The "Jesus Family Tomb" Statistics: Further Developments

This post is a follow up to The correct interpretation of Dr. Andrey Feuerverger's 1:600 odds calculation and Tomb Statistics: Feuerverger Responds, which cited Feuerverger's The Tomb Computation.

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Joe D'Mello, author of the first above mentioned post, responds to Feuerverger's response as follows:

Dear Professor Feuerverger,

Thanks for your reply! I can certainly understand the need for a collective reply since you must be deluged with e-mail inquiries. I sincerely apologize for adding to your e-mail overload by replying to this message, but I feel professionally compelled to do so. I have read with interest your calculation and your recent explanation of it (in `The Tomb Computation'). Your explanation reinforces my understanding of your computation, but my issue is with the INTERPRETATION of your computation floating around in the media. For example, the Discovery Channel site makes the following claim (exact quote from http://dsc.discovery.comconvergence/tomb/about/about.html): Discovery Channel: "It comes down to a matter of statistics. A statistical study commissioned by the broadcasters (Discovery Channel/Vision Canada/C4 UK) concludes that the probability factor is 600 to 1 in favor of this tomb being the tomb of Jesus of Nazareth and his family."

After reading your computation and explanation, I remain convinced that your statistical computation supports the following claim:

Statistically Correct Claim: "It comes down to a matter of statistics. A statistical study commissioned by the broadcasters (Discovery Channel/Vision Canada/C4 UK) concludes that the probability factor is 600 to 1 in favor of this tomb being the tomb of Jesus of Nazareth and his family, on the condition that the Jesus family had a family tomb to begin with."

(In other words, you have computed a conditional probability.) It goes without saying that statistically, logically, and semantically the two claims are a world apart, and the first claim as stated by Discovery Channel is a subtle and shameful attempt to mislead the public. Your computation, as it appears to me, does not "adjust" for the whole Jewish populace that lived in the area in question during the entire time period in question, but only "adjusts" for the 1,000 tombs found in the area! Do you agree with the corrected claim above? If you do, I hope you will consider it your professional responsibility to ensure that your findings are correctly communicated by Discovery Channel.

If you don't agree with my corrected interpretation, please reply with a brief one-sentence email saying that you don't. In that case, I will await your more detailed peer-reviewed paper (which you refer to in `The Tomb Computation') and will cease to send you any further e-mails until then.

By the way, I am copying Dr. Mark Goodacre, Associate Professor in New Testament at the Department of Religion, Duke University, North Carolina, on whose award-winning New Testament Gateway blog (http://ntgateway.com/weblog/) I have challenged the INTERPRETATION of your computation (see Friday, March 2, 2007 entry). If you could join us on that blog to discuss the interpretation of your computations by the media (or send Dr. Goodacre a response for him to post there), I would be truly delighted! I am also copying asktedkoppel@discovery.com (Ted Koppel's e-mail question bucket) because I had sent my interpretation of your computations to him earlier this week.

Best regards,

Joe D'Mello

As a result of this, Andrey Feuerverger today wrote to Joe D'Mello to agree that he was "essentially correct on two points" and to say that he has changed his web page accordingly, to quote:

A `null hypothesis' can be thought of here as asserting that this cluster of names arose purely by chance under random sampling from the onomasticon. The alternative hypothesis is the opposite of this, in some sense. It is not in the purview of statistics to conclude whether or not this tombsite is that of the New Testament family. Any such conclusion much more rightfully belongs to the purview of biblical historical scholars who are in a much better position to assess the assumptions entering into the computations. The role of statistics here is primarily to attempt to assess the odds of an equally (or more) `compelling' cluster of names arising purely by chance under certain random sampling assumptions and under certain historical assumptions.

In this respect I now believe that I should not assert any conclusions connecting this tomb with any hypothetical one of the NT family. The interpretation of the computation should be that it is estimating the probability of there having been another family at the time whose tomb this might be, under certain specified assumptions.
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We assume that this tombsite observation represents the `best' of many `trials'. It is estimated that there are approximately 4000 inscribed male ossuaries and somewhat fewer than half as many inscribed female ossuaries in existence. The number of `trials' is then taken as being approximately 1000. The computations do not take into account families who could not afford ossuary burials or who did not have sufficient literacy to have their ossuaries inscribed.