Monday, September 10, 2007
Talpiot Tomb Statistics Article
Probability, Statistics, and the Talpiot Tomb
Kevin T. Kilty, Ph.D., P.E.,
Mark Elliott, Ph.D.
It's already been noted by several people, including James Tabor and Darrell Bock, the latter with some interesting comments on Yoseh. I would like to comment on this article myself in due course, but I am working through a backlog at the moment and may not have time for a little. I look forward to comments from the statistical experts who earlier weighed in on this topic.
Labels: statistics, Talpiot tomb
Wednesday, March 28, 2007
Talpiot Tomb Various
Bayes' Theorem and "The Jesus Family Tomb"
I have been lucky to be able to listen to the experts talking about the statistics in an email discussion initiated by James Tabor and featuring Randy Ingermanson, Jay Costs, Joe D'Mello and others.
Meanwhile, Robert Gundry has a guest post on Bruce Fisk's Crossings:
Robert Gundry on the physicality of Jesus' resurrection in earliest Christian proclamation
The post responds to James Tabor, partly on the Talpiot Tomb but also on The Jesus Dynasty. Speaking of James Tabor, you can now read a helpful summary of his thinking about the tomb on his blog:
The Talpiot Jesus Tomb: An Overview
This overview has brought about a series of responses by Darrell Bock on Bock's Blog, on Historical Context, Statistics, Inscriptions and Tabor's Hypotheticals.
In a March 13 post on Talpiot Tomb Various, I noted Michael Heiser on the ossuaries found at Dominus Flevit:
I want to draw your attention—and the attention of scholars and interested parties who read your blog—to a SECOND site that has all those names. In 1953-1955, Bellarmino Bagatti excavated the site of Dominus Flevit (“The Lord wept”) on the Mount of Olives. The excavation uncovered a necropolis and over 40 inscribed ossuaries – including the names of Mary, Martha, Matthew, Joseph, Jesus. These ossuaries are not, as far as I can tell, in Rahmani’s catalogue. I’m guessing the reason is that they are not the property of the Israel Antiquities Authority (see Rahmani’s Preface). The necropolis was apparently used ca. 136 BC to 300 AD. Here is a link that discusses the site. A few scanned pages of Bagatti’s excavation report (written in Italian) can be found here as well.Now Antonio Lombatti emails:
I teach Medieval History (my field of research is the cult of Christian relics) and, while reading your excellent NT Blog, I came across the quotation of the Dominus Flevit excavations. There you quoted the Bagatti and Milik 1958 book which is, unfortunately, in Italian. Well, I am Italian... I got it and read it carefully. And I found out that on the 34 ossuaries Bagatti and Milik found there were (also) the following names: Jesus, Mary, Joseph, Judas, Mathew, Martha and... Mariame.The humour is still coming too. Chris Brady links to a delightful cartoon Tomb of Star Trek and there are plenty of places that crack the inevitable but still funny joke that the one thing that would have convinced them that this was Jesus' tomb would have been the discovery of a bracelet in there reading "WWID?"
But, above all, the names Mary and Mariame were inscribed on the same ossuary and were found in the very same loculus. And, last but not least, the inscriptions were in GREEK.
It is worth mentioning too that discussion of the Talpiot tomb continues apace on the ANE-2 list, including regular contributions from Joe Zias and James Tabor.
Labels: ossuaries, statistics, Talpiot tomb, TV documentaries
Friday, March 16, 2007
Discovery Website Adjusts Tomb Claims
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I just checked the Discovery Channel website and noticed that all three changes have been made.
