Should We Calculate Prior Probabilities to Determine if Jesus Was Resurrected?

Post Author: Bill Pratt

I am aware that there are philosophers who employ Bayesian analysis to determine probabilities that historical events occurred, but I am becoming skeptical of the value of these analyses.  A Bayesian analysis requires a calculation of the prior probability that a historical event occurred, without considering any of the evidence we have that the event occurred.  But how we do calculate prior probabilities for a historical event?

I think the problem was clearly illustrated in a debate between Greg Cavin and Mike Licona.  Cavin mounted an attack on the resurrection of Jesus by arguing against the prior probability of it.  Remember that prior probability calculations ignore the actual evidence for the event.  Here is Licona’s summary of Cavin’s argument (note: Greg Cavin has contacted me and denied that he made the argument presented below, so I have edited the comments below to represent a generic argument made by a generic atheist named Bob; even if Cavin did not make this argument, I have heard arguments like it made plenty of other times by other atheists):

[Bob’s] first argument is the probability that Jesus rose is astronomically low, since, even if God exists, he doesn’t have a tendency to raise people from the dead. In support he said that, of the estimated 100 billion people who have lived and died on the Earth, the historical evidence is inadequate to suggest that any have been raised from the dead. So, even if the historical evidence for Jesus’ resurrection were good, there would still be only a 1 chance in 100 billion that Jesus was raised.
Bob argues that the prior probability of Jesus rising from the dead is 1 in 100 billion.  Given this low prior probability, there is no need to even look at the evidence for the resurrection of Jesus.  The evidence doesn’t matter because it can never overcome 1 in 100 billion odds.  Here is Licona’s response:
I replied that historians don’t use prior probabilities in historical inquiry.  One cannot calculate the prior probability that the U.S. would drop nuclear bombs on Japan during WWII, since in all of human history no nation had dropped a nuclear bomb on another before or since WWII.  Moreover, I’ll be 51 in two weeks.  That’s a lot of days in my life. Yet Sunday was the first day I had ever spent in Temecula, California. Given my “tendency” not to go to Temecula, one should conclude that I wasn’t there that evening.  Historians examine a historical report then look at the evidence for the event occurring.  Thus, prior probabilities are the wrong tool for historical inquiry.  It’s like using a calculator for an archaeological dig.
I think Licona’s response is compelling.  You cannot determine whether a historical event occurred without actually examining the evidence for it.  Calculating prior probabilities may be an interesting exercise, but I doubt that it is the best way to approach historical inquiry.  It just doesn’t matter that resurrections are rare.  In fact, even Christians claim that resurrections are rare in history.  But that fact just has no bearing on whether Jesus rose from the dead.
  • Should we or can we? I don’t think we need to, except to make a point to the skeptic. But I do think we can. That happens to be the big project I’m working on that I’ve mentioned here several times before. Problem is that everywhere I’ve seen it done, it was arbitrary. It needs to be done in an intelligent way with multidimenstional probabllity distributions taking into account when probabilities are not independent. Again, I’ve seen probabilities mutliplied that are not independent. It also has to take into account probabilities of any given detail not being true based on all evidences. It must be truly honest and unbiased. I propose to do it as it is done in target indentification algorithms for targets where there is no training data, but only characteristics of a hypothetical target that needs to be picked out of the noise. The noise can give a false conclusion and its character must be taken into account as well. I believe that most of the conclusions of the skeptic come about because the noise has led them astray. But, maybe my beliefs have been the result of noise. So, it must be comprhensive and honest to be of value.

  • Walt,
    I’m definitely looking forward to your approach to this topic. Keep me posted!

  • Rusty Southwick

    If their theory is suggesting that a rare occurrence can never happen a first time, then it’s flat-out self-contradictory. How many prior big bangs were there? No, I mean prior to the first one. Uh, yeah. By definition, every first occurrence of something has to have zero preceding events of the same kind. And by definition, every repeated event in history always had a first time. Ergo, cogito some more on that one. The difficulty would then arise in trying to show that Christ’s resurrection could in no way be the first time. Good luck in trying to demonstrate that.

  • I guess the difference is “the historical evidence is inadequate to suggest that any have been raised from the dead”. We HAVE evidence for the dropping of the nuclear bomb.

    “Moreover, I’ll be 51 in two weeks.”
    Right, and given known mortality rates, we can work out fairly well at any given stage of Licona’s life how likely he was to reach the age of 51. We can also calculate the probability of him making it to

  • Walt Tucker: The noise can give a false conclusion and its character must be taken into account as well. I believe that most of the conclusions of the skeptic come about because the noise has led them astray.

