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A heated controversy has broken out over the alleged discovery of the tomb of Jesus and his family. Experts in many related fields have weighed in and, since a statistical analysis was presented in support of the claim, I’m going to throw in my two cents’ worth as well. As you can tell from this post's headline, I don’t think the statistical support proves anything.
In the documentary, University of Toronto statistician Andre Feuerverger calculates that the chances of the names being found together are 600 to one.
He said that the Maria on one of the ossuaries is the mother of the Jesus found on another box, that Mariamne is his wife and that Joseph — inscribed as the nickname Jose — is his brother.
Jesus' mother was known after his death as Maria, the Latin form of Mary, as more Romans became followers. Mariamne is the Greek form of Mary. Mary Magdalene is believed to have spoken and preached in Greek. Jose was the nickname used for Jesus' little brother.
Furthermore, the tomb is the only site where ossuaries have been found with the names Mariamne and Jose, the documentary's creators claim.
CTV got the man’s first name wrong: It’s really Andrey. His home page at the University of Toronto gives no indication of interest or expertise in religion or archaeology. His listed publications all pertain to highly technical (not to say arcane) mathematical statistics.
An outline of Dr Feuerverger’s calculations is posted at The Discovery Channel’s The Lost Tomb of Jesus pages. The website is presented almost entirely in Flash animation, making it quite difficult to download or even print off the contents. Also, most of the pages do not have unique URLs. So, to document the location of the statistical information, I have to describe the steps necessary to find the page. Here goes:
From the Lost Tomb of Jesus home page, click on “Explore the Tomb”, the second item in the list of tabs to the left of the tomb photo. This will take you to a page headed “Explore the Evidence”. (After this point, individual pages do not have unique URLs.)
Click on “Enter the Tomb”, immediately above tomb photo. When the next page has loaded, click on “Supporting Evidence” at the bottom right of the main window. When the next page has loaded, click on “Statistical Evidence”, the fourth item in the list to the left of the main text.
This is the full text:
Statistics Overview
Dr Andrey Feuerverger, Professor of statistics & mathematics at the University of Toronto, has concluded A [sic] high statistical probability that the Talpiot tomb is the Jesus Family tomb.
In a study, Feuerverger examined the cluster of names in the tomb.
This involved multiplying the instances that each name appeared during that time period with the instances of every other name.
To be conservative, he then divided the number by the statistical standard of 4 (or 25%) to allow for unintentional biases in the historical sources.
He then further divided the results by 1,000 to account for all tombs that may have existed in First Century Jerusalem.
Taking into account the chances that these names would be clustered together in a family tomb, this statistical study concludes that the odds — on the most conservative basis — are 600 to 1 in favor of this being the JESUS FAMILY TOMB. A statistical probability of 600 to 1 means that this conclusion works 599 times out of 600.
Statistics Tables
Frequency of names:
Jesus Son of Joseph: 1 in 190
Mariamne: 1 in 160
Matia: 1 in 40
Yose: 1 in 20
Maria: 1 in 4Initial Computation: 1/190 x 1/160 x 1/40 x 1/20 x ¼ = 1/97,280,000
Second Computation: Eliminating Matia since he is not explicatively [sic] mentioned in the Gospels:
1/190 x 1/160 x 1/20 x 1/4 = 1/2,400,000Third Computation: Adjusting for unintentional biases in the historical sources:
2,400,000 / 4 = 600,000Fourth Computation: Adjust for all possible First Century Jerusalem Tombs:
600,000 / 1,000 = 600Probability Factor = 600 to 1
The second sentence refers to a “study” which I have searched for without success. It is definitely not posted at Dr Feuerverger’s website and, as far as I can determine, it is not posted anywhere else on the internet.
To me, this looks like something dashed off on the back of an envelope in five minutes. Moreover, Dr Feuerverger has simply taken someone else’s word that the tomb is genuine and that the names listed were found therein. The probability estimate is based on uncritical acceptance of the reports of others as to the contents of the tomb.
Several crucial but unexamined assumptions lie behind this computation, which I think an academic mathematician should have spelled out. These assumptions are all extremely tenuous.