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Dr. Andrey Feuerverger, professor of statistics & mathematics at the University of Toronto, has concluded a high statistical probability that the Talpiot tomb is the JESUS FAMILY TOMB.changed to
Dr. Andrey Feuerverger, professor of statistics at the University of Toronto, has concluded (subject to the stated historical assumptions) that it is unlikely that an equally "surprising” cluster of names would have arisen by chance under purely random sampling.===========
Taking into account the chances that these names would be clustered together in a family tomb, this statistical study concludes that the odds – on the most conservative basis – are 600 to 1 in favor of this being the JESUS FAMILY TOMB. A statistical probability of 600 to 1 means that this conclusion works 599 times out of 600.changed to:
Taking into account the chances that these names would be clustered together in a family tomb, this statistical study concludes that the probability under random chance of observing a cluster of names as compelling as this one within the given population parameters is 600 to 1, meaning that this conclusion works 599 times out of 600.===========
"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."changed to
A statistical study commissioned by the broadcasters (Discovery Channel/Vision Canada/C4 UK) concludes that the probability factor is in the order of 600 to 1 that an equally "surprising" cluster of names would arise purely by chance under given assumptions.---------------
Labels: ossuaries, statistics, Talpiot tomb, TV documentaries
Thursday, March 15, 2007
Talpiot Tomb Statistics Update
The Statistics Behind "The Tomb"
Jack Poirier
This may be a good occasion to bring together in one place the other major articles on the statistical case:
Statistics and the "Jesus Family Tomb"
Randy Ingermanson
Examining the "Jesus Tomb" Evidence
Jay Cost
The Improper Application of Statistics in "The Lost Tomb of Jesus"
Stephen Pfann
Talpiot Tomb: Statistics
Includes several posts by Joe D'Mello
The last of these links is to all the material relevant to the statistical case from this blog, including several guest posts by Joe D'Mello, in interaction with Andrey Feuerverger, whose most recent statement is on his homepage.
Labels: ossuaries, statistics, Talpiot tomb, TV documentaries
Tuesday, March 13, 2007
Talpiot Tomb Various
I want to draw your attention—and the attention of scholars and interested parties who read your blog—to a SECOND site that has all those names. In 1953-1955, Bellarmino Bagatti excavated the site of Dominus Flevit (“The Lord wept”) on the Mount of Olives. The excavation uncovered a necropolis and over 40 inscribed ossuaries – including the names of Mary, Martha, Matthew, Joseph, Jesus. These ossuaries are not, as far as I can tell, in Rahmani’s catalogue. I’m guessing the reason is that they are not the property of the Israel Antiquities Authority (see Rahmani’s Preface). The necropolis was apparently used ca. 136 BC to 300 AD. Here is a link that discusses the site. A few scanned pages of Bagatti’s excavation report (written in Italian) can be found here as well.Meanwhile, I've just received an updated version of Jack Poirier's article on the statistics and the tomb. It is to appear on Jerusalem Perspective Online but isn't there yet. As Jim West points out, Stephen Pfann has announced a re-reading of the "Mariamenou Mara" inscription -- see Scholar: 'Jesus Tomb' documentary got it wrong on CNN. And the SBL Forum carries responses by James Tabor to Jodi Magness and Christopher Rollston and to Jonathan Reed. On his blog, he promises breaking news.
I have one more thing to do, to complete my list of Errors and Inaccuracies later today. There are quite a lot still to get through. I am grateful to hear today from James Tabor that these have been reported back to those responsible for the site with a view to making corrections and adjustments.
Labels: ossuaries, statistics, Talpiot tomb, TV documentaries
Correction on Discovery Tomb Website
==================
Discovery Channel has made one correction!
Note that the following paragraph from the 'Tomb Evidence' PDF file:
Taking into account the chances that these names would be clustered together in a family tomb, this statistical study concludes that the odds – on the most conservative basis – are 600 to 1 in favor of this being the JESUS FAMILY TOMB. A statistical probability of 600 to 1 means that this conclusion works 599 times out of 600.has now been changed to
Taking into account the chances that these names would be clustered together in a family tomb, this statistical study concludes that the probability under random chance of observing a cluster of names as compelling as this one within the given population parameters is 600 to 1, meaning that this conclusion works 599 times out of 600.I believe that this is an acknowledgement that the computed 600:1 odds really have no direct bearing to whether or not this is the family tomb of Jesus. It is very disappointing to note that Discovery is using a misleading play on words even in this "corrected" version. Notice that they are using the statistical term "population" (in this case the name combinations on the inscribed ossuaries in the roughly 1,100 family tombs) in a manner that the majority of readers will interpret as the "Jews who were living in the area at the time". There is a big difference! The odds would be much less with that latter interpretation!
While I am clearly happy that a change has been made - at least we are moving in the right direction - there are two other paragraphs (below) that are still not corrected, and I have e-mailed Dr. Feuerverger again inquiring why these were not changed. I hope that this will be the beginning of many changes that Discovery will make to correct inaccurate statements on their sites. Inaccuracies don't make for good and healthy debates!
