Jun 29 2012

The Jesus Tomb and Bayes’ Theorem

Finally, a mathematician actually gets the math right on the Jesus Tomb hypothesis. Conclusion? We have not found the tomb of Jesus. For those who already know the backstory and want to jump right to it, read Bayes’ Theorem and the “Jesus Family Tomb” by physicist Randy Ingermanson. He approached the problem like a physicist dealing with any old problem in data analysis (the problem is not so much different from how particle accelerator data are analyzed). He was assisted by political scientist Jay Cost, another who has good experience running Bayesian models like this. This expands on Ingermanson’s work on this published under peer review as Randall Ingermanson, “Discussion of: Statistical Analysis of an Archaeological Find,” Annals of Applied Statistics 2.1 (2008): 84-90 (responding to Feuerverger).

Backstory: James Tabor and some others have been pushing the claim that a tomb uncovered in the Talpiot district of Jerusalem (hence now called the Talpiot tomb) is the actual burial place of Jesus (and we not only have his “coffin,” but his DNA! As well as evidence he had a child named Judas by Mary Magdalene, also buried therein, also with her DNA!), and they published a book and a documentary arguing their case. (I’m just being colloquial. The tomb’s not full of coffins, of course, but ossuaries, a cultural analog). They had a mathematician backing them (Dr. Andrey Feuerverger), but his math has been consistently bogus from day one. For example, even though we have vastly better odds of randomly getting a name in a group of ten-to-thirty bodies than in a group of five, he kept running the math for five, even though there were ten-to-thirty bodies buried in that tomb. He also adopted a number of dubious (and some outright refuted) factual assumptions (for example, regarding the names of the women in the tomb: see, as one instance, the penultimate paragraph of my previous article on this tomb). By these devices, he found the odds were 600 to 1 in favor of this being the actual tomb of Jesus.

What happened: Ingermanson and Cost apply the correct math (Bayes’ Theorem, valid historical premises, proper treatment of variables, and correct mathematical models, e.g. acknowledging that more than five people were buried there). They find that by standard historical assumptions, the odds are 1 in 19,000 against the Talpiot tomb being the tomb of Jesus, and even by more generous assumptions the odds are 1 in 1,100 against (I put my own assumptions into their model and came up with 1 in 200 against), while even the most fanatical “I desperately want this to be the tomb of Jesus” estimator can only get odds of 1 in 18 that the Talpiot tomb is the tomb of Jesus. Thus, it probably isn’t, even if we are ridiculously generous to the hypothesis that it is.

So much for that. Done and dusted.


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  1. 1
    Jason Goertzen

    Perhaps you didn’t get the memo, Richard. Bayes’ Theorem can’t be used for this sort of thing. *rolls eyes*


    1. 1.1
      Richard Carrier

      Thanks. Yes, memo to anyone reading that: This is exactly the kind of thing BT can be used for. It is in fact the only mathematically correct way to answer the question of how likely this name cluster is on chance alone vs. any particular causal theory.

      As for the article you link to (in case anyone is curious–eye roll was indeed appropriate), it has nothing to do with this case or anything comparable to it. All it does is make weird rambling objections to things I say about completely different kinds of historical questions. And since it ignores most of what I do say about that, and gets wrong a lot of what I say as well, it’s kind of useless even if we were talking about those other questions here.

  2. 2

    Dr. Carrier,

    Would you say your book dealing with Bayes’ Theorum is a good place to learn about it, or would one be better off learning/researching it elsewhere before trying to tackle your material? (For the layman, in this instance.)

    1. 2.1
      Richard Carrier

      My book (Proving History) is actually the best place to start (it references the more advanced resources if you want more), because I wrote it specifically so that laymen and humanities majors could understand it, using nothing more than the simplest sixth grade math (there are a few things in the book more complex, but they are tucked into narrow corners and not essential to the rest).

      No one else to my knowledge has ever done that. All other discussions of BT presume more advanced scientific or mathematical knowledge or vocabulary, and often don’t even have other folks in mind at all, or when they do, don’t really understand what’s needed to put things in terms they will find familiar.

