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Bayes' Theorem And The "Jesus Family Tomb"

Publication of the book The Jesus Family Tomb in late February, 2007, sparked a media firestorm. Could it be that the actual tomb of Jesus of Nazareth had been found in a suburb of Jerusalem? The book's authors, Simcha Jacobovici and Charles Pellegrino, believed it has. The book was followed up by the showing of a related documentary on the Discovery Channel on March 4, 2007.

The reaction to the book/documentary was intense, and things got particularly hot around the blogosphere. A number of folks criticized the probabilities quoted by Simcha and Charlie in the book. They alleged that the odds were "600 to 1" that this is in fact the tomb of Jesus of Nazareth. As support, they cited the calculations of Prof. Andrey Feuerverger, of the University of Toronto.

I read the book as soon as I could get a copy and thought hard about the calculations presented there. Because I have extensive experience in computing probabilities of such "remarkable events," I did my own set of calculations and posted them on this web site in an article titled Statistics and the Jesus Family Tomb. My conclusion was that the tomb seemed very unlikely to be the family tomb of Jesus of Nazareth.

The article quickly earned a lot of notice around the web, even getting me several mentions on the blogs of Dr. James Tabor and Dr. Mark Goodacre, two noted scholars.

Shortly after my article appeared, I received an email from Jay Cost, a graduate student in political science at the University of Chicago. Jay had written an influential article on the Real Clear Politics web site noting the importance of Bayes' Theorem to the issue. In his email to me, Jay reiterated his comments on Bayes' theorem and also asked some pointed questions about my calculations.

That email prompted a long and intense discussion between me and Jay on the statistics of the Jesus family tomb. At first, I was skeptical of his comments, but after doing some analysis, I quickly decided that he was correct -- there was more to say about the Jesus family tomb. After many hours of talking, we have fused his ideas with mine. I can now report our conclusions.

I should note that Jay also introduced me to Dr. James Tabor, one of the leading players mentioned in the book The Jesus Family Tomb. Prof. Tabor has strongly urged the academic community to give the tomb hypothesis a fair chance.

I agree. There is nothing to gain by dismissing the whole idea out of hand, merely because it was proposed by a documentary producer. Either the tomb once contained the body of Jesus of Nazareth or it didn't. Dr. Tabor and I agree that the issue needs to be studied carefully, without fear of where it will lead. We disagree on a number of issues, but he has become a valued friend. Jay and James have also introduced me to a number of other experts on the subject. And a few other experts took the initiative to contact me. Those folks have helped me define what is generally agreed on and what points are subject to judgment calls.

Downloads

Jay Cost and I have written a detailed report of our analysis and conclusions, which we have published as a PDF file titled: "He Is Not Here" Or Is He? Along with this article, I created a spreadsheet that does all the calculations described in our article. You can easily change the assumptions in the calculations by adjusting numbers in the spreadsheet to see how it affects the results.

Download the PDF document "He is Not Here" Or Is He? to read our detailed analysis.

Download the Excel spreadsheet JesusCalculations.xls to replicate our calculations.

The article is unfortunately a bit technical. If you don't want to read through all the math, then this page will summarize the line of argument and show you some selected conclusions.

A Review of the Evidence

It's impossible to describe ALL the evidence for the alleged Jesus family tomb. Here, I'm going to review those parts of the evidence that I want to model mathematically.

In 1980, an ancient tomb was found in Jerusalem containing 10 ossuaries. Since ossuaries were only used from about 20 B.C. until A.D. 70, we can assume the bodies belong to Jerusalem residents from that era. We can also assume that this was a FAMILY tomb, because the usual practice then was to bury several generations of families in the tomb over the course of time.

The tomb was excavated by several Israeli archaeologists, including Joseph Gath, Amos Kloner, and Shimon Gibson. Gath died a year later, but Kloner and Gibson are well-known Israeli archaeologists who remember the excavation.

Of the 10 ossuaries, 6 were inscribed with names. These names read:

  • Jesus son of Joseph (Aramaic: Yeshua bar Yehosef)
  • Mary (Aramaic: Maryah)
  • Mary (Greek: Mariamenou e Mara)
  • Joseph (Aramaic: Yoseh)
  • Matthew (Aramaic: Matyah)
  • Judah son of Jesus (Aramaic: Yehudah bar Yeshua)
The inscription "Jesus" is badly scratched and nearly illegible, but most scholars agree that it should be read as Jesus. 

The inscription "Judah son of Jesus" is VERY legible, and that convinced the excavators that the "Jesus" inscription should really be read as "Jesus."

