I’ve written up my rant more seriously here. Here’s the new abstract:
Bayesian inference is one of the more controversial approaches to statistics. The fundamental objections to Bayesian methods are twofold: on one hand, Bayesian methods are presented as an automatic inference engine, and this raises suspicion in anyone with applied experience. The second objection to Bayes comes from the opposite direction and addresses the subjective strand of Bayesian inference. This article presents a series of objections to Bayesian inference, written in the voice of a hypothetical anti-Bayesian statistician. The article is intended to elicit elaborations and extensions of these and other arguments from non-Bayesians and responses from Bayesians who might have different perspectives on these issues.
And here’s how the article concludes:
In the decades since this work and Box and Tiao’s and Berger’s definitive books on Bayesian inference and decision theory, the debates have shifted from theory toward practice. But many of the fundamental disputes remain and are worth airing on occasion, to see the extent to which modern developments in Bayesian and non-Bayesian methods alike can inform the discussion.
In answer to many of the earlier commenters: yes, I have replies for the criticisms. But I didn’t want to put them here because I worried that they would inhibit the flow of discussion that I’d like to see come from this article. I will post my replies at some point (at which time I’m sure they’ll be a disappointment, after all the hype).
Dr. Gelman, do you think it is better to submit this paper to a non-Bayesian journal (or even better, non-statistics journal) to reach a broader readership? After all, those who read Bayesian Analysis do not need more discussion on this.
Yu,
My thought was the opposite–that Bayesians do not always seriously engage with the fundamental non-Bayesian arguments. Also, I had a suspicion that if I sent it to a non-Bayesian journal it would not be accepted for publication. I would think that "Bayesian Analysis" is the perfect place to publish an article about criticisms of Bayesian inference. After all, the journal is online so non-Bayesians can read it too!
i'm very curious to know which arguments you think ought to be "ultimately accepted in some settings." can't wait to read your response.
Amusing, and parts of it do raise serious issues, but surely the bit about irrelevance of stopping times should only be in the April Fools version – especially the hilarious line, "Unfortunately for the Bayesian theory, the p-value does change when you alter the stopping rule, and no amount of philosophical reasoning will get you around that point".
The most amusing/shocking objection to Bayesianism I've come across, in the discussion of a paper in an old conference proceedings (can't remember the reference now), is that it's just so simple. How can one expect to build up an academic discipline of statistics, with lots of tenured professorships, big research grants, etc., when all one is doing is just specifying a model and prior, and then turning the crank of conditional probability? Surely people will recognize how easy it is, and not keep the money coming. Of course, this commenter must not have realized that the computational problems alone will keep us happily employed for the forseeable future…
By the way, thanks for the nice comments on the work of Longhai and myself on high-order interactions!
"…the journal is online so non-Bayesians can read it too!"
I understand why you said this, but my first thought was, "non-Bayesians don't read paper journals?"
I am curious about the stopping rule viz-à-viz psychics. IIRC, choosing when to end the experiment gives them the power to manipulate p-values and get "significant" results. Are Bayesian statistics better for investigating, say, a would-be mind reader?
How about we try some lab experiments, where we assign people some data and parameters to estimate, randomly assign them to use Bayes methods or not, and they see which group is more accurate?
Robin,
Good points. We statisticians don't practice what we preach. We're always telling other people to do random sampling, experimentation, adjustment of comparisons, and so forth. But then for ourselves, we just mouth off and make recommendations based on personal anecdotes.