Rejoinder of: Statistical analysis of an archeological find

The Annals of Applie d Statistics 2008, V ol. 2, No. 1, 99–112 DOI: 10.1214 /08-A OAS99REJ Main articl e DO I: 10.1214/ 08-AOAS99 c  Institute of Mathematical Statistics , 2 008 REJOINDER OF: ST A TISTICAL ANAL YSIS OF AN AR C HEOLOGICAL FIND By Andrey Feuer verger University o f T or onto I th ank all th e discussants for their many critiques and comments, and for their considerable efforts. Many of the p oin ts raised are ones with which I (at least in part) agree. It therefore seems easiest to first deal w ith a num b er of p oints with wh ic h I don’t agree. First, F uc hs states (and Ben tley app ears to assume) that my analysis is do cumented in a b o ok and in a mo vie, neither of w h ic h I ha ve authored. In fact, it is do cumented only in my pap er whic h references neither of these, and neither d o es it reference an y deve lopmen ts wh ic h occur red subsequent to m y w ork. Alt hough I will need to co mmen t on one suc h d ev elopment b e- lo w, I ot herwise confine this reply to the con tents of m y pap er and to those commen ts of the discussants whic h app ear within this issue of the Annals . In particular, I a void b eing drawn here into discussions concerning representa- tions made elsewhere by others, or to an y matters alluded to by discussants that are p eripheral to the cen tral and substanti v e statistica l issues of the problem. Nothing in th is work wa s ever intended to cause offence to any one. In my view, the statistical problems h ere are of metho dological interest, and the sub ject matter is one of historical and arc h eologica l significance. I f this tom b is not that of the NT f amily (as ind eed it ma y not b e) then archae- ologic al work could still one da y unearth a tom b that is and the question of wh at statistics migh t th en con tribute tow ard suc h a pursu it could then b ecome imp ortant. I also wa nt to s a y that m y pap er do es n ot—as some discussants in timate— claim that the T alpiy ot tom b “is most likel y that of the NT f amily .” What it tries to do is dev elop to ols to assist sub ject m atter exp erts in their work of ga uging the v eracit y of an y suc h clai ms. The fu nction of statistics h ere is to h elp out in the d iffi cu lt historical an d arc heological work. The critical role whic h historical assumptions pla y here means that such calls are not ours to mak e; and lik e F uchs, I to o refr ain from passing judgmen t on the Received F ebruary 2008; revised F ebruary 2008. This is an electro nic reprint of the o riginal ar ticle published by the Institute of Mathematical Statistics in The Annals of A pplie d Statist ics , 2008, V ol. 2 , No. 1, 99 –112 . This repr int differs from the origina l in pag ina tion and typogr aphic detail. 1 2 A. FEUER VERGER sub ject matter issue of whether this is or is not the NT tombsite. Of course, after the fact, it is easy to gain a sharp ened app reciation for th e safet y of a “nihilistic” app r oac h, one th at—as H¨ ofling and W asserman put it—pr o vides no answers. Ho w ev er, the in tellectual temptations p osed by a problem of th is nature are su rely to o great to simply set aside. Me aning of surprise. T ur ning to some sp ecific issues raised by th e dis- cussan ts, I think it is imp ortan t to distinguish more carefully b et wee n “in- teresting” or “relev ant” collections of names, and what I ha ve defin ed as b eing “su rprising” collections of names. If a NT tombsite actually exists, it is certainly within the realm of prior p ossibilities that it conta ins within it only the most common ren d itions for the names of p ersons who migh t b e recog nizable to us. W ere this so, n o purely statistical pr o cedure would then b e able to “detect” it b ecause such collections of names wo u ld not o c- cur rarely enough in the general p opulation to allo w an y p ro cedure at least an opp ortunity to attain significance—that is, w e then could n ever kno w. Indeed, only if the actual bu rials had taken place u nder rarer relev an t rendi- tions of the names (and only if in a tomb of a certain size) could there ev er b e a chance to “dete ct” it statistic ally . In other w ords, some historical and arc heological “go o d fortune” w ould also b e r equired. Both H¨ ofling and W asserman, as we ll as F u c hs , app ear to misin terp ret m y defin ition of “sur p risingness” and its in ten t. In fact H¨ ofling and W asser- man state that “the RR statistic b ecomes more significan t if broad name catego ries are b eing sub divided into sp ecial n ame ren d itions, ev en if th e particular name renditions are not relev ant .” But that do es not tak e int o accoun t that the s p ecialness of a name rendition is p ermitted to count only if it is r elev ant, and only if it app ears in a p resp ecified nested list of in creas- ingly more sp ecialized (i.e., “rarer and more relev an t”) name ren ditions. The r areness alone of a n ame rend ition (ev en if it corr esp onds to a generic name category deemed to b e highly relev ant) is not of essence. When H¨ ofling and W asserman state that “in terested observers would surely argue that a tom b is interesting if there is an y w a y at all of m atching the names found to p otentia lly interesting n ames,” th ey bypass the fact that such matc hings will b e relativ ely to o probable to b e significant if they w ere to o ccur un - der the most common renditions for the names. Likewise, F uc h s su ggests in an example that, had the T alpiy ot tom b con tained a Salome in lieu of the Mariamenou [ η ] Mara inscription, it would hav e b een consider ed still more surpr ising ev en though