      There is of course no way to make it as easy as pie, since sound reasoning is always to some extent complicated. But I think anyone who would be commenting on a blog post like this is going to be smart enough to understand it. I do think there could be a book that (in concept) explains Bayesian reasoning in even simpler terms, but it would have to be a book devoted to nothing else. And no one has written it yet.

  3. 3

    Isn’t this actually a no-brainer???

    If history’s goal is to study what PROBABLY happened in the past, then obviously the case to be made involves probability.
    It is very well established that the mathematically correct way of dealing with probabilities is Bayes’ Theorem.

    So then, whats all the fuss about ??

    1. 3.1
      Richard Carrier

      Preach, brother. Preach.

    2. 3.2
      J. Quinton

      Some people seem to think that probability only applies to uncertainty in regards to future events…

  4. 4
    Jerry Lutgen

    Can you tell us what assumptions you did use to get your 1 in 200 result?

    1. 4.1
      Richard Carrier

      0.5 prior probability that Jesus had a child (i.e. 50/50), i.e. I set an F1 of 0.5; plus the same relative probability that he was reburied in Talpiot as anyone else (i.e. nothing whatsoever counts against that hypothesis, such as that he would more likely be reburied in Nazareth or–being poor–not at all), i.e. I set an F2 of 1. Everything else I left at default. Result is slightly better than 1 in 200 if 10 people in all were buried in Talpiot tomb A, declining to slightly below 1 in 250 if 35 were. And we know the body count was higher than 10.

  5. 5
    Eliyahu Konn

    I am not sure what you are arguing for or against as I am not sure what Tabor and the rest who think the tomb is that of “J.” Scientifically one can argue for the existence of a man based upon physical evidence such as bones, tombs, engravings, credible documents, but this case requires special care. It is of little doubt that a man did exist, who was a Jew, who had a following, and presently and accurately is described as having been observant to Torah Judaism. His name was Yehoshua – Hebrew, Yeshua – Aramaic. Such happens to be the name found on the ossuary in question in Talpiot along with many other names that texts (in the Greek but which can be translated accurately into both Hebrew and Aramaic) identify with this Hebrew-Israeli-Jewish man. Is that who we are talking about? Or are we talking about the name “J” which is of dubious etymology and which for centuries has been associated wrongly with the other man who would have had bones, could have had a tomb, and could have been buried in Talpiot? The name “J” of course, can not have bones according to the story, at least not on earth. They must exist if they do in a state completely foreign to science. And so of course there is no proof for the unprovable. But science if it is not a trick by a perfect Creator would be something trustworthy to find a real man. If you haven’t gotten my point yet, stop naming a real man Yeshua, the one on the ossuary, “J.” It is a complete and utter impossibility to make sense of this without knowing the 1st century history of Israel and containing that history within science. Belief in science is seeing and repeating. You can do that for all men in history since they all live and die and their bones stay here. The Ze*us-Hor*us-Jup*iter-”J” myth is going down. The case will close. Try this page: http://netzarim.co.il/Museum/MusFram.htm

    1. 5.1
      Richard Carrier

      Sorry. I don’t understand your question at all.

      FYI, they (Tabor et al.) claim the odds of there being such a tomb complex by chance accident is 600 to 1 against (i.e. 0.0017 or 0.17% or almost one fifth of one percent). But the more accurate calculation shows the odds are quite the other way around: the actual odds of there being such a tomb complex by chance accident is nearly 100%. We can only quibble about how near (e.g. even the most favorable assumptions still place it around 95%).

  6. 6

    Considering that even the gospels claim that Jesus wasn’t buried in his family’s tomb, which would have been in Bethlehem or Nazareth (which didn’t exist at the time but that’s what the book says), but that of someone else’s (Joseph of Arimathea) why would this even be considered to be Jesus’ tomb?

    Except out of desperation?

