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Γ-Minimax: A Paradigm for Conservative Robust Bayesians

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Robust Bayesian Analysis

Part of the book series: Lecture Notes in Statistics ((LNS,volume 152))

Abstract

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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Authors
  1. Brani Vidakovic
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Editors and Affiliations

  1. ESCET-URJC, Tulipan s/n, 28933, Mostoles, Madrid, Spain

    David Ríos Insua

  2. CNR IAMI, Via Ampere 56, I-20131, Milano, Italy

    Fabrizio Ruggeri

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Vidakovic, B. (2000). Γ-Minimax: A Paradigm for Conservative Robust Bayesians. In: Insua, D.R., Ruggeri, F. (eds) Robust Bayesian Analysis. Lecture Notes in Statistics, vol 152. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1306-2_13

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  • DOI: https://doi.org/10.1007/978-1-4612-1306-2_13

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-98866-5

  • Online ISBN: 978-1-4612-1306-2

  • eBook Packages: Springer Book Archive

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