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On a recent post asking about self-identified Bayesians (most comprehensive list: ISBA) there were great answers, yet little was mentioned about the drive towards unification. Except from Andrew Gelman, a lot of the referenced authors were of "settled" historical importance.

Some divisions have been etched between so-called "subjective or personalist" Bayesians (Dennis Lindley, Michael Goldstein) and "objective or default" (James Berger, José Maria Bernardo) advocating a more integrative approach, and blurring the boundaries between Frequentists and Bayesians.

It seems as though the controversy centers around whether the use of objective (or un-informative) priors would negate to some extent the idea of the Bayesian prior by giving precedence to the likelihood (the data) over prior beliefs. Yet, you can read from Andrew Gelman, "In BDA, we express the idea that a noninformative prior is a placeholder: you can use the noninformative prior to get the analysis started, then if your posterior distribution is less informative than you would like, or if it does not make sense, you can go back and add prior information". Further it is apparent that their use has become very prevalent in applications such as MCMC.

So is the seemingly widespread use of objective priors de facto unifying Bayesians and Frequentists despite philosophical discrepancies?

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    $\begingroup$ Objective Bayes approaches remain within the Bayesian paradigm and do not seek frequentist validation, so I would reply no to your question. $\endgroup$ – Xi'an Sep 16 '15 at 13:17
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    $\begingroup$ I remember you helped me in the past, and I've read your profile. Honestly, is there a point in keeping this question? or is it in any way obvious, disconnected, or otherwise better erased? $\endgroup$ – Antoni Parellada Sep 16 '15 at 13:21
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    $\begingroup$ There is nothing ridiculous in the question!, so you can keep in open. I however believe there is no clear answer as there is no clearcut division between objective, weakly informative, non-informative and reference Bayesian approaches. $\endgroup$ – Xi'an Sep 16 '15 at 14:19

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