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Optimal Properties of Some Bayesian Inferences

Bob the biologist sent me the link to this paper by Evans and Shakhatreh:

We [E & S] ]consider various properties of Bayesian inferences related to repeated sampling interpretations, when we have a proper prior. While these can be seen as particularly relevant when the prior is diffuse, we argue that it is generally reasonable to consider such properties as part of our assessment of Bayesian inferences. We discuss the logical implications for how repeated sampling properties should be assessed when we have a proper prior. We develop optimal Bayesian repeated sampling inferences using a generalized idea of what it means for a credible region to contain a false value and discuss the practical use of this idea for error assessment and experimental design. We present results that connect Bayes factors with optimal inferences and develop a generalized concept of unbiasedness for credible regions. Further, we consider the effect of reparameterizations on hpd-like credible regions and argue that one reparameterization is most relevant, when repeated sampling properties and the prior are taken into account.

I should read this–it seems related to the “weakly informative priors” stuff. But for now I’ll stick it on the blog where I hope I won’t forget it. At least it gets it out of my inbox!

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