Rejoinder of: Statistical analysis of an archeological find

I thank all the discussants for their many critiques and comments, and for their considerable efforts. Many of the points raised are ones with which I (at least in part) agree. It therefore seems easiest to first deal with a number of points with which I don't agree.

First, Fuchs states (and Bentley appears to assume) that my analysis is documented in a book and in a movie, neither of which I have authored. In fact, it is documented only in my paper which references neither of these, and neither does it reference any developments which occurred subsequent to my work. Although I will need to comment on one such development below, I otherwise confine this reply to the contents of my paper and to those comments of the discussants which appear within this issue of the Annals. In particular, I avoid being drawn here into discussions concerning representations made elsewhere by others, or to any matters alluded to by discussants that are peripheral to the central and substantive statistical issues of the problem. Nothing in this work was ever intended to cause offence to anyone. In my view, the statistical problems here are of methodological interest, and the subject matter is one of historical and archeological significance. If this tomb is not that of the NT family (as indeed it may not be) then archaeological work could still one day unearth a tomb that is and the question of what statistics might then contribute toward such a pursuit could then become important.

I also want to say that my paper does not-as some discussants intimateclaim that the Talpiyot tomb “is most likely that of the NT family.” What it tries to do is develop tools to assist subject matter experts in their work of gauging the veracity of any such claims. The function of statistics here is to help out in the difficult historical and archeological work. The critical role which historical assumptions play here means that such calls are not ours to make; and like Fuchs, I too refrain from passing judgment on the subject matter issue of whether this is or is not the NT tombsite. Of course, after the fact, it is easy to gain a sharpened appreciation for the safety of a “nihilistic” approach, one that-as Höfling and Wasserman put it-provides no answers. However, the intellectual temptations posed by a problem of this nature are surely too great to simply set aside.

Meaning of surprise. Turning to some specific issues raised by the discussants, I think it is important to distinguish more carefully between “interesting” or “relevant” collections of names, and what I have defined as being “surprising” collections of names. If a NT tombsite actually exists, it is certainly within the realm of prior possibilities that it contains within it only the most common renditions for the names of persons who might be recognizable to us. Were this so, no purely statistical procedure would then be able to “detect” it because such collections of names would not occur rarely enough in the general population to allow any procedure at least an opportunity to attain significance-that is, we then could never know. Indeed, only if the actual burials had taken place under rarer relevant renditions of the names (and only if in a tomb of a certain size) could there ever be a chance to “detect” it statistically. In other words, some historical and archeological “good fortune” would also be required.

Both Höfling and Wasserman, as well as Fuchs, appear to misinterpret my definition of “surprisingness” and its intent. In fact Höfling and Wasserman state that “the RR statistic becomes more significant if broad name categories are being subdivided into special name renditions, even if the particular name renditions are not relevant.” But that does not take into account that the specialness of a name rendition is permitted to count only if it is relevant, and only if it appears in a prespecified nested list of increasingly more specialized (i.e., “rarer and more relevant”) name renditions. The rareness alone of a name rendition (even if it corresponds to a generic name category deemed to be highly relevant) is not of essence. When Höfling and Wasserman state that “interested observers would surely argue that a tomb is interesting if there is any way at all of matching the names found to potentially interesting names,” they bypass the fact that such matchings will be relatively too probable to be significant if they were to occur under the most common renditions for the names. Likewise, Fuchs suggests in an example that, had the Talpiyot tomb contained a Salome in lieu of the Mariamenou [η] Mara inscription, it would have been considered still more surprising even though its RR value would then have been higher. In fact, based on the definition of surprisingness, had a Salome been found in lieu of the Mariamenou inscription, the cluster might conceivably be described as being more relevant, but (in view of how common Salome was as a name) it certainly would not have been mor

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