But, “a prior is a prior is a prior” is formally true but disastrous in practice – the prior (and data model) can miss-represent the reality one is trying to learn about so badly as to make any analyses assuming them harmful. So developing peer review expertise for priors is badly needed (which I wrote about in Two cheers for Bayes 1996 https://www.ncbi.nlm.nih.gov/pubmed/8889349 ).

Also, I think you find these ideas used by Mike Evans solution to Lindley-Jeffreys paradox.

Keith O’Rourke

]]>Thank you. The main messages here are that (a) there is no principled way to rank priors, i.e., “a prior is a prior is a prior”, and (b) probability statements are made relative to the probability model induced by the prior choice of the prior (!), which means that comparing priors via their outcome is not particularly meaningful. Comparing posteriors with the same priors, if this is what you mean by “across studies”, is relevant.

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