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by Alan M. Zaslavsky, Eric T. Bradlow
http://fourps.wharton.upenn.edu/ideas/pdf/99-005.pdf
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Abstract:
In a Bayesian model, we de ne an outlier as an observation which is \surprising" relative to its predictive distribution, under the model, given the remainder of the data. Hence \outlyingness " can be measured by the posterior predictive p-value of any interesting scalar summary of the (possibly multivariate) observation. For this calculation, we exclude the case of interest from the data, analogously to studentization of regression residuals. When Bayesian inference about the parameters is conducted by drawing a sample from their posterior distribution, as with a Markov Chain Monte Carlo sampler, the p-value can be calculated by reweighting the sample to re ect deletion of the target observation and then drawing from the predictive distribution. Therefore the case-deletion weighting methods of Bradlow and Zaslavsky (1997a) are useful. Avariety of outlier checks are illustrated using hierarchical models for two data sets, a standard linear hierarchical model for rat growth and a complex ordinal model for survey data with nonignorable missing responses. 1
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