Two weeks ago there was a press conference with James Cameron (the creator of Titanic, the highest-grossing, most-nominated and receiving most Oscars of all movies to date). Those credentials tend to be taken seriously when a documentary claims they discovered the tomb of Jesus. The documentary was a serious success – James Tabor (one of the advisors) reports 4.1 million viewers.
One of the key pieces of evidence was a statistical calculation that those names must have belonged to Jesus’ family – you can read more about it from the source, Andrey Feuerverger. A quantitative investigation into those claims has appeared in Scientific American (with some of my involvement) and later in the Wall Street Journal column and blog. These articles stress the importance assumptions behind the calculations. But there is more interesting detail to what is going on.
First, there is a lot of confusion about “those names are frequent”. Of course, Feuerverger did take that into consideration. The real problem is in the interaction between the names on the coffins and the contents of the coffins, which is a simple example of a probability calculus. Let me thus walk through the calculations [PDF].
It’s not a problem to think that Jesus had a tomb: indeed, he was said to be buried. The authors assumed the probability to be 1/1,000 – meaning that one of the tombs was surely Jesus Christ’s. This is fine, we denote it as P(Tomb=Jesus)=1/1,000. Easily, P(Tomb=Random)=999/1,000. It is also not a problem to assume the probability of that particular choice of names out of all possible ones to be 1/600,000. We denote it as P(Names|Tomb=Random) = 1/600,000
P(Names|Tomb=Jesus)=1.0 is a major can of worms – we need this assumption to compute the probability P(Tomb=Random|Names). Why? The probability is computed through the Bayes rule:
P(Tomb=Random|Names) = P(Names|Tomb=Random) P(Tomb=Random) / (P(Names|Tomb=Random) P(Tomb=Random) + P(Names|Tomb=Jesus) P(Tomb=Jesus))
Here P(Names|Tomb=Jesus) = 1, P(Tomb=Jesus) = 1/1,000, P(Names|Tomb=Random) = 1/600,000, P(Tomb=Random) = 999/1,000. P(Tomb=Random|Names) corresponds to odds of about 1 in 600, but only if you agree with the other numbers.
First, to assume that the bones inside the “Jesus” ossuary are Jesus Christ’s would be inconsistent with the hard-line interpretation of the Ascension – that Jesus Christ physically ascended to heaven, so his bones aren’t there – they would want this probability to be zero based on the properties of the tomb. Note that not all Christians believe in physical Ascension, but those who do would assign the probability of Jesus having a full ossuary to 0 (but I don’t know if the ossuary was full or not, I’m assuming it was full). Secondly, hard-line Christians are quite ignited over the implication that Jesus would have a wife and a child, as is the case with this particular tomb. Instead, they would claim that the probability is zero, because the idea of a married Jesus with a wife and a child would be contrary to their understanding of the Bible.
Feuerverger went beyond what I would have gone, so my guess in Scientific American was wrong. The probability of 1/600,000 is reasonable and safe: it’s the probability that a random tomb would carry those names. The number of 1,000 is also safe: it’s the number of tombs. But using the Bayes rule to come up with the probability that the tomb is a random find is no longer safe. Why? Because it is based on P(Names|Tomb=Jesus) – you’re opening a Pandora’s box of trouble.
As for other lessons learned, when you talk with a journalist, don’t explain things that *he* would understand it, explain it so that *everyone* would understand, because you’re going to be quoted and you don’t want to sound as eggheaded as I have. Also, try to keep the answer within a sentence or two. In the past I’ve had the chance to edit the final version, but you can’t count on it.
In coming up with the 1/600,000 figure, did they think about the possibility of correlation between choices of names? In the U.S., John, Joshua, Ezekiel, and Mary are more likely to be combined than John, Alexander, Irving, and Tiffany.
Eric, I don't think they did: the data on frequencies for that period is already hard enough to find, but the data on correlations should be even harder.
There seems to be an assumption that all tombs are known. But I suspect there is a alot of censoring, in that many tombs have not yet been found yet, or have been destroyed. In my own community, portions of an old pioneer graveyard were recently found, and it was realized that a state highway, built 30 years ago, must have gone right through it.