Miracle of the Shroud IV - The Phantom Image

[JayUtah]

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

Agreed, and fatal to the method. The cardinal rule of Bayesian estimation is that it's only as good as the prior. This is why it's so popular with fringe claimants who, faced with a dearth of actual evidence, try some pseudo-mathematical razzle-dazzle to produce a number they think makes their claims seem less overtly made up.

 

[Jabba]

Blood/What difference does it make?

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.

Hugh,
- The formula I gave (with the extra parentheses) is the Bayesian formula for determining the "posterior probability" of a hypothesis given some new info relevant to the hypothesis. More specifically, it is the formula that pertains to a true-false issue -- a hypothesis vs its complement. Here, the two hypotheses are 1) the shroud is authentic, and 2) the shroud is not authentic.

- I didn't really follow your reasoning before, assumed it was correct, and proposed what I thought might explain it...
- That didn't work.
- I'll be back after I think more about your reasoning.

 

[JayUtah]

The formula I gave (with the extra parentheses) is the Bayesian formula for determining the "posterior probability"

No it isn't. It superficially resembles it, but is wrong.

of a hypothesis given some new info relevant to the hypothesis.

You left out the part where Bayesian inference of posterior probability extends a prior probability, which in this case you just made up. The degree to which the prior probability has been properly formulated is the nearly exclusive determinant of whether the posterior probability has any meaning. When I say you don't understand what Bayesian modeling is meant to achieve, I'm not just whistling "Dixie."

I'll be back after I think more about your reasoning.

Irrelevant. You plucked your numbers out of thin air and you don't want anyone discussing the fact that you did.

 

[Mojo]

Hugh,
- The formula I gave (with the extra parentheses) is the Bayesian formula for determining the "posterior probability" of a hypothesis given some new info relevant to the hypothesis. More specifically, it is the formula that pertains to a true-false issue -- a hypothesis vs its complement. Here, the two hypotheses are 1) the shroud is authentic, and 2) the shroud is not authentic.

Jabba, how did you factor the carbon dating into your prior probability? Please show your working.

 

[pgwenthold]

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.

Absolutely. Maybe it is an issue of Bayesian or something, and I certainly am not an expert in Bayesian statistics, but if that is the conclusion from Bayesian statistics, it's complete ********. On the other hand, I am confident that Bayesian statistics are not complete ********, so the answer is that it is being applied incorrectly.

The biggest issue has to be the question of how big of a sample we are talking about. For example, if there are only two measurements, one says it is 90% that the answer is A and 10% chance it is B, and the other measurement says there is a 50% chance that is A and 50% chance it is B, then that is one thing. The probability that the answer is B is not going to be 50%, but is is going to be a higher than 10%.

But if I have 10 measurements and the conclusion of those 10 measurements is that there is a 90% chance that the answer is A and a 10% chance the answer is B, making a measurement that says it is 50/50 does not change that much at all. What is more likely? That the 10 measurements all fall in the minor probability? Or that the outcome that can be 50/50 is consistent with the other 10 measurements?

It's clearly the latter. If I have 10 looks that all say something is green, and along comes and says "it can be either red or green", that doesn't mean it is 50/50. It means that it's green. Now, admittedly, that is assuming the observations are all of comparable quality. However, if you have one measurement in there that is far more accurate than all the others, then that could trump it. If there is something that looks green but when you do an absorption measurement and find that the thing has an absorption peak in the 450 - 550 nm range, you can say, "objectively, this red, because it absorbs green." Hey, it might just be an optical illusion, and in that case, those 10 looks where it looked green were indeed wrong.

But notice in this example, the outlying observation is not 50/50, it's 100% clear that it is red.

Now, back to the shroud. The BEST measurement we have is the 14C date. And it is much, much more than 90%. Heck, take out the 14C dating and it's still far and away in favor of the middle ages. Now, you throw something like "there's limestone on it, which can be 50/50" it doesn't change the conclusion at all. It's perfectly consistent the middle ages date. It doesn't make it just as likely to be authentic in the least.

 

[JayUtah]

On the other hand, I am confident that Bayesian statistics are not complete ********, so the answer is that it is being applied incorrectly.

Or applied to meaningless input.

The biggest issue has to be the question of how big of a sample we are talking about.

Bayesian methods don't work that way. It's a departure from measured statistical outcomes, and it includes the formal notion of "likelihood," which is akin to probability but not as linearly formulated. You can think of a likelihood function for some model as the set of all possible probability density functions for all the ways a model can be constructed for some case. Bayesian formulations general "cut" through the multidimensional aspect of the likelihood function at one favored set of parameters.

Now, back to the shroud. The BEST measurement we have is the 14C date. And it is much, much more than 90%.

