## leave Bayes factors where they once belonged

**I**n the past weeks I have received and read several papers (and X validated entries)where the Bayes factor is used to compare priors. Which does not look right to me, not on the basis of my general dislike of Bayes factors!, but simply because this seems to clash with the (my?) concept of Bayesian model choice and also because data should not play a role in that situation, from being used to select a *prior*, hence at least twice to run the inference, to resort to a *single* parameter value (namely the one behind the data) to decide between two distributions, to having no asymptotic justification, to eventually favouring the prior concentrated on the maximum likelihood estimator. And more. But I fear that this reticence to test for prior adequacy also extends to the prior predictive, or Box’s p-value, namely the probability under this prior predictive to observe something “more extreme” than the current observation, to quote from David Spiegelhalter.

October 31, 2019 at 4:01 pm

[…] of these predictions can be rigorously assessed using Bayes factors (Wagenmakers, 2017; but see the blog post by Christian Robert, further discussed below). In order to evaluate the empirical success of a […]