Discussion of: Statistical analysis of an archeological find

The Annals of Applie d Statistics 2008, V ol. 2, No. 1, 57–65 DOI: 10.1214 /08-A OAS99D Main articl e DO I: 10.1214/ 08-AOAS99 c  Institute of Mathematical Statistics , 2 008 DISCUSS ION OF: S T A TISTICAL A NA L YSIS OF AN AR C HEOLOGICAL FIND By Camil Fuchs T el Aviv University 1. Introdu ction. The starting p oin ts of F euerverger’s pap er are b oth ex- citing and promising: A scien tific puzzle of ma jor imp ortance is settled by a no vel statistica l approac h . The pu zzle is related to the re-analyzed inscrip- tions on th e ossuaries from an ancien t tom b from Jerusalem unearthed in 1980. The new analysis, also do cumente d in a b o ok [Jacob ovic i and Pelle - grino ( 2007 )] and a do cumenta r y movie [Cameron ( 2007 )], claims that the inscriptions ind icate that this ma y b e the bu rial site of the New T estamen t (NT) family . Undoub tedly , if v alidated, a disco v ery with p oten tial to stir ma jor in terest b oth in a cademic a s w ell as in religious circles. A t this p oin t, the sta tistical method ology is called to settle the con trov ersy and a new statistica l approac h is d ev elop ed t o handle the intrica cies of the complex problem. The resu lts p resen ted in the pap er seem to justify the prior excitemen t. In terms of the n ew appr oac h, the defined leve l of “sur prisingness” for the cluster of names in the tom b is found to b e ve ry h igh, that is, under the sp ecified pro visos, there is a ve ry lo w probabilit y that a random sample of suc h ossuaries con tains a cluster of names which is more su rprising than the cluster foun d. F urthermore, wh en the p robabilities related to the lev el of surp risingness are translated into the classical terms of conditional o dd s ratios, the o dds that t he T alpiot t om b is th at of th e NT family are also found to b e v ery high. It seems lik e the statistical methodology succeeded in se ttling the con tro- v ersy , and the ve rdict is in fa vor of the tom b b eing the NT family tomb. In the p ro cess, a new approac h was dev elop ed to settle cases in whic h judgment has to b e rendered on whether or not a multiple c h aracteristics even t is or is not a result of random draws. On a p ersonal note, I confess that I w ould ha ve b een very pleased to b e able to conclude my discussion with t wo p ositiv e statemen ts: (a) that I foun d Received Octob er 2 007. This is an electronic repr int of the original ar ticle published by the Institute of Mathematical Statistics in The Annals of Applie d Statistics , 2008, V o l. 2, No. 1, 57 –65 . This reprint differs fr om the original in pagina tion a nd t ypo graphic detail. 1 2 C. FUCHS the results co nvincing and w e can sec ond Prof. F euerverge r’s claim that the tom b is most likel y that of the N T family , and (b) that the new app roac h is preferable to the existing metho ds in deciding whether the tested ob ject is the sp ecial one. Unfortunately , to anticipat e the findings detailed b elo w, despite the initial excitemen t and the p ersonal preferences, I find m yself in disag reemen t w ith the results and the conclusions. As for the new approac h, it may ev olv e and pro ve b eneficial, although not n ecessarily p referable to existing metho ds. I b eliev e its prop erties ha v e ye t to b e inv estigat ed. 2. The statistical analysis. Let us fi rst b riefly review the relev an t statisti- cal f eatures in F euerv erger’s approac h and their application to the particular data set. The justifications of the ab o v e-menti oned con ten tions are pr esented in this con text. The an alogue of a null hypothesis H 0 is defi ned to b e th e assertion that the observ ed configur ation of names (on th e ossuaries in the tombsite) arose b y purely r andom d r a ws from the onomasticon. T h e alternativ e H 1 is p resen ted as “an opp osite of H 0 relev an t to the “NT hypothesis” that the