On information measures and prior distributions: a synthesis
This paper suggests a new approach to reconciling, in a systematic way, all inferential methods that maximize a specific criterion functional to produce non-informative and informative priors. In particular, Good's (1968) Minimax Evidence Priors (MEP), Zellner's (1971) Maximal Data Information Priors (MDIP) and Bernardo's (1979) Reference Priors (RP) are seen as special cases of maximizing a more general criterion functional. In a unifying approach Good-Bernardo-Zellner's priors are introduced and applied to a number of Bayesian inference problems, including the Kalman filter and Normal linear model. Moreover, the paper focuses, under plausible conditions, on the existence and uniqueness of the solutions of the derived optimization problems.
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