CASE INFLUENCE ANALYSIS IN BAYESIAN-INFERENCE

We demonstrate how case influence analysis. commonly used in regressio n, can be applied to Bayesian hierarchical models. Draws from the join t posterior distribution of parameters are importance weighted to refl ect the effect of deleting each observation in turn: the ensuing chang es in the posterior distribution of each parameter are displayed graph ically. The procedure is particularly useful when drawing a sample fro m the posterior distribution requires extensive calculations (as with a Markov Chain Monte Carlo sampler). The structure of hierarchical mod els, and other models with local dependence, makes the importance weig hts inexpensive to calculate with little additional programming. Some new alternative weighting schemes are described that extend the range of problems in which reweighting can be used to assess influence. Appl ications: to a growth curve model and a complex hierarchical model for opinion data are described. Our focus on case influence on parameters is complementary to other work that measures influence by distances b etween posterior or predictive distributions.