tombsite is that of the NT family .” An intermediate formulatio n (with w eak er H 1 ) is also present ed, with H 0 b eing th e assertion th at all p ossible tom b s comparable to that of T alpiot arouse under random assignment of names and H 1 is the ev ent that among the such p ossible tombs, one unsp e cifie d tom b is that of the NT family . With resp ect to th e in termediate H 1 and for v arious prior- lik e pr obabilities, F euerverge r assesses from the H 0 -tail a rea the o d d s r atios of the even t that the T alpiot tom bsite is that of the NT family . The data from the T alpiot tomb includes six in scrib ed ossuaries with the follo wing inscriptions: #1: M αριαµη ν oυ [ η ] M αρα , #2: , #3: , #4: , #5: , #6: transliterated as: #1: Mariamene [ η ] Mara, #2: Y ehuda son of Y esh ua, #3 : Mat y a, # 4: Y eshua son of Y oseph, #5 : Y oseh, #6: Marya. A t least some of the names are reminiscen t of the names related to th e NT family . As a first step in determin in g ho w significan t o r (in terms of the prop osed approac h) h o w “surp r ising” is this fin d, o ne has to assess ho w common were those names in the vicinit y of Jer u salem in the late Second T emple p er io d. T able 1 presents the frequencies and the relativ e frequencies of the generic names out of the total compiled male and female nonfi ctitious names from ossuary an d n on-ossuary sources [Ilan ( 2002 )]. F urthermore, the table also presents the fr equencies and relativ e frequencies of the relev an t renditions of Mary/Mariam and Y oseph from ossuary sources. Under the pr op osed approac h , the d ata analysis conditions on b oth the n u m b er of inscrib ed ossu aries and their gend er d istribution, as well as on DISCUSSI ON 3 T able 1 F r e quencies of the name d inscr ib e d in the T alpi ot ossua ry All sources Ossuary sources Relative Relative Generic name F re quency frequ ency Rendition s F requency frequen cy F e male Mary/Mariam 74 0.233 Mariamene 1 0.023 Mary a 13 0.295 F emales— 317 T otal ossuaries— 44 T otal all sources F emales n amed Mariam Male Y eh u d a 171 0.068 Y esh ua 101 0.040 Mat ya/Mattit yahu 62 0.026 Y oseph 221 0.088 Y oseh 7 0.152 Males— 2509 T otal ossuaries— 46 T otal all sources Males named Joseph the generational sequence in tw o of the four male ossuaries. Ho w ever, the basic analysis deals only w ith th e inscriptions from five ossuaries, with the Y eh ud a son of Y esh ua ossuary b eing discarded. No w, the new app r oac h defines “an a p riori defined” m easur e of “sur - prisingness” related to th e H 0 – H 1 con tinuum. The “surprisingn ess” v alue of a particular configuration increases as the configuration is in some resp ect closer to H 1 . The reci pro cal form of th e “ surprisin gness” v alue is defined as “relev an ce an d rareness” (RR v alue). “Relev ance” refers to membersh ip in an a priori list of candidates for inclusion in an NT tom bsite, and “rareness” is d efined relativ e to an a priori list of nested p ossible name renditions f or eac h suc h candidate. The initial relev ant lists are s u pp osed to include names whic h are reasonable to assume that th ey hav e p oten tial to b e found in a NT family tomb, based on a set of a-pr iori form ulated hyp otheses. The rel- ev an t lists h a ve to refl ect those hyp otheses. In add ition, the r elev an t lists are a lso allo wed to include unrelated names, d efined as “Other,” as p ossibly b elonging to p ersons ab out whom there are no reco rds. The p opulation and the sample are stratified, and separate a priori li sts of tom b cand id ate name renditions are compiled by gender. In the analysis of the T alpiot data the follo wing assum ingly a pr iori lists of tom b cand idate name rend itions for men and w omen are pr esen ted: Men: Y oseph, Y esh u a, Y oseh, James and “Other ” W omen: Mary Magdalene (denoted MM or Mariamene), Mary a, Mariam, Salome and “Other ” 4 C. FUCHS Th us the Mat ya fr om