Miracle of the Shroud IV - The Phantom Image

[Jabba]

Blood/What difference does it make?

...Unfortunately, I can't see the rationale behind your multiplying and dividing. I've been doing a bit of experimenting with coins to try to work out what we need. Would you be so kind as to check my working?

The probability of three fair coins falling all heads is 1/8. However, if we are told that one of the coins has a 75% chance of being two-headed, then the probability of the three coins falling all heads is (1/8 * 2) * 3/4 = 3/16. I multiplied the original probability by 2 as, by separating one of the coins, the probability of the other two both falling heads is doubled.

That seems to work. It also works with two coins. The probability of two fair coins falling all heads is 1/4. However, if we are told that one of the coins has a 75% chance of being two-headed, then the probability of the two coins falling all heads is (1/4 * 2) * 3/4 = 3/8.

In more general terms, the probability of x coins all falling heads is 1/2^x, assuming ignorance of the chance of any coin being double-headed. If one of them has a 75% chance of being double headed, the chance becomes:

(1/2^x) * 2 * 3/4

Now let's use your figures.
You give P(A) as 0.1, and therefore P(~A) as 0.9, which is generously in favour of non-authenticity, and you give L(x|A) as 0.95 and L(x|~A) as 0.5, which is debatable.

So, the probability of the Shroud being authentic, given a 50/100 chance of limestone, is 10/100. However, if we are told that there is an 95/100 chance of limestone being present, then the probability of the Shroud being authentic is 10/100 * 2 * 95/100 = 1900/10000 = 19/100.

If this is correct, then why do we have to divide by anything?

Many thanks to anybody who has got this far!

Hugh,
- In hopes of clearing this up easily -- you already did the dividing, but in several steps? The Bayesian formula does it all in one step?

 

[JayUtah]

The Bayesian formula does it all in one step?

Your use of Bayesian models is not probative of anything relevant to your claims because you simply made up the numbers you introduced into it. And lest there is any lingering confusion or doubt, yes I am accusing you of making them up out of thin air. You mentioned that you would address this. Please do so without further delay.

 

[JayUtah]

The inability to view any kind of evidence except as supporting one's preconceived position is spreading, I see,

This harks back to the warning I gave you some weeks ago. Regardless of what experience you may have had at other forums, this one is likely to be more contentious. That is, rather than nonpartisan discussion, this forum focuses on debate -- taking up a position and defending it against inquiry. That does not mean you can't effectively discuss weaknesses in your own position. But to avoid confusion it would be wise to label them as devil's advocacy.

 

[hugh farey]

Hugh,
- In hopes of clearing this up easily -- you already did the dividing, but in several steps? The Bayesian formula does it all in one step?

No, Jabba, I did no dividing at all. I multiplied the original probability (not considering limestone as significant) of 0.1 by the likelihood that limestone would appear on an authentic Shroud (0.95), and achieved 0.095. I doubled this on the basis that previously the presence of limestone was not considered a determining factor either way (probability 0.5), but now I think that if a factor has not been considered at all, then the multiplication by 2 is unnecessary.

Anyway, the formula that works for coins (!) is:

P(A|x) = L(x|A)*P(A)

so where does the rest of your equation come from?

 

[JayUtah]

...so where does the rest of your equation come from?

Apparently from a misguided attempt to normalize for the totality of the event space. His formulation is wrong, but I won't say more. (I've realized he's usurped my comments to date to make it seem like he's the one being instructive.)

Don't be fooled. The overriding problem with Jabba's newfound attempt at statistical modeling is that he's simply plucked his inputs out of thin air. No formulation, correct or otherwise, produces anything other than a transformation of Jabba's personal degree of belief, turning it into a thinly disguised circular argument.

Fringe argumentation often seeks to avoid discussing the critical problems of an argument by focusing on irrelevant minutia.