The Greek inscription "Mariamenou e Mara" has provoked a LOT of controversy. "Mariamenou" is a rare form of the name Mary. It is in the genitive case (it's a possessive) of the diminutive name "Mariamenon". So the best translation of this might be "Belonging to little Mary" or "Belonging to dear Mary." The center word "e" is taken by many scholars to be an abbreviation for "aka". There is a question of how to read "Mara". This is a known abbreviation of "Marta". But it could also be translated as a feminine form of "Master". The masculine form would be "Mar" and this is the common equivalent for "Mr." today in Israel.

In the book The Jesus Family Tomb, Simcha and Charlie argue that this inscription should be read "Belonging to Mariamene, also known as The Master." They further argue that Mariamne was the "real" name of Mary Magdalene, as proved by the fourth-century Gnostic book "The Acts of Philip." They quote Dr. Francois Bovon of Harvard University to support their claim that Mary Magdalene's real name was Mariamne. A critical point of Simcha and Charlie's thesis is that the inscription "Mariamenou e Mara" should be understood, with very high probability, to be "Mary Magdalene."

Most scholars flatly disagree. There are numerous problems, which I reviewed in my previous article. Since this an important issue, I'll review them here:

  • As Dr. Bovon has said in one of his articles on the subject, "I do not believe that Mariamne is the real name of Mary of Magdalene."
  • The Acts of Philip is nearly four full centuries after the time of Jesus, and it has no historical value. It's fiction.
  • The "Mariamne" in the Acts of Philip is ALSO identified at the same time as Mary of Bethany. But Mary of Bethany is an entirely different historical person than Mary Magdalene.
  • The name on the ossuary is in fact "Mariamenon", not "Mariamne".
  • In the New Testament, Mary Magdalene's name is spelled "Maria", exactly the same spelling as Mary the mother of Jesus, and Mary of Bethany. There is no reason to believe that "Mariamenon" was a unique identifier for Mary Magdalene.
For all of these reasons, it's really impossible to argue that the ossuary inscribed "Mariamenou e Mara" must have once contained Mary Magdalene. This is a historical question to be resolved by New Testament scholars. Since I'm not a New Testament scholar, I'll simply repeat what the consensus is. "Mariamenou e Mara" could be ANY Mary who lived in ancient Jerusalem. There is no reason to connect this name to Mary Magdalene.

Of course, it is POSSIBLE that the "Mariamenou e Mara" ossuary contains Mary Magdalene. We can't rule that out. All we can say is that this particular form of the name Mary does not make it MORE likely to refer to Mary Magdalene.

We note here that DNA evidence shows that the "Jesus" ossuary and the "Mariamenou e Mara" ossuary are not maternally linked. So "Mariamenon" is not the mother or sister of the Jesus of the tomb. Most likely, "Mariamenon" is connected to the family by marriage. She might be the wife, sister-in-law, aunt, niece, or other in-law relation of the Jesus of the tomb.

There are many who would ask at this point, why in the heck are we even talking about this? Isn't it obvious that Jesus of Nazareth was raised from the dead and ascended to heaven and that his body can't possibly be buried in some tomb somewhere?

Well, yes, it's "obvious" to most Christians. The problem is that it's not at all obvious to anyone else. That is a faith assertion. Many Christians would argue that it's a faith assertion backed by solid historical evidence. Still, it's a faith assertion. In this article, I'll show how to do the calculations so that you either use this faith assertion or you don't -- it's up to you.

Aside from faith assertions, there are some strong reasons to question whether Jesus of Nazareth could possibly be buried in this particular tomb. I'll refer you to Dr. Jodi Magness' article Has the Tomb of Jesus Been Discovered? Even if Jesus was NOT raised from the dead, Dr. Magness argues that this particular family tomb is a poor candidate for his final resting place.

This is not a faith assertion, it is a historical judgment, and a disputed judgment at that. I'll show how to account for this historical judgment in our calculations. You can make your OWN judgment on this issue and see the results for yourself.

The Tomb Hypothesis

Based on the above evidence, Simcha Jacobovici and Charles Pellegrino hypothesized that the tomb might be the tomb for the family of Jesus of Nazareth. They believed that this would not upset many Christians. They guessed wrongly on that. Many Christians got VERY upset.

But tempers have no place in a scientific investigation. The question is a valid one to ask: Could this be the family tomb of Jesus of Nazareth? What are the odds?

We have only the following to help us estimate the odds:

  • The evidence of the tomb
  • Historical judgments
  • Faith assertions
Please note that there is some fuzziness here, since BOTH historical judgments AND faith assertions are subjective elements -- which we'll call "fuzzy factors". But the evidence of the tomb is pretty darned objective. Wouldn't it be interesting if the evidence of the tomb was strong enough to make a decision REGARDLESS of the fuzzy factors?

