In Martin et al (2003), we suggested an approach to general robustness studies in Bayesian Decision Theory and Inference, based on ε-contamination neighborhoods. In this note, we generalise the results considering neighborhoods based on norms, specifically, the supremum norm for utilities and the total variation norm for probability distributions. We provide tools to detect changes in preferences between alternatives under perturbations of the prior and/or the utility and the most sensitive direction.
En Martin et al (2003) propusimos una aproximación a estudios de robustez en análisis bayesiano, basada en entornos ε-contaminados. En esta nota, generalizamos los resultados considerando entornos basados en normas, empleando, específicamente, la norma del supremo para las utilidades y la norma de variación total para las distribuciones de probabilidad. Proporcionamos herramientas para determinar cuánto podemos perturbar la utilidad o probabilidad originales sin que cambie la alternativa óptima y la dirección de perturbación más sensible.
@article{urn:eudml:doc:40988,
title = {Optimal alternative robustness in Bayesian Decision Theory.},
journal = {RACSAM},
volume = {97},
year = {2003},
pages = {407-412},
mrnumber = {MR2126239},
zbl = {1065.62005},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40988}
}
Ruggeri, Fabrizio; Martín, Jacinto; Ríos Insua, David. Optimal alternative robustness in Bayesian Decision Theory.. RACSAM, Tome 97 (2003) pp. 407-412. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40988/