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I disagree with Tyler Cowen regarding a so-called lack of Bayesianism in religious belief

Tyler Cowen writes:

I am frustrated by the lack of Bayesianism in most of the religious belief I observe. I’ve never met a believer who asserted: “I’m really not sure here. But I think Lutheranism is true with p = .018, and the next strongest contender comes in only at .014, so call me Lutheran.” The religious people I’ve known rebel against that manner of framing, even though during times of conversion they may act on such a basis.

I think Cowen’s missing the point here when it comes to Bayesianism. Indeed, as an applied Bayesian statistician, I’m not even “Bayesian” in Cowen’s sense when it comes to statistical inference! Suppose I fit some data using logistic regression (my go-to default when modeling survey data with Mister P). I don’t say “logistic regression is true with p = .018, and the next strongest contender comes in only at .014, so call me logistic.” What I say is that I use logistic regression because it works for the problems I work on, and if it has problems, I’ll change the model. I also might want to try some other models as a robustness check. But Bayesian reasoning doesn’t at all require that I assign probabilities to my models.

Or, in a different direction, we can resolve Cowen’s problem by thinking of religious belief as analogous to nationality. Being an American doesn’t mean that I say that Pr(Americanism is true) = .018 or whatever. It’s just an aspect of who I am. This framing becomes particularly clear if you think of interactions between religion and nationality, such as Irish Catholic or Indian Muslim or whatever. And then there are Episcopalians, which from a doctrinal perspective are very close to Roman Catholics but are just part of a different organization. There’s a lot of overlap between religion and nationality. Another way to put it is that sticking with your own nationality, or your own religion, is the default. You can switch religions if there’s another religion you really like, or because you have some other reason (for example, liking the community at one of the local churches), but that’s not a statement about which religion is “true.”

To loop back to statistics, I suppose someone might talk Bayesianly about the probability that a particular religion is best for him/herself, but that’s not at all the same as the probability that the doctrine is true.

Cowen is frustrated by what he sees as “lack of Bayesianism” in religious beliefs that he observes, but I think that if he had a fuller view of Bayeisanism this would all make sense to him. In my recent paper with Hennig we talk about “falsificationist Bayesianism.” The idea is that a falsificationist Bayesian performs inference conditional on a model—that is, treats the model as if it were true—and then uses these inferences to make decisions while keeping an eye out for implications of the model that conflict with data or don’t make sense. From a Bayesian perspective, if a prediction “doesn’t make sense,” this implies that it’s in contradiction with some piece of prior information that may not yet have been included in the model. As we move forward in this way, we continue to update and revise our model, occasionally revamping or even discarding the model entirely if it is continuing to offer predictions that make no sense. This sort of Bayeisanism does not seem so far off from many forms of non-fundamentalist religious belief.

P.S. to all the wiseguys who will joke that Bayeisanism is a religion: Sure, whatever. The same principle applies to statistical methods and frameworks: we use them to solve problems and then alter or abandon them when they no longer seem to be working for us.


  1. Statsgirl says:

    I wonder what statisticians would answer if asked to give P(Bayesianism is true)?

  2. Eric says:

    Is it possible you’re reading too much into Cowens reference to Bayesianism specifically and miss what – to my mind – is an attempt to describe the lack of probabiluty estimates of Christianity’s central truth claims? … Or truth claims specific to different denominations, for that matter. What is the p = for Christ existing? … Being baptized by John the Baptist? … Being crucified at the hands of Pontius Pilate? And, importantly, rising from the dead?

    Christianity differs from American and Americanism because, at least at the very core, they rely on truth claims which can be evaluated on the basis of the texts that are available to us. Of course, Christianity (as Cowen rightly points out) is absolute dependent on what country your born into, parenting etc., but few people would admit that they are Christian simply because they were born in the US. Or, if they did, I would expect them to call themselves cultural Christians.

    Being a believing Christian, which is what we’re talking about based on Cowen’s post, means accepting certain truth claims. Those claims can be evaluated statistically, and Bayesianism would lend itself nicely to it. Of course, the problem would be interpreting/analyzing the sources to estimate these probabilities, but that’s another story.

  3. Vladislav Malik says:

    Add to this:

    Religions change (eg, Christian mysticism/meditation revival, Reform Judaism, etc)
    Religions are internally diverse (eg, Trappist monk vs. Regular Joe Catholic)
    Religions borrow from each other and share a lot (eg, read Living Buddha, Living Christ by Thich Nhat Hanh)

  4. BenK says:

    What he seems to want is ‘fractional belief.’ It is a weird interpretation, perhaps, of intersectionalism, in which all the religious identities are on a single axis that sums to 1.

