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December 2016 New Classes of Priors Based on Stochastic Orders and Distortion Functions
J. Pablo Arias-Nicolás, Fabrizio Ruggeri, Alfonso Suárez-Llorens
Bayesian Anal. 11(4): 1107-1136 (December 2016). DOI: 10.1214/15-BA984

Abstract

In the context of robust Bayesian analysis, we introduce a new class of prior distributions based on stochastic orders and distortion functions. We provide the new definition, its interpretation and the main properties and we also study the relationship with other classical classes of prior beliefs. We also consider Kolmogorov and Kantorovich metrics to measure the uncertainty induced by such a class, as well as its effect on the set of corresponding Bayes actions. Finally, we conclude the paper with some numerical examples.

Citation

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J. Pablo Arias-Nicolás. Fabrizio Ruggeri. Alfonso Suárez-Llorens. "New Classes of Priors Based on Stochastic Orders and Distortion Functions." Bayesian Anal. 11 (4) 1107 - 1136, December 2016. https://doi.org/10.1214/15-BA984

Information

Published: December 2016
First available in Project Euclid: 27 November 2015

zbMATH: 1357.62102
MathSciNet: MR3545475
Digital Object Identifier: 10.1214/15-BA984

Subjects:
Primary: 62F15
Secondary: 60E15

Keywords: Bayesian sensitivity , class of priors , distortion functions , robust Bayesian analysis , Stochastic orders

Rights: Copyright © 2016 International Society for Bayesian Analysis

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Vol.11 • No. 4 • December 2016
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