The exercise Jabba is attempting is to project from a prior degree of belief (expressed as a probability in Bayes, but not measured as one) to a posterior (i.e., new) degree of belief based on his notions of the applicability of parameters such as the presence of limestone. Basically it seeks to answer the question, "If I believe H to a certain degree, and this new information X would apply to a certain degree, then to what degree can my belief change if that new information turns out to be the case?"

Obviously such methods are only as good as your quantification of prior belief and of the intermediate applicability. Frequentist-mode statistics can help you do that -- and should. Plucking numbers out of thin air, even in Bayesian methods, is very sketchy practice. That's why fringe claimants like it. Because Bayes works with a different definition for probability, they can pretend math helps them by expressing their belief as a Bayesian probability and giving it a spin around the hamster wheel.

But as you and others are homing in upon, the belief in a ten-percent figure for the probability of authenticity amounts to claiming (in the frequentist sense) that three independent labs not only got false-negative results for the specimen, but got the same false-negative result. That sort of thing is quantifiably estimable, but Jabba has not done the exercise to estimate it. He says his guesses for the important numbers in his model are "educated guesses," but he has provided nothing more rigorous than handwaving to support the alleged education.

 

[MRC_Hans]

Are we not being a little unfair on Jabba?

Considering his history here, I don't think so

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

No. Considering the state of the evidence, it is ridiculous.

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 shroud has spent at least 700 years in churches, castles, an similar edifices which are generally full of limestones, at least in the form of decorations, but often as the walls themselves. No matter what its origin, it would be very surprising NOT to find traces of limestone on it.

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

The problem is both.

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.

It is not only absurd, it is wrong. The origin of the shroud is not a lottery. And the probabilities are not serial.

Hans

 

[hugh farey]

Hugh,
- The formula I gave (with the extra parentheses) is the Bayesian formula for determining the "posterior probability" of a hypothesis given some new info relevant to the hypothesis. More specifically, it is the formula that pertains to a true-false issue -- a hypothesis vs its complement. Here, the two hypotheses are 1) the shroud is authentic, and 2) the shroud is not authentic.

That's very helpful, Jabba. I Googled the Bayesian formula for determining the posterior probability of a hypothesis, and found it at https://en.wikipedia.org/wiki/Bayesian_inference, under the heading, "Probability of a Hypothesis".

Here the equation is:
P(H1|E) = P(E|H1)*P(H1) / ( P(E|H1)*P(H1) + P(E|H2)*P(H2) )

Whereas yours was:
P(A|x) = L(x|A)*P(A) / ( L(x|A)*P(A) + L(x|~A)*P(~A) )

Now I find what seems to be a computational error. You give the last two terms as L(x|~A)*P(~A), or in numbers, 0.5*0.9. However, when you calculate the product of 0.5*0.9, you get .0475, instead of the correct figure of 0.45. This makes serious inroads into your eventual probability.

Your final figure is:
P(A|x) = 0.95*0.1 / ( (0.95*0.1) + (0.5*0.9) )
= 0.095 / (0.095 + 0.0475)
= 0.667, or a 2:1 chance that the Shroud is authentic.

The correct calculation is:
P(A|x) = 0.95*0.1 / ( (0.95*0.1) + (0.5*0.9) )
= 0.095 / (0.095 + 0.45)
= 0.174, or a 1:6 chance that the Shroud is authentic.

Is that right?

Of course, you already think the Shroud is, say, 80% likely to be authentic, and were being deliberately kind to those who disagree. In that case, the final probability is increased to 94%, which you would no doubt think encouraging. But then, most of the commenters on this site think it is less than 1% likely to be authentic, in which case, using the same formula, it becomes less than 2% instead. The evidence of the limestone doesn't really make much difference to either point of view.

 

[Maurice Ledifficile]

The chance that the cloth in question is actually a shroud used to wrap the body of one Jesus H. Christ in the first century is 0 (zero).

 

[JayUtah]

The evidence of the limestone doesn't really make much difference to either point of view.

The point I made last week, even before Jabba debarked upon this irrelevant mathematical fantasy.

 

[hugh farey]

The chance that the cloth in question is actually a shroud used to wrap the body of one Jesus H. Christ in the first century is 0 (zero).

Would you care to explain why this figure is any less of a guess than Jabba's 10%?

 

[pgwenthold]

Would you care to explain why this figure is any less of a guess than Jabba's 10%?

Because the chances of the image on the shroud resulting from wrapping a cloth around a body is 0%. It CANNOT be done. Impossible to do.

Jabba likes to claim how no artist has ever reproduced the shroud as evidence for authenticity. However, he always forgets to mention that not only has no one reproduced even the image on the shroud, much less the shroud itself, by wrapping a cloth around a body. And for good reason: it cannot be done. It's simple cartography.

Unless, of course, you want to invoke the probability of a miracle occurring...

 

[Kid Eager]

Before we go any further, what is the assurance that the Bayesian method is being used correctly?

