale model as a medical example, even if it's a totally odd-ball case. when sometimes you, but usually analytics, physics guy, and the Dog have explained how we can think about the Book of Mormon in baysian terms, it's pretty clear, if I think we're just talking about it as it should be, and not when adding the weird constraint of filtering everything through the "facts of coe's book", adding in that curve ball turns something difficult but tractable into a brain teaser.

[_Lemmie]

Actually, of all your technical posts this is the clearest one.

I'm glad to hear you feel I am improving.

[_Lemmie]

You are correct, i have referred to parts of it, but there is one piece of technical information I hesitated to add.

You had the sense something should sum to one, and you are correct, but it is not the top and bottom of a single likelihood ratio. It is the total statements B true and B not true under a given hypothesis, so that is the two denominators of the two different LR ratio set-ups (based on considering the 2x2 matrix that medical diagnostic tests used to determine LRs for false positives and false negatives).

In other words, it is equivalent to the denominator of the LR that supports Book of Mormon historical (LR < 1) and the denominator of the LR that supports Book of Mormon fictional (LR > 1) that must sum to one.

P(B true | Book of Mormon not fiction) + P(B not true | Book of Mormon not fiction) = 1

If the first term = almost 1, which the Dales defined as such, the second term MUST = almost 0, and therefore the smallest LR in support of fictional Book of Mormon MUST be a number approaching infinity ( because dividing by a number approaching zero), therefore, a single positive Llikelihood ratio is enough to overcome ALL 131 LRs less than one.

Sorry, it is so technical, I'll try to demonstrate better in a future post. That's why it is so irritating to see the Dale's mis-use the math, they really don't know what they are doing. AT ALL. I cut them some slack before, but now they have asserted that the denominator allows for both hypotheses, AND they confirmed they are using the medical diagnosis format, therefore they have to conform to the theoretical constraints of the math.

But your instincts are correct that some probabilities must add to 1. Just not the top and bottom of the likelihood ratio.

Hey Lemmie,

At some point, perhaps you could write and post a little online test covering Bayesian inference so folks who have diligently studied the posts on this thread would have an opportunity for some "continuing education credits". (No need to worry about open book - if one doesn't have this stuff down cold, no normal colleague or book I have seen is going to help much.)

You could challenge DCP to post the test on the Interpreter website, or over at SeN, so the Dales and interested faithful readers over there could take it.

To make it interesting, you could suggest that the Dales either "Pass the Test or Pull the Paper".

Just a thought in case you might be interested.

Thank you, DrW, I do like teaching math, but the stories of mopologists going after people in real life just horrifies me, so I doubt I will do much beyond chatting here with my friends.

I do like your title of "pass the test or pull the paper," as I am really getting the sense that the authors are using surface manipulations of interesting techniques, all the while having no understanding of the underlying theory.

[_Physics Guy]

Maybe the world could use a better primer on Bayesian inference. It looks to me as though it would be hard to learn about Bayesian inference for the first time from the Wikipedia article on the topic, because the article plunges into technical details pretty quickly without much explanation of what the terms actually mean.

Perhaps the problem is that there are too many enthusiasts about Bayes who are actually a bit confused about it, and they're all allowed to edit Wikipedia. So if anyone writes a clear and simple explanation of some point, some confused enthusiast will think it's wrong and change it. For a passage to survive, it has to be obscure enough to intimidate all the confused enthusiasts.

[_Philo Sofee]

The interesting thing is, every tie I explained Bayes Theorem to people from RIchard Carrier's book Proving History, people were saying even he didn't know what he was talking about. His book on Jesus, one of the most fascinating I have ever read, whether you agree with it or not, it is utterly incredible to read, the use of Bayes in it has also been said to be just outright wrong. Soooooo, I literally do not know whether Bayes has ever been used correctly or not. And anyone who writes about it will be told the same thing, they are doing it wrong. I wonder if anyone actually knows the right way to apply Bayes to any other subject than medical.

[_Physics Guy]

My feeling is that Bayes's theorem is hard to use correctly because it's so simple. It's a one-line theorem that uses nothing but obvious logic. So to me what that means is that it's perfectly correct as far as it goes, but it really doesn't go very far because you're still stuck with having to supply good logical reasoning and that's still hard to do.

People who get really excited about Bayes's theorem are usually excited about having a mathematical magic power that will somehow deliver rigorous conclusions without their having to make solid arguments. But spinning straw into gold is for Rumpelstiltskin, not Bayes. Bayes is a very simple machine that won't do anything to make bad arguments better. It can be an excellent way to present good arguments clearly, but the work of constructing the good arguments in the first place still has to be done and Bayes won't help you with that.

The dark side of Bayesianism is that it gives innumerate people a delusion of rigor. They've done math! They've used numbers! So their lousy arguments have to be right!

The people who actually understand how Bayesian inference works often don't even need it. When the data are really inconclusive it doesn't matter very much what formalism you use in which to say that. Ditto when the data are conclusive. Sometimes there can be data that aren't obviously conclusive but if you look closely they're more strongly suggestive than one might at first think. Or vice versa, data that appear to be strongly suggestive might really be much less clear. Bayes can be good for revealing those cases, if you use it really carefully.

Otherwise Bayesian probabilities are just a particular language for expressing simple logic. For people who are comfortable with math it's an elegant language but you can generally say all the same things in other ways if you want. So Bayes is usually optional, as far as I can see.