    • Steve J says:

      You think summing probabilities to 1 is weird? How else would it work? Non-believers usually aren’t sure about anything. When religious people say they are sure about their beliefs it is hard for us to comprehend that.

  5. Jeffrey Bowers says:

    Not sure this is relevant to the quote, but it is possible to use Bayesian statistics as a tool but deny the view that the brain is a Baysian device. People act un-Baysian all the time (is that the frustation?). This is the point we make in the following paper.

    Bowers, J.S., & Davis, C.J. (2012). Bayesian just-so stories in psychology and neuroscience. Psychological Bulletin, 138, 389-414.


  6. Guive says:

    I see this a lot, people calling the practice of assigning in an apparently arbitrary way probabilities to propositions (p(Lutheranism is true)=.018) and calling that bayesianism. I can’t imagine how you would actually calculate the probability that Lutheranism is true and arrive at .18 and have that be meaningfully different from .21.

    • Kyle C says:

      Yes, if you believe truth concepts apply to religion at all, it seems like a clear case of Keynesian/Knightian uncertainty.

    • Eric Rasmusen says:

      Not a problem at all. The essence of Bayesianism is that new information changes one’s optimal decisions. If the probabilty of rain rises from .18 to .21, some people will change their minds and carry their umbrellas. If it’s Lutheranism, some Calvinists will decide it’s worth reading a book about why Lutherans are right on the sacraments and Calvinists are wrong.

  7. Dale Lehman says:

    I believe this misses the whole point of much of Cowen’s work. To show how learned he is, he loves to throw around terms such as Bayesian, and it achieves the objective of getting lots of blog attention. That post got around 300 comments, with around 100 of them addressing the Bayesian reference. Mission accomplished!

  8. Ben Prytherch says:

    I think maybe atheists / non-believers should just quit with this whole “justify your belief to me using the same methods I use to justify my own beliefs” game. I know Cowen’s post was in direct response to a question about his lack of faith, so fair play to him I suppose. But it’s pretty annoying.

    • Steve J says:

      I don’t think non-believers require the same methods I think we are asking for any method at all. Having some sort of method would at least allow us to understand how you evaluate one religion against another. At this point most believers realize there is no methodical way to justify their belief so they resort to faith/hope/etc. Trust me it is annoying both ways.

      • Ben Prytherch says:

        “At this point most believers realize there is no methodical way to justify their belief so they resort to faith/hope/etc”

        I agree, and my experience very few will deny this. The issue for non-believers (and I’m a non-believer) is that we just can’t fathom how anyone would think that “faith” is an acceptable reason for believing anything.

        In my opinion, subjecting religious claims to empirical scrutiny is fine in response to people who use religious belief to make empirical claims. This certainly happens, and when it does, fair game. But most religious believers don’t do this (side note: I don’t consider “there is a heaven that I will go to when I die” or “God watches over us all” to be empirical claims). The religious people I know just say something like “I have my faith and that’s enough for me”. I really don’t see the point in arguing with them over this, and I definitely don’t see the point in asking them to assign probabilities to their religious beliefs.

        • Steve J says:

          I somewhat agree with you but it is infrequent that believers will make any empirical claims so while your logic makes sense it doesn’t really matter. The claims they regularly make are moral claims which they justify with their faith. If you find asking a believer the odds they are right annoying then how do you feel about claims about women’s rights being backed up by “God said so”? Again the annoyance has got to go both ways.

          I don’t get the desire to be “fair” to the intellectually challenged. Keep in mind these people have designed systems that allow them to perform evil acts righteously that result in punishment for those outside their circle.

          • Martha (Smith) says:

            This sounds like you are talking about *some* believers, but not all.

          • Ben Prytherch says:

            I agree with Martha, and I also take the point regarding moral claims. I’m not giving a pass to those who claim divine permission to treat someone else badly. I don’t think most religious people are like this, at least in the US, but certainly the ones who are do a good job of bringing attention to themselves. I don’t have an interest in being “fair” to this subset.

            I still think that asking them for a rational (and in particular empirical) justification of their religious beliefs is pretty pointless. And probably the most effective counter-arguments against evil in the name of religion are going to come from other religious people – their arguments carry some weight with one another, silly as they may sound to those of us on the outside looking in.

  9. max says:

    Andrew, can you comment on the idea that it’s “more rational” to have “partial beliefs” or “beliefs with degrees of confidence” attached to them than “outright” beliefs? Can we get rid of the “outright” or “full” beliefs and replace them with more accurate representation that hugs reality closer? I think the “rationalist” crowd advocates some kind of “bayesian salvation through the degrees of faith”

    • Guive says:

      I think Andrew’s point in this post is that it isn’t really meaningful to talk about degrees of belief in this way. Like believing in Lutheranism not only commits you to the truth of certain propositions, it also means you believe certain causal theories about how the world works, which you can’t really partially believe. What does it mean to have 18% belief that the world was created in 7 days? Or that salvation is by faith alone? For me it’s really hard to make sense of an 18% belief in those things. Also the numbers seem like they’re always going to be very arbitrary. What computations got Cowen to .18? None, obviously he just made it up, and idk what other way there is of getting to a probability for Lutheranism being true.

      • grumbler says:

        “What does it mean to have 18% belief that the world was created in 7 days?”

        It means that I don’t know for certain, but I think the probability that the world was created in 7 is 18%. Similarly, I don’t for for certain, but I think the fair die in the other room has a 6 facing up, with a probability of 16.7%. OK, maybe not the best example since any other number has the same probability. But I could say I believe the pair of dice add up to 7, since that is the likeliest scenario. Anyway, I am surprised no one has noticed the parallels here to Pascal’s wager.

        But you are right, there are no computations used. It’s all made up since there are so many things unquantified and unquantifiable.

        • Guive says:

          I like the parallel with Pascal’s wager.

          I think my point was more that it’s hard to imagine really believing that, as opposed to saying something like 18% of the evidence supports Lutheranism. The way you interpret new evidence is contingent on the previous theories you hold about the world and I’m not sure how that would look for an 18% Lutheran. Maybe more partial beliefs but I sorta suspect people don’t really think that way.

          • max says:

            “What computations got Cowen to .18? None, obviously he just made it up, and idk what other way there is of getting to a probability for Lutheranism being true.”

            How do people in the industry get the “degrees” for their Bayesian models or parameters? Dont they in some sense “just make it up”?

      • Olav says:

        I have no difficulty with having partial beliefs over various religious views (treating those views as truth claims — which I do — rather than simply views about my own identity). Obviously it would be arbitrary to assign very precise numbers, but I can still give rough estimates. And at least for me, it’s helpful to do so. I’m roughly 70-80% atheist and 20-30% religious. And conditional on some religion being true, I’m much more confident of Christianity than I am of Scientology, though my absolute confidence in each is quite low. These numbers aren’t due to some sort of computation, but are rather facts about my epistemic state (chiefly arrived at through introspection and my evaluation of what I take to be the available evidence). Obviously, all these numbers are scientifically worthless, but they’re still perfectly meaningful, at least to me.

  10. Jonathan says:

    But people do perform Bayesian style analysis on beliefs. They match their prior to their reality as it develops and adjust their beliefs and if things get really disparate then they change churches, maybe to a new location, or maybe they lapse or maybe they even convert, depending on how deeply the difference between posterior and prior run. You come to beliefs through family and that constructs priors which you carry into adulthood and as you develop as a person then you apply those priors to the experiences of the beliefs and see how they match. That is Bayesian. What is nonsensical is the idea that you should or could rank this or that faith by some sort of truth measure which is applied to judge which faith you should follow. That’s not Bayesian at all. It’s the kind of vacant intellectual exercise one sees in plays and novels. But we all do map faiths to our priors … that’s what faith is to most of people, a set of priors you inherit and develop.

  11. Olav says:

    I’m not so sure about your analysis of either religious belief or of your own use of Bayesian models! I don’t think religious people (even non-fundamentalists) typically treat their religion as a revisable and even discardable model that they do not assign a truth value to or that they only consider “best for me” — In many cases they really think their religion (or “model”) is true. At the very least they will typically think their religion is “best for everyone” in some more objective sense.

    Similarly, even if you don’t assign a probability to a model, implicitly you trust some models more than others, perhaps because they have a scientific justification or proven track record, and this trust isn’t just a reflection of your attitude that the model is “best for me” in some superficial pragmatic sense; it’s a reflection of your belief that the model actually tracks something real in the phenomena you’re studying — it’s “close to the truth” in the relevant sense, even if not strictly speaking true. Moreover, that kind of trust comes in degrees, so even if you may put the most a priori stock in a linear model for a particular phenomenon, you may at the same time be open to the possibility (i.e. also have some degree of trust) that a model with, say, some of its variables (say log-)transformed would be better.

