Robust Bayesian Analysis
Robust Bayesian analysis aims at overcoming the traditional objection to Bayesian analysis of its dependence on subjective inputs, mainly the prior and the loss. Its purpose is the determination of the impact of the inputs to a Bayesian analysis (the prior, the loss and the model) on its output when the inputs range in certain classes. If the impact is considerable, there is sensitivity and we should attempt to further refine the information the incumbent classes available, perhaps through additional constraints on and/ or obtaining additional data; if the impact is not important, robustness holds and no further analysis and refinement would be required. Robust Bayesian analysis has been widely accepted by Bayesian statisticians; for a while it was even a main research topic in the field. However, to a great extent, their impact is yet to be seen in applied settings. This volume, therefore, presents an overview of the current state of robust Bayesian methods and their applications and identifies topics of further in terest in the area. The papers in the volume are divided into nine parts covering the main aspects of the field. The first one provides an overview of Bayesian robustness at a non-technical level. The paper in Part II con cerns foundational aspects and describes decision-theoretical axiomatisa tions leading to the robust Bayesian paradigm, motivating reasons for which robust analysis is practically unavoidable within Bayesian analysis.
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Ranges of Posterior Expected Losses and eRobust
Topics on the Foundations of Robust Bayesian Analysis
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additional algorithm alternative application approach approximation assess Association assume Bayes Bayesian robustness Berger bounds changes class of priors computational concentration consider constraints contaminations corresponding decision defined denote density derivative described discussion elicitation estimation et al example expected factor failure finite fixed function given gives global important indicator inference influence interest issue Journal Lavine leading likelihood linear local analysis loss loss function marginal mean measure methods mixture Moreno nonparametric normal Note observed obtained optimal parameter particular possible posterior predictive prior distribution probability probability measures problem quantile quantity random range reasonable References reliability respect Ríos Insua robust Bayesian analysis Ruggeri rule sampling sensitivity solution space specified Springer-Verlag standard Statistics Table testing theory tion uncertainty unimodal variable Wasserman York