    I am curious as to what you consider “noise.” Can you give some examples of “noise” regarding the Resurrection of Christ that has led me astray?

    I know it may seem selfish to ask only about me, but I am not interested in “noise” like the swoon theory—not applicable to me. Or “noise” like “You are predisposed to not believe in miracles,”—again completely inapplicable to me. I am looking for specific historic claims I make surrounding the Resurrection you would consider “noise.”

    Not too unreasonable, I think, considering I am a skeptic, I have studied the Resurrection and I presume you would consider my conclusion—it didn’t happen—as “astray.” *wink*

  • Dagood,

    I’ll have to be brief since I am between meetings. But in short, the conclusion is not based on the truth of a small set of individual facts, but is based on a collective whole that has more to do with the conclusion of a world view in which the details must be consitent, than that any one thing happened. So, the resurrection has a low probability if the Christian worldview is not probable based on the world as it is understood, and it has a high probability if the Christian worldview is highly probable. The “noise” is the uncorrelated data of the world that masks the real world data used to arrive at the worldviews. The noise had to be filtered and the buik of the problem is filtering it without destroying the data that represents the reality we want to know, and as well, not constructing a picture that only exists in the noise. Noise does not persist. Whereas the real data does. As example of noise is looking at all world myths and automatically putting Christian writings in the same category without looking at it in the contexts. Analyzed alone, it may be most likely that Christian “myths” are no different than others. The only way to analyze it is to look at the correlations of the bigger picture hypotheses. What world view is most probable based on how well its understanding of the world maps unto what is observed. WIthout the analysis, we each have a “gut” feeling based on our experiences. We can be fooled by “gut” feelings. So, an unbiased analysis is necessary.

  • Walt Tucker,

    I confess—your response makes no sense to me whatsoever. For example:

    Walt Tucker: So, the resurrection has a low probability if the Christian worldview is not probable based on the world as it is understood, and it has a high probability if the Christian worldview is highly probable.

    Since the Christian worldview is based upon the resurrection as a historical event, isn’t this sentence redundant?

    More: The ‘noise’ is the uncorrelated data of the world that masks the real world data used to arrive at the worldviews….Noise does not persist. Whereas the real data does.

    Is “the noise” actual data, false data, perceived data, unknown data?

    I would agree we should not rely upon false information…is that what you are claiming “noise” is? If so, I would ask what false information I am relying upon regarding the resurrection claim?

  • The noise is information which by itself can lead to false conclusions.

    The ressurection is only one element of the Christian worldview. The whole world has to be taken into account. It is only one piece of a puzzle. By itself, it doesn’t give the whole picture, but it is vital part of the picture. By looking at the whole, we can decide whether we are intepreting the resurrection correctly.

  • Boz

    Did you know that there are three steps in a bayesian analysis? The first step is to estimate the prior probability. The second step is to assess the strength of the evidence. The third step is to combine these two results to determine the posterior probability.

    In that quote in the OP, Mike Licona is deliberately misunderstanding the process of bayuesian analysis.

    This is another strawman.

  • Boz,

    I don’t think Licona is deliberately misunderstanding the process, but he is at least saying that an over simplified calculation for something based on a decision is pointless. That’s not a strawman, but a point that the calculation as done is pointless.

    I think everyone has been doing that calculation in the wrong way. Per Calvin’s method (if Licona described what he is doing correctly), you can’t calculate the probability that dead people rise from the dead as a prior probability for the condition that God raised Jesus from the dead. Properly considering the way the resurrection works, the resurrection of Jesus would be insignificant if it was common for people to rise from the dead apriori anyway. The apriori calculations must take into account much more than just that dead people do or do not naturally rise from the dead. The claim never was that Jesus rose from the dead naturally in the first place. So, natural resurrections are not an apriori condition for Jesus’ resurrection, but should only be one part of several conditions that need to be involved to support the test! For God to raise Jesus from the dead, you also have to have the probabilities that God exists, that we have the story correctly passed down, that Jesus existed, and so on. And these probabilties are not independent of each other and can’t just be multiplied together. Rather, a multidimensional probabilty density function has to be developed that is multiplied by a priori probabilities that are carefully calculated taking into account any correlations between them. This is not a simple thing to do and Licona is mostly making that point, except I think he is being too pessimistic about it. But given it has been a fruitless endeavor to date and it complicated, he isn’t unwarranted in his claim. (Besides, I’m not sure he has the mathematical background to know whether it makes sense to do or not.)

