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.
Original language | English (US) |
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Pages (from-to) | 156-164 |
Number of pages | 9 |
Journal | Biometrics |
Volume | 68 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2012 |
Keywords
- Discrepancy measures
- Markov chain Monte Carlo
- Model checking
- Model criticism
- Model hierarchy
- Posterior-predictive density
ASJC Scopus subject areas
- Statistics and Probability
- General Biochemistry, Genetics and Molecular Biology
- General Immunology and Microbiology
- General Agricultural and Biological Sciences
- Applied Mathematics
MD Anderson CCSG core facilities
- Biostatistics Resource Group