its RR v alue wo u ld then ha ve b een higher. In fact, based on the definition of sur prisingness, had a Salome b een foun d in lieu of the Mariamenou inscription, the cluster migh t conceiv ably b e describ ed as b eing more relev an t, but (in view of ho w common Salome was as a name) it certainly w ould not ha v e b een more surp rising, th at is, it would n ot ha v e pro v id ed a greater evidentiary v alue (under ou r p ro visos). REJOINDER 3 Other misinterpr etations. F uc hs also remarks that if a Simon had b een found in the tom b instead of the Mat ya, our RR v alue, and hence our tail areas, would ha ve b een unc hanged ev en though that S imon might h a ve b een a brother of Jesus. No w one can certa inly carry out analyses allo wing for the brother Simon to b e a candidate for a NT tom b. Th e reason we did not do so, ho w ever, is th at Simon is pr esumed to h a ve died sub sequen t to the time (70 CE) when the practice of ossuary burial ce ased. If this is so then it is ap p ropriate to hav e, as F u c h s pu ts it, “ignored that inscription.” F uc hs also states that assigning an RR v alue of 1 to n ames in the “Other ” catego ry means that su c h names w ill not con tribu te to the RR v alue of a cluster, the implication b eing that su c h names are then simply ignored by our pro cedur e. This actually is not so. Such v alues of 1 d o in fact con tribute in the sense of b eing v alues m u c h higher than w ould hav e o ccurr ed had r elev ant names b een encounte red instead. (As wel l, s uc h v alues of 1 for “Other” also affect our null distrib u tion.) And in any case, we hav e also allo wed for v alues exceeding 1 via the device of a disqu alifier list, but w e did not imp lement suc h a list since no su c h n ames app eared in-sample; disregarding such names w as ther efore conserv ativ e. One referee of the pap er had stated that merely including the T alpiy ot names within the onomasticon n ecessarily biases our resu lts. I d o not agree that this is the case. An y and all a v ailable names may and should in fact b e used to aid in the p ro cess of constructing the pr esp ecified cate gories of name rend itions and nesting them according to “relev ance and rareness.” What is imp ortant is that this pro cess b e carried out without reference to whic h of the n ames actually originated from within the tom b. F uc hs ment ions that the RR v alue for the T alpiy ot tomb u ses on ly fou r out of the six inscrib ed ossu aries on accoun t of the fact th at the Mat y a ossuary only cont ributes a 1 to th e RR v alue for the tom b. T h at view is n ot ent irely correct. As noted abov e, the Mat y a ossuary renders the RR v alue for the tom b muc h h igher than it wo u ld hav e b een had a more r elev ant name b een encoun tered in its place, and in turn th is results in a considerably increased tail area (for the RR v alue) un der the n ull distribution. Th e situation with resp ect to the s ixth inscription (i.e., Y eh u da bar Y eshua) will b e tak en up separately b elo w; for the momen t w e only note that, in effect, this inscription also con tribu tes an RR v alue of 1. A hyp othesis testing issue. F uc h s states that “A set of rules w h ic h weig h p ositiv ely (i.e ., with a co efficien t less than 1) names exp ected und er H 1 , but do es not we igh negativ ely names whic h are unexp ected under H 1 , is lik ely to yield biased results in fa v or of H 1 ” and that “this pro cedu r e is at least qu estionable.” K adane’s critique of the RR measure p oin ts in a related direction. Intuitiv e as suc h remarks may seem, how ev er, they are not entirely correct. First, a s long as a test statisti c is sp ecified a priori (in p articular, 4 A. FEUER VERGER without making reference to the data), and as long as its d istribution un der the n u ll h yp othesis is sp ecified correctly , the resulting test will b e unbiase d in the sen s e of having its stated leve l of significance. E ssen tially , only the p ow er of the test will b e at issue—a consider ation that leads u s to seek pr o cedures with high abilit y to d iscriminate. S econd, our allo wance for a disqu alification set do es to some exten t p ermit certain names to w eigh negativ ely; the reason w e did not implemen t suc h a set (as men tioned p reviously) wa s only b ecause Mat y a w as n ot considered to b e a disqualifying n ame so that our c h oice not to do so w as conserv ativ e. (In fact, the Mat y a name w as view ed to b e neutral.) Con trary to F u c hs’ assertions, th ere is n othing questionable ab out our actual pr o c e dur e . The matter of the Y ehuda inscription will b e discuss ed separately b elo w. Post ho c infer enc e. F uchs do es p oin t out correctly that “the a priori na- ture of th e proviso s is amongst the most imp ortant pr emises” of the an alysis. He f urther states that “The o v erall impression is that the in evitable exp osure to the d ata affecte d the definition of the proviso s.” Concernin g the degree to whic h the pro visos w ere truly a priori, he adds: “It is d ifficult to accept that . . . the elemen ts . . . ha v e indeed b een so sp ecified.” On s u c h p oin ts I am certainly symp athetic to the general nature of the concerns raised by the discussant s and ther efore revisit certain of the ‘pro visos’ in the discussions b elo w . It is indeed true h er e that p rior exp osure to the data w as in evitable, and th e principle is well under s to o d that b iases result if data is used w h en setting up an inference. In fact, th e b est w e ha ve b een able to do was to stress the fact that the data has b een seen. And we also tr ied, b oth conscien tiously and h