"Dr. Andrey Feuerverger, professor of statistics & mathematics at the University of toronto, has concluded a high statistical probability that the Talpiot tomb is the JESUS FAMILY TOMB."AND
"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."
====================
Labels: ossuaries, statistics, Talpiot tomb, TV documentaries
Saturday, March 10, 2007
Adjustments to Discovery Website Statistics Claims
Discovery to Update Website Claims (PDF)
And I excerpt the major part of it here:
---------------
Date: Friday, March 9, 2007
I am pleased to state that as a result of several e-mail exchanges I have had with Dr. Andrey Feuerverger over the past few days, and a phone conversation with him this morning which confirmed our informal understanding reached by e-mail yesterday, he has agreed that the following two statements made on Discovery Channel’s website:
1. “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.” (from http://dsc.discovery.com/convergence/tomb/about/about.html)ARE NOT A CORRECT INTERPRETATION OF HIS STATISTICAL COMPUTATIONS. He has also confirmed for me that, at his urging, Discovery Channel has agreed to “undertake the required updates to their website”. As evidence of this, I have appended at the end of this message the relevant portions of the last few emails I exchanged with Dr. Feuerverger.
2. Dr. Andrey Feuerverger, professor of statistics & mathematics at the University of Toronto, has concluded a high statistical probability that The Talpiot tomb is the JESUS FAMILY TOMB. In a study, Feuerverger examined the cluster of names in the tomb …… Taking into account the chances that these names would be clustered together in a family tomb, this statistical study concludes that the odds – on the most conservative basis – are 600 to 1 in favor of this being the JESUS FAMILY TOMB. A statistical probability of 600 to 1 means that this conclusion works 599 times out of 600.
(from http://dsc.discovery.com/convergence/tomb/explore/media/tomb_evidence.pdf)
Dr. Feuerverger indicates that an accurate interpretation of his results are to be found at his recently updated “Tomb Computation” link on his University of Toronto website. Please note the following excerpts from that website:
A. It is not in the purview of statistics to conclude whether or not this tomb site 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.
B. 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.
C. 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, and does not take into account families living outside of the Jerusalem area.
I wish to thank Dr. Feuerverger immensely for his efforts to ensure that the viewing public receives the honest and truthful reporting they are entitled to! I also hope and trust that Discovery Channel will follow suit and retract these inaccuracies quickly. As I have stated before, my efforts were never aimed at defending Christianity, because I truly believe that all religions must and will eventually reconcile themselves with science and our God-given reason. It is not Christianity that is at stake here but the honest and enlightened use, application, and interpretation of science and reason. Discovery Channel’s unqualified assertions that the 600:1 odds are specifically associated with the tomb in question being that of the New Testament Jesus family are, in my opinion, untenable and inaccurate in light of the clarifications on Dr. Feuerverger’s website.
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Labels: ossuaries, statistics, Talpiot tomb, TV documentaries
Friday, March 09, 2007
The Numbers Guy on the Talpiot Tomb Calculations
Odds of 'Lost Tomb' Being Jesus' Family Rest on Assumptions
Carl Bialik
. . . "As you pile on more assumptions, you're building a house of cards," says Keith Devlin, a Stanford mathematician and NPR's "Math Guy." (Scientific American also challenged the calculation on its Web site.) . . . .The article doesn't tell us much more than we already knew, but it does help to underline the point that I have been making since my post last week on The Statistical Case for the Identity of the "Jesus Family Tomb", viz. that any statistical calculation is only as good as the data fed to the statistician; the numbers are only as good as the assumptions they are based on, and here there are major problems with those assumptions.
. . . . "I wouldn't be comfortable coming up with a number like this, because the general audience will not understand that it is very, very subjective," says Ivo Dinov, assistant professor of statistics at the University of California, Los Angeles . . . .
. . . . He still hasn't provided full documentation of his calculation, saying he'd wait until his paper, not yet completed, is accepted by a journal. "There is a mismatch between how the media works and how academia works," Prof. Feuerverger says. "Obviously it would have been a whole lot better if I had completed the paper" before the documentary aired . . . .