We'll see if that's possible. But let's forge on ahead. The reason we suspect that this tomb might POSSIBLY be the family tomb of Jesus of Nazareth is that so many of the names are familiar to us from the Gospels. Jesus had a mother named Mary. Probably 3 or 4 other women in his inner circle were also named Mary. Jesus' father was named Joseph. He had four brothers named James, Joseph, Judah, and Simon. He also had at least two sisters, traditionally known as Mary and Salome. Unfortunately, we can't say how good those traditions are, since they don't go back to first-century sources.

We should note that Matthew is both the name of a disciple of Jesus AND a great-grandfather. Most historians don't consider this relevant. A family tomb typically contained people of the extended family, including slaves. There is no particular reason to expect the disciples of a rabbi to be buried in his family tomb. Nor is there good reason to expect a great-grandfather from Nazareth to be dislocated. So the consensus on all sides is to ignore Matthew.

An important point is that history knows nothing of any children of Jesus of Nazareth. The Jesus of the tomb had a son named Judah. It is POSSIBLE that Jesus of Nazareth had a son that we never heard about. But how probable is it? Once again, we're faced with a judgment call, yet another "fuzzy factor" that we need to deal with.

Is the math going to be able to handle all these fuzzy factors? Maybe. Maybe not. The only way to know is by doing the calculations. Let's consider a couple of "extreme cases" in order to see some examples of when the math would be pretty definite.

The Calculus of Jesus

Suppose that the tomb was just outside the walls of first-century Jerusalem and had the following names inscribed on the ossuaries:

  • "Mary, mother of Jesus"
  • "James, son of Joseph, brother of Jesus, from Nazareth"
  • "Judah, son of Joseph"
  • "Joseph son of Joseph, brother of Jesus"
  • "Simon, son of Joseph, from Nazareth"
  • "Mary of Magdala"
Wouldn't you agree that this would be FREAKIN' GOOD EVIDENCE that you'd found the family tomb of Jesus? 

Yes, you would. Why? Because this is a virtually perfect match to the historical record. It agrees with many known facts. It doesn't disagree with any known facts. The only thing that could make it stronger would be if the Mary, Judah, and Joseph inscriptions also said "from Nazareth" and if the Judah and Simon inscriptions specified "brother of Jesus". But honestly, that level of corroboration isn't necessary. And nobody would quibble about including Mary Magdalene in the tomb, even if she wasn't part of the immediate family. Since Mary was a wealthy woman, it would be plausible that she paid for the tomb. If we found this tomb, every reasonable person would agree that the tomb matches the historical record almost exactly.

The point here is that names are good indicators, but it's far more convincing to see the relationships spelled out too. And a couple of place names to indicate where these people came from is even stronger yet. Ossuaries sometimes do give these kinds of information.

Suppose instead that the tomb was in Chicago and had the following names inscribed on the ossuaries:

  • "Douglas son of Raymond"
  • "Elizabeth"
  • "Lizzie, native Chicagoan"
  • "Bilbo Baggins"
  • "Ricardo son of Douglas, Cubs fan"
  • "Freddie"
Is there anybody on the planet who would imagine that this is the family tomb of Jesus of Nazareth? LOL, no way! Why? Because there are no matches. The tomb doesn't match the historical record AT ALL.

Finally, suppose you found a tomb near old Jerusalem that had 10 ossuaries, and all of them were blank. No names at all. Would you leap to the conclusion that this IS DEFINITELY the family tomb of Jesus?

Nope. There's no evidence of that.

Would you insist that this is DEFINITELY NOT the tomb of the family of Jesus?

No, that wouldn't make any sense either.

The problem is that you'd have NO EVIDENCE. It's reasonable to think that some family members of Jesus are buried somewhere around Jerusalem. But there's no reason to think that this tomb of blanks is more OR less likely to be their final resting spot.

What we've seen above are the three main kinds of factors to consider in our "calculus of Jesus":

  • "Jesus factors"
  • "Not-Jesus factors"
  • "Neutral factors"
A "Jesus factor" is a fact about the tomb that MATCHES what we believe we know about Jesus of Nazareth. It may be only one small fact, but the point is that it matches what we know. For example, we believe we know that Jesus' immediate family had the names Mary, James, Joseph, Judah, and Simon. We believe we know they came from Nazareth. We believe we know that Jesus' legal father was named Joseph. We believe we know that Mary Magdalene was close to Jesus. It's true that we can't be ABSOLUTELY certain of any of these facts, but our best available evidence says that they are true, and we have no grounds for doubting them.

A "Not-Jesus factor" is a fact about the tomb that VIOLATES what we believe we know about Jesus of Nazareth. We believe that we know that Jesus was NOT named Douglas, his father was NOT named Raymond, and that he never lived anywhere near Chicago. We believe that we know that he had no relatives named Elizabeth, Lizzie, Bilbo, Ricardo, or Freddie. Again, we can't be ABSOLUTELY certain that none of these held true, but we have no evidence at all in favor of any of them, and we have no grounds for expecting any such evidence.