ard, and on a b est efforts basis, to construct our inference to b e as a priori as possib le in the circumstances. The exten t to whic h we h a ve su c- ceeded or n ot in this task is one which eac h reader u ltimately m ust jud ge for themselv es. F or regardless of the degree of ob jectivit y any analyst may w ish or seek to cla im in carry in g out an anal ysis u nder suc h circumstances, no con vincing or irrefu table p ro of of suc h ob jectivit y can ev er b e offered. Th is is the p erennial p roblem of pr e- versus p ost-ho c inference, and the presen t statistica l problem provides a go o d example of it. It is also the reason why I tried to b e so careful to isolate and exhib it all of the assum p tions under whic h the analysis was carried out. Mariamenou ne e d not b e Mary M agdalene. Before addressing th e cri- tiques to m y p r o visos, there is one f u rther item that needs to b e clarified. F uc hs intimate s that the RR v alue assigned to the Mariamenou [ η ] Mara inscription m eans that this n ame must then n ecessarily r efer to Mary Mag- dalene. (A related remark is also m ade by Ben tley .) This in terpretation is not correct. That RR v alue resu lted from that v ersion of the n ame h a ving b een considered, on an a p riori basis, to b e the m ost ‘rare and relev an t’ REJOINDER 5 rendition of the h er name from amongst those names that w e know. (But on this p oin t, note the fur ther discussion b elo w.) It assumes no more than that only one w oman ha ving the generic name category of Mariam out of ab out ev ery 44 such wo men could legitimate ly hav e b een called by that ren- dition, and th at Mary Magdalene was among those wh o could so b e called. In p articular—although that p ossibilit y w as w eighed into the pro cess when deciding up on our a priori nested rendition categories—it certainly was not assumed that the Mara in the inscription must b e an honorary title, only that it might b e. F or if that we re assumed one m u st surely agree w ith F uchs (and Bentle y) that no statistical analysis wo u ld then b e r equ ired. W e now turn our focus to some of our v arious pr ovisos starting with the ones asso ciated with Mary Magdalene. Mary Magdalene as a priori c andidate. With resp ect to Mary Magda- lene, there are at least t wo distinct considerations. The first of these is the matter of h er inclusion on our list of a priori candidates for a NT tom b. O f course, this is primarily a historical iss u e, not a statistical one, and as suc h needs to b e v etted through disp assionate su b ject matter exp ertise. While sensitivities surr ou n ding this p oint render th e sc holarly work more difficult, I really do not s ee h o w one can exclude her from that list. T his is in no wa y tan tamount to an y assumptions ab out to whom, if an yo ne, s h e ma y hav e b een married. Th e p erceptions of Mary Magdalene ha vin g b een un c haste apparen tly originates with Po p e Gregory th e Great in the last decade of the sixth cen tury and h as no basis at all in the NT—a p oint that ev en the V atican conceded in 1969. Her presence is felt b oth prominently and s trate- gically throughout the NT accoun ts. She is the piv otal fi gure and primary source for th e resurr ection. She accompanies Jesus o ver su bstant ial distances and ov er a substantia l p erio d of time. Sh e ev en app ears, fr om the account s, to ha ve b een highly acti v e in Jesus ’ ministry . She is present at the cruci- fixion, and also at the bur ial wh ere (in view of the like ly n atur e of suc h rituals in that era) one would exp ect only intima tes of the family to attend. Indeed, she is also cited as ha ving b een in the v icinity of the tombsite on m u ltiple occasions. So, on balance—and in view of the p ossibilit y that she ma y ha ve b een buried in the Holy Land—I really d o not s ee ho w on e can realisticall y exclude h er from at least b eing a c andidate for a NT tom b site. One must a void a certain b lurring of logic that can o ccur inadv er tently here: The inclusion of Mary Magdalene on an a priori list of candidates f or a NT tom bsite is not equiv alen t to assertin g that she must actually b e found in suc h a tom b . It only sa ys that she is, a p riori, among the plausible c andi- dates . The distinction b et wee n these must not b e blu rred by th e o ccurrence of the Mariamenou [ η ] Mara ossuary within our d ata. Of course, there is no obligation on an y one’s part to accept the argument we mak e here; if one c ho oses to omit Mary Magdalene as an a priori candidate then the impact 6 A. FEUER VERGER of that c h oice is clear: no statistica l analysis applied to the T alpiyot d ata w ould then att ain s ignificance. Names f or Mary Magdalene. Wit h resp ect to the second k ey considera- tion p ertaining to Mary Ma gdalene, the situatio n is more problematic. A t the time I d id the an alysis my “due diligence” in r esp ect of constructing an a priori nested list of name renditions for Mary Magdalene included suc h elemen ts as the f ollo wing: (a) The itemization of the 80 kno wn ren d itions for the ge neric n ame of Mariam as recorded in Ilan ( 2002 ). (b) The meaning of the Ar amaic word “mara”; sp ecifically , Ilan (pp. 392 and 423) states: “Mara means ‘lord, master’ in Aramaic.” (c) An in ference, based on (a) and (b), that of th ese 80 name renditions for Mariam, the extraordinary Mariamenou [ η ] Mara one ma y provide an arguably tigh ter “fit” to Mary Magdalene than any of the other 79. (d) The reference b y Hipp olytus, aroun d 175 CE, in his Refutations, to a particular Mariamne wh o was legitimat ely a “mara” in the Aramaic sense of that word. (e) The u n w av