. . . . . "When I was doing the calculation, I was naively unaware of the extent to which the filmmakers might be depending on the ultimate result of it," he says. "I did carry out the calculation in every good faith. I hoped it would be interpreted in that light."
Labels: ossuaries, statistics, Talpiot tomb, TV documentaries
Sunday, March 04, 2007
The "Jesus Family Tomb" Statistics: Further Developments
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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
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.
Labels: ossuaries, statistics, Talpiot tomb, TV documentaries
Tomb Statistics: Feuerverger Responds
The Tomb Computation
The latest version of this is dated today, 4 March. Feuerverger's response confirms my concerns, earlier mentioned, about the assumptions that went into the statistical calculations. I was concerned especially about the way that "Mariamne Mara" and "Judas son of Jesus" were being dealt with. It seemed to be that "Mariamne Mara", far from being treated as a neutral or a non-match element, was actually being used as the "Ringo" piece of data, i.e. the really distinctive name that was clinching the identification, something that is highly problematic for reasons stated here and in other places on multiple occasions. And "Judas son of Jesus" was regarded simply as a neutral piece of data, not a non-match of such decisive importance that it should in fact have been radically detracting from the overall probability. In the light of these concerns, now note the following important elements in Feuerverger's response. He rightly makes clear that: "The results of any such computations are highly dependent on the assumptions that enter into it" and lists as one important assumption the following:
We assume that `Marianemou e Mara' is a singularly highly appropriate appellation for Mary Magdalene. Note that this important assumption is contentious and furthermore that statistically this assumption drives the outcome of the computations substantially.Note too:
We assume that the presence of Matya does not invalidate the find but we assign no evidentiary value to it (other than factoring in its combinatorial role). We also assume that the Yehuda son of Yeshua ossuary does not invalidate the find but we ignore it in the computations. This last assumption is contentious.Later, he also notes:
The apparent absence of `negatives' in the finding, i.e. of archeological details that would in and of themselves invalidate `the hypothesis' or that would appear to lessen its likelihood.Well, Judas son of Jesus is just the kind of "negative" which, I have argued, should have seriously detracted from the alleged plausibility. The fact that it was not factored into the assumptions governing the calculations remains highly problematic.
As I see it, the problem with all of this goes back to the difficulty of Jacobovici mediating the discussion between archaeologists, biblical scholars and statisticians. The data that Feuerverger is working with is data that already has a particular spin on it, data that is cherry picked and manipulated. This is an unacceptable basis for a strong statistical analsysis.
Labels: ossuaries, statistics, Talpiot tomb, TV documentaries
Saturday, March 03, 2007
The Jesus Family Tomb: Some Further Thoughts
To make a valid statistical argument, you shouldn't start with the names in the tomb you have already , observe that some of them resemble names from the NT, and then conclude, based on statistics, that this exact combination of names is very unlikely and must be the very same individuals. Instead, you need to start with the whole basket of names that we have for Jesus's family (of which Mary Magdalene is not one). This list includes: Jesus, Joseph Sr., Mary, Zacharias, Elizabeth, John, James, Joseph Jr., and Simon. This is 9 individuals. And if you really want to speculate about non-relatives (like Mary Magdalene) named in the Bible who might under some circumstance have been buried in a tomb with them, the list would only lengthen considerably, because objectivity would demand that Mary #2 not be the only name considered. Then it would have to be calculated statistically, based on the known frequency of names and known number of family tombs that would have existed at the time (not merely those we have found), just how many such tombs would have collocations of each permutation of these names. I must believe that a tomb with 10 ossuaries that only contained 3 out of the initial 9 names--3 very common names--along with one outside the 9, cannot be that unlikely.Also in comments, Matt Page writes:
I'm not sure you are quite right about the statistics, your comments have more to do with the way those statistics are taken and interpreted.Not quite. My comments are more to do with the evidentiary basis for the statistics, i.e. the information that was fed to Feuerverger, which I regard as (a) incomplete (Matia and Judas son of Jesus are not neutral data) and (b) misleading (Mariamne Mara is not a name given to Mary Magdalene, or Mary Anyone Else from the Gospels, nor -- if it were -- is anyone in Jesus' family given that name). So my complaint is not about what they did with the statistics but what they did before they had started with the statistics, i.e. the information fed to the statistician, hence my use of the term "cherry picking". Matt continues:
The probability of a certain cluster occurring (Jesus, Joseph, Mary, Joses, James) within a group of 10 is not affected by other names that may or may not also be present. What the filmmakers are trying to say is that this combination alone is so unlikely that this must be the tomb of THE Jesus. The rest really is trying to explain the unusual data within that given frame.I think this accurately conveys what the film-makers are claiming, but it is flawed, not only because there is no James, but also because clustering becomes increasingly less impressive relative to the size of the sample. So it is clearly more likely to get the names in question occurring in a group of seven named ossuaries than it is in a group of three -- and so on. Michael Turton expresses the problem, also in comments, in the following useful way:
the real question is: what are the odds that a tomb with ten ossuaries is going to contain a half dozen names that might be construed as significant in an NT context? In other words, if they had found Joseph, Joses, James, Andrew, and Peter, it would have been just as suggestive. So would Mary, Barabbas, Cleophas, John, and Saul. Or James, Andrew,.... there must be tens of thousands of such combinations -- especially, as Mark points out, if you get to cherry pick your data set.Meanwhile on Deinde, Danny Zacharias suggests that the film-makers are aware of the problem over "Judah son of Jesus" and so suggest that this is the beloved disciple, with some spurious exegesis to get one there.
