Is Bayesian Inference a Religion?

Time for a provocative post.

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:

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

To repeat: I am not referring to most Bayesians. I am referring to a small subgroup. And, yes, this subgroup does treat it like a religion. I speak from experience because I went to all the Bayesian conferences for many years, and I watched witty people at the end-of-conference Cabaret, perform plays and songs that merrily mocked frequentists. It was all in fun and I enjoyed it. But you won’t see that at a non-Bayesian conference.

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.”

It is my belief that Dennis agrees with me on this. (If you are reading this Dennis, and you disagree, please let me know.) Here is my evidence. Many years ago, there was a debate about whether to start a Bayesian journal. Dennis argued strongly against it precisely because he feared it would make Bayesian inference appear like a sect. Instead, he argued, Bayesians should just think of themselves as statisticians and send their papers to JASA, the Annals, etc. I think Dennis was 100 percent correct. Dennis lost this fight, and we ended up with the journal Bayesian Analysis.

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.