  • Boz

    The deliberate misunderstandings in the OP are (1) “So, even if the historical evidence for Jesus’ resurrection were good, there would still be only a 1 chance in 100 billion that Jesus was raised.” , and (2) “Given my “tendency” not to go to Temecula, one should conclude that I wasn’t there that evening.”.

    I agree with you Walt Tucker that more needs to be taken in to account, and I look forward to seeing this document you have been foreshadowing.

  • Walt Tucker,

    Thanks for the response. I guess (being a historian in nature) I was looking for specifics along the lines of historical analysis to determine the likelihood of a claimed historical event. (Notice Dr. Licona’s comparison utilizes such analysis.)

    Normally, I am pretty good at getting the gist of what someone is claiming (I have to be in my occupation), whether I agree with it or not. I am still completely befuddled what you mean by “noise.”

    It sounds as if you are saying, “If you assume Christianity is true, then claims within Christianity (such as the resurrection) have a high probability of occurring.” But that can’t be right, because this would so obviously be begging the question.

    I guess I will wander away in confusion.

  • Dagood,

    The idea is to not be assuming as much as possible. Noise causes one to make assumptions that may or may not be correct. (My dots that look like a line example.) Noise is what muddy’s the picture and we want to know the true picture. When you or I look at the data relevant to whether the resurrection is true or false, we make assumptions. The only way I see to know whether the assumptions are valid is to look at the bigger picture. Anybody can say almost anything about a limited data set. The noise is our own experiences and preconceptions distorting our perception. So, to know whether the resurrection is true requires looking beyond only the data for the resurrection.

  • What do you mean by saying he is deliberately misunderstanding? Do you mean that he understands bayesian analysis, but that he is delberately misleading people about what it is?

  • Boz

    I say that because the mistakes are so basic, so obvious. It’s like getting 12 times 13 wrong.

    So, either he has no idea what bayesian analysis is, and these are just newbie mistakes. Or he does know what bayesian analysis is, and is deliberately misunderstanding it, perhaps for rhetorical effect.

    Or perhaps this is a verbatim transcript from a speech, (not a written article), and he mis-spoke.

  • Todd

    I’m no mathemetician, so please correct me if I misstep, but let’s do a quick calculation using the Bayesian simple form I got from wiki for a single event where P(A|B) = P(B|A) P(A) / P(B). We shall only need to ascertain P(B), I think. However, Where P(A) is the number of trials where A (human death) has happened; A = infinity. P(B) is the number of trials where B (resurrection) has occurred in proportion to A; B = 0. Therefore P(A|B) = 0. Is my interpretation correct?

    I think this only strengthens the skeptic viewpoint and puts Christianity back in the same place as usual; needing to prove that resurrection is possible… until then it would seem mathematics would be the tool of the skeptic.

  • Todd, that is not correct.

    First, you can’t do such a problem based only on P(B). You need to know P(B/A) and P(A).

    Second, for the math you used, infinity divided by zero is not zero, it is an undefined number that is determined through use of limits.

    Third, if you are trying to solve for the probability of the resurrection, you can’t do it based only on a sampling of human beings who have died. The reason is that the resurrection is based on the fact that people do die normally and that resurrections do not normally occur. It is a unique event by definition where the context has to be taken into account. If you were trying to calculate the probability that people naturally rise from the dead, then you would be correct to calculate that from the probability that people naturally die alone. Your conditional is different in this case.

    Until the skeptic properly frames P(B/A), then can’t made a case against the resurrection. The calculation you have proposed and that of Cavin is oversimplified and is only based on someone rising from the dead naturally, not as a result of God raising them supernaturally. Thus, the conditional needs to be set up considering the quality of the information which says there was a resurrection, the probability that there is a God, etc., etc. That is not so simple – and that IS Licona’s point.

  • Boz, I am the one who mentioned bayesian analysis, not Licona. Calculating prior probablity is one step required to do a baysian analysis, and Licona is pointing out that calculating prior probabilities for unique historical events is perilous. He gave examples to show why this is the case. I don’t see any misunderstandings on my part or Licona’s part. Any skeptic who tries to use prior probabilities to disprove the resurrection, as Licona and Walt have pointed out, is on very thin ice.