James Tabor, the scholar most closely associated with the documentary, has a useful post on the Flawed Statistics & Ossuary Names and news of the Ted Koppel show to air on Sunday after the documentary, and featuring James Tabor as well as Darrell Bock, who also mentions it. A quick word about the tone of James Tabor's posts on The Jesus Dynasty Blog: he is setting a high standard for civil and respectful discourse. It is a pleasure to see the non-polemical tone and others could learn from it.
If you are getting a bit fed up of the whole thing, there is some great humour around. Jon Steward on the Daily Show is a must see -- go to The Daily Show website. Thanks to several people who have drawn attention to this, e.g. Joe Weaks on the Macintosh Biblioblog. Or on Paleojudaica, Jim Davila mentions Scott ("Dilbert") Adams' humour on the same issue. And one of my favourite comments in my blog was the person who remarked, "What is the likelihood that Jesus would have named his son Judas, of all names . . . "!
There are several more things I would like to mention. My email inbox is choc-a-bloc. So please be patient. More later.
Labels: ossuaries, statistics, Talpiot tomb, TV documentaries
Friday, March 02, 2007
The correct interpretation of Dr. Andrey Feuerverger's 1:600 odds calculation
Available here as PDF
I would particularly like to draw your attention to the request for additional data below. Does anyone know a good place for the collection of the relevant pieces of data? Thanks.
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The correct interpretation of Dr. Andrey Feuerverger's 1:600 odds calculation
Joe D'Mello
There has been plenty of discussion focused on the validity of the numbers and the assumptions used in Dr Andrey Feuerverger's calculation that results in a 1:600 odds claim. While that discussion is certainly interesting, there is a more fundamental issue associated with the very interpretation of this 1:600 odds calculation.
I am a mathematician or, strictly speaking, a former mathematician. After earning my Ph.D. in mathematics from
First, I would like to point out that Dr. Andrey Feuerverger's calculation is nothing very fancy, involving only very basic mathematical probability that is taught in many undergraduate programs and business schools. It is conceptually no deeper than a problem I could include on a take-home final exam for my MBA students. Actually, several decades ago, when I was a teaching assistant at the State University of New York, I remember giving my undergraduate freshman class problems that required this level of understanding of mathematical probability.
Second, I am willing to accept the 1:600 result that Dr. Andrey Feuerverger has computed. However, it is the INTERPRETATION of this 1:600 result that is of crucial significance here. The media are touting this 1:600 result as:
Interpretation A: “There is only a 1 in 600 chance that this is NOT the Jesus family tomb.” OR, equivalently, “There is a 599 in 600 chance that this IS the Jesus family tomb.”
This interpretation is mathematically, statistically, and semantically flawed, and I am sure that Dr. Andrey Feuerverger is well aware of that. I am really shocked that an individual of his stature would not set the record straight on this and try to make sure that the public knows the correct interpretation. Then again, the truth does not always make for good business or popular TV. Using numbers and language precisely often runs contrary to the goals of advertising! It is generally more advantageous to advertisers to word numerical results and statistical findings in a manner that appears precise and impressive without necessarily being so.
