Gamma-Minimax: A Paradigm for Conservative Robust Bayesians

Brani Vidakovic, Duke University

In this paper a tutorial overview of Gamma minimaxity ($\Gamma$-minimaxity) is provided. One of the assumptions of the robust Bayesian analysis is that prior distributions can seldom be quantified or elicited exactly. Instead, a family of priors, $\Gamma$, reflecting prior beliefs is elicited. The $\Gamma$-minimax decision-theoretic approach to statistical inference favors an action/rule which incorporates information specified via $\Gamma$, and guards against the least favorable prior in $\Gamma.$ This paradigm falls between Bayesian and minimax paradigms; it coincides with the former when prior information can be summarized in a single prior, and with the latter when no prior information is available (or equivalently, possible priors belong to the class of {\it all} distributions).

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