Bayesian Balderdash

A post or two ago, I suggested that people giving presentations of the authenticist view of the Shroud should avoid the use of Bayesian statistics, which although are actually quite useful predictive calculations based on prior factual knowledge, are often badly misrepresented as accurate derivations of probability based on nothing more than guesses. This was very forcefully expostulated against by Dale Glover, in a subsequent podcast of his own, who assumed I was thinking of him and called me clueless, profoundly ignorant, and out of my league. Oh dear. Dangerous words.

I wasn’t thinking of Dale Glover, as it happens, as although he has performed some such Bayesian manipulations regarding the Resurrection of Christ, I don’t recall that he has done the same regarding the Shroud. I was thinking of Giulio Fanti, whose analysis is published at shroud.com/fanti2en.pdf, and Tom Dallis, who presented his ideas in a discussion with Guy Powell, at youtube.com/watch?v=B_p9x4izRKI. But if the cap fits…

Anyway, the rest of this little comment is based on all these worthy opponents being absolutely correct, on my debasing myself in humble apology, and submitting, exactly as directed by their expertise, the following Bayesian analysis of my own.

Is the Shroud authentic or medieval? Following the experts, I initially assign a probability of 50% to each one.
Hypothesis 1 (Authentic): The Shroud of Turin is the burial cloth of Jesus Christ (1st century AD).
Probability of Hypothesis 1 = 0.5.
Hypothesis 2 (Medieval): The Shroud of Turin is a medieval artifact (13th-14th century AD).
Probability of Hypothesis 2 = 0.5.

Now we select evidence that might help refine the probabilities.

Evidence 1: Radiocarbon Findings (C-14 Dating). The 1988 radiocarbon dating of the Shroud by three independent laboratories (Oxford, Zurich, Tucson) dated samples from the Shroud to between 1260 and 1390 CE with 95% confidence. The findings were published in one of the most prestigious peer-reviewed scientific journals in the world, and although a very slight refinement of the confidence level has been demonstrated since then, the leading proponents of authenticity today accept that the radiocarbon levels were measured with accuracy and precision.

The Probability of this Evidence being reliable if the Shroud is actually authentic is very low. I’m giving it 1%.
The Probability of this Evidence being reliable if the Shroud is actually medieval is very high. I’m giving it 99%.

Evidence 2: The d’Arcis Memorandum. In 1389, Pierre d’Arcis, Bishop of Troyes, wrote a memorandum to Antipope Clement VII, stating that the Shroud exhibited in Lirey, France, was a “cunningly painted” fake, and that the artist had confessed. Neither the Pope nor the owner of the Shroud claimed that the Shroud was authentic for a hundred years after its emergence at Lirey, and every exhibition was accompanied by a formal declaration that it wasn’t.

The Probability of this Evidence being worthwhile if the Shroud were actually authentic depends on whether the bishop and Pope knew what they were talking about. Ignorance or dishonesty could play a part. I’ll give this 10%.
The Probability of this Evidence if the Shroud is medieval is very high. 95%.

Evidence 3: Walter McCrone’s Ochre Findings. In 1990, in the well-respected peer-reviewed journal Accounts of Chemical Research, Walter McCrone described finding red ochre and vermilion on the Shroud, consistent with it being a medieval painting.

The Probability of this Evidence being true if the Shroud were actually authentic is minimal, although it could have been touched up. I’ll give this 5%.
The Probability of this Evidence if the Shroud is medieval is very high. 95%.

Evidence 4: Textile Expert Findings (Four-Shaft Treadle Loom). The textile experts to examine the Shroud (e.g. Vial, Tyrer, Vercelli), mostly inclined towards authenticity, but have generally supposed that a treadle-loom, unknown in the 1st century, must have been used to weave the cloth, and the only attempt ever made to weave some Shroud-like material on a warp-weighted loom resulted in the weaver declaring it impossible.

The Probability of this Evidence being valid if the Shroud were actually authentic is small but not vanishingly so. 30%
The Probability of this Evidence being valid if the Shroud is medieval is high. 90%.

Right! Here we go!

The Probability of a Hypothesis being true given some extra Evidence [ P(H|E) ] is found by taking the Probability of the Evidence supposing the Hypothesis to be true [ P(E|H) ] and multiplying it by the originally assumed Probability of the Hypothesis [ P(H) ], and then dividing the product by itself [ P(E|H) x P(H) ] plus the Probability of the Evidence supposing the Hypothesis to be false
[ P(E|~H) ] multiplied by the originally assumed Probability of the opposite Hypothesis [ P(~H) ].

Or to put it symbolically:

What could be simpler? The last terms on the top and bottom row are the first estimates we decided on at the beginning: 50% for Medieval, 50% for Authentic.

The first terms on the top and bottom row are the probabilities that the evidences are true, assuming the Shroud is medieval: 0.99 for Evidence 1, 0.95 for Evidence 2, 0.95 for Evidence 3 and 0.90 for Evidence 4.

0.99 x 0.95 x 0.95 x 0.90 =0.804

And finally, suppose the Shroud is authentic, then the probabilities of the Evidences are pretty meagre: 0.01 for Evidence 1, 0.10 for Evidence 2, 0.05 for Evidence 3 and 0.30 for Evidence 4.

0.01 x 0.10 x 0.05 x 0.30 = 0.000015

So here’s the total calculation:

By scrupulously following the guidance of my elders and betters (well, betters; I don’t think any of them are elder), we see that the probability of the Shroud being medieval is:

And I don’t think anyone can argue with that, can they?