If you read through Dr. Andrey Feuerverger’s calculation at the end of the PDF file on the Discovery Channel website, it is clear that he is restricting his “population” (in a statistical sense) to the roughly 1,000 tombs found in the geographic area in question. He is not basing his calculation on the overall Jewish populace in the area and the time period in question. So, the correct interpretation of his 1:600 odds calculation is:
Interpretation B: "There is a 1 in 600 chance that this particular cluster of names would occur in one of the roughly 1,000 tombs discovered so far"
An alternative but equivalent (to B) interpretation of the 1:600 odds result is:
Interpretation C: "If the Jesus family did indeed have a family tomb (that was among the 1,000 found), then there is a 599 in 600 chance that this particular tomb found is indeed that of the Jesus family"
Clearly, these latter and correct interpretations (B and C) would not sell the TV program very well! What Dr. Andrey Feuerverger has calculated here is known in probability theory as a “conditional probability” (more about that later!). This means that you are calculating the probability of one event on the condition that another has occurred.
If Cameron wants to invoke probability to make his point - and I commend him for trying to do that – then the more relevant probability that he should have gone after is:
“Suppose that (for argument's sake) the cluster of names in question did in fact occur in Jesus' family (assuming that Mariamne was part of that family). Then, what is the probability that there would be at least one other Jewish family in the geographic area in question that had the same name cluster?”
I suspect that if this probability is calculated it would burst Cameron’s bubble and sink his story faster than the Titanic! I would be happy to calculate this probability but would need (ideally) the following data:
1. The name cluster that would make sense to work with (based on the facts known to leading New Testament scholars)
2. The frequencies of these names from a gender perspective. For example: 1 out of every 6 women was named Mary, 1 out of every 12 males was named Jesus, etc.
3. The appropriate geographic area and time period (example: 10 to 110 AD) to consider for this calculation and the population of males and females in that area during that entire time period
4. The percentage of families at that time that would have had family tombs
If I could get help assembling this data, I will be able to quickly compute the probability.
There is another avenue one can take here that uses Dr Andrey Feuerverger's own calculation to calculate a probability far more relevant to Cameron’s claim! To explore that avenue, let’s get back to the notion of conditional probability! Recall that the correct 1:600 odds interpretation is:
Interpretation C: "If the Jesus family did indeed have a family tomb (that was among the 1,000 found), then there is a 599 in 600 chance that this particular tomb found is indeed that of the Jesus family"
Those of you mildly comfortable with quantitative concepts and probability terms should be able to follow the next few computations. The others can just skip the computations and read the text conclusions.
Let B be the event that the 1,000 (approximately) family tombs found to date in the area in question included the Jesus family tomb among them; and let A be the event that the particular tomb found is that of the Jesus family. In the language of probability, Dr. Andrey Feuerverger has calculated:
P(A|B) (read as “the probability of A given that B has occurred”) and he estimates it to be about 599/600
We know from classical probability theory that
P(B) * P(A|B) = P(A and B) (* stands for multiplication)
Now, P(A and B) is the probability that the Jesus family had a family tomb AND that the tomb discovered is that of the Jesus family. Note that the media are taking P(A|B) (Feuerverger’s 599/600 number) and wording it in a manner that makes it appear to the general public that it is in fact P(A and B). This is a fallacy and an out right deception! It behooves Dr. Andrey Feuerverger as a respected member of the academic community to set the record straight here.
To calculate P(A and B) we would need to estimate P(B) and THEN use Dr. Andrey Feuerverger’s 599/600 number. Note that several experts, including Professor Amos Kloner (of
P(B) * P(A|B) = P(A and B)
We see that P(A and B) = (1/10) * (599/600) = 0.1 (approximately). This immediately slashes the probability of the discovered tomb being that of the Jesus family down to 0.1 or 10%. In other words, there is then only a 10% chance that the discovered tomb belongs to the Jesus family – a number not likely to draw a runaway TV audience for Cameron!
Finally, I would like to note that, in the spirit of intellectual honesty and fairness, I sent two e-mails to Dr. Andrey Feuerverger at his
I would really love to have an open and honest discussion (maybe on this blog!) with Dr. Andrey Feuerverger and find out if he agrees or disagrees with what I have claimed above. If anyone can induce him to enter into a discussion that would be great!
