Prior Influence in Bayesian Statistics

Michael Lavine
Duke University

Nov 30 1988

One paradigm for sensitivity analyses in Bayesian statistics is to specify a reasonable class of priors and to compute the corresponding class of posterior inferences. This paper introduces density bounded classes of priors and shows how to compute the corresponding upper and lower bounds on posterior and predictive expectations. By treating the prior as a probability measure on the set of all possible distributions on the sample space, or on the set of all possible regression functions, this paradigm offers a unified approach to analyzing sensitivity to the prior, to the family of distributions on the sample space and to the family of regression functions.


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