ering opinion of Rahmani, and of some other h ighly re- garded epigraphers (e.g., Leah Di S egni), that the f u ll inscription on ossu ary #1 w as intended to refer to a single ind ivid ual only . (f ) The article by F rancois Bo v on ( 2002 ) ident ifying the Mariamne in the Acts of Ph ilip as Mary Magdalene, and id en tifyin g P h ilip as h er br other. And fin ally: (g) Information pro vided to m e (but n ote the discussions b elo w) that Professor Bo v on—a highly resp ected sc holar and exp ert on this sub ject— w as on record as ha vin g authent icated that Mariamne w as most lik ely the actual name of Mary Magdalene. I w as, of course, also aw are of the fact that the inscription Mariamenou [ η ] Mara had o ccurred within the tom b, and obvio u sly also of the fact that suc h information m ust b e disregarded when forming a priori assumptions. Ho we v er there is as w ell a concomita nt piece of inf orm ation of a s eemingly ancillary kin d , and not ent irely unrelated to our conditioning on th e tom b’s configuration. Namely , it is kno wn that the Mariamenou [ η ] Mara inscription w as rendered in Greek, but that it o ccurred within a tom bsite conta ining fi v e other inscrib ed ossuaries all of wh ic h were rendered in Aramaic. Ho w and if suc h a p iece of inform ation may b e used in forming a pr iori assumptions is not entirely clear to me and I lea ve this as a question f or r eaders to consider. Similar issues also arise in resp ect of su c h considerations as the nature of the actual in cisions and so on. I also p oin t out in passing—although th is should n ot b e regarded as being an a p r iori observ ation—that to the b est REJOINDER 7 of my kno w ledge, Mary Magdalene is th e only h istorical p ersonage who was ev er referr ed to by the generic n ame of Mariam com b in ed with the Hebrew letter “n u n,” and that s h e is referr ed to in that w a y in t wo d istinct sources (Hipp olytus and the Acts of Philip). The con tro versies resulting f r om the airing of the do cu m en tary film w as a u n ique eve n t in the cont ext of any statistical problem I had ev er d ealt with, and wen t b ey ond what I might realisticall y ha v e b een able to p r epare for. Schola rs and others who were in vol v ed in an y wa y were sub jected to pressures that sometimes made it difficult to discern where the actual facts la y . S p eaking for myself, I was intereste d only in the facts. Th e s tory of the crucifixion h as held sw a y o ve r the h istory of humanit y for s ome 2000 y ears. It therefore seemed worth while to sta y th e course that happ enstance had led me to, and to ste adfastly pursue the facts to whatev er w ould b e their logica l conclusion. Bovon ’ s clarific ation . This brin gs us to the su b ject of the clarifications subsequently issued b y Professor Bo von. There is no doubt whatev er no w that th ese were n ot retractions in resp onse to p r essures n or w ere they moti- v ated by a recognition of the p ossible uses which migh t b e m ade of su c h wo rk. In fact, Bo von’s clarifications are those of a serious sc holar wh ose remarks— ha ving inadv erten tly b een misinte rpreted by Jacob o vici—w ere conv ey ed to me out of con text. T o qu ote from Bo von’s statemen t to the So ciet y of Bib- lical L iterature: “I do not b eliev e that Mariamne is the r eal name of Mary of Magdalene. Mariamne is, b esides Maria or Mariam, a p ossible Greek equiv alen t, attested b y Joseph us, O rigen, and the A cts of P hilip , for the Semitic Myriam.” “Mariamne of the A c ts of Philip is part of the ap ostolic team w ith Philip and Bartholomew; she teac hes and baptizes. In the b eginning, h er faith is stronger than P h ilip’s faith. This p ortray al of Mariamne fits v ery well with the p ortra ya l of Mary of Magdala in the Manic hean Psalms, the Gosp el of Mary , and Pistis Sophia. My in terest is not historica l, but on th e lev el of literary traditions.” Without b enefit of the last elemen t, that is, (g), of th e itemization ab ov e, I d o not r egard the assumption A.7—concerning the most appropr iate n ame rendition for Mary Magdalene—as b eing equally adequately justified by the remaining elemen ts (a) through (f ) on that list. In particular, this means that w e cannot (on the basis of our RR pro cedure) sa y that the T alpiyo t find is statistically significan t in an y m eaningful wa y . Readers who wish to form their o wn ju dgemen t on this should note that the germane question here is n ot whether or not Mariamne w as the actual name of Mary Mag- dalene, b u t whether or n ot we are justified—on an a priori b asis—to sa y that the rendition Mariamenou [ η ] Mara pr o vides a b etter fit to the name of Mary Magdalene than any of the others, w hilst b earing in mind that sh e is rep eatedly r eferred to in the NT as h a ving come from Migdal, and is not 8 A. FEUER VERGER referred to th er e as Mariamne. W e shall see b elo w, ho w ever, that this matter is not yet closed. The Y ehuda ossuary. No w let us deal with the matter of the s ixth ossuary—the admittedly p roblematical one inscrib ed Y ehuda bar Y eshua. When I en countered th is d ata set I d id not at fi r st h a ve a clear idea of ho w that datum should b e dealt w ith in an analysis and I tenta tiv ely set it aside. It w ou ld b e fair to sa y that the apparen t implications su ggested by that ossuary w ould hard ly ha v e found any m en tion of or allo w ance for in m y list of a priori assum p tions f or sev eral r easons, not the least of w hic h b eing that suc h a p ossibilit y wo u ld not eve r hav e o ccurred to me. After the RR approac h ev olv ed, it b ecame clear to me that this sixth