Date: Wed, 28 Feb 2007 08:59:07 -0800 (PST)
From: Joe D'Mello
Subject: Fwd: Request for assumptions & calculations
To: andrey@utstat.toronto.edu
CC: president@utoronto.ca
Dear Professor Feuerverger,
Since I did not hear back from you on the email I sent yesterday (copy below), I sent a formal request today to Discovery Channel requesting the assumptions and details underlying your calculations, and am also copying your president, Dr. David Naylor, on this email. I'm sure that as a respected faculty member of a university of worldwide repute, any professional assertions you make, especially in matters that have profound historical significance, will have sound documentation and analysis, and will pass the highest levels of academic scrutiny and peer review.
The brief numerical calculation in the pdf document on The Discovery Channel website raises more questions than it answers, and it appears to me that the logic is flawed. However, I cannot be sure unless I can inspect the detail and assumptions underlying your calculations. Will it be possible for you to send me these? Better still, could you kindly post that detail (at a level comparable to that of a scholarly research publication) on the Discovery Channel website, so that fellow academics can have the opportunity to understand and appreciate your work?
Best regards,
Dr. Joe D'Mello
Joe D'Mello
Date: Tue, 27 Feb 2007 08:49:19 -0800 (PST)
From: Joe D'Mello
Subject: Request for assumptions & calculations
To: andrey@utstat.toronto.edu
Dear Professor Feuerverger,
As a fellow mathematician I am sending you this email to request your calculations (and associated assumptions) for the probability numbers being circulated in the media about the 600:1 odds (attributed to your calculations) that the tomb belonged to Jesus's family. I am generally suspect of media coverage, and want to get the real scoop directly from you, so I can get a better understanding of the assumptions and the true interpretation of these odds. I would appreciate any information you can provide in this regard.
Best regards,
Joe D'Mello
Labels: ossuaries, statistics, Talpiot tomb, TV documentaries
Thursday, March 01, 2007
The Statistical Case for the Identity of the "Jesus Family Tomb"
Before beginning, let's get the key information at our fingertips. The Statistics claim is discussed at Monday's Press Conference (Discovery Channel Website, links on left), in Simcha Jacobovici's interview (especially Parts 3-4), in the Tomb Evidence PDF from the Discovery site (go to p. 13), and in three pages on the Jesus Family Tomb website headed Probability, The Football Field and Probability: Principles Adopted.
The major part of the case that the Talpiot tomb is Jesus' family tomb is based on a statistical claim. It is thought to be so unlikely that this cluster of names, so familiar from the New Testament record, would show up by accident that the identification of this tomb with the family of Jesus is on firm ground. What are the chances, they ask, that one would find a Jesus son of Joseph together with a Maria, a Mariamne and a Jose? Their answer is that the chances are something like 600:1 on a conservative estimate. The identification between this tomb and Jesus' family is all but certain.
I think this case is severely flawed. The essential problem, as I see it, is that the matches between the Talpiot tomb and the early Christian literary record are factored into the calculations in a positive way, but the non-matches are simply ignored, or treated as neutral. This will not do. If a case is built up on the notion that a remarkable cluster of names in a given places matches with a known cluster of names in another place, it is essential that the non-matches are taken seriously too, all the more so when some of the non-matches are not only non-matches but also contradict the literary record. The non-matches are simply absent from the statistical calculations here. The non matches in question are three, and the first of these needs to be underlined because it is being treated not only as a match but as one of the key matches:
- There is no reliable historical tradition that Jesus was married to a woman called Mariamne (or for that matter Mary, Salome, Joanna or anyone else). It is important to underline this. It is an unexamined assumption that lies behind all the film-makers' discussion of the "family tomb". The ultimate source of this is, I am afraid, popular fiction like The Da Vinci Code. I would not want to assume that the film-makers' research here was deficient by suggesting that The Da Vinci Code was the source of their information but remarkably, they are actually citing it in their remarks in favour of the identification, as if The Da Vinci Code is here giving shared knowledge.* Now given that no reputable historian of Christian origins seriously thinks that Jesus was married to Mary Magdalene (or anyone else, as far as we know), the presence of a Mariamne in the tomb can in no way be allowed to be a part of the statistical calculations here. We cannot assume unevidenced data in setting up the calculation. If the statistical calculation is to have any validity at all, we must work only with the known quantities.
