Bayesian Model Checking with Applications to Hierarchical Models
Roi Weiss · eScholarship (California Digital Library) · 2011
In a Bayesian model with proper prior, all functions of the parameters and data are known. After observing the data, the joint prior specification of data and parameters can be checked by comparing the posterior of any function of the parameters to its assumed prior. This paper gives checks for missing predictors, goodness-of-fit, and over-diffuseness of the prior. The approach is illustrated in a hierarchical random effects model. Key Words: Bayesian Data Analysis, Diagnostics, Goodness-of-Fit, Longitudinal Data, Outlier, Quantile-Quantile Plots. 1 Introduction. This paper introduces a general approach to Bayesian model checking. Like previous authors (Box, 1981; Chaloner and Brant 1988; Dey, Gelfand, Vlachos and Schwarz 1994; Gelman, Meng and Stern 1996; Meng 1994; Rubin 1984), we may consider a model suspect when some residual or checking function g, a function of the data Y and/or parameters `, is far from an appropriate measure of center, Robert E. Weiss is Assistant Professor...