ossuary #3 is consid ered as “Other” (one of those p ossibly b elonging to p er s ons ab out whom ther e are no records), a nd Mari- amene [ η ] Mara is added to t he w omen’s list as b eing “the most sp ecific app ellation to Mary Magdalene from among those kno wn.” As can b e seen from T able 1 , this is the only such exact rendition of Mariam among the recorded n ames. The R R v alue of a datum or of a subset of data is defined as the adjusted relativ e frequ en cy of o ccur r ence of the comp onents under indep endent ran - dom samp lin g from the onomasticon. The RR for a g eneric n ame is it s relativ e frequency , while the RR v alue for a particular rendition of a generic name is computed as a pro duct of the name’s o veral l r elativ e frequency and t he relat iv e frequ ency fr om ossuaries sources of the particular rendition within the generic name. F or some particular configur ations, quite complex (and relativ ely reaso nable) defin itional adj ustment s imp osed b y H 1 are used in the computation of the RR v alues. In particular, a prized b on us is applied when Y oseph is the father and Y eshua is the s on with the RR-v alue b eing divided by 1.2. Under the su ggested approac h, the names defin ed as “Other” r eceiv e an RR v alue of 1, and th u s hav e no effect on the pro du ct whic h yields th e RR v alue f or the entire clus ter. As exp ected, and as illustrated b elo w, a sample’s RR v alue is critically affected b y the t wo ma jor features of the approac h : the defin ition of th e a priori list and the v alue give n to names d efi ned as “Other.” T able 2 presen ts the RR v alues for the cluster of names found in the T alpiot tom bsite. W e can see that Mat y a is assigned an RR of 1, while the ossuary #2 is discarded (with its t wo n ames, Y ehuda and Y esh u a, bu t the name Y eshua do es app ear in the table from ossuary #4). The p ro du ct of the individ u al RR-v alues yields 1 . 74 × 10 − 8 . F ollo wing the division by the p rized b onus factor of 1.2, the RR-v alue for the cluster is 1 . 45 × 10 − 8 . Clusters with a similar configuration (i.e,. tw o female and three male ossu aries, wher e on e male ossuary has t w o men in father–son generational ali gnmen t) and with a lo wer RR v alue are consid er ed to b e more “surprising” than the studied tom bsite. Out of the n 1 and n 2 male and female p ersons in the p opu lation, the tot al p ossib le num b er of suc h samples is n 4 1 · n 2 2 and the total n u m b er of v alid samples (wh ic h pass pre-sp ecified “realit y” requirements) is β n 4 1 · n 2 2 with β < 1. In th is case, n 1 = 250 9 , n 2 = 317 and F euerve rger found that β = 0 . 906, yielding β n 4 1 · n 2 2 = 1 . 981 · 10 12 . Among them a prop ortion of 5 . 89 × 10 − 7 , o r about 1 / 1,821,00 0 ha v e an RR v alue lo w er than 1 . 45 × 10 − 8 . The siz e of the estimated p opulation who could ha ve b een inte rred in ossuaries includ es ab out 4,400 males and 2,200 females. Dividing those v alues in to the studied configuration of 4 male and 2 f emale inscr ip tions we obtain an estimate of 1,100 p oten tial “trials” with whic h the T alpiot tom b site has to b e compared. DISCUSSI ON 5 The p -v alue for testing th e alte rnativ e that among the co m parable p ossi- ble tom b s one unsp e cifie d to m b is th at of the NT family is assessed by the probabilit y that at least one among the 1,100 w ould hav e an H 0 -tail area less or equal to 5 . 89 × 10 − 7 . This prob ab ility is b ound ed ab o ve by 1 / 1,655. F or the Ba y es-type computation of th e p osterior probabilit y th at this is indeed the NT f amily tom bsite, F euerverge r defines b y θ the (p rior) probab ility th at an NT family tom b would consist of a cluster of with an RR v alue as su r- prising as that at T alpiot. F or θ = 1 , 0 . 