  • Boz

    The obvious mistakes are: (1) “So, even if the historical evidence for Jesus’ resurrection were good, there would still be only a 1 chance in 100 billion that Jesus was raised.” , and (2) “Given my “tendency” not to go to Temecula, one should conclude that I wasn’t there that evening.”.

  • “He gave examples to show why this is the case.”
    They were poor examples. We can say that lots of other people have reached the age of 51 and that lots of other people have visited Temecula, and that Licona has visited lots of other places. Therefore neither events are unusual. A better analogy for rising from the dead would be the probability of Licona flapping his arms and FLYING to Licona, or travelling to Pluto, or reaching the age of 510. Instead he offers quite unremarkable events.

  • That is a good point Andrew! But I take Licona’s comment to be that “even” historical events such as the ones he mentioned are difficult to caculate, let alone the resurrection, which Cavin over simplified. I’ll admit though, that he didn’t quite say it that way, but I think that is what he meant.

  • Asylo_Sophia

    I just have to say that I was actually at the debate (an
    eyewitness), and Cavin’s argument is being- borderline fraudulently-
    misrepresented on this blog. Cavin never insisted that historical data is irrelevant,
    but actually presented a sophisticated and elaborate example of why the resurrection
    hypothesis is inadequate to explain those facts. For those of you who were
    actually at the debate you will remember how Cavin proposed the “Atoms/Schmatoms”
    dilemma to Licona as a challenge to his resurrection hypothesis; a dilemma, by
    the way, that Licona never responded to.

    Furthermore, not only does this blogger misrepresent Cavin’s
    argument, but fails to grasp an understanding of how Bayesian analysis must be
    applied to history. I can’t help but think that this blogger is just
    piggybacking on what Licona has suggested. Having actually attended the debate,
    I know that Licona’s understanding of Bayes’ Theorem is flimsy, as he continues
    to dismiss it as only dealing with priors; this is not only incorrect, but
    extremely irresponsible as a scholar.

    I find it fascinating that a debate which occurred on
    7/1/2012 can lead to such great misrepresentations and confusion of the truth. This
    particular instance alone should raise a red flag for anyone considering the
    reliability of the gospel accounts!

  • Asylo,

    I was not at the debate, so you may well be right. I disagree with Licona’s understanding of Baye’s Theorem, but do see it typically misused by skeptics against the resurrection as well as many of those who try to use it in support of the resurrection. So I cannot make an assessment of what Cavin is doing beyond what was said above. If used properly, the Bayes theorem can be very valuable at assessing the reality of the resurrection. Many conditionals must be taken into account and they are not all independent and simply multiplied together as most do.

    What is a schmatom? My training is in physics and I have never heard of such a thing and could find nothing about it on the internet (other than for the word to be used a couple fimes) .

    Also, your eyewitness testimony goes to show how eyewitnesses are important for getting at the truth even if there are several vantage points (maybe especially if there are mutliple vantage points). The above account in the blog I’m sure is second hand or mutliple hand and thus not an eyewitness account. As such, unless we have reason to not to take your word at face value, your statement about the red flag on the reliability of the gospels with this blog as an example of confusion is defeated as a result of your posting. The accuracy of human testimony and the existence of an agendas in one’s rhetoric can go into the Baysian calculation, but alone, in absence of other details, it means little to whether there was or was not an actual resurrection.

  • Andrew Ryan

    “What is a schmatom?”

    It’s not a thing! You’ve never heard someone say “Hey, problems schoblems!”. Or if someone says “Watch out for the speed bumps”, and the other guy will reply “Speed bumps sheed bumps”. Or famously in the Rocky Horror Show song, “Planet Schmanet Janet”.

    It’s just a turn of phrase, I guess Jewish in origin. This doesn’t help with the atoms dilemma, but I guess you need to here what the dilemma actually was.

  • Thanks Andrew. I guess I’ve heard that a few times, but you are right in that it doesn’t help with knowing what the dilemma is.

  • You need to go back and re-read the post and re-read the comments under the post. Licona said nothing about Bayes’ Theorem; I did. I mentioned it because I know that prior probabilities play a significant role in a Bayesian calculation (it’s in the numerator).

    Having read Licona in other places, he definitely understands Bayes’ Theorem, so your claiming that he does not is simply false.

    Licona’s point was that relying heavily on prior probabilities to determine whether a historical event occurred is not the way historians work. If Cavin actually did use the example of 100 billion people not rising from the dead as evidence against Jesus’s resurrection, then he was making a ridiculous argument, and everything in this blog post stands.