    1. 6.1
      Richard Carrier

      They have an elaborate theory. But their basic rebuttal is, “We can’t rule it out. Especially since the Gospels are mostly myth anyway. So why are you harshing our mellow with all this negative energy, man?”

      Note that Tabor has long been an advocate of the view that Jesus was actually a rich Davidic heir attempting to establish a dynasty and had a son to that end. Thus he is starting from the assumption that they were a wealthy family with dynastic ambitions who set up shop in Jerusalem to pursue them after his death. (See The Jesus Dynasty. There’s a reason they called the book about the tomb The Jesus Discovery. Get the hint?)

      Tabor would say this tomb verifies his theory. That’s why he needs it to be authentic.

      (BTW, most experts, by far, are wholly unconvinced by recent attempts to dispute the existence of an inhabited Nazareth or Bethlehem at the time. And many do think Jesus would most likely have ended up buried in Jerusalem, but not in a family grave, but a mass pauper’s grave, most likely without any name or marking.)

    2. 6.2

      ‘harshing our mellow’

      Love it.

      Back to lurking.

    3. 6.3
      David Stockhoff

      (BTW, most experts, by far, are wholly unconvinced by recent attempts to dispute the existence of an inhabited Nazareth or Bethlehem at the time. And many do think Jesus would most likely have ended up buried in Jerusalem, but not in a family grave, but a mass pauper’s grave, most likely without any name or marking.)

      Richard, I have run into this theory and I’m curious where I can read about the skeptical experts’ response to it.

    4. Richard Carrier

      Which theory (I referenced several) and which side of the argument are you interested in?

  7. 7

    I’m trying for half an hour to post a message that this is a false problem. In Haaretz from 28,2012 “Naked Archaeologist`finds signs Jerusalem cave was used to bury Jesus`disciples” was published that that is not the Tomb!

    1. 7.1
      Richard Carrier

      I don’t understand your comment.

    2. 7.2

      Well, I am trying to post a linck to the Haaretz article (Naked Archaeologist finds signs Jerusalem cave was used to bury Jesus disciples) where Jacobivici admitted that that is not the Tomb of Jesus.

    3. Richard Carrier

      The article you have in mind is about Talpiot tomb B, not tomb A. It looks to me that Jacobovici remains adamant that Jesus was buried in tomb A (the one my article here is referring to), and claims that his disciples were buried in tomb B. I discuss that claim and its lack of merit here.

    4. 7.3

      The true Sepulchre, has always been known, Romans built a pagan temple over it and Constatin built one of the first Christian churches the Church of the Holy Sepulchre. So what is the purpose of this discussing?

    5. Richard Carrier

      That tomb has long been held by scholars to be a fabrication, initiated by Helen (Emperor Constantine’s mother, tasked by him with “finding” Christian holy sites and building them up for his propaganda campaign). There is no honest basis for it being genuine. And for that reason, another tomb location was “identified” in the 19th century, The Garden Tomb. But that has no basis either (except being an actual ancient graveyard). Nevertheless, many of the faithful regard it as the true burial site.

      The matter is complicated by the fact that Jesus is unlikely to have remained where he was initially buried anyway.

      The Gospel accounts collectively depict a temporary warehousing of the body; the actual burial could only be performed a day later (which the Gospels do not mention and thus seem unaware of), and would be elsewhere (in the official graveyard of the condemned reserved for all who were convicted of capital crimes by the Sanhedrin), thus explaining why the tomb he was put in Friday night was empty Sunday morning. See The Empty Tomb, chapter 10.

      Or if only Mark is correct, or if all of the Gospels are making up their stories, then Jesus would have been buried in that Sanhedrin graveyard straightaway, which would be a large complex designed to house the corpses of hundreds of criminals at a time. But after about a year, his bones would be collected and cleaned and deposited elsewhere to await resurrection. Probably a mass pauper’s grave; although his family would then have the right to take his bones and bury them with his family (which would most likely be in Nazareth), they might have been too poor, too dead, or too fearful of returning to take on that duty, or the body may have gotten lost for poor marking, deliberate or otherwise [or it may have been stolen: see The Empty Tomb, chapter 9]; or if the family were of a sect that held to the belief the first Christians most likely did, that God did not resurrect a person from their bones but created an entirely new body for them, as some Jews did indeed believe and the first Christians do appear to have believed [see The Empty Tomb, chapter 5], then they would not believe in reburial and thus would not have even wanted to reclaim the body, and thus would have left it for the court to relocate his bones with other unclaimed corpses.