5 and 0.1, the p osterior p r obabilities are 0.9994, 0.9988 and 0.9940, resp ectiv ely . In a n utsh ell, the exp osition ab o ve reviews the basics of th e new prop osed approac h as app lied to the sp ecific d ata set. 3. The a p riori hyp otheses. As emphasized, the foundation for the anal- yses is a set of “hyp otheses, assumptions and c onditions up on whic h t he computations are carried out, collectiv ely n amed as the proviso s.” The pa- p er pr esen ts detailed explanations and jus tifications for the f eatures in th e pro v isos and p erforms sensitivity analysis un der some v ariations of the pro v i- sos. W e concen trate here on th e b asic proviso s and the resu lting conclusions. Undoubtedly , the p osterior p robabilities are impressive and seem to suggest that this is indeed the tom bsite of the NT family . Ho we v er, are the p ro visos reasonable? And more imp ortan tly , were the pro v isos sp ecified and w ere the analyses carried out according to the stated premises of the n ew appr oac h? And if n ot, what is the lik ely effect of the deviations f rom those premises? The a priori nature of the pro visos is amo ng the most imp ortan t premises of the new app roac h. In this con text, let us revisit fi r st the issue of the female names conta ined in the pr esumably a pr iori list of candidates. 3.1. The female nam es in the a prior i list o f c andid ates. Th e list of p oten tial c andidates includes the names Mariam and Salome “commonly b eliev ed to b e” J esu s’ sisters, Mary a (Jesus’ mother), and Ma ry Mag da- lene. Th e addition of Mary Magdalene is explained by th e fact that Mary Magdalene was “presen t a t the burial ritual.” The con tention th at Mary Magdalene’s ossuary is presumed to b e that inscr ib ed as Mariamene [ η ] Mara is justified by stating that Mariamne is “the most sp ecific a pp ellation to Mary Magdalene from among those kno wn.” But it is d ifficult to av oid the feeling that in a truly a pr iori compiled list, the probabilit y of addin g p ersons whose relation w as only that they we re “pr esen t at the burial ritual” and had n o familial relationship, were lik ely to b e quite lo w . (The iss u e of p ossible familial relationship is discussed , b u t the addition of the name is not b ased on it.) Moreo v er, the addition of the particular rendition of th e name to the list giv es a clear imp ression that after observ in g the data, the list wa s b iased in fa v or of H 1 . 6 C. FUCHS T able 2 RR-values for the cluste r of names in the T alpiot tombsite All sources Ossuary sources RR Name on Relative Relative Ossuary ossuary Generic name frequency Re n ditions frequency F e male #1 Mariamene Mary/Mariam 0.233 Mariamene 0.023 0 . 0053 = 0 . 23 · 0 . 02 #6 Mary a Mary a 0.29 5 0 . 0690 = 0 . 23 · 0 . 30 Male #2 Y eh u d a Y eh u d a 0.068 Discarded #4 Y esh ua Y esh ua 0.040 0.0403 #3 Maty a Mat ya/Mattit yahu 0.026 1 #4 Y oseph Y oseph 0.088 0.0881 #5 Y oseh Y oseph 0.088 Y oseh 0. 152 0 . 0134 = 0 . 09 · 0 . 15 F u rthermore, since th e particular rend ition is in the relev an t list, the in - scription Mariamenou [ η ] Mara is n o w pr esented as b eing a un ique rendition of Mariam b oth from ossuary as w ell as from nonossuary sour ces. The as- signed RR v alue to that name is 1.68 / 317, w ith the lar gest effect on th e o ve rall RR v alue. Clearly , if there is evidence that the elegan tly rendered ossuary inscrib ed Mariamenou [ η ] Mara is indeed the ossuary of the Mary Magdalene, the fin ding is sensational by itself. But if w e only use the sta tis- tical evid en ce, the fact that the effect on the o v erall result of the ins cription Mariamenou [ η ] Mara (w h ose p resence on the list is at least more am b iguous than the other names) is problematic, to sa y the least. W ere Mariamenou [ η ] Mara treated as “Other,” the o ve rall RR v alue w ould ha ve b een 188 times higher, w ith the corresp onding effect on the computed p -v alue. The effect of the inscription Mariamene [ η ] M ara also illustrates a further significan t deviation from the initial