Local Predictive Influence in Bayesian Regression

Michael Lavine
Duke University

Nov 30 1989

In 1986 Cook presented the idea of local influence to study the sensitivity of inferences to model assumptions: introduce a vector ω of perturbations to the model; choose a discrepancy function δ to measure differences between th original inference and the inference under the perturbed model; study the behavior of δ near ω=0, the original model, usually by taking derivatives. Cook gives an example where ω is a vector of case weight perturbations in a linear regression. Johnson and Geisser (1983) measure influence in Bayesian linear regression by the Kullback-Leibler divergence between predictive ditributions. The current work is a synthesis of Cook and Johnson and Geisser, using Kullback-Leibler divergence between predictive distributions as the discrepancy function in a local influence analysis of a Bayesian linear regression.


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