> Bayesian methods are not easy to use, I agree. But that's because they're trying to answer much more meaningful (but harder) questions than frequentist ones
I think your view about the difference between Frequentist and Bayesian methods is wrong. There is this rant I like from Larry Wasserman [1] on the subject:
My opinions have shifted a bit. [...] Bayes-Frequentist debate still matters. And people — including many statisticians — are still confused about the distinction. I thought the basic Bayes-Frequentist debate was behind us. A year and a half of blogging (as well as reading other blogs) convinced me I was wrong here too. And this still does matter.
My emphasis on high-dimensional models is germane, however. In our world of high-dimensional, complex models I can’t see how anyone can interpret the output of a Bayesian analysis in any meaningful way.
I wish people were clearer about what Bayes is/is not and what frequentist inference is/is not. Bayes is the analysis of subjective beliefs but provides no frequency guarantees. Frequentist inference is about making procedures that have frequency guarantees but makes no pretense of representing anyone’s beliefs. In the high dimensional world, you have to choose: objective frequency guarantees or subjective beliefs. Choose whichever you prefer, but you can’t have both. I don’t care which one people pick; I just wish they would be clear about what they are giving up when they make their choice.
[...]
Of course, one can embrace objective Bayesian inference. If this means “Bayesian procedures with good frequentist properties” then I am all for it. But this is just frequentist inference in Bayesian clothing."