Posterior predictive model checking in hierarchical models

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Robustness of linear mixed‐effects models to violations of distributional assumptions (2020, background): “Ideally, these features should be motivated by biological interest but should not be parameters for which the model is optimized (Sinharay & Stern, 2003).”
Validation of Software for Bayesian Models Using Posterior Quantiles (2006, background): “Model checking is another important area of research and is discussed, for example, by Rubin (1984), Gelman et al. (1996), Bayarri and Berger (1999), and Sinharay and Stern (2003).”
A Bayesian chi^2 test for goodness-of-fit (2004, unknown): “…extent, the computations required to approximate A’s sampling distribution are as complicated as, or even more complicated than, similar techniques used to approximate the sampling distribution of discrepancy functions used in posterior-predictive model checks [e.g., Sinharay and Stern (2003)].”
X-ray spectral modelling of the AGN obscuring region in the CDFS: Bayesian model selection and catalogue (2014, background): “Posterior-based approaches are diverse, and can be overly conservative (see e.g. Sinharay & Stern 2003).”