A "neutral factor" is a fact about the tomb that is equally likely to be true of Jesus or any other person in some large group of men. For example, we have no idea whether Jesus was right-handed or left-handed. If we found a tomb with a left-handed man, that would not weigh at all in our calculation of whether we had found Jesus. We don't know how tall Jesus was. If we found a man of average height, that would tell us nothing about whether we had found Jesus.

Here is an important point. Both the "Jesus factors" and the "Not-Jesus factors" are relative. A "Jesus factor" can be strong or weak, depending on how specifically it indicates Jesus. A "Not-Jesus factor" can be strong or weak, depending on how specifically it counter-indicates Jesus . Let's look at some examples.

An ossuary that says "James, son of Joseph, brother of Jesus, from Nazareth" would be a strong "Jesus factor." The reason is because the odds of finding somebody to fit this description BY CHANCE are very low. We know for a fact that Jesus' brother James did fit that description so the odds are very low of finding a second man who also fits it. The probability of finding this ossuary in the family tomb of Jesus of Nazareth is a LOT higher than the probability of finding it in some randomly chosen tomb.

An ossuary that says "Judah" would be a weak "Jesus factor". It is true that Jesus had a brother named Judah. But so did many other men in ancient Jerusalem. So a family tomb of Jesus of Nazareth would likely have a Judah in it. But a family tomb of any other Jesus also has a pretty good chance of having a Judah too. The probability of finding a Judah in the family tomb of Jesus of Nazareth is SOMEWHAT higher than the probability of finding a Judah in some randomly chosen tomb.

An ossuary that says "Eleazar" would be a neutral factor. Nobody in the immediate family of Jesus was named Eleazar, but it's plausible that in his extended family, somebody would have that name. It's just as likely that he'd have a cousin named Eleazar as that anyone else in Jerusalem would have a cousin with that name. The probability of finding an Eleazar in the family tomb of Jesus of Nazareth is ESSENTIALLY THE SAME as the probability of finding an Eleazar in some randomly chosen tomb.

An ossuary that says "Yosi the Priest" would be a weak "Not-Jesus factor". The reason is that Jesus did not come from a priestly family. So none of his immediate family could be priests. It is true that a sister or cousin might have married a priest. But the fact remains that finding a priest in the family tomb of Jesus is just a bit less likely than finding one in some other randomly chosen family tomb. (It's less likely because we are guaranteed to have several people in a family tomb of Jesus who are NOT priests, whereas we have no such guarantee in a randomly chosen family.)

An ossuary that says "Jesus son of Simon" would be a strong "Not-Jesus factor." The legal father of Jesus is Joseph according to all the historical records we have. It is POSSIBLE that Joseph of Nazareth had a secondary name Simon. It just isn't likely, given the records we have. So finding the name "Jesus son of Simon" on the ossuary of Jesus of Nazareth is a lot less likely than finding it on the ossuary of some other man named Jesus. If you find a "Jesus son of Simon" in a tomb, you'd be better off claiming this was a member of the extended family than claiming you'd found Jesus of Nazareth. That way, your "Jesus son of Simon" would become a neutral factor.

Let's review the evidence we have. There are six ossuaries, each with an inscription. We can classify these as follows:

  • Jesus son of Joseph: fairly strong "Jesus factor"
  • Mary: weak "Jesus factor"
  • Mary: weak "Jesus factor"
  • Joseph: weak "Jesus factor"
  • Matthew: neutral factor
  • Judah son of Jesus: strong "Not-Jesus factor" or neutral factor, depending on whether you call this the son of Jesus of Nazareth or the son of some other Jesus in the extended family
We also have two other facts to account for:

  • Bones of Jesus: very strong "not-Jesus factor" if you believe that Jesus' body was resurrected; neutral factor otherwise
  • Location of the tomb 3 miles from ancient Jerusalem: fairly strong "not-Jesus factor, depending on which historian you listen to
The situation looks very complicated. We have some strong "Jesus" AND "Not-Jesus" factors. We have several weak "Jesus factors". And some of these come with options that let us convert strong factors to neutral factors. How are we supposed to put all these together and come to a decision?

The answer is that we should do the best we can with the information we have. And I believe that the best we can do is to use Bayes' Theorem.

Bayes' Theorem

Bayes' Theorem is a way of improving an initial probability estimate in light of new information. As an example, imagine a gambling game in which you bet on the outcome of two dice. You're betting you'll get snake-eyes -- two 1s. The only way this can happen is if each die comes up a 1. The odds of this happening are 1 in 36, because each die can come up in 1 of 6 different ways.