      Any of these scenarios already has a higher probability than what Tabor and gang are claiming.

    6. 7.4

      Personally I love nothing more than to hear an atheist, useing the old “long debunked” argument. In my 3 years career as blogger and youtuber. I heard this argument so many times, particularly in zeitgeist anti Christian type, issues that it just does not impress me .

      Regarding the Holy Sepulchre

      No! We are nowhere near a scholar unanimity, you see the vast majority of historians thought in the last century, that, that is not the tomb becouse the Jesus’ tomb should be outside the city walls. The problem is that we do not know where the walls were exactly in that historical period. However it should be taken into account that, this tomb was not a common grave but the tomb of “a rich man from Arimathaea”, the tomb could therefore be positioned in a privileged place very close to the citie walls.

      Now a little history…”That tomb ” is not a fabrication, initiated by Saint Empress Helen becouse Elena has only found the Cross the tomb was already thought to be there. In reality the Church is composed of three connected churches built over the three different holy sites, the a rotunda, called the Anastasis, is the tomb that was already thought to be there St. Helen & Macarius I of Jerusalem just identified the burial place, as being Jesus.

      Now about the atheist myth namely that the Joseph of Arimathea would have thrown the body the next day, the righteous Joseph of Arimathea was a member of the Jewish Sanhedrin and a secret disciple of Jesus’ (Matt. 27:25; John 19:38). Jews have very strict rules on the handling of a deceased body, no Jew would have just thrown the body of another Jew and especially a Sanhedrin member that was at the same time a friend of the deceased and his family.

      On the presence of the tomb on the original place (outside or inside the walls) here is another dilemma, the Tomb surrounding rock was cut away, and the Tomb was encased in a structure that is called the Edicule. A very widespread practice in the Orthodox Church, where no church can be built without a relic that is placed in or under the altar. Therefore we do not know 100% if the tomb was not moved to be placed inside the church.

      On the “The Empty Tomb Jesus Beyond The Grave” book, I do not consider it to be authoritative, and wikipedia even less.

      The best argument for the authenticity of the Church of the Holy Sepulchre is the “Orthodox Tradition”, as any sacred tradition, tends to be very accurate. Even less sacred tradition as “Trojan War” have been proven to be based on real events, to the amazement of skeptics. (I hope you know the story)

    7. Richard Carrier

      Please try actually reading the references I cited before trying to argue against their conclusions. Everything you have said is either mooted by them or refuted by them.

    8. 7.5

      Richard Carrier says:
      “Please try actually reading the references I cited before trying to argue against their conclusions”
      I am a poor man,I can not afford to buy that book, and anyway they do not send them to the young EU countries. Their conclusions is all I have.
      Richard Carrier says:
      “Everything you have said is either mooted by them or refuted by them”
      This is no surprise, atheist are debunkers this is what they do their job if you wish…Protagoras & Sextus Empiricus argue that any argument can be opposed by a another. So as a historian I have no time to read all the marginare books, supporting a predetermined conclusion.
      The facts remain:
      The area of the Tumb was brought within the city walls in 41-43 AD,in 135 AD the Roman Emperor Hadrian built a Temple of Venus over the site regarded as holy by Christians and in doing so claiming the site for the traditional Roman religion.The first thing that Constantine would have made is to investigate the local Christian tradition, because the chosen site was inconvenient and expensive, moreover a building had to be demolished and not just any building but the Temple of Venus built over the site by Hadrian ( at this time Constantine was still Pontificus Maximus of the traditional Roman religion). The topographical elements of the church’s site are compatible with the John Gospel descriptions, (John 19:17) and the fact that the tomb had to be close (John 19:41-2).
      According to historians Eusebius of Caesarea! (c. 260-341). and Socrates Scholasticus the local Christian community of Jerusalem worship this site until 66 AD
      An early tradition associated the site of the Crucifixion and the Resurrection as the center of the world. The building incorporated into the pseudo Tomb of David considered to be an first century Judeo-Christian synagogue is oriented not towards the Temple Mount ( as traditionally)., but towards the site of the Holy Sepulchre!, north with a slight easterly deviation of several degrees toward the Temple Mount!
      As historians one of the best sources, are always found in the local oral traditions if the local oral tradition, gave a toponym to a plain, such as “the citadel” well somewhere buried it must be a citadel. People do not invent traditions without a base. The early Christians in Palestine worshiped this place Eusebius was very clear. If your boys say it was all a lie, then they have a much bigger problem on their hands, they have to explain the origin of the tradition, and to bring evidence that it was a false tradition. For example, protests of Christian bishops that Constantine was building his church in the wrong place (where there was no cemetery,and no Golgotha). see here more!

