Testing Small Variance Priors Using Prior-Posterior Predictive P-values
Muthen and Asparouhov (2012) propose to evaluate model fit in structural equation models based on approximate (using small variance priors) instead of exact equality of (combinations of) parameters to zero. This is an important development that adequately addresses Cohen’s (1994) “The earth is round (p < .05)”, which stresses that point null-hypotheses are so precise that small and irrelevant differences from the null-hypothesis may lead to their rejection.
A prior predictive loss function for the evaluation of inequality constrained hypotheses
In many types of statistical modeling, inequality constraints are imposed between the parameters of interest. As we will show in this paper, the DIC (i.e., posterior Deviance Information Criterium as proposed as a Bayesian model selection tool by Spiegelhalter, Best, Carlin, & Van Der Linde, 2002) fails when comparing inequality constrained hypotheses.