Suppose you throw the dice and you want to know if you won or not. You can't see the dice, but your friend down at the other end of the table tells you that he can see one of them and it's a 1!

That's great news! In order to get snake-eyes, you just need that other die to be a 1 also. The odds of that, GIVEN THE NEW INFORMATION YOU HAVE, are now 1 in 6.

On the other hand, if your friend had reported to you that one of the dice was a 3, then you'd give up hope. There is no way to get snake-eyes if one die is a 3. So the probablity of getting snake-eyes is now 0, GIVEN THE NEW INFORMATION YOU HAVE. It can't happen.

Bayes' Theorem tells you how to adjust probabilities as you learn new information. Typically, you start with a naive probability estimate based on very little information and then revise it by adding in the effects of the new information. It doesn't matter what order you consider each piece of information -- you get the same result every time.

Let's see how this applies to the Jesus family tomb. We can begin with just the one fact that we noted above, that there is an ossuary with the name "Jesus son of Joseph." Scholars estimate that in first-century Jerusalem, there were a few hundred men named "Jesus son of Joseph." Depending on the estimate you use, there might be 1000 or so, or even more. Let's take 1000 as the estimate, because that's a good round number. (In Simcha and Charlie's book, they estimated 1008.)

If there were 1000 men named "Jesus son of Joseph", then one might think that any of them could be just as likely to be the Jesus of the tomb as any other. But not so fast! That would mean that Jesus of Nazareth has odds of 1 in 1000 to be the man of the tomb. As we noted above, Jesus of Nazareth is LESS likely than a normal man on the street of being buried in this tomb. Different people are going to argue about "how much less", but most will agree that it is less.

How to settle this impasse? The answer is easy. We just create what I call a "fuzzy factor" that represents "how much less". We'll name this "fuzzy factor" F1, and we'll insist that it should be between 0 and 1. If you believe that Jesus ascended to heaven and can't possibly be in the tomb, then you can set F1 to be 0. The historian next to you might believe that Jesus was likely buried in a trench grave right outside Jerusalem, and is therefore only 10% likely to have been taken the 3 miles to Talpiot to this family tomb. That historian can set F1 to be 0.1. There may be other historians who insist that Jesus was just as likely as anyone else to be in that tomb. They can set F1 to be 1.

No matter what you choose for F1, we now have a probability that Jesus of Nazareth is in the tomb. The probability is F1/1000. No matter what number you assign to F1, this formula gives you the probability that Jesus is in that tomb.

Once we have that probability, Bayes' Theorem tells us how to revise it in light of the other information in the tomb. There are really only two things we have to calculate, based on the two possible cases:

  • Case 1: Jesus of Nazareth is definitely in the tomb. We need to calculate the probability that we'd see the five other names on the ossuaries, given that Jesus' immediate family members are among the bodies in the tomb.
  • Case 2: Jesus of Nazareth is definitely not in the tomb. We need to calculate the probability that we'd see the five other names on the ossuaries, given that those names are chosen at random from the names common in Jerusalem.
Once we have this information, Bayes' Theorem tells us how to combine the numbers to get a refined estimate of the probability that Jesus of Nazareth was buried in this tomb.

I'm not going to go into infinite detail on how to make these calculations. I've explained it carefully in the PDF article on this web site. Let me just give you a flavor of what goes into it.

First of all, we need to deal with that inscription "Judah son of Jesus." That is a "Not-Jesus" factor. When we say that, we mean that we're more likely to see a "Judah son of Jesus" in a randomly chosen tomb than we are to see it in the tomb of Jesus of Nazareth. The odds of finding this particular name aren't high, but we really don't care about that fact. All we care about is how much LESS likely it is to find this name in the tomb of Jesus of Nazareth than to find it in somebody else's tomb.

There is no way to compute this! It's a judgment call. So let's now create a new "fuzzy factor" F2 that tells the RELATIVE probability that Jesus of Nazareth had a child as compared to a randomly chosen man of Jerusalem. Most people would guess that F2 is pretty low. Some might set it to 0. Others might guess it to be 1%. A few might even say that it's 100%. We don't need the value in order to set up the problem! It's a fuzzy factor, after all.

Remember that the tomb had at least 10 bodies, and maybe a lot more. The archaeologists estimated 35 people were buried in the tomb. That was a guess based on experience with other tombs. Nobody knows. But there were at least 10. We have names for 6 of them. Besides Jesus and Judah, there were two women and two men. And they had a remarkable set of names.

Actually, we need to define just what's so remarkable about those names. They are remarkable because several of them coincide with near family members of Jesus of Nazareth.