- There is no reliable historical information that anyone called Matia was related to Jesus' family. The film-makers appear to be aware of this, and talk about the possibility that he might be a relative by marriage, perhaps one of Jesus' sister's husbands. (At the press conference, it is even suggested that he might have been the Gospel writer). One cannot allow negatives like this to be left out of consideration. The Matia ossuary is a non match with any of the data we have about Jesus' family and it cannot be left out of the calculations. In other words, this is not simply a piece of neutral information that one can leave to one side. It needs to be given negative weight, to detract from the probability that this is Jesus' family tomb.
- There is no reliable historical information that a character called Judas son of Jesus was connected with the Jesus movement. Indeed, this is evidence that contradicts the literary record in a striking way. Let us be clear about how important the appearance of this character is. There is no record of Jesus having any children, and so the evidence here contradicts the identification of the tomb as Jesus' family tomb. It will not do to say that our evidence is incomplete, or that this is an argument from silence, or that we should not rule out the possibility that Jesus had children. The point is that the case being made by the film makers is a case built up on the basis of an alleged remarkable match between one set of data (the names on the ossuaries) and another set of data (the early Christian record). Where that is the basis of the case, it is essential that non matches between the sets of data are taken as seriously as the matches, all the more so where non-matches actually contradict elements in the early Christian record.
One can view the data that was given to Feuerverger on the Discovery website, in the PDF packet of documentation, where the grounds for the statistical analysis are given. It is clear from this that the task he was given was to work out the probability of a certain cluster of names occurring, where in each case all known examples of the given name in the given period were divided into all known naming possibilities in the given period. And the names he worked with were Jesus son of Joseph, Mariamne, Maria and Joseph. The name Matia was initially factored in too, and then removed "since he is not explicatively [sic] mentioned in the Gospels". But the problem is not just that Matia is not mentioned as a family member in the Gospels, it is that the greater the number of non-matches, the less impressive the cluster becomes. Or, to put it another way, it stops being a cluster of striking names when the cluster is diluted with non-matches. Mariamne needs to be taken out of the positive calculation and instead treated as a non-match; Matia needs to be treated as a second non-match; Judas son of Jesus needs to be treated as contradictory evidence. These three pieces of data together detract radically from the impressiveness of the given cluster.
At the risk of labouring the point, let me attempt to explain my concerns by using the analogy of which the film-makers are so fond, the Beatles analogy. This analogy works by saying that if in 2,000 years a tomb was discovered in Liverpool that featured the names John, Paul and George, we would not immediately conclude that we had found the tomb of the Beatles. But if we also found so distinctive a name as Ringo, then we would be interested. Jacobovici claims that the "Ringo" in this tomb is Mariamene, whom he interprets as Mary Magdalene and as Jesus's wife, which is problematic (see Mariamne and the "Jesus Family Tomb" and below). What we actually have is the equivalent of a tomb with the names John, Paul, George, Martin, Alan and Ziggy. We might well say, "Perhaps the 'Martin' is George Martin, and so this is a match!" or "Perhaps John Lennon had a son called Ziggy we have not previously heard about" but this would be special pleading and we would rightly reject such claims. A cluster of names is only impressive when it is a cluster that is uncontaminated by non-matches and contradictory evidence.
In short, including Mariamne and leaving out Matia and Judas son of Jesus is problematic for any claim to be made about the remaining cluster. All data must be included. You cannot cherry pick or manipulate your data before doing your statistical analysis.
* One example of this is Jacobovici's interview, Part 4, where he says: "There are two Marys in Jesus' life, as everybody knows, one is his mother, you know, the Virgin Mary, and the other is, Mary Magdalene, you know, post Da Vinci Code everybody knows Mary Magdalene." There are actually at least four Marys in the Gospels, not two: (1) Mary mother of Jesus, (2) Mary Magdalene, (3) Mary sister of Martha, (4) Mary of James and Joses, and (5) Mary of Clopas, though (1) and (4) may be the same person, or (4) and (5) may be the same person. None of these is described as Jesus' wife.
Labels: ossuaries, statistics, Talpiot tomb, TV documentaries
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