      I forgot how they use BB Codes

    9. Richard Carrier

      Nice. “Any argument can be opposed by another, therefore there is no valid argument against anything.” Do you not see how crazy your reasoning is?

      The area of the Tumb was brought within the city walls in 41-43 AD

      State your source for this information–and not some website just claiming it: I mean an actual ancient source or archaeological report that confirms this claim is true.

      the Roman Emperor Hadrian built a Temple of Venus over the site

      Only according to a Christian legend begun under Constantine. There is no evidence that what temple was built over had any connection to Jesus whatever. It was simply declared so by the minions of Constantine sent on a mission to create Christian pilgrimage sites for state propaganda.

      the local Christian community of Jerusalem worship this site until 66 AD

      Quote Eusebius and Socrates saying this. (Good luck with that.)

      And nice job ignoring everything else I said. Fact remains, by law Jesus’ body would have been removed from its Friday resting place and buried in the Sanhedrin court graveyard reserved for criminals (or he would have been buried there straightaway, either way, a mass grave complex that in no way resembles the Church of the Holy Sepulchre).

  8. 8

    ALERT: I’m going to get all Popperian here

    I can agree with Jason that Bayes Theorem isn’t some magic method: you can’t just throw in a few reasonably plausible probabilities and “prove” X.

    This is correct, just as you cannot just throw a few reasonable sounding premises together and “tada!” prove the existence of God (e.g. William Lane Craig’s methodology). Just as intellectualism (the “rationalism” of Decartes, Leibniz etc.) yields little and can be very misleading; a “probabilityism” yields just as little and can be very misleading.


    That people over-reach with logic doesn’t mean that you don’t need logic or, still less, cannot use logic. Logic is still used and needed in drawing conclusions about what would be the case were a statement to be true. These conclusions can be compared to the world to see if what would be the case is the case. Logic is also used to draw out what a theory entails to see if it makes sense and that it is consistent. That is to say that we use logic to [Austrian accent] criticise our theories not to justify them. [/Austrian accent]


    That is precisely what Ingermanson and Cost did. They showed (very clearly, to my mind) that for “this is almost certainly Jesus’ tomb” to be true facts about the world would have to be very different to how we believe them to be.

    The objection to the use of Bayes Theorem in this way strikes me as very similar to “different ways of knowing”: that, because you can’t prove a claim of type X by method Y, claims of type X are not subject to criticism by method Y.

    1. 8.1
      Richard Carrier

      Just to be clear, I think Jason was joking.

      The guy who isn’t joking is Hoffmann (whom Jason linked to), but good luck discerning an intelligible argument there (which isn’t already answered and resolved in my book, which he purports to be criticizing).

      Nevertheless, your comment is quite correct.

      (Except that I don’t accept the premise that “claims of type X can be subject to criticism by method Y but can’t be proved by method Y” when claims of type X are provable in any empirical sense. If method Y can show that X is false when X is false, then it can show that X is true when X is true. As long as Y is a suitably robust method. And BT is.)

