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Biometrika 1995 82(1):223-225; doi:10.1093/biomet/82.1.223
© 1995 by Biometrika Trust
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MISCELLANEA

A note on bounded influence in Bayesian analysis

LUIS R. PERICCHI and BRUNO SANSÓ

Centro de Estadística y Software Matemático, Departamento de Matemática, Universidad Simón Boliva Apartado 89.000, Caracas 1080-A, Venezuela

Let {chi} be a single observation from a distribution having unknown location parameter {theta}. Dawid (1973) provided sufficient conditions for the posterior distribution of {theta} to approach the prior distribution as {chi} tends to infinity, so that an outlier has bounded and vanishing influence on the posterior distribution. We present a result closely related to Dawid's theorem. This enables us to consider priors and likelihoods for the location problem which have bounded but nonvanishing influence on posterior moments. Examples are given.

Key Words: Bayesian analysis • Bounded influence • Robust Bayes • Location parameter


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