For starters, both women bear the name "Mary" (or some variation on it). That's remarkable because Jesus' mother was named Mary. What is not particularly remarkable is that there's a second Mary, because we don't know for sure that there were two Marys in Jesus' immediate family. So it's remarkable that AT LEAST ONE of the two women should be named Mary.

The names are also remarkable because one of the two men has the name of a brother of Jesus. One of the men is named Joseph, but the truth is that we'd have been just as happy to get any brother of Jesus -- James, Simon, or Judah would have done just as well.

We want to estimate the probability that at least one of the two women were named Mary. Roughly a quarter of all women were named Mary, so the odds are pretty good that if you choose two women from a random collection of women, then you'll get at least one. The odds for this are computed exactly in our technical article.

Please note that the family tomb of Jesus would be different, though! We are defining the family tomb of Jesus to have his mother Mary in it, plus a number of other women whose names we can only guess. So IF the tomb is the family tomb of Jesus, then when we choose which women will go into the ossuaries with names, there's a lot higher likelihood that at least one of them will be named Mary. Again, the exact odds are calculated in our technical article.

A similar situation holds with the two ossuaries containing Matthew and Joseph. One of those is the name of a brother of Jesus. What are the odds of randomly choosing two men of Jerusalem and finding one of them named after a brother of Jesus? We calculate the odds of this in our technical article.

There is another "fuzzy factor" that gets introduced here. We have one ossuary with the name "Jesus son of Joseph". If this were the family of Jesus, we wouldn't expect his father Joseph to be in the tomb (he'd likely be buried years earlier in Nazareth). We would expect his brother to be there, though. But if this ISN'T the family of Jesus, then there's a fair chance that the father Joseph WOULD be in the tomb. And there's a fair bet that there'd be a brother named after the father there too.

So in either case, the number of "Josephs" in the tomb is likely to be a bit higher than in a typical tomb. In the tomb of Jesus of Nazareth, we can confidently set the number of extra Josephs to be 1. (1 brother, no father.) For the tomb of any other "Jesus son of Joseph", we define a new "fuzzy factor" F3 to be the number of extra Josephs that we would expect based on various sociological factors. We can't easily evaluate these sociological factors, but we can be confident that F3 is between 0 and 2. (Because any man named "Jesus son of Joseph" can have at most 1 father buried with him and at most 1 brother named Joseph buried with him.)

Once F3 is defined, we can now compute the probability of finding one men out of two in the tomb who has the name of a brother of Jesus. We've done that in the technical article that goes with this page.

In order to do these kinds of calculations, we need to know the probabilities that a randomly chosen man or woman in Jerusalem would have a particular name. Let's talk about that next.

A Note On Name Frequencies

We don't have census data for ancient Jerusalem. What we do have are some surveys taken from various sources that list how often certain names appear. Two lists have been compiled by Israeli scholars, one by Dr. Rachel Hachlili and one by Dr. Tal Ilan. The lists don't agree exactly, but they agree approximately. The numbers we need are as follows:

Brother's Name Percentage
(Hachlili)
Percentage
(Ilan)
Simon 21% 10.24%
Joseph 14% 9.21%
Judah 10% 7.13%
Jacob (James) 2% 1.79%
Mary 21.4% 25.4%

Since we don't know which of these sets of numbers is more accurate, we'll run our calculations using both sets. We'll get different answers for each set, and that'll give us a range of possible answers to our question.

Results

The technical article associated with this page shows how to put everything together into a final answer. There are a number of unknown parameters that go into this, but once you specify each of these, our equation uses Bayes' Theorem to combine the numbers into an ESTIMATE of the probability that the Jesus of the tomb is Jesus of Nazareth.

Here is a list of the unknown parameters that you need to supply in order to get an answer:

  • N: The number of people living in Jerusalem. Most historians would guess between 30,000 and 80,000 for this number.
  • g: The number of complete generations who lived and died during the time ossuaries were used. Since ossuaries were only used for about 90 years, this number should be between 1 and 3. (Considering that a generation is born, lives, and dies in somewhat less than 70 years.)
  • Whose name frequencies will we use: Rachel Hachlili's or Tal Ilan's?
  • F1: The relative probability that Jesus of Nazareth had a child, as compared to other men of his generation. This fuzzy factor should be between 0 and 1.
  • F2: The relative probability that Jesus of Nazareth might have been buried in a tomb near Talpiot, as compared to other men of his generation. This fuzzy factor should be between 0 and 1.
  • F3: The number of "extra Josephs" that you would expect in a randomly chosen tomb that contains a man named "Jesus son of Joseph". This fuzzy factor should be between 0 and 2.
That's all! Make those six choices and everything else in our equations is determined. If you would like to run the calculations yourself, go right ahead and download the spreadsheet. You'll find six purple cells near the top of the page. Change the values in those cells and you'll see a graph of the results, plotted versus the number of bodies in the tomb. (Remember, the archaeologists estimated that there were between 10 and 35 bodies in the tomb.)