The first assumption is that the tomb of Jesus and his family exists. Given other readily available historical information, the probability of that has to be considered minute.
Secondly, it has been assumed that the four (or five) names found in the tomb are the actual names of the members of Jesus’ family. In particular, the computation assumes that Jesus married Mary Magdalene (supposedly Mariamne in the tomb inscription). If those two did not marry, then the computation is obviously pointless and absurd. I don’t believe there is any credible historical evidence that Jesus married anybody.
Thirdly, Dr Feuerverger has assumed that the names given to him are all accurate transcriptions of what is written in the tomb. In a lengthy post on that very question, New Testament scholar Ben Witherington demolishes any claim that the names presented by Dr Feuerverger are the names actually inscribed in the ossuaries.
Just for the record, I’m not familiar with the adjustment factors of 4 and 1000 applied in step three and four. I stand to be corrected, but they look to me like arbitrary numbers.
In sum, Dr Feuerverger’s probability calculation is one big example of begging the question. He has assumed what he purports to prove. Assuming that Jesus was buried in a tomb with brother Yose, mother Maria, and wife Mary Magdalene, the calculation indicates that there is a 99.8% probability that Jesus’ tomb has been found. If those assumptions are not correct, then the tomb will never be found because it does not exist in the first place.
h/t for Ben Witherington link: Thinking Christian
Previous related post: From our bulging “How not to do statistics” file
Good work, Scott.
I like this other statement from the CTV article:
“John Marshall, a religious studies professor at the University of Toronto, said he’d like to know how a family from Galilee would have ended up being buried in Jerusalem.”
Since the movie Titanic, people should know that James Cameron does not do history well. He is not good with facts. But the strange thing is that there are people out there who are foolish enough to believe every word of this kind of junk.
The first assumption is that the tomb of Jesus and his family exists.
I would unpack that a little. The analysis assumes that there is a tomb that Jesus and his family were together buried in and that such tomb is extant.
Other elements that seem to me to decrease the probability:
4. No one in Jesus’ family that we know of was named Matthew, and several important names we do know in his family are not here, including James/Jacob and Simeon/Simon. James was even known to have spent his whole life in Jerusalem and seems to have died there, so why wouldn’t he be in this tomb? This does change the calculations considerably.
5. What is the likelihood that Jesus’ family was buried near Jerusalem (rather than Galilee) and in the same tomb with him if all along they’d been pretending that his body wasn’t around?
6. Doesn’t the calculation assume more than just the combination of names but a particular spousal relation between this Jesus and one of the women and between this Joseph and the other of the women? We do not know that, but I think the numbers assume we do.
7. To assume this Mariadne might be Mary Magdalene, other judgments were made that some have questioned, which might mean their unlikeliness should be factored in. One involves the connection between one of her names and the meaning “master”.
8. If this theory is correct, then something extremely unlikely must have happened. Lots of people who knew full well that Jesus’ body was sitting in a tomb somewhere were dying for a belief that he was raised from the dead and had ascended to heaven. That is unlikely enough that any calculations as to the likelihood of this combination of names appearing needs to be help up against the considerable probability that Jesus, if his body still existed somewhere, would not have been with bodies of anyone related to the people who were going around advertizing him as having been resurrected and ascended.
There are several things that strike me as odd about this calculation. The first may be a simple misunderstanding on my part, but isn’t Yose an alternate spelling for Joseph? If that is the case, is there good reason to believe that the Joseph that Jesus is the son of is _not_ Yose. If that’s the case, the presence of Yose is most definitely not an independent variable, and should not be included in the probability calculation. Finding Joseph, Jesus the son of Joseph, and Judah the son of Jesus all in the same tomb really only gives us one independent variable, Jesus son of Joseph, to connect to the Jesus of the Bible. If, for some reason, it is unlikely that Yose and Joseph are the same person, they are still related names, and having a Yose and a Joseph in the same family are still not independent probabilities.
Second, if I understand correctly, in this tomb there were way more than these four people, something on the order of thirty-five. Why were just these names chosen? Let’s redo the odds, except I just calculate that in a tomb of thirty-five random first century Jews, there will be (at least) one Mariamne, one Mary, one Yose, and one Jesus son of Joseph.