ossuary w as actually b eing incorp orated within th e computations in a particular w ay . As indicated in S ection 14 of the pap er , the analysis may in fact b e carried out allo wing for th e presence of a generationally aligned sequence of the form “A son of B son of C” w ith the youngest of this trio “not counting” to ward the RR v alue due to our lac k of kno wledge ab out any father-and -son pair b oth dying within the 30–70 CE timeframe. Of course, this still lea ves open the question of asso ciated a pr iori assu mptions. If one ascrib es to certai n theo- logica l in terpr etations later placed up on the historical ev ents, the decision is clear: the outcome observed must b elong to the disqualification set, and the matter is closed. If one do es not so ascrib e, the situation b ecomes more difficult, for then one must in terpr et the historical records as b est one can to assess the plausib ility of s u c h an outcome, and address such qu estions as the follo wing: W ould a un ion in suc h an instance ha v e b een sanctioned? W as it— in that er a—viewed as improp er to father a son? Did Jesus adv o cate against it for either self or follo we rs? If th er e w ere a son, w ould there hav e b een a r ecognized th r eat to his life? W e cannot answe r these or other suc h questions on b ehalf of the r eader. C er tainly the NT do es not record any union or an y son (although muc h other inf ormation is left u nprovided as w ell). As for the statistica l analysis based on RR, what w e can sa y is that in assigning an RR v alue of 1 to the sixth ossuary , our pr o cedure in effect acts with ab s olute n eutralit y on this question. Some extensions. A few method ologica l p oin ts seem w orth noting. In- stead of presp ecifying nested collect ions of name rend itions one can (for eac h candidate individu al) p reassign n umer ical RR or surpr isingness ratings to eac h of the onomasticon en tries un der th eir generic name. Only comparativ e (not numerical) v alues wo uld actually matter, and the RR computation for an encoun tered rendition would then b e based on the “ta il area” resulting within the generic name category . Since many en tries in the generic col- lection will hav e identica l ratings, the r esulting “discreteness” of the tail REJOINDER 9 areas w ould ac t m uc h as in our nested collections approac h but w ould al- lo w for somewhat greater flexibilit y . Note also that w e could allo w for th e existence of rare rend itions as y et unknown. F or an y candidate individual, the rareness of any suc h r enditions wo u ld at most b e (in the order of ) that of a sin gle unique en try in th e onomasticon. W e should remark h ere that a certain amount of v ariabilit y in our results is attributable to the fact th at name prop ortions are derived from the onomasticon w hic h itself constitutes only a sample; Mortera and Vicard prop ose one metho d for assessing su c h v ariabilities. Other explanations and c onc erns. Although many of the d iscussan ts fo- cus on criti ques to the analysis that might ha v e b een an ticipated to arise out of theologic al groun ds, S tigler allud es to some which stem from nont heo- logica l sources. F or example—although the circumstances of the fi nd assu re us that the tom b had b een und isturb ed for many ce n tu ries—w e do kn ow that the T alpiyot tom b had b een accessed at some p oin t in antiquit y . While it seems implausible to assume undue efforts on the part of those who did so, sup p ose they h ad found ther e only five of our six inscrib ed ossuaries an d “recognized” th e n ames on them. Migh t they n ot hav e though t it amusing to then tak e one of the un inscrib ed ossuaries there and cru dely s cr atch up on it the name Y esh u a bar Y ehosef u sing an implement at h and? As for Stigler’s reference to Sh erlo c k Holmes’ dog who did not bark, I did ind ep endently pursu e the matter of why the placemen t of the ossu aries among th e ko chim had n ot b een noted and concluded that this like ly h ad o ccurred only on ac- coun t of th e general circum stances of the fin d and of Gath’s u n timely death up on wh ic h th at p otentia lly priceless piece of information w as p ermanently lost. It must b e remem b ered that the arc haeologi sts who w ere sent there w ere not statisticians, th at they could hardly hav e anticipat ed the n ature of the questions that w ould later arise from this dut y , that they had limited time insid e a tom b co n taining only seemingly t ypical n ames, and th at the messy Y esh ua inscription could h ard ly hav e b een decipherable to them at first. In fact one could (follo wing up on a comment made b y Bird) argu e equally (although for what I b eliev e are go o d reasons I do n ot) that the length y p erio d w hic h elapsed b et we en the time of the tom b’s d isco ve ry , and the time of the p ublication of its details, provides a y et con trasting in s tance of the dog not barking. Stigler also raises the matter of our sp ecialized indep endence assum ption A.9. Our concerns, as wel l as our reasoning ab out th is assumption, w ere discussed in Sections 7 and 14 of the pap er. But in b ringing this data set to the atten tion of the statistical communit y , it wa s und er s to o d that qu estions whic h m erit fu rther s tudy would arise from it and the issue of cross-sectional indep en d ence is one of them. Here the question is not whether or not this assumption is true; w e know that it is not. T he question is wh ether the 10 A. FEUER VERGER nature of that dep endence affects the null distribution in an essentia l and nonconserv ativ e manner. I r efrain f rom an y rejoinders to S tigler’s