Goodness-of-fit diagnostics for Bayesian hierarchical models |
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Authors: | Yuan Ying Johnson Valen E |
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Institution: | Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas 77030, USA. |
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Abstract: | This article proposes methodology for assessing goodness of fit in Bayesian hierarchical models. The methodology is based on comparing values of pivotal discrepancy measures (PDMs), computed using parameter values drawn from the posterior distribution, to known reference distributions. Because the resulting diagnostics can be calculated from standard output of Markov chain Monte Carlo algorithms, their computational costs are minimal. Several simulation studies are provided, each of which suggests that diagnostics based on PDMs have higher statistical power than comparable posterior-predictive diagnostic checks in detecting model departures. The proposed methodology is illustrated in a clinical application; an application to discrete data is described in supplementary material. |
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Keywords: | Discrepancy measures Markov chain Monte Carlo Model checking Model criticism Model hierarchy Posterior‐predictive density |
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