a priori definition of “surp rise” relativ e to H 1 . If th e alternativ e H 1 is that this tom bsite is that of the NT family , the “surpr isingness” sh ould indeed b e assessed with resp ect to H 1 and not (only) with resp ect to th e frequency table of the names. T o illustrate this p oint consider a c han ged configuration of only the thr ee male inscriptions, from (Y esh ua son of Y oseph, Y oseh and Mat ya) to (Y oseh son of Mat ya, Jacob and Y oseph). Note that there is no Y esh ua, and Y oseh is the son of an arbitrary Mat ya. Although a priori th e c hanged configur ation is by no means a serious candid ate for b eing the NT family tom bsite, under the su ggested metho d th e new configuration would h a ve had a lo wer RR v alue than the actual one, that is, a h igher “surpr ise.” DISCUSSI ON 7 3.2. “ Other ” and disqualifying names. No w let us add ress other features of the pr esumably a p riori selected relev an t lists. The relev an t lists are al- lo we d to include any n um b er of names d efined as “Other” as p ossibly b e- longing to p ersons a b out whom we ha v e no reco rds, with in dividual RR v alue of 1. Usin g this ru le, th e author computes the o ve rall RR v alues as a pro du ct of the RR v alues of only four out of the six inscrib ed ossuaries (!). The ossuaries inscrib ed as Y eh u da son of Y eshua (#2) and Mat y a (#3), although discus sed at length, con tribute n othing to th e computation of the o ve rall RR v alue. F ollo wing the rules set up b y the su ggested approac h , this pro cedur e is at least questio nable. A set of rules whic h weigh p ositiv ely (i.e., with a co efficient less than 1) names exp ected und er H 1 , bu t do es not we igh negativ ely names which are u n exp ected und er H 1 , is lik ely to bias in fav or of H 1 . Also, and con tinuing the previous p oint, it is men tioned th at “. . . the list of p ersons (b ut not n ecessarily names ) th at w ould disqualify the tombsite as b elonging to the NT family includes Joseph, S imon, and Y ehuda” (as the p ersons’ death did not o ccur in the relev an t p erio d of time, bu t the names ma y b elong to other p erson s ab out whom w e h a ve no records). But if, sa y , an ossuary inscrib ed “S im on ” wo uld ha ve b een found in that tom bsite (sa y , instead of that of “Mat ya ”) ho w could w e hav e kn o wn whether it b elongs to “that” Sim on (b rother of Jesus) or not? According to the “surp risingness” approac h, we wo uld ha ve ignored that inscription, as b elonging to “Other” (as b elonging to a p erson about whom w e ha ve n o records) and set the relev an t co efficien t to 1. Th e calculated p -v alue wo u ld ha ve b een exact ly as in the presen t case . Ho w can one th us judge the relev ance to H 1 and render judgment ab out disqualifying? The o v erall impression is that the inevitable exp osure to the data affecte d th e defin ition of the p ro visos in fav or of H 1 . 4. An other analysis. I men tioned ab o ve that the inclusion of MM in th e relev an t list h as a sub stan tial effect on the o v erall results and conclusions. W e can get an idea of th e order of magnitud e of that effect b y comparing the results present ed in F eur v erger’s pap er with th ose yielded b y another Ba y esian analysis p erformed on the same data by Kilty and Elliot ( 2007 ). They consider th e name Mariamene [ η ] Mara as irrelev an t, and treated it iden tically to the n ames on the ossuaries inscrib ed Y ehuda s on of Y eshua, and Mat ya. Th eir computation is based on a listing of 32 scenarios of com- binations of names one migh t exp ect to find in a NT family tombsite, based on Jesu s’ b r others and mother. All the scenarios h a ve to in clude the Y eshua son of Y oseph (in any rendition), and are assumed to b e equally probable. The a p osteriori probabilit y that this is in d eed the tom b site of the NT family giv en the data is estimated b y Kilty and Elliot as 0.487, v ery different from the v alues of well ab ov e 0.994, d educed fr om the o dd s ratios mentio n ed in F eu er verger’s article. 