references to Bruno and Galileo fin ding s uc h remarks to o fr igh tening to even con tem- plate. Explanations based on coincidence sh ou ld also not b e ov erlo ok ed; in d eed, p erhap s these d ata can b e assessed und er the framew ork of Diaconis and Mosteller ( 1989 ). Within the con text of coincidence, o dd s of 1000 to 1 are hardly uncommon. Th ree “coincidences” wei ghed substantiv ely in our anal- ysis. One is the ossu ary of Y eshua b ar Y ehosef. Another is the matc h to the rare name version Y oseh. And the th ird is th e remark able Mariamenou [ η ] Mara inscription. Th ere are, how ev er, also three f urther coincidences that (for r easons stated in the pap er) I did not incorp orate in the anal ysis b ut nev erth eless seem wo r th n oting. Th e first of these is th e generational align- men t of the three names Y ehosef, Y eshua and Y eh u da, with the alignmen t at T alpiy ot b eing the only one among the six not immed iately inconsisten t with the NT family . Th e seco nd is the seemingly suggestiv e choice , among the six ossu aries, on whic h the Greek script actually o ccurred, with the other fiv e ha ving b een in Aramaic. And the th ir d is the suggestiv e c h oice for wh ic h of the six ossuaries b ore the messiest inscription—that c hoice b eing seem- ingly consisten t with some theories that m ight b e adv anced to accoun t for the empt y tom b. Finally , there is ye t on e f urther coincidence: The youngest mem b er of the generationally aligned ossuaries—namely Y ehuda—has the same name as the y oun gest (or second yo ungest) brother of Jesu s , with th e accoun ts of Mark and Matthew ha vin g cu riously r ev ersed th eir tw o names. Let u s no w address s ome sp ecific fu r ther matters r aised by the discussan ts. H¨ ofling/Wa sserman ’ s first metho d. In the “Differen t Approac h” p ro- p osed by H¨ ofling and W asserm an, the most essen tial difference actually lies in th e treatmen t it accords to the differen t name versions. In particular they “lump tog ether different ve r sions of names” arguin g “that a tom b is in teresting if ther e is any wa y at all of matc h ing the found names to p oten- tially interesting names.” Unfortunately , for common names, “in teresting” will not b e enough; there will b e lit tle opp ortun it y for detec tion (i.e., the p ow er will b e lo w through ou t all of the alternativ e) unless the renditions whic h o ccur m atch more sp ecifically to the NT individu als, and if the sp eci- ficness of such renditions is appropriately accoun ted for. A manifestation of this is that their calculation is “in v ariant under splitting names into sub cat- egories,” while our calculation (wh ich attempts to account for th e degree of rareness and r elev ance among the p ossible renditions) is not. T h us, h ad an inscription su c h as (say) “Y esh ua of Nazareth, son of Y ehosef ” o ccurred in the tom b, their computations w ould b e indifferent to an essential asp ect of the name. Incidentall y , H¨ ofling and W asserman are not correct in suggesting that what I hav e computed is “the p robabilit y of getting this s et of names.” REJOINDER 11 Bayesian notions. Sev eral referees argue in fav or of a Bay esian appr oac h, something I tried to a v oid due to the great div ergences exp ected amongst priors (some of which ha ve b een influenced b y theologic al considerations). Also, I do not en tirely u n derstand K ad an e’s remark ab out viola tion of the lik eliho o d principle. Kadane app ears to s uggest that the uncertain ties in d e- ciding b et w een whether a n u ll h yp othesis is false or whether a rare ev en t has b een observed is merely an artifact of the frequent ist appr oac h. It seems to m e, how ev er, that no p urely statistical metho d can ev er circum ven t its analogue for “t yp e 1 error.” F urther, in allo win g a p r ior to place a zero probabilit y on a d iscrete eve n t, K adane highlights a d ifficult y that can arise in a pu rely classical Ba yesian approac h , unless one tak es to its extreme the view that “coherence” alone must su ffice. I t is also not en tirely clea r to me ho w s tr aigh tforwa rd it w ould b e to implement LR pro cedu res of the t yp e Mortera and Vicard advocate. Th e Ba yesian approac h p rop osed by H¨ ofling and W asserm an, h ow ev er, d o es on fi rst glance app ear to lead to results com- parable to those of a f requent ist appr oac h, as long as the assumptions und er whic h the tw o approac hes are implemen ted—in particular the assump tions concerning the renditions for the r elev ant names—are tak en to b e similar. Ba y esian-lik e ideas ma y of course also b e used to rationally com bine s ub jec- tiv e b eliefs ab out individ u al assumptions into a p laus ib ilit y for the collection of all assumptions. O u r approac h has b een, ho w ever, f or the RR m etho d to act as a m easuring device, to b e tuned by the inv estigator in accordance with h is or h er exp ert assum ption set. Bentley. Ben tley is co rrect in s tating that m y analysis assumes that a NT tomb m igh t exist, bu t I do n ot f ully agree w ith him that m y analysis is conditioned on the assu mption that suc h a tom b must exist with probab ility one. Also, while it ma y b e fair of Ben tley to argue with the estimates I used for the num b er of tom bsites in J erusalem, I am not a ware of any exp ert opinion su ggesting that the tru e num b er of tom bsites is greatly in excess of the n umb er s I had used. Ben tley’s critiques regarding the Mariamenou [ η ] Mara inscription are well take n and this matter h as b een dealt with at length in our discussions ab o ve. I f , in spite of my lab ors, Bentle