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I heard that Bernardo Priors are better versions of Jeffrey's prior that work in multi-dimensions & match frequentist confidence intervals.

Apparently they also dodge many paradoxes of other reference priors. I'm wondering which they avoid & which (if any) they still encounter?

profPlum
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  • There is not "better" or "worse" in the choice of so-called non-informative priors. See e.g. my points in https://stats.stackexchange.com/a/20535/7224 – Xi'an Aug 24 '23 at 08:47
  • If there is no better or worse then how do you choose one? I mean I realize that no prior is perfectly uninformative...

    But right now I guess I'm mostly interested in which prior avoids the most paradoxes.

     – profPlum Aug 24 '23 at 21:25
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    This is the wrong question, in that priors cannot be compared from a Bayesian viewpoint. Even though the sensitivity of a specific inference to the choice of the prior can be ascertained. Concerning "paradoxes", it is unclear what you are alluding to. For me the main paradox of reference priors is that they depend on the division between parameters of interest and nuisance parameters, when the Bayesian approach should model the entire parameter space all at once. – Xi'an Aug 25 '23 at 12:50
  • @Xi'an from Stéphane Laurent's answer to the question link you posted. He says: "Maybe Bernardo's reference prior could not be considered as the "best" choice of a noninformative prior but could be considered as the most successful one. Theoretically it overcomes many paradoxes of other candidates." – profPlum Aug 25 '23 at 21:59
  • Could you explain (or add refs/links) to the paradoxes you refer to? – kjetil b halvorsen Mar 27 '24 at 14:26
  • This question is based on Stéphane Laurent's answer to the question link posted by Xi'an. But for example the principle of indifference (uniform prior) isn't actually uniform because you need to apply it to a particular parameterization. But it can be non-uniform to different parameterizations (hence motivation for Jeffrey's prior). I'm asking if any 'paradox' like that still exists in Bernardo priors. – profPlum Mar 27 '24 at 14:47

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