 

[Slowvehicle]

Apparently from a misguided attempt to normalize for the totality of the event space. His formulation is wrong, but I won't say more. (I've realized he's usurped my comments to date to make it seem like he's the one being instructive.)

Don't be fooled. The overriding problem with Jabba's newfound attempt at statistical modeling is that he's simply plucked his inputs out of thin air. No formulation, correct or otherwise, produces anything other than a transformation of Jabba's personal degree of belief, turning it into a thinly disguised circular argument.

Fringe argumentation often seeks to avoid discussing the critical problems of an argument by focusing on irrelevant minutia.

With the greatest of respect, Mr. Savage's totrtuous misuse of his version of "Bayesian" statistics is not "new-found", but the same inept misapplication he attempted to pass off in the "Immortality" thread...

 

[JayUtah]

With the greatest of respect, Mr. Savage's totrtuous misuse of his version of "Bayesian" statistics is not "new-found", but the same inept misapplication he attempted to pass off in the "Immortality" thread...

So I saw. By "newfound" in this context I mean relatively new to this thread. Hugh effectively shot down the limestone argument by correctly noting that its presence on the cloth is indicative neither of authenticity nor of forgery. Jabba, flagrantly ignoring that, argued that it would be more likely for an authentic cloth to have limestone than for a forged one. He has attempted to disguise what is an obviously and flagrantly begged question by couching it in pseudo-mathematics, encoding his assumptive reasoning in likelihood figures plucked out of thin air.

 

[Jabba]

Blood/What difference does it make?

Your use of Bayesian models is not probative of anything relevant to your claims because you simply made up the numbers you introduced into it. And lest there is any lingering confusion or doubt, yes I am accusing you of making them up out of thin air. You mentioned that you would address this. Please do so without further delay.

Jay,
- I'm not making these up out of thin air.
- The exact numbers chosen are indeed guesses. However, they are educated guesses -- which is what Bayesian statistics is all about.

- If we know the history of an artifact, our guess as to the microscopic debris to be found on it would be more likely accurate than our guess did we not know its history.
- The likelihoods I suggested reflect that principle.
- The exact numbers I chose are where the educated guesses come in. What numbers would you chose?

 

[HighRiser]

So I saw. By "newfound" in this context I mean relatively new to this thread. Hugh effectively shot down the limestone argument by correctly noting that its presence on the cloth is indicative neither of authenticity nor of forgery. Jabba, flagrantly ignoring that, argued that it would be more likely for an authentic cloth to have limestone than for a forged one. He has attempted to disguise what is an obviously and flagrantly begged question by couching it in pseudo-mathematics, encoding his assumptive reasoning in likelihood figures plucked out of thin air.

Well... How else would he prove that the shroud is real?

 

[HighRiser]

Jay,
- I'm not making these up out of thin air.
- The exact numbers chosen are indeed guesses. However, they are educated guesses -- which is what Bayesian statistics is all about.

- If we know the history of an artifact, our guess as to the microscopic debris to be found on it would be more likely accurate than our guess did we not know its history.
- The likelihoods I suggested reflect that principle.
- The exact numbers I chose are where the educated guesses come in. What numbers would you chose?

The numbers you have chosen have not been vetted by anyone who has seen your work on how the numbers were arrived at to begin with.

This is because you haven't done shown the work.

 

[Craig4]

Jay,
- I'm not making these up out of thin air.
- The exact numbers chosen are indeed guesses. However, they are educated guesses -- which is what Bayesian statistics is all about.

- If we know the history of an artifact, our guess as to the microscopic debris to be found on it would be more likely accurate than our guess did we not know its history.
- The likelihoods I suggested reflect that principle.
- The exact numbers I chose are where the educated guesses come in. What numbers would you chose?

Why are you guessing about microscopic debris when so much has been done and written about regarding material on the cloth?

Why don't you tell us about what you know about the artifact?

 

[MRC_Hans]

- If we know the history of an artifact, our guess as to the microscopic debris to be found on it would be more likely accurate than our guess did we not know its history.