y wishes to b e critical of them, he is within h is rights. Nonethele ss —lest Be n tley’s commen ts regarding James T ab or b e misconstrued—I wish to sa y that in m y discussions w ith Professor T ab or I f ound him alwa ys to b e a sc holar of imp eccable integrit y . Some of Bentley’ s comments, for example his closing remarks ab out archeolo gists and archeolo gy b eing no w at o d ds with statis- tics and with statisticians admittedly mak e for prov o cativ e and dramatic reading; un fortunately pressu res of time d o not p ermit me to en ter in to suc h d eb ates. 12 A. FEUER VERGER Ingermanson. Ingermanson energetically pr esen ts “the case against” for essen tially eac h one of the assu mptions un der whic h my computations w ere carried out. Although his critiques seem o ccasionall y o verzea lous to me, they do pro vide a useful c hec klist of items that s hould b e consid ered b y an yone who seeks to arriv e at a fully informed opinion ab out the T alpiy ot tomb. Needless to sa y , an analysis of such data needs to b e carried out u nder assumptions th at are r easonable and defensible, ev en th ough n o single as- sumption can ever b e regarded as absolutely u nassailable. Ha ving already discussed many of such matters in m y pap er and throu gh ou t this r eply , I do not rep eat those argu m en ts here, but instead return to t w o sp ecific items. The first item concerns the treatmen t of the n ame Y oseh m entioned b y In- germanson (as w ell as others). I add here tw o add itional p oin ts to those already made in th e pap er. First, su rnames were not t yp ical in that era and exceedingly common names (su c h as Y ehosef ) w ould n ot h a ve pro vided adequate differen tiation amongst individuals. In that resp ect, one needs to b ear in mind the distinction b et w een wh at we commonly r efer to as b eing a “nic kname” v ersus a name rend ition or v ariant that is in itself intended to act as an actual name. (An instance of this may , e.g., ha v e occurr ed in the case of the NT family .) S econd, there is no singleton Y eh osef inscription o ccurring within this tom b. Th erefore suc h a seemingly more “formal” or more “resp ectful” version for Y oseh wo u ld ha ve b een a v ailable for u se by the family without an y risks of confusion but they c hose not to use it. The sec- ond item concerns the name of the mother. I tak e issue with the ob jections Ingermanson (and others ) raise regarding the a priori “rarer and more rele- v ant” r endition of her name u sed in my analysis. The ve ry earliest historical reference to h er app ears in Mark 6:3: “Is this n ot the carp enter/builder, the son of Maria, the brother of. . . ” The second earliest reference also o ccur s in Mark when he men tions Maria as b eing at th e cross, although whether or not this Maria (“the mother of James and Joseph”) is mean t to b e Jesus’ mother is not en tirely certain. The third earliest historical reference to her app ears in Matthew 1:18: “. . . when His mother Maria h ad b een b etrothed to Joseph. . . ” (Lu k e d o es not use the form Maria b ut r ather Mariam, h o wev er Luk e is historically a significant ly later source.) DNA and other ev i denc e. Mortera and Vicard r aise the q u estion of why DNA evidence was not collected and assessed m ore broadly and indicate some p ossible uses of such data. Bird alludes to some related matters as w ell. Ha ving had reserv ations, suc h as about the risks of con tamination, these were evidentia r y p oin ts I decided not to pu rsue. I understand that it is, in any ev ent, the case that suc h data cannot actually b e obtained. While I appreciate the reasons b ehind such concerns, I also b elieve that Bird ma y b e making more of the m iss ing ten th ossuary than ma y actually b e wa rran ted b y the facts. REJOINDER 13 Critiques. The critiques of the discus san ts encompass b oth the metho d- ology and the assump tions un der w h ic h it is b eing applied. Th e vigor of their remarks rep resen ts an imp ortant comp onent of the scientific p ro cess when results seen to b e con trov ersial are b eing assessed. Although some of the discussan ts hold strong prior views on th e sub ject matter, all critiques do nev ertheless need to b e consid ered on their o wn merits. So far as the metho dology itself is concerned, I think I ha ve add ressed the main p oin ts that ha ve b een raised; how ev er, the situation regarding the assumptions is necessarily different. T h ese need to b e v etted by disp assionate sub ject mat- ter exp ertise. It is a cur ious and p erhaps u nique feature of this pr oblem, ho wev er, that th e b o dy of su b ject m atter exp ertise h er e is itself divided along v ery particular lines. A symp osium. In January 2008, at ab out the time I prepared this reply to discussion, I had the p rivilege to attend The T h ird Princeton S ymp osium on Ju daism and Chr istian Origins held in Jeru s alem. Sev eral of the sessions at this conference w ere connected to matters relev ant to ev aluating the con- text of the T alpiy ot tom b. Among the s u b ject matter participan ts th ere w orkin g p rimarily with historical approac h es, some indicated th at they d id not r egard the T alpiy ot tom b’s b eing th at of the NT family as an imp ossi- bilit y . All of the participants ho w ever (m yself includ ed) indicated that they did not regard that p ossibilit y as h a ving b een p ro ven. The most in teresting session there—relativ e to the r equiremen ts of our statistical analysis—w as one on the epigraph y of the T alpiy ot ossu aries dur ing wh ic h the Mariamenou [ η ] Mara inscription was discussed . As might b e exp ected, n o consensus