Wasserman on Bayesian religion

30 Jan, 2015 at 18:10 | Posted in Statistics & Econometrics | 4 Comments

There is a nice YouTube video with Tony O’Hagan interviewing Dennis Lindley. Of course, Dennis is a legend and his impact on the field of statistics is huge.

At one point, Tony points out that some people liken Bayesian inference to a religion. Dennis claims this is false. Bayesian inference, he correctly points out, starts with some basic axioms and then the rest follows by deduction. This is logic, not religion.

I agree that the mathematics of Bayesian inference is based on sound logic. But, with all due respect, I think Dennis misunderstood the question. When people say that “Bayesian inference is like a religion,” they are not referring to the logic of Bayesian inference. They are referring to how adherents of Bayesian inference behave.

(As an aside, detractors of Bayesian inference do not deny the correctness of the logic. They just don’t think the axioms are relevant for data analysis. For example, no one doubts the axioms of Peano arithmetic. But that doesn’t imply that arithmetic is the foundation of statistical inference. But I digress.)

The vast majority of Bayesians are pragmatic, reasonable people. But there is a sub-group of die-hard Bayesians who do treat Bayesian inference like a religion. By this I mean:

They are very cliquish.
They have a strong emotional attachment to Bayesian inference.
They are overly sensitive to criticism.
They are unwilling to entertain the idea that Bayesian inference might have flaws.
When someone criticizes Bayes, they think that critic just “doesn’t get it.”
They mock people with differing opinions …

No evidence you can provide would ever make the die-hards doubt their ideas. To them, Sir David Cox, Brad Efron and other giants in our field who have doubts about Bayesian inference, are not taken seriously because they “just don’t get it.”

So is Bayesian inference a religion? For most Bayesians: no. But for the thin-skinned, inflexible die-hards who have attached themselves so strongly to their approach to inference that they make fun of, or get mad at, critics: yes, it is a religion.

Larry Wasserman

For some more thoughts on the limits of the Bayesian approach, Stephen Senn’s You May Believe You Are a Bayesian But You Are Probably Wrong is a good read.


  1. I note this with some amusement. Senn wrote: “You May Believe You Are a Bayesian But You Are Probably Wrong” Whether you are a Bayesian or not is not a question of an event, but of a hypothesis. The distinction between Bayesian and frequentist probability is whether a hypothesis has a probability. Senn says yes, so he is a Bayesian. 😉

  2. OC, charges of religiosity can be made against some Fisherians, as well. Also, randomization could be considered as a ritual of that religion. 😉 And defining probability as the ratio of an infinite series of possible events could be called mumbo jumbo. I mention that not as an indictment of non-Bayesian statistics, but to illustrate that name calling is easy and unproductive.

    Feynman, in his first autobiography, tells about a psychology graduate student who asked him about a proposed experiment and Feynman told her that the first thing to do was to replicate the previous experiment upon which the new experiment was based. The student’s professor, however, said not to bother with replication, because, “We already know that.” OC, he meant that the previous experiment had gotten statistically significant results at the 5% level. Bayesians would have avoided such a fundamental error, because they know that there is a inescapable subjective component to statistics. (And today, over a half a century later, psychologists are focused on the question of replicability.)

    Part of what I found attractive about Bayesian statistics is that it was more skeptical and less inclined to such overstatement. Would parapsychology have gained the degree of respectability that it enjoys today without null hypothesis testing?

    • Yes, the problem is the misuse of the maths, not the maths. In both cases there is a widespread practice of going well beyond what the logic supports.

  3. You do not have to be a Bayesian to believe that uncertainties are always adequately represented by probability distributions. In so far as Bayesian inference is logic it seems true, useful and harmless. The problem seems to me a special case of a more widespread phenomenon: we want a tool that we can legitimately apply, we only have one tool, so we use that tool and defend its use against all comers. The logicality of Bayesianism is irrelevant: it is its applicability that matters.

    Perhaps we need to re-consider the alternatives in Keynes’ Treatise?

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