Title: Bayesian model checking: A comparison of tests,
Abstract: Two procedures for checking Bayesian models are compared using a simple test
problem based on the local Hubble expansion. Over four orders of magnitude,
p-values derived from a global goodness-of-fit criterion for posterior
probability density functions (Lucy 2017) agree closely with posterior
predictive p-values. The former can therefore serve as an effective proxy for
the difficult-to-calculate posterior predictive p-values.