8 C. FUCHS The comparison b etw een Kilt y and Elliot’s resu lts and th e a p osteriori probabilities computed by F euerverger illustrates the effect of the inclus ion of Mariamene [ η ] Mara in F euerv erger’s list. Ob viously , other analyses of this data set are p ossible and in deed some are presen ted in articles p osted on the in tern et. I refer to Kilt y and Elliot’s article, since unlike others, they mention that th ey agree in principle with F euerverger’s conclusions and their in ten- tion in writing the article w as to sh o w that the cluster of name is “hard ly what a p erson should exp ect to fi nd r andomly .” They fur th er state that their figure is “quite comparable to F eu erv erger’s co nclusion ev en though the t wo are done from v ery d ifferen t standp oin ts.” T he statement seems to b e inaccurate, probably based on fragmen tary information of F euerverger’s results. 5. S ome final remarks. F euerve rger emph asizes the p ro visos for the ca l- culations, and men tions that the conclusion and the measure of su rprising- ness are based on a particular—bu t not uncont ested—set of assumptions. He men tions that “as lo ng as the definition of surprise is sp ecified fully and a priori, th e resulting appro ximate “tail area ” will essentia lly b e v alid.” It is difficult to accept that in this case, the elemen ts of the new approac h whic h are men tioned in the p ap er that ha ve to b e a priori sp ecified (the h yp othesis for the p roblem, the measur e of sur prisingness, the list of p ossible candi- dates, and the lists of nested p ossib le name r endition for eac h candidate), ha ve indeed b een so sp ecified. Th e final sentence in the pap er ca ndidly , and in m y o pinion v ery correctly , p oints to th e w eak est link in the foundation of the en tire exp osition and conclusions: “It is the presence in this b urial ca v e of the ossuary of Mariamenou [ η ] Mara, and the m ysteries concerning the iden tity of t he w oman kno wn as Mary Magdalene, that hold th e k ey for the degree to whic h statistic al analysis w ill ultimately pla y a substantiv e role in determining whether or not the bur ial ca ve at East T alpiot happ ens to b e that of the family of Jesus of Nazareth.” Let me re-phrase this sen tence: “If the o ssuary inscrib ed Mariamenou [ η ] Mara is in deed the ossu ary of the Mary Magdalene from the New T esta- men t, then, giv en th e other n ames inscrib ed on the other ossuaries and the assumptions presen ted in the p ap er, we can state with a v ery h igh d egree of confidence that that is the tom bs ite of the NT family .” I agree to suc h a statemen t. Th e only problem is th at no statistical ex- p ertise is necessary to reac h such a conclusion. If indeed, an ossuary pr oven to b e that of Mary Magdalene was to b e f ou n d, and in the same tom bsite w ere also to b e found ossuaries inscrib ed as Y eshua son of Y oseph, Y oseh and Mary a, it is u nlik ely that the arc heologists and the h istorians wo u ld app eal to stat isticians for help. In suc h a c ase, as men tioned, the ossuary o f the Mary Magdalene w ould hav e b een by itself an imp ortan t historical relic. DISCUSSI ON 9 On the other hand, if we don’t ha ve that level of confid ence regarding the Mary Magdalene ossuary , we hav e to r ely on statistical analysis. Unfortu- nately , in my opinion, the stated p rinciples of setting the assump tions we re not follo wed, b oth in the presumably a priori compilation of th e relev an t lists as well as in th e defi n ition of the RR v alues (which allo ws discarding data whic h ma y p oin t to w ard H 0 and assigns “surprisin gness” v alues based the rareness of name fr equencies r ather th an the actual closeness to H 1 ). The re- sulting effect on the conclusions reac h ed is dr amatic. Indeed, the