At least 1 Mariamne: 10.38%
At least 1 Mary: 99.07%
At least 1 Yose: 58.77%
At least 1 Jesus son of Joseph: 8.81%
Assuming that the presence of Yose is an independent variable, the probability of finding all four in a tomb is 0.54%. If it’s not, then the odds are closer to 1%.
Now, if you want to prove something, show me that these people are connected in the way proposed by this presentation. Then, the odds start to work out the way they suggest.
Thanks for the comments.
Jeremy and Donald, the points you raise concerning the rest of Jesus’ family named in the NT are very good. Why were ossuaries with their names not also discovered in the tomb? And who are the otherwise unknown others whose names were were found therein?
There are ways of taking those problems into account in estimating statistical probabilities, but Dr Feuerverger did not do that. If he had, though, his calculation wouldn’t look like a five-minute back-of-the-envelope job.
A little statistics and the tomb of Jesus…
Have you been following the story of the Tomb of Jesus? I haven’t been following it in detail, I’ll admit, just reading the odd blog post here and …
[...] Our bulging “How not to do statistics” file just filled up and burst [...]
[...] Now we have the names and the statistics. Their conclusion is “that the probability factor is 600 to 1 in favor of this tomb being the tomb of Jesus of Nazareth and his family.” Others, once again, have looked at the stats, I point you especially to Magic Statistics: Our bulging ‚ÄúHow not to do statistics‚Äù file just filled up and burst and a follow up at Back of the Envelope: A little statistics and the tomb of Jesus (which also discusses the issue of Mary Magdalene) as well as Darrell Bock: Fun with Numbers, Key Stats Reconsidered. They aren’t very impressed. Even the statistical consultant to the film Dr. Andrey Feuerverger think the film didn’t lead people to the right conclusions about his statistics. He also noted one thing that I was thinking about: There are certain additional facts regarding this archeological find which are of interest, but the precise ways in which they may or may not enter into statistical computations are debatable. Examples of these include [Ed. Note: I only include one of his examples]: [...]
Let’s suppose for a moment that one accepts that there are four names in common between the documented Jesus family and the ossuary inscriptions: Jesus son of Joseph, Mary and Jose (I exclude Mariamne since, as others have noted, Mary Magdalene is not part of the known family of Jesus of Nazareth). I think Feuerverger‚Äôs approach of multiplying the frequencies is fundamentally problematic.
Suppose by illustration, a society had exactly six names: ‘one’, ‘two’, … ’six’. and these names all occurred with equal frequency. Now suppose we had documentation of a family with two brothers named ’six’ and ‘five’ and then a tomb is found with ossuary inscriptions that read ’six’ and ‘five’. Feuerverger‚Äôs approach would seem to be to take 1/6 and 1/6 and multiply them to come up with 1/36 and conclude that this is the probability of a tomb with this configuration.
The problem here is that mutliplying frequencies this way implies ORDER. The actual probability of a two-inscription tomb containing a ’six’ and a ‘five’ is more like 1/18. (If one thinks of rolling dice, the first die could be ’six’ and the second one ‘five’ or vice versa.) (Actually, the probability is likely higher than 1/18 because in family groups names are not randomly assigned — two brothers would not typically both have the same name.)
In the case of the Talbiot tomb, one could perhaps make a case for multiplying the frequencies for ‘Joseph’ and ‘Jesus’ because of the implied order. In other words, in both the documented history and in the tomb, Joseph is the father and Jesus the son. We would not have a match with a tomb that said ‘Joseph son of Jesus’.
However, in the case of Mary and Jose, the relationship in the tomb is not specified. This makes use of simple multiplication absurd.
In the case of the hypothesized brother, for example, consider that the filmmakers would have claimed a ‘match’ had this fourth ossuary said ANY of Joses, James, Simon or Judas. This does not seem to be taken into account in the calculation at all. Surely a more reasonable approach would have been to sum the frequencies of all four of these names to come up with a group frequency for this hypothesized ‘brother’ ossuary.