Γ-Minimax: A Paradigm for Conservative Robust Bayesians

In this chapter a tutorial overview of Gamma minimaxity (Γ-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, Γ, reflecting prior beliefs is elicited. The Γ-minimax decision-theoretic approach to statistical inference favors an action/rule which incorporates information specified via Γ and guards against the least favorable prior in Γ. 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 all distributions).

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