Statistical Clouds, Fuzziness, and Ockham’s Razor
There has been a lot of discussion regarding statistical methods as applied to the names on the ossuaries in the Talpiot tomb. I offer here a short clarification, and refer folks to more extensive discussions, if anyone is interested, on earlier entries on this Blog. These are easily located by a search for the term “statistics.”
The confusion, as I understand it, has had to do with the use, or perceived misuse, of “statistics” on onomastic data of this type. Dr. Feuerverger does not need me to defend him or his incredible accomplishments and intellect. His Bio speaks for itself. I regret that things got very confused with the way in which Feuerverger’s work was intially reported by Discovery. That has now, thankfully, been clarified on both the Discovery Web site and the home page of Dr. Feuerverger thanks to the helpful input of Joe D’Mello and other statisticians who contacted both Dr. Feuerverger and Discovery.
I am not a statistician but I have consulted with several, including Feuerverger, as well as a half dozen others who have been critical of his conclusions, as well as my own posts on the subject. We have had an exceptionally open and friendly give-and-take through private e-mail over the past few weeks. My own position is the following.
I do not think it is possible to construct any meaningful statistical model that will tell us whether this tomb, or any other, might be the hypothetical Jesus of Nazareth family tomb. There are simply too many variables and no one could account for them all, or even anticipate them. Who would be in such a tomb? Where would it be located? How large would it be (inner family only or wider circles)? Would ossuaries likely be plain or decorated? Would inscriptions be Aramaic or Greek or both? And so on and on it goes. The point is we can neither know nor accurately imagine any of these things? The list of potentially factored variables could be infinite.
The function of statistics with regard to onomastics is to establish simple probabilities. That is, what is the likelihood that this particular cluster of names (taken either in generic form, e.g. Yehoshua/Mariam/Yehosef or nickname form Yeshua/Maria/Mariamene/Yose) might occur more than once? That is it. In my own work I have preferred to be conservative and use generic forms of the names in the Talpiot tomb, forms that are then much less rare than those we actually have. But the calculations are firm and the method is sound.
For example, if we had a tomb with the four most common male and female names: Joseph, Judah, Mary, and Salome, with no patrynomic tags, we might have hundreds of tombs with such a cluster based on standard name frequency data for 2nd Temple Palestinian Judaism. These data hold up quite well for ossuaries as well as other onomastic data (literary, inscripitions) taken as a whole (Rahmani compared with say Tal Ilan, or Hachlili).
In the case of the Talpiot names, the data show that this cluster, in these relationships, would not occur more than once, even in a high estimate of Jerusalem population over several decades/ generations. Such a conclusions does not establish mathematically the probability that this is the Jesus of Nazareth family tomb. It has to do with the rarity of the cluster. In other words, it is a response to the oft repeated claim–”oh, the names are common,” with the implications that any number of tombs of the period might contain this same configuration of names. This is the approach that Fuchs used in accessing how common it would have been to have a “James son of Joseph, brother of Jesus.” The probabilities can be worked out with precision and the data on frequency of name distributions is sound and reliable. Essentially, this is what Feuerverger’s work on probability involves, though he did factor in various caveats in order to be as conservative as possible in his calculations. This is the Ockham’s razor of probability theory.
Randy Ingermanson and others have suggested that a more Bayesian model be used on the Talpiot inscriptions but I think the task is exceedingly problematic in that it rests up an infinitely variable prediction of possibilities and expectations, many of which are historically disputable, that are impossible to gauge in a quantifiable way. I surely do not want to prejudge these efforts and I look forward to seeing any results, but in terms of method and task, the two approaches are “apples” and “oranges.” I wonder if we will be any nearer to saying anything mathematically about the names in this tomb fitting, or not fitting, an imagined tomb of Jesus of Nazareth than we are at present. As I see it, the identification task has not to do with mathematics or probability, but with proposopography, the kind of thing that Rollston and Bauckham have begun to explore. If one can show that these names either fit, or do not fit, what we as historians might posit as a hypothetical “Jesus family tomb,” then we have something to discuss. Thus our tasks when it comes to the names are: epigraphy, statistics, and finally, history or prosopography.