narrator in the mo vie [Cameron ( 2007 )] announ ced that F euerv erger’s mo d el concludes that “there is only one c hance in 600 that the T alpiot tom b is not the Jesus family tom b, if Mary Ma gdalene can b e link ed to Mariamene.” Later, in an in terview on th e Scientific Americ an website [Mims ( 2007 )], F euerv erger is quoted as sa ying that “I did p ermit the num b er one in 600 to b e used in the film. I’m prepared to stand b ehind that but on the u nderstandin g that these n u m b ers w ere calculated based on assumptions that I was aske d to use ,” a statemen t far r emo ve d fr om the r igorous demand of a pr iori assu m ptions. [On h is w ebp age, F euerverger ( 2007 ) ment ions that th e qu otations in the in terview are “suffi ciently accurate to b e considered fair”.] In spite of the fact that, in m y opin ion, the analysis of the “surp risingness” based on the configu r ation of names f ailed to yield the stated conclusions, I refrain in this article from passing ju dgmen t on the sub ject matter issue of whether or n ot this is the tom b site of the NT family . F u rthermore, not withs tanding the reserv atio ns from the analyses applied to the d iscussed d ata, I applaud the b old initiativ e take n in th e discussed pa- p er to d ev elop a new approac h to tac kle a problem charact erized by a degree of complexit y that precludes th e straigh tforw ard app lication o f the classical h y p othesis fr amew ork. The general pr oblem of rending ju dgmen t on wh ether a multiple c h aracteristics observ ation represents the p ursued sp ecific en tity or it is just the result from r andom dra w s is interesting and in triguing. Cases of disputed p aternit y and DNA matc hing come to mind in this con- text. Unlik e the T alpiot case, in those cases a standard for comparison is a v ailable. The new app roac h and concepts of “sur p risingness,” “relev ance” and “ rareness” may ev olve and pro ve b eneficial in c ases in whic h there is no suc h standard exists. Classical method s, u s ually b ased on Ba yesia n analysis are a v ailable for those cases, but their application ma y b e d ifficult in complex situations. If the new approac h is to b e applied, its p erform ance needs to b e compared to existing metho ds in situations in wh ic h it is kno wn whether the n u ll hyp oth- esis (or the analogous null hypothesis) is correct. I think that th e features of the approac h still n eed to b e inv estigated theoretically or by sim ulations under v arious cond itions of complexit y . In an y case, the assu mptions ha ve to b e pre-sp ecified to ensure v alid resu lts and a v alid comparison. 10 C. FUCHS REFERENCES Ja cobo vici, S. and Pellegrino, C. (2007). The Jesus F ami ly T omb: The Disc overy, the Investigation, and the Evidenc e That Could Change History . Harp erCollins, San F rancisco. Cameron, J. (2007). T he Lo st T omb of Jesus . Discov ery Channel, March 4, 2007. Ilan, T. (2002). L exic on of Jewish Names in L ate A ntiqui ty , Part 1 : Palestine 330 BC E– 200 C E. Mohr Siebeck, T ubingen. Kil ty, K. T. and Elliot, M . (2007). Probabilit y , statistics and the T alpiot tom b . A v ail- able at http://www .lccc.wy. edu/Index.aspx?page=547 . Mims, C. (2007). Q&A with the statistician who calculated the o dds th at this tom b belonged to Jesus—An interview with the profess or who esti- mated the probability that a p articular tomb could hav e b een the fi nal rest- ing place of a family other th an that of Jesus. Scientific Americ an Website http://sci am.com/ar ticle.cfm?articleID=13C42878- E7F2- 99DF- 3B6D16A9656A12FF . Feuer ve rger, A. (2007). Dear statistical colleagues. T ext page. Av ailable at http://fis her.utsta t.toronto.edu/andrey/OfficeHrs.txt . Dep ar tment of S t a tistics and Opera tions Research Ra ymond and Beverley Sackler F acul ty of Exact Sciences Tel A viv University Rama t A viv , Tel A v iv Israel 69978 E-mail: fuch s@post.tau.ac.il