We'll show some sample cases here that cover the gamut fairly well.

Case 1: A "Typical" Historian

We're not sure what a "typical historian" might be, or even if such a creature exists. But we chose numbers that we thought would be fairly non-controversial:

  • N = 50,000: (People in Jerusalem.)
  • g = 2: (The number of generations.)
  • Tal Ilan's name frequencies.
  • F1 = 1%: (The relative probability that Jesus of Nazareth had a child.)
  • F2 = 50%: (The relative probability that Jesus of Nazareth might have been buried in a tomb near Talpiot.)
  • F3 = 1: (The number of "extra Josephs" in a tomb with a "Jesus son of Joseph".)
Results are plotted for a body count ranging from 10 to 36:

Conclusion: This "typical" historian would estimate odds of about 1 in 19,000 that this is the family tomb of Jesus of Nazareth.

Case 2: A Historian Who Very Badly Wants The Tomb to Belong to Jesus of Nazareth

The numbers are chosen in every case to be as favorable as possible to the "tomb hypothesis, no matter how absurd the assumptions might be from a historical perspective:

  • N = 30,000: (People in Jerusalem.)
  • g = 1: (The number of generations.)
  • Tal Ilan's name frequencies.
  • F1 = 100%: (The relative probability that Jesus of Nazareth had a child.)
  • F2 = 100%: (The relative probability that Jesus of Nazareth might have been buried in a tomb near Talpiot.)
  • F3 = 0: (The number of "extra Josephs" in a tomb with a "Jesus son of Joseph".)
Results are plotted for a body count ranging from 10 to 36:

Conclusion: This "ultra-advocate" historian would estimate odds of about 1 in 18 that this is the family tomb of Jesus of Nazareth.

Case 3: A Historian Who Leans Toward Choices That Would Make the Tomb Belong to Jesus of Nazareth

The numbers are chosen in every case to be quite favorable to the "tomb hypothesis, but staying within the bounds of historical reasonableness:

  • N = 50,000: (People in Jerusalem.)
  • g = 2: (The number of generations.)
  • Tal Ilan's name frequencies.
  • F1 = 10%: (The relative probability that Jesus of Nazareth had a child.)
  • F2 = 80%: (The relative probability that Jesus of Nazareth might have been buried in a tomb near Talpiot.)
  • F3 = 1: (The number of "extra Josephs" in a tomb with a "Jesus son of Joseph".)
Results are plotted for a body count ranging from 10 to 36:

Conclusion: This "leaning-toward" historian would estimate odds of about 1 in 1,100 that this is the family tomb of Jesus of Nazareth.

Case 4: A Historian Who Leans Toward Choices That Would Make the Tomb NOT Belong to Jesus of Nazareth

The numbers are chosen in every case to be quite unfavorable to the "tomb hypothesis, but staying within the bounds of historical reasonableness:

  • N = 80,000: (People in Jerusalem.)
  • g = 2: (The number of generations.)
  • Rachel Hachlili's name frequencies.
  • F1 = 0.1%: (The relative probability that Jesus of Nazareth had a child.)
  • F2 = 10%: (The relative probability that Jesus of Nazareth might have been buried in a tomb near Talpiot.)
  • F3 = 2: (The number of "extra Josephs" in a tomb with a "Jesus son of Joseph".)
Results are plotted for a body count ranging from 10 to 36:

Conclusion: This "leaning-against" historian would estimate odds of about 1 in 5 million that this is the family tomb of Jesus of Nazareth.

Case 5: A Christian Who Insists That the Only Option is That Jesus of Nazareth Ascended to Heaven

Only one number matters in this case:

  • F2 = 0%: (The relative probability that Jesus of Nazareth might have been buried in a tomb near Talpiot.)
Results are plotted for a body count ranging from 10 to 36:

Conclusion: This Christian would estimate that it is impossible that this is the family tomb of Jesus of Nazareth.

Conclusions

Depending on your assumptions, you will get a wide range of possible answers to the question: "What is the probability that the Jesus of the tomb is Jesus of Nazareth?" But the range is not unlimited. For most choices of assumptions, even very liberal choices, the odds fall below 1 in 1,000. In some cases, they are far below that. We were able to make some extreme choices in order to get the probability estimate up above 5%, but we doubt that very many historians would want to defend those choices.

We know this is not the final word on the subject. We are quite willing to listen to critiques of our analysis and improve it, if necessary. If you have suggestions, feel free to email me on my Contact page on this site.