    If Cavin never said anything about 100 billion dead people being evidence against the resurrection, then I may have misinterpreted Licona, or maybe he misheard Cavin. If that is the case, please let me know.

  • Hi Bill — Cavin’s PowerPoint slides from the debate are now available here.

  • News Alert: Scientists have proven the Bible False

    And God said, Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years: 15 And let them be for lights in the firmament of the heaven to give light upon the earth: and it was so. 16 And God made two great lights; the greater light to rule the day, and the lesser light to rule the night: he made the stars also. –the Bible

    The ancient Hebrews and therefore the early Christians believed that above the earth, God had created a “firmament” or domed ceiling, upon which he hung the sun, moon, stars, and planets. Heaven was directly above this “ceiling”.

    Let’s now look at the story of the Ascension of Jesus:

    When he (Jesus) had said this, as they were watching, he was lifted up, and a cloud took him out of their sight. 10 While he was going and they were gazing up toward heaven, suddenly two men in white robes stood by them. 11 They said, “Men of Galilee, why do you stand looking up toward heaven? This Jesus, who has been taken up from you into heaven, will come in the same way as you saw him go into heaven.” -The Bible

    If you lived in the first century AD and believed that heaven was just on the other side of the firmament or “ceiling” above the earth, then it would be very consistent with your worldview to believe that if Jesus was going to return to heaven, all he had to do was to ascend past the clouds and he would soon reach the “ceiling” of the firmament, to which are hung the planets, the sun, and moon, and he then would pierce the firmament to enter heaven. And if one can look up and see the planets and stars, then these heavenly objects must be within a day’s travel time. You would know this by common sense: if you can see a mountain in the distance, chances are you can reach it in a day’s time. So believing that Jesus could ascend to heaven, at a speed slow enough for his disciples to watch him ascend into the clouds, would be completely consistent with this world view.

    The problem for the Bible, and for Christians who believe that the Bible is the inspired, inerrant word of the Creator, is that this worldview has been proven absolutely false by modern science. There is no firmament. Jesus could not have reached the outer reaches of the universe to enter heaven moving at a speed at which humans could watch him ascend. Scientists have demonstrated that for a rocket or space ship to reach the next closest galaxy to our own, the Andromeda Galaxy, it would take two million LIGHT YEARS to get there!

    Unless Jesus entered a tractor beam once he got into the clouds, a tractor beam that “beamed him up” to heaven like Captain Kirk would regularly do on Star Trek…Jesus…at this very moment…is in outer space, putting along, somewhere between earth and the Andromeda Galaxy. Bombshell! Jesus hasn’t made it to heaven yet! Jesus is not sitting at the right hand of God the Father as the Bible claims.

    Thus, scientists have proven the Bible false.

    Trust science, my friends, not the scientifically ignorant superstitions and legends of ancient peoples, nor their holy books, full of preposterous supernatural claims.

  • Gary, there are a lot of assumptions in there about what is going on, what the firmament was understood to be, and where heaven is. I think the only thing science has discreted is your interpretation of all of that. I’m not aware of any scientific papers that actually prove the Bible false. If you can prove scientifically there was no creation, there is no design, that evil doesn’t exist, and that Jesus did not rise from the dead, then I think you have a case. I trust science. My degree is in physics. But I also have a subsequent degree in philosophy and know how easy it is to creat what is called a strawman and then knock it down. The strawman is not the real argument. Some will say that science has proved there is no design, that evil does not exist and that Jesus did not rise from the dead, but it actually hasn’t. Rather, it is an interpretation of the data from the preconceived notion that such things are not true. All of the laws of nature are just as true for a world that is designed and where evil exists. That men don’t normally rise from the dead just goes to make the case how unique Jesus’ rising was. You have to make a pretty large group of people out to be liars and deceivers to say it didn’t happen. It is possible for a small group, but not likely for a large group. Many people knew Jesus and many of them saw him after he was supposed to be dead. Seeing him ascend is pretty bizarre, I will admit. But since we weren’t there, it is rather presumptious to say for sure such a thing didn’t happen. It isn’t just a story that was passed down like many myths, but an actual event that many claimed to have seen with their own eyes. Before Christian faith can be laid to rest, someone has to prove the resurrection didn’t happen since that fact, not details of the ascension, is what it is based upon. It does make sense that things were written in ancient time in terms they understood. That doesn’t make it false.