Some red meat for the Bayesians

Eric Archer forwarded this document by Nick Freemantle, “The Reverend Bayes—was he really a prophet?”, in the Journal of the Royal Society of Medicine:

Does [Bayes’s] contribution merit the enthusiasms of his followers? Or is his legacy overhyped? . . .

First, Bayesians appear to have an absolute right to disapprove of any conventional approach in statistics without offering a workable alternative—for example, a colleague recently stated at a meeting that ‘. . . it is OK to have multiple comparisons because Bayesians’ don’t believe in alpha spending’. . . .

Second, Bayesians appear to build an army of straw men—everything it seems is different and better from a Bayesian perspective, although many of the concepts seem remarkably familiar. For example, a very well known Bayesian statistician recently surprised the audience with his discovery of the P value as a useful Bayesian statistic at a meeting in Birmingham.

Third, Bayesians possess enormous enthusiasm for the Gibbs sampler—a form of statistical analysis which simulates distributions based on the data rather than solving them directly through numerical simulation, which they declare to be inherently Bayesian—requiring starting values (priors) and providing posterior distributions (updated priors). However, rather than being of universal application, the Gibbs sampler is really only advantageous in a limited number of situations for complex nonlinear mixed models—and even in those circumstances it frequently sadly just does not work (being capable of producing quite impossible results, or none at all, with depressing regularity). . . .

The looks negative, but it you read it carefully, it’s an extremely pro-Bayesian article! The key phrase is “complex nonlinear mixed models.” Not too long ago, anti-Bayesians used to say that Bayesian inference was worthless because it only worked on simple linear models. Now their last resort is to say that it only works for complex nonlinear models!

OK, it’s a deal. I’ll let the non-Bayesians use their methods for linear regression (as long as there aren’t too many predictors; then you need a “complex mixed model”), and the Bayesians can handle everything complex, nonlinear, and mixed. Actually, I think that’s about right. For many simple problems, the Bayesian and classical methods give similar answers. But when things start to get complex and nonlinear, it’s simpler to go Bayesian.

(As a minor point: the starting distribution for the Gibbs sampler is not the same as the prior distribution, and also that Freemantle appears to be conflating a computational tool with an approach to inference. No big deal—statistical computation does not seem to be his area of expertise—it’s just funny that he didn’t run it by an expert before submitting to the journal.)

Also, I’m wondering about this “absolute right to disapprove” business. Perhaps Bayesians could file their applications for disapproval through some sort of institutional review board? Maybe someone in the medical school could tell us when we’re allowed to disapprove and when we can’t.

P.S.

Yes, yes, I see that the article is satirical. But, in all seriousness, I do think it’s a step forward that Bayesian methods are associated with “complex nonlinear mixed models.” That’s not a bad association to have, since I think complex models are more realistic. To go back to the medical context, complex models can allow treatments to have different effects in different subpopulations, and can help control for imbalance in observational studies.

1 thought on “Some red meat for the Bayesians

  1. The remark in that paper, by a Bayesian, that multiple comparisons are OK seemed very cavalier. My impression is that multiple comparisons is a difficult area for both frequentists and Bayesians. I am not familiar with the alpha spending approach, so I can't judge whether frequentists have a good approach there. Could you comment on the difference between Bayesian and frequentist approaches to multiple comparisons?

    Blaise

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