I see a whole bunch of equations flying around, but if I recall an article I read recently, improper use can be used to shoehorn any belief into being likely (which appears to be the motivation in this thread, given OP's prior performance in the immortality thread).

Will see if I can locate the article.

Meanwhile, I can't help but feel that this thread descending into using Bayesian methods is an indication that all arguments have been exhausted, so taking refuge in a forest of parentheses is the final redoubt.

 

[John Jones]

Before we go any further, what is the assurance that the Bayesian method is being used correctly?

I see a whole bunch of equations flying around, but if I recall an article I read recently, improper use can be used to shoehorn any belief into being likely (which appears to be the motivation in this thread, given OP's prior performance in the immortality thread).

Will see if I can locate the article.

Meanwhile, I can't help but feel that this thread descending into using Bayesian methods is an indication that all arguments have been exhausted, so taking refuge in a forest of parentheses is the final redoubt.

I agree, but never under estimate the power of the Fringe Reset

 

[JayUtah]

Before we go any further, what is the assurance that the Bayesian method is being used correctly?

None. It is assuredly being used incorrectly.

Meanwhile, I can't help but feel that this thread descending into using Bayesian methods is an indication that all arguments have been exhausted, so taking refuge in a forest of parentheses is the final redoubt.

It is an indication that, like all fringe claimants, Jabba is wallowing in irrelevant minutia so that he can maintain the illusion of continuing the debate and participating without actually contributing anything relevant or advancing the discussion.

 

[hugh farey]

Because the chances of the image on the shroud resulting from wrapping a cloth around a body is 0%. It CANNOT be done. Impossible to do.

I think it is important to a skeptical website not to fall into exactly the same errors of reasoning as the arguments it seeks to refute, don't you? The epithet "straw man" is often bandied about, I think to represent an argument that is easily refuted, but is not, in fact proposed by the holders of the argument you wish to refute. I do not think any autheniticist thinks that Shroud was 'wrapped' around a body in order to produce the image, so assuming that they do, and denouncing it as impossible, is a classic "straw man". Jabba's arguments have many weaknesses, and I hope he will recognise that 0.9 * 0.5 does not equal 0.0475, but responding like for like is unlikely to persuade him, or any other authenticist reading this thread to change his mind.

 

[pgwenthold]

I think it is important to a skeptical website not to fall into exactly the same errors of reasoning as the arguments it seeks to refute, don't you?.

Nonsense.

It's simple cartography. Wrapping a cloth around a 3d body will not give that image.

If you equate that with the made up, baseless percentages that Jabba uses, then you are as much of an apologist as others have accused you of being.

To call it "exactly the same error" is complete ********.

 

[Jabba]

Blood/What difference does it make?/Bayesian Statistics

That's very helpful, Jabba. I Googled the Bayesian formula for determining the posterior probability of a hypothesis, and found it at https://en.wikipedia.org/wiki/Bayesian_inference, under the heading, "Probability of a Hypothesis".

Here the equation is:
P(H1|E) = P(E|H1)*P(H1) / ( P(E|H1)*P(H1) + P(E|H2)*P(H2) )

Whereas yours was:
P(A|x) = L(x|A)*P(A) / ( L(x|A)*P(A) + L(x|~A)*P(~A) )...

Hugh,
- I may not be telling you anything new, but their equation is for comparing two different hypotheses (H1 and H2). The equation I've been using is for comparing a hypothesis and its complement.
- I probably should have used their terms, however, and expressed my equation as
P(H|E) = P(E|H)*P(H)/(P(E|H)*P(H)+P(E|~H)*P(~H))
- "H" being that the shroud is authentic.

 

[Slowvehicle]

Nonsense.

It's simple cartography. Wrapping a cloth around a 3d body will not give that image.

If you equate that with the made up, baseless percentages that Jabba uses, then you are as much of an apologist as others have accused you of being.

To call it "exactly the same error" is complete ********.

Not to mantion:

The ¹⁴C dating (dayenu!) is only one of the indications that the CIQ is an artwork. For instance, the Byzantine style of the cartoon; the anatomical impossibilities (including the self-contradictory "fixes" of manipulating a body in rigor); the mis-representation of the behavior of the "blood" (including the defiance of gravity); the provenance of the artifact (and the lack thereof); the chang in appearence of the CIQ over the last 7 centuries; all of these are strong (very strong) arguments against this particular cloth bearing the death-likeness of the body of a person not reliably demonstrated to exist.

If "Bayesian" "statistics" is to be used, those, too, must be calculated into the final range of probabilities...

 

[hugh farey]

It's simple cartography. Wrapping a cloth around a 3d body will not give that image.

Another thing we skeptics should do is to read what people say, and respond to that, and not what we think they might have said.
In short, I agree with you. Wrapping a cloth around a 3d body will not give that image. But then, no authenticists think that was how the image was made, so you are refuting an argument that is not held by the people you wish to refute. That is what a 'straw man' argument is.