Bayesian model checking: A comparison of tests

TL;DR

This paper compