Carrier: Understanding Bayesian History

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by Neil Godfrey

Richard Carrier addresses two online criticisms of his book, Proving History: Bayes’s Theorem and the Quest for the Historical Jesus, in a new blogpost, Understanding Bayesian History.

I took time out from my own chapter by chapter reviews of the book to read a history of Bayes’ Theorem by Sharon McGrayne, The Theory That Would Not Die. I’d like to return to discussions of Bayes’ rule with that additional reading background. One thing that stands out from reading the way Bayes’ theorem has been successfully applied and the social and political struggles it has had for open acceptance (it has much more often been covertly accepted) until today is that the more complexities and nuances their are impinging upon any question, the more appropriate is the use of Bayes’ theorem to help resolve them. That means that those arguments that history is too complex for Bayes to be of use fail to understand that it is complexity and nuance of so many unknown quantities that Bayes assists us in handling.  McGrayne’s book also shows us that some of the arguments used against Bayes today are identical to the ones that were used long ago until they were eventually proven unfounded.

Carrier is responding to criticisms by an atheist-mathematician-with-New-Testament-interests on Irreducible Complexity.

Richard Carrier writes:

When Ian isn’t ignoring the refutations of his own arguments in the very book he’s critiquing, he is ignoring how applications of Bayes’ Theorem in the humanities must necessarily differ from applications in science (again for reasons I explain in the book), or he is being pointlessly pedantic and ignoring the fact that humanities majors need a more colloquial instruction and much simpler techniques than, for instance, a mathematical evolutionist employs.

To illustrate these points . . .




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Neil Godfrey

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  • 2012-10-10 12:37:03 GMT+0000 - 12:37 | Permalink

    I think you meant to have more of this post after the jump. Maybe an HTML error? I hope it’s something easily fixed and you didn’t lose anything.

    • 2012-10-10 21:44:03 GMT+0000 - 21:44 | Permalink

      Nothing lost. Just wanted to post something I thought worth attention but lacked the time to expand with my own reflections on it all. Can’t post a thousand words every day 😉

  • Ian
    2012-10-12 08:31:13 GMT+0000 - 08:31 | Permalink

    Hi Neil, I think you may be rather misunderstanding the issues.

    Among a few other things, I’ve applied Bayesian probability to demographic reconstruction in large ecommerce systems, financial models of commodity pricing, and (as part of my PhD) the dynamics of genetic regulatory networks. All these are systems that are highly complex, very nuanced, and depend on statistics that are often poorly reflective of the underlying variables. There are many situations where Bayesian probability is very useful. Several of the cases in McGrayne’s (super math-light) book fit exactly the same case. Her story is told as a hero’s journey for journalistic effect, but the idea that Bayesian reasoning can do anything, and anyone who says it doesn’t apply to some domains will be steamrollered by its conquest is a naive one.

    There are places where probability theory is useful, and others where other similar models can be useful. I’ve done more with what are called ‘fuzzy logics’ which use 0-1 ranges to represent philosophical vagueness, rather than confidence. The math is a bit different, but the upshot is similar. But there are others where the errors inherent in a Bayesian calculation can swamp the information one gains from it. This is provable, and I’ve seen in cases where conclusions are indeterminable. Areas where most inputs behave this way are not amenable to Bayesian analysis (though other methods may apply). Bayes’s Theorem is not the one ring to rule them all.

    The problem is, when you’re tied to a particular position, it is easy to see anyone putting forward anything that supports your position as right, and anyone challenging them as wrong. The poster that Richard quotes extensively in his post, for example, has spent a long time discussing these issues on my blog and while his criticisms of my review were specific, has an opinion of Bayes’s Theorem’s usefulness in history that is entirely consistent with mine.

    While it can be tempting to cheer your friends, and boo your perceived enemies, it is harder to actually work on getting to the bottom of the criticism, and seeing if it has merit. A dalliance of knowledge in an area, can be very misleading.

    • 2012-10-12 08:57:57 GMT+0000 - 08:57 | Permalink

      Hi Ian. My own past posts on Carrier’s discussion of Bayes’ theorem will explain where I see the primary value of its application for historical studies.

      There I also address some criticisms of Carrier’s views that I am sure even you would consider ill-informed. It is in that context that I wrote my post. These other critics of Carrier’s views may well support your conclusions but as you yourself say, one must be on guard against the tendency to see anyone who puts forward something that supports your position as being right and anyone challenging them wrong. (You will notice many posts on this blog that are indeed critical of arguments for general views I support — my interest is not to crusade for particular views but to understand certain questions, so I am very conscious and try to be on guard against embracing arguments simply because they support my views. I have been critical of Carrier and other “mythicists” on other issues, too.)

      So I think it’s more constructive to avoid gratuitous ad hominem assumptions and stick to arguing the case. Such extensive rhetoric does not encourage me to think you can rely upon the logic of your case alone.

      Not being a mathematician myself my post was brief in order to direct interested readers to Carrier’s response to criticisms that are surely well known thanks to McGrath’s promotion of them.

      • Ian
        2012-10-12 09:20:29 GMT+0000 - 09:20 | Permalink

        Thanks Neil, I was responding to “That means that those arguments that history is too complex for Bayes to be of use fail to understand that it is complexity and nuance of so many unknown quantities that Bayes assists us in handling.” which I took to be a criticism of my “arguments that history is unamenable to Bayes’s Theorem”.

        If my criticism of Carrier didn’t motivate that, then that’s fine. If it did, then I respectfully suggest you have misunderstood the criticisms of Bayes’s Theory in history.

        The ad homs were an unnecessary addition, I agree. But they cut both ways. James McGrath’s (and others) ‘promotion’ of my posts on this is indisputably motivated by the fact that I am saying things they want to hear! And controvery aside, it might be worth noting that I enjoyed Carrier’s book, outside the mathematical bits, (and said so on my blog) because it fitted in with many of my own biases, particularly on the use of Criteria.

        Always happy to have the discussion.

        • 2012-10-12 09:42:19 GMT+0000 - 09:42 | Permalink

          Hi again Ian. That sentence was directed most directly at the attacks by Joseph Hoffmann and Stephanie Fisher on Carrier’s thesis. Their criticisms are remarkably reminiscent of some of the less informed rhetoric that McGrayne documents being leveled against the theorem throughout its history — and also suggestive that they have not really read Carrier’s work in any depth or with any comprehension anyway.

          I would never myself enter into the fray of arguments over the details of mathematics. I try to understand as much as I can but must rely upon those more skilled than I to present their cases clearly for lay people to allow me to either lean one way or reserve any judgment altogether. I would never commit myself dogmatically to any complex mathematical argument because I am not qualified to do so. I also think your might have your own potential for bias against the nonhistoricity of Jesus — that is not a personal criticism, but another reason for an outsider to be extra cautious with arguments from your side as well as Carrier’s.

          I see anything that can be used as a tool to assist laying out one’s assumptions and alternative views as “a good thing” — to the extent that such a process leaves me wondering why even bother with Bayes after all of that. (But of course Richard’s argument is that it is all too rare to find scholars who are as comprehensively aware of the full complexities needing to be addressed to make a sound case.) I have found a couple of preliminary exercises I have attempted with Bayes “interesting”. But I have yet to read through the remainder of the book before I can say anything more.

          • Ian
            2012-10-12 09:57:42 GMT+0000 - 09:57 | Permalink

            “I also think your might have your own potential for bias against the nonhistoricity of Jesus”

            Yes, though I think is insidious. I am not just biased against arguments for nonhistoricity (a bias which I choose, based on my conclusions on the matter), but I have bias against unrelated arguments made by people who advocate nonhistoricity. I am likely to take things you say less seriously, than say James McGrath, because we disagree on a key issue that has defined ‘sides’. And vice versa, you are likely to begin approaching what I think with a greater degree of skepticism, because of that same disagreement. Of course, we can both compensate for this to a certain extent if we try, but 90% of the iceberg, I suspect, is subconscious.

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  • Malcolm
    2012-10-16 13:07:57 GMT+0000 - 13:07 | Permalink

    FWIW, I’ll add my $0.02, as the “poster that Richard quotes extensively in his post.” Ian’s original posts contained a number of criticisms of Carrier’s book that focused on stylistic issues. There were a few allusions to more serious mathematical problems, but they weren’t spelled out. So my original post on Carrier’s blog was just a list of all the points Ian made and, in some cases, my response to them. The purpose of my posting that was for Carrier to respond, not me, so I didn’t give my opinions about all of Ian’s points, some of which I somewhat agreed with and others for which I was neutral. Later Ian and I discussed mathematical difficulties in applying BT to history, and we came up with more serious ones than were mentioned in his previous posts and my comments on Carrier’s blog, and these are the focus of Ian’s 3rd post on the subject as well as recent comments by us on Carrier’s blog.

    So while I think that Ian’s original review of Carrier’s book is not particularly damning for it, the weaknesses in applying BT to history that we have identified still have not been completely addressed by Carrier. While I certainly have my biases and tendency to favor arguments by people with whom I agree, in this case they may not be playing that much of a role since I am, like you and Carrier, “biased” against the HJ hypothesis.

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