    2. 8.2
      Jason Goertzen

      Hehe. Richard is right–I was joking. I actually was about to post, when I added the “*rolls eyes*” because I realized that the sarcasm might not come across otherwise.

      The last thing I want is to be associated with Hoffmann’s recent treatment of mythicism–and of Richard Carrier’s position in particular. It’s a train wreck.

    3. Richard Carrier

      Jason Goertzen:

      I actually was about to post, when I added the “*rolls eyes*” because I realized that the sarcasm might not come across otherwise.

      No, it wouldn’t have! So thanks for that.

      The problem with text is its flat affect. That’s why we need clues added in like that, to replace inflection and body language. I say this just for everyone’s benefit: people, what Jason did, do that. :-)

  9. 9
    Tony Lloyd

    Just to be clear, I think Jason was joking.

    Oops! I missed the sarcasm (what comes of not paying attention to the URL for an, otherwise, pseudonymonous blog).

    Apologies to Jason.

  10. 10
    Richard Carrier

    Note: Kevin Kilty and Mark Elliott have (sort of) a response to Ingermanson, also using a Bayesian model (see here for the latest entry, which links to earlier commentaries here and here).

    They do not provide a working model for others to tinker with, however, and only state that their results come out to a “probability of the tomb being that of the Jesus family” of “either 47%, if we assume Yoseh to be a rare name and that of one of the brothers of Jesus; or, it is only 3% if we treat Yoseh as just a variant of the more common Joseph.” They are essentially using the most credulous assumptions in Ingermanson’s model, and in doing so get a 1 in 33 chance this is the tomb of Jesus Christ (which means: they find it isn’t), unless we bank on “Jose” being a critical connection to the family of Jesus (although even then they get less than an even chance this is the tomb of Jesus, which is not what Tabor and gang have been claiming).

    It should be pointed out (because they do not) that the NT manuscripts don’t even agree the name in question was “Jose” (Jose or Joses): Codex Sinaiticus reads “Joseph” for this brother in Mark 6:3, and many manuscripts of Matthew 13:55 also read thus. Many manuscripts of Mark also read Iôsê (ditto Matthew), which is grammatically incorrect in Mark and possibly was corrected by assuming it was supposed to be Iôsês and thus (in the genitive) Iôsêtos, when more likely the single letter phi was accidentally dropped, and the original read Iôsêph. Or of course it was the other way around and adding the phi was the correction. But in any case, there is no secure certainty that Jesus even had a brother named “Jose” (assuming the Gospels are even reliable records of his family to begin with).

    Likewise, Kilty and Elliott denounce the suggestion that Jose and Joseph would be distinguished when more than one Joseph was being buried together (as at Talpiot), but give no good reason to reject that assumption. Surely the choice to use the short name here has no statistical relationship to whether this is the family of Jesus Christ or just any family with two men named Joseph.

    Combining both points, their focus on “Jose” as a rare form is unfounded, IMO.

  11. 11

    Dr. Carrier

    Speaking of empty tombs and historicity, I just watched your 2004 debate with Mike Licona and truly enjoyed your presentation. You definitely brought your “A” game that night. Licona came across as sounding like a William Lane Craig clone, utterly lost in the sublunar realm of biblical literalism.

  12. 12

    Dear Dr Carrier

    When paul uses the word ‘buried’ in corinthians, does that connote inter’d in the ground? Or in a Rock?

    Or is such inferencing not worth it?


    1. 12.1
      Richard Carrier

      The word there is ambiguous as to the mode of burial. But in Jewish lore of the time, Adam was buried in the ground (actual soil) located in the third heaven (i.e. in outer space), where the Garden of Eden was now located (complete with soil, trees, and celestial plants and animals), the same third heaven Paul claims he (or someone “he knows”) had visited (in 2 Cor. 12). We also know each of the heavens contained buildings and structures and thus could contain tombs, too. So we cannot decide the matter of historicity from that passage alone.

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