Yes, OK. And this, apart from the math, is what is wrong with your calculation.

You must evaluate the options on the same basis. You cannot assume one as a known and the other as an unknown, and then use the result to rate their probability.

Hans

 

[MRC_Hans]

The inability to view any kind of evidence except as supporting one's preconceived position is spreading, I see, and does not seem to apply only to authenticists. Jabba's logic is catching.

Jabba's logic? .... Where?

More seriously, the fact that not everything is known about the Shroud does not weaken the evidence that it is medieval, but it stimulates worthwhile discussion.

It may do, but it does not support Jabba's position.

Charles Freeman suggests than an ordinary well-known artefact could 'become' a holy relic if a miracle was suddenly associated with it. However, although I do think a painted sheet could suddenly become 'sanctified', I don't think it could suddenly become the Shroud of Christ, unless a) no one knew where it had come from and b) it was attested to by a number of bishops.

Both correct. Any artefact could become holy if associated with a miracle (and, back then, miracles could be easily arranged). However, it could not become a specific object, like the shroud of Christ, except by FIAT, by being declared to be. (Which could also be arranged)

I don't think this happened with the Shroud. Nor do I think an attempt to introduce such a holy relic in such a small and otherwise insignificant village not far from a major cathedral was a sensible idea, which is why I don't think the Shroud was made for Lirey church. I think it possible therefore that Geoffroy de Charny brought it back from one of his excursions (and why not while held for ransom in England?) as an interesting artefact of no particular sanctity, and then after he died it was suddenly produced by some not too far-sighted clerics as the Shroud. The only thing that holds me back is d'Arcis claiming that it had been attested by the artist who painted it. Did Bishop Henri enquire as far as England for provenance? It's possible, but pushing our scenario beyond the quite likely into sheer guesswork.

That is the word.

Hey, ho. More crap, I expect... Pearls before swine, caviar to the general and all that....

Just a word of advice: Provocation can be productive, insults will not.

Hans

 

[JayUtah]

The exact numbers chosen are indeed guesses. However, they are educated guesses

No, they aren't. They're just guesses. More specifically, they're just quantifications of your desired belief, manipulated in a deceptive and inappropriate way to convey the illusion of rigor.

which is what Bayesian statistics is all about.

No, Bayesian statistics are about quantified belief that accepts uncertainty. You simply encoded your predetermined belief regarding the state of the system in the numbers you chose and tried to pretend that uncertainty worked out in your favor. As I said, you dink around in the mechanics of Bayesian inference, but you don't know what any of it means.

If we know the history of an artifact, our guess as to the microscopic debris to be found on it would be more likely accurate than our guess did we not know its history.

No. You postulated two of several possible histories and arbitrarily assigned likelihoods to them based on preferential consideration of applicable variables. Hugh tried to explain to you what was wrong with this, but you directly contradicted him and plowed ahead with your own preconceived notion.

The likelihoods I suggested reflect that principle.

Asked and answered. The discussion you point to that alleges to have examined this simply recites your preconceived notion of likelihood. Several people called you on it at the time, but you ignored it and continue to ignore it.

The exact numbers I chose are where the educated guesses come in. What numbers would you chose?

I wouldn't at all, because I don't agree that Bayesian analysis is appropriate to this question. Haven't you been listening to anything people have tried to tell you for the past week? Someone else proposed different numbers and asked you to refute them. You simply pointed back to your original treatise. That's no different than simply insisting that you're right.

 

[Spektator]

Someone--I think Hugh--wrote to the effect that "If the Shroud is medieval, then it was made by someone, at somewhere, for some reason, using some method."

To demonstrate the inadequacy of reducing everything to a yes/no, binary proposition, take the opposite of that: "If the Shroud is not medieval, then it was not made by anyone, nowhere, for no reason, using no method."

That leads inevitably to the statement that "The Shroud is medieval."

