Concentration function and sensitivity to the prior |
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Authors: | Sandra Fortini Fabrizio Ruggeri |
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Affiliation: | 1. istituto di Metodi Quantitativi, Università ?Luigi Bocconi?, Italia 2. Istituto per le Applicazioni della Matematica e dell'Informatica, Consiglio Nazionale delle Ricerche, Italia
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Abstract: | Summary In robust bayesian analysis, ranges of quantities of interest (e. g. posterior means) are usually considered when the prior probability measure varies in a class Γ. Such quantities describe the variation of just one aspect of the posterior measure. The concentration function describes changes in the posterior probability measure more globally, detecting differences in probability concentration and providing, simultaneously, bounds on the posterior probability of all measurable subsets. In this paper, we present a novel use of the concentration function, and two concentration indices, to study such posterior changes for a general class Γ, restricting then our attention to some ∈-contamination classes of priors. |
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Keywords: | Concentration function Bayesian robustness ∈ -contaminations Gini's area of concentration Pietra's index |
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