Objections to Bayesian statistics
I remember reading Andrew Gelman's blog on 1 April 2008. The title of the post was "Why I don't like Bayesian statistics''. Seeing as how Gelman's work is pretty Bayesian, I was a bit confused until I realized it was April Fool's Day. Gelman edited this blog post and published it in Bayesian Analysis, a journal specifically for all things Bayesian. You can find the article as well as 4 comments and a rejoinder here. There are no truly anti-Bayesians here, but the articles give a look into some of the questions of Bayesian analysis that are answered and some that are not.
I did learn a few things while reading these articles. One in particular stands out. The comment is in reference to most Bayesian analysis using conjugate priors out of convenience rather than truly representing prior information. These conjugate priors are typically used for computational reasons. Kadane points out that any prior can be well approximated by mixtures of conjugate priors. Using these mixtures allows accurately capturing prior information, but also retaining computational simplicity.
Finally, I'll end this post with a quote that comments on the objective versus subject statistical analysis debate that appears in non-Bayesian as well as Bayesian statistical analyses.
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Statistics is made of subjective procedures that yield objectively testable results.
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