was reac hed in that s ession, bu t one r emark ab le p ossibility emerged of w hic h few mem b ers in the audience (whic h consisted of n onstatisticians) grasp ed the immediate s ignifi cance. Th at p ossibilit y , raised by Jonathan Pr ice—a classi- cal Greek ep igrapher (among other qualifications)—w as that this inscrip tion had b een done by one hand, that it lik ely r eferred to a single individu al, and that it sh ou ld likely b e read as “Mariam also kn o wn as Mara,” the presum p- tion b eing that Rahmani misr ead an intended και as an ν oυ ending in the first name together with an η και , and that the και in this instance was in tend ed to signify a double name. (See Figure 1.) W ere that the case, it seems to me th at the element (g) of our “due diligence” list ab o v e could then b e sup p lan ted b y one that w ould n o w b e consider ab ly stronger still. It is w orth men tioning h ere that the classical Greek epigrapher Roger Bagnall had earlier indep endent ly arriv ed at a s imilar reading: “Mariam, also called Mara,” findin g Rahmani’s reading to b e “not acceptable,” b ut prop osing that Mara ma y hav e b een intended as a short form of Maria, although “some uncertain ty remains” (quoted fr om a J une 2007 e-mail comm u nication). Un - fortunately , the (spiraling) m ultiplicit y of readings and in terpretations for that inscription, and the nature of the relativ e uncertain ties among them, 14 A. FEUER VERGER mak es it difficult to giv e u nequivocal preference to an y one of th e r eadings, and until further w ork and consensus establishes at least th e correct reading of this inscrip tion (let alone any correct in terpretation of it) further progress along this fr on t seems unlikely . One p ossibilit y that had not o ccurred to me w as raised b y a participan t [Claude Matlofsky] and seems w orth noting h ere. Namely , that the T alpiyo t tom b might also fit th e profile of the f amily of J esus’ b rother Y oseh. Under that scenario, Y oseh wo uld ha ve named a son after his slain b rother, bu t the assumption A.8 ab out Y oseh and Y eh osef b eing necessarily distinct individ- uals would h a ve to b e su sp en d ed. It b ears p oin ting out h ere that statistical ‘evidence’ of the nature describ ed in my pap er, ev en if significan t, cannot automatica lly b e used to also identify the actual p ersons bur ied in the tom b, nor an y of their relati onships to eac h other; these are separate inferentia l problems. Some opinion s and c oncluding r e marks. During the cours e of this w ork I h a ve had o ccasion to meet many of the individu als in v olve d in this matter, including Andr e Lemaire wh o “discov ered” the J ames ossuary , Oded Golan who o wns it and who kindly p ermitted me a priv ate viewing of part of his remark able an tiquities collection, Shimon Gibson and Amos K loner b oth of whom (along with th e late Y osef Gath) w ere p resen t at the T alpiy ot find in 1980, as well as with a num b er of other k ey p ersons. In such m eetings I tried to gather information, or at least to f orm impr essions, ab out some of th e nonstatistical asp ects relev ant to the analysis. A few such observ ations ma y b e wo rth mentio ning here. First, opinion on th e authent icit y of the James ossuary is d ivided so I ha ve no basis in forming a judgement on that matter. Either wa y , if th e James ossuary p ro venanced to the T alpiy ot tomb (as some ha ve clai med) th e statistical imp lications w ould b e non trivial. Ho wev er, in m y opinion there is at present n o credible evidence to tie that ossuary to the T alpiyo t tom b. Second—although no one who has witnessed fi rst hand the in tensity that can b e engendered b y this sub ject matter w ould deny that suc h an ev entualit y sh ould, at the v ery least, b e momen tarily considered— the p ossibilit y of an y “co v er-u p” of facts by the arc h eologists in volv ed strike s me as b eing p ure fiction. Th e dynamics for s u c h a thing to h a ve tak en place simply we re not there. Th ird, a story made headlines w h en the wido w of Y osef Gath ann ounced that her late husband kn ew and h ad told her that he had disco vered the tom b of Jesus, and that h e wa s deeply concerned ab out the p ossib le rep ercussions of th at find. Ha ving b een present at the ev ent during wh ich s he made this statemen t, I found it easy enough to gather sufficien t in f ormation to lead me to b e concerned that this could hav e b een an in stance of “false memory syndrome”; I am therefore inclined discoun t that in formation. REJOINDER 15 A few participan ts at the P rinceton sym p osium ind icated that it migh t b e worth while to carry out furth er exca v ations at the T alpiyot tombsite and in particular at another imm ed iately adjacen t tomb. While it is alwa ys p ossible that su c h further w ork might lead to more definitiv e answ ers, it is also the case that Israeli laws are v ery strict ab out matters that p ertain to disturbin g burial sites. Th erefore, un less evidence comes to ligh t to in v alidate the T alpiy ot fi n d, this, it seems to me, is wh ere matters are like ly to rest for some time to come. REFERENCES Bov on, F. (2002). Mary Magdalene in th e A cts of Phi lip. I n Which M ary?—The M arys of Early Christian T r adition ( F. Stanley Jones, ed .) 77–89. So ciety of Biblic al Liter atur e Symp osium Series 19 . So ciety of Biblical Literature, Atlan ta. Diaconis, P. a nd Mo steller, F. (1989). Method s for stu dying coincidences. J. Amer. Statist. Asso c. 84 853–861. MR1134485 Ilan, T. ( 2002). L exic on of Jewish Names i n L ate Antiquity , Part 1 : Palestine 330 BCE– 200 CE . Mohr Sieb eck, T u bingen.