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Criticism of a Hierarchical Model Using Bayes James H. Albert

Summary: Criticism of a Hierarchical Model Using Bayes
James H. Albert
Bowling Green State University
May 21, 1996

This paper analyzes a data file of heart transplant surgeries performed in the United States
over a two­year period. A Poisson/Gamma exchangeable model is used to learn about
the underlying death rates for 94 hospitals. There are concerns about the suitability of
this hierarchical model, including the need for a hierarchical structure, the existence of
outliers, the choice of prior hyperparameters, the need for a covariate in the model, and the
manner in which exchangeability was modeled. Each concern motivates the construction
of alternative models and Bayes factors are used to compare the existing model with the
alternative models. Graphical displays are used to check the sensitivity of the posterior
analysis with respect to model perturbations and plots of Bayes factors are used to criticize
these perturbations.

1 Introduction
1.1 Heart transplant mortality data


Source: Albert, James H. - Department of Mathematics and Statistics, Bowling Green State University


Collections: Mathematics