Fair point! I guess I’m also saying that frequentist properties of Bayesian inferences could (justifiedly) be interesting to the Bayesian.

]]>thanks!, I have difficulties in putting a mathematical definition upon “objective” (the ultimate paradox for the president-elect of the Objective Bayes session of ISBA, isnt’it?!)

]]>Esp. given the above quote! I find it rather surprising that this old saw of a claim of frequentism to objectivity resurfaces there. There is an infinite range of frequentist procedures and, while some are more optimal than others, none is “the” optimal one (except for the most baked-out examples like say the estimation of the mean of a normal observation).

I don’t think frequentism is objective in the sense of providing an optimal-for-everyone procedure, but it does consider objective properties of any given procedure. To the extent that a Bayesian can interpret sampling-type probability at all, looking at, say, the coverage properties of a credible interval (given a particular prior) seems perfectly valid, objective, and unobjectionable to me.

]]>“What prior evidence are we using? None, as it turns out! With 6033 parallel situations at hand, we can effectively estimate the relevant prior from the data itself”

Then goes on to poo-poo on uninformative priors when the empirical bayes approach is implicitly using an uninformative hyperprior. I do think that multilevel modeling / empirical bayes is often the right approach in these high dimensional estimation scenarios, but at the end of the day, it’s still just a bayesian model. One is still making a decision about the characteristics of the hyperprior, not to mention the functional form of the prior distribution and other aspects of the model.

I’m also perplexed that he doesn’t critcize this idea of “optimal estimators”, since he did so much work with stein estimation. One of my takeaways from stein’s paradox is that one form of optimality (e.g. unbiasedness) comes at the cost of other forms of optimality. In applied scenarios the price one pays for “optimal” estimators (e.g., overestimation of statistically significant effects) often makes them highly suspect to use in practice.

]]>I cannot understand how this is interesting enough for a science column. Anyone who’s done statistics for more than a short time can probably do a “one man play” version of the argument at the drop of a hat. It’s always the same!

When it comes down to it, both work when the data has information, neither work (or both work depending on your point of view) when it doesn’t. It always comes down to make assumptions, ride assumptions, check assumptions, repeat.

Incidentally, when I was in UC Santa Cruz, David Draper showed me an old book on inference that recommended using the unbiased estimator, but often negative, estimator of a variance (I’m failing to remember the context, but it was fairly classical) because unbiasedness was judged to be more important than positivity.

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