    • Martha (Smith) says:

      Olav said, “I don’t think religious people (even non-fundamentalists) typically treat their religion as a revisable and even discardable model that they do not assign a truth value to or that they only consider “best for me” — In many cases they really think their religion (or “model”) is true. At the very least they will typically think their religion is “best for everyone” in some more objective sense.”

      I’m not convinced; I think of “my religion is true” as characterizing fundamentalism.
      Also, “My religion is best for everyone” doesn’t even characterize all fundamentalist religions — some fundamentalists think they belong to a “chosen people”.

      This view is probably influenced by the fact that I grew up in a non-fundamentalist religion, and have seen lots of people “migrate” in their religious beliefs.

      • Olav says:

        Point taken on the “chosen people” part. But I do think most non-fundamentalists regard their religion as more or less true, although they may be willing to concede that some of the details might be wrong. I mean, if you don’t actually believe there was a person named Jesus, and that Jesus was God, and that he rose from the dead and will one day return to earth — if you don’t think these claims are literally true, then in what sense can you be said to be a Christian?

        That’s not to say people don’t ever revise or even discard their religious beliefs. They do. Also, some religions are clearly more permissive in the range of metaphysical views they allow among their adherents (e.g. liberal Judaism). However, I don’t think it’s the case that most religious people (even non-fundamentalists) view their religion as just a pragmatic tool whose truth value (or rough truth value) is completely irrelevant to them. That was my main disagreement with Andrew.

        • Andrew says:


          Maybe you’re right—indeed, it could well be that many religious people’s beliefs in Adam and Eve, Noah, etc., is on par with the beliefs of Daryl Bem and Satoshi Kanazawa, say, regarding their theories. Belief in all these cases is a matter of thinking and acting with a certain frameworks, with no direct evidence required. (There’s indirect evidence in all these cases: the Bible is a real book and it does mention Adam and Eve, and Bem and Kanazawa have real published papers which claim evidence for their theories; but in none of these cases is there direct evidence outside the documents that present the stories in question.)

          But let’s get back to Cowen’s quote that got this discussion going: “I’ve never met a believer who asserted: ‘I’m really not sure here. But I think Lutheranism is true with p = .018, and the next strongest contender comes in only at .014, so call me Lutheran.'” I’m no expert in religious doctrine so I could well be wrong on the details here, but I’m assuming that Lutherans, like other Christians, hold that there was a person named Jesus, and that Jesus was God, and that he rose from the dead and will one day return to earth. I’m still skeptical of the claim that what separates most Lutherans from Methodists, Catholics, Baptists, etc., is belief in whatever doctrines that happen to characterize these different denominations.

          • Eric Rasmusen says:

            Cowen is wrong— there are plenty of people like that. But you are right, also, that most people adhere to a denomination for reasons other than belief in its doctrine. Most member do not even *know* the doctrine of their denomination— they just trust the pastor about all tht intellectual stuff.

  12. I prefer characterization ‘absolutism’& ‘relativism’ b/c beliefs are expressed differently in different contexts, in my observation. So some refined scale may be appropriate. But not sure whether Bayesian scale is appropriate.

  13. sam says:

    one way of looking at faith / religion is a degenerate prior – no amount of information can shift peoples beliefs

  14. Carlos Ungil says:

    I find interesting that the expression “non-fundamentalist religious belief[s]” has only been used a dozen times in the past according to Google.

  15. Eric Rasmusen says:

    Nice Sunday morning topic!

    Hume criticized theological statements that were unconnected to sense impressions as vacuous, which is indeed a big problem. Other theological statements are simple statements of fact, though, true or false, if hard to verify, e.g. did Jesus of Nazareth rise from the dead after 3 days and appear bodily to the Apostles, or not?

    I Corinthians 14. says, 2 Now if Christ be preached that he rose from the dead, how say some among you that there is no resurrection of the dead? 13 But if there be no resurrection of the dead, then is Christ not risen: 14 And if Christ be not risen, then is our preaching vain, and your faith is also vain. 15 Yea, and we are found false witnesses of God; because we have testified of God that he raised up Christ: whom he raised not up, if so be that the dead rise not. 16 For if the dead rise not, then is not Christ raised: 17 And if Christ be not raised, your faith is vain; ye are yet in your sins. 18 Then they also which are fallen asleep in Christ are perished. 19 If in this life only we have hope in Christ, we are of all men most miserable.

    You can apply Bayesian thinking to a theory like Lutheranism or Evolution as well as to a fact like the Resurrection or the partial descent of modern humans from Neanderthals, but defining what the probability is over, and what the event space is, gets tricky. Also, equivocation becomes easy and will happen even by accident rather than by design, and “No true Scotchman…” gets to be a problem.

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