No offense to Hugh intended. I know that such reasoning (if it even deserves to be called reasoning) is completely unfair and is silly--but to impose numbers just for the sake of supporting an already-reached conclusion is just as silly, and just as unfair.

 

[MRC_Hans]

Someone--I think Hugh--wrote to the effect that "If the Shroud is medieval, then it was made by someone, at somewhere, for some reason, using some method."

To demonstrate the inadequacy of reducing everything to a yes/no, binary proposition, take the opposite of that: "If the Shroud is not medieval, then it was not made by anyone, nowhere, for no reason, using no method."

That leads inevitably to the statement that "The Shroud is medieval."

No offense to Hugh intended. I know that such reasoning (if it even deserves to be called reasoning) is completely unfair and is silly--but to impose numbers just for the sake of supporting an already-reached conclusion is just as silly, and just as unfair.

I don't think Hugh meant that. The shroud, being basically an artefact, was always made by someone, somewhere, some time, for some reason, using some method. The question is who, where, when, why, and how.

And either scenario (authentic, medieval) answers some, but not all, of those questions.

Hans

 

[hugh farey]

Are we not being a little unfair on Jabba?

He gave the probability of the Shroud being authentic as 10%. Given that he is a confirmed authenticist himself; I think that's generous.

Assuming the Shroud to be authentic, he gave the likelihood of its having limestone crumbs on it as 95%. I think that's perfectly fair, given that, if it is a burial cloth, and the tombs around Jerusalem are made of limestone, which they are, it would almost certainly have made contact with the tomb.

The problem is not his probabilities, guesswork though they are, but his calculation. If I were so convinced of the medieval provenance of the Shroud as to give that a probability of 99%, but thought that, even if it were medieval, the likelihood of it having limestone on it was only 50%, then immediately the probability of the Shroud being medieval drops to 49.5%, which is absurd. It may be that all that dividing stuff accounts for that, but I'm afraid I don't understand where that comes from.

 

[Steve]

Are we not being a little unfair on Jabba?
He gave the probability of the Shroud being authentic as 10%. Given that he is a confirmed authenticist himself; I think that's generous.

Assuming the Shroud to be authentic, he gave the likelihood of its having limestone crumbs on it as 95%. I think that's perfectly fair, given that, if it is a burial cloth, and the tombs around Jerusalem are made of limestone, which they are, it would almost certainly have made contact with the tomb.

The problem is not his probabilities, guesswork though they are, but his calculation. If I were so convinced of the medieval provenance of the Shroud as to give that a probability of 99%, but thought that, even if it were medieval, the likelihood of it having limestone on it was only 50%, then immediately the probability of the Shroud being medieval drops to 49.5%, which is absurd. It may be that all that dividing stuff accounts for that, but I'm afraid I don't understand where that comes from.

no

 

[zooterkin]

He gave the probability of the Shroud being authentic as 10%. Given that he is a confirmed authenticist himself; I think that's generous.

Given that he's yet to produce a shred of evidence in favour of authenticity, that's incredibly generous.

 

[JayUtah]

The problem is not his probabilities, guesswork though they are, but his calculation.

Both are the problem, and I have a very low tolerance for people who attempt science, perform it incompetently, and somehow feel that the attempt somehow justifies lending undeserved rigor to the answer. Those of us who work in science and technology require the rigor of mathematics and the formalism of estimation to achieve and maintain credibility in our work. We go to extreme lengths collectively to make sure it is done right, employing a process of painstaking review and cross-checking It is better not to do mathematics at all than to go through the motions of it improperly and thereby convey a false sense of reliability.

Given that it took efforts on my part that bordered on violating the MA just to get him to acknowledge there was something that needed discussing, and given that he tried to ride my coattails early on in order to hide his incompetence, I don't think we're being nearly hard enough on him. If he wants to attempt rigor he will be held to those standards. Time has shown he generally cannot meet those standards, but I feel zero sympathy for that. This is how bad ideas get properly thrown into the bin.