Open Access
February 1996 Local sensitivity of posterior expectations
Paul Gustafson
Ann. Statist. 24(1): 174-195 (February 1996). DOI: 10.1214/aos/1033066205


We investigate the degree to which posterior expectations are sensitive to prior distributions, using a local method based on functional differentiation. Invariance considerations suggest a family of norms which can be used to measure perturbations to the prior. The sensitivity measure is seen to depend heavily on the choice of norm; asymptotic results suggest which norm will yield the most useful results in practice. We find that to maintain asymptotically sensible behaviour, it is necessary to reduce the richness of the class of prior perturbations as the dimension of the parameter space increases. Jeffreys' prior is characterized as the prior to which inference is least sensitive.


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Paul Gustafson. "Local sensitivity of posterior expectations." Ann. Statist. 24 (1) 174 - 195, February 1996.


Published: February 1996
First available in Project Euclid: 26 September 2002

zbMATH: 0853.62026
MathSciNet: MR1389886
Digital Object Identifier: 10.1214/aos/1033066205

Primary: 62F15
Secondary: 62F35

Keywords: $L^p$-norm , Classes of probabilities , Fréchet derivative , Jeffreys' prior , local sensitivity , robustness

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 1 • February 1996
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