Acknowledgments

We are indebted to a number of people for useful discussions on this topic. Not all of them will agree with our conclusions, so we take full responsibility for any errors in this article. We thank: Joe D'Mello, Mark Goodacre, Gary Habermas, Michael Heiser, John Koopmans, Stephen Pfann, John Poirier, Chris Rollston, James Tabor, David Tyler, Ben Witherington III. Undoubtedly, we have forgotten somebody. If you deserve an acknowledgment, please email me in a violent rage, and I'll be happy to add you to the list.

Useful Links

If you want to read more about the alleged Jesus family tomb, check out these pages, which I have listed in roughly chronological order:

  • The web site created by Simcha Jacobovici and company to provide evidence alongside the documentary and book.
  • The "Tomb Evidence" PDF file that was originally posted on the web site of the Discovery Channel, summarizing Simcha Jacobovici's evidence for the tomb. This PDF file contains a page title "Statistics Overview" that claims to represent the calculations of Dr. Andrey Feuerverger. A year later when Feuerverger's article was published in The Annals Of Applied Statistics, it became clear that Jacobovici had badly misrepresented Feuerverger's work. 
  • Prof. Ben Witherington's blog. Dr. Witherington is a New Testament scholar who wrote the book on the famous ossuary that reads "James, son of Joseph, brother of Jesus".
  • Prof. Mark Goodacre's blog at NT Gateway. Dr. Goodacre is a well/known New Testament scholar and he's done a fair and even/handed treatment of the subject.
  • Jack Poirier's article on "The Statistics Behind The Tomb"
  • Randy Ingermanson's first simple spreadsheet analysis of the statistics of the tomb, which appeared on March 3, 2007
  • An article by Dr. Jodi Magness, "Has the Tomb of Jesus Been Discovered?," arguing that the family of Jesus of Nazareth is unlikely to have owned the family tomb in East Talpiot that has been called the "Jesus family tomb. Prof. Magness teaches at the University of North Carolina, Chapel Hill, and specializes in Early Judaism.
  • Dr. Michael Heiser's web site. Mike wrote a paper on the Jesus family tomb ossuaries back in 2003, when few other people were looking at the subject. Mike has a Ph.D. in Biblical Hebrew and Semitic Studies and I've known him since the bad old days when the Bible code was hot.
  • Prof. James Tabor's blog. Dr. Tabor is another well/known Biblical Studies scholar, and he's argued strongly that the evidence in favor of this being the tomb of Jesus of Nazareth is a lot stronger than most people are giving credit.
  • Randy Ingermanson's second, more complicated spreadsheet analysis of the statistics of the tomb, which appeared on March 26, 2007
  • The technical article by Jay Cost and Randy Ingermanson using Bayes' Theorem to analyze the tomb, posted on March 26, 2007
  • Stephen Pfann's article on "The Improper Application of Statistics In The Lost Tomb of Jesus"
  • Stephen Pfann's article "How Do You Solve a Problem Like Maria" analyzing how often the New Testament writers use the names Maria and Mariam.
  • Stephen Pfann's article "Yoseh Can You See?" analyzing the occurrences of Yoseh and Yehosef in the original sources.
  • The Codex blog of Prof. Tyler Williams has been following the story with interest and has a good collection of links. At the time the controversy erupted, Dr. Williams was the chair of the Religion and Theology Department at Taylor University College in Edmonton.
  • Francois Bovon has posted a short article on the SBL web site clarifying his position on the identification of Mariamne with Mary Magdalene.
  • Jay Cost has written a nice summary article on the Jesus family tomb. Jay was the first to bring in Bayes' Theorem to the discussion.
  • Dr. William Dembski, famous for his work on Intelligent Design, has written an article on "The Jesus Tomb Math" which you can find on his Design Inference web site. The article is co/authored with Robert J. Marks II.
  • Kevin Kilty and Mark Elliott have written an article using Bayes' Theorem that analyzes the tomb using a simple model. Their probability estimate ranges from about 6% to about 48%, depending on which assumptions they make.
  • Prof. Andrey Feuerverger's article in The Annals of Applied Statistics summarizing his original calculations.
  • Randy Ingermanson's discussion article in The Annals of Applied Statistics responding to Feuerverger's article.
  • The other referees' discussion articles in The Annals of Applied Statisticsresponding to Feuerverger's paper.
  • Feuerverger's response to the referees in The Annals of Applied Statisticsin which he said clearly that he does not believe that his original calculations are statistically significant.
  • Randy Ingermanson's calculations posted as a supplement on the web site of The Annals of Applied Statistics estimating that the tomb has less than a 2% probability of being authentic.

I'm sure I've forgotten (or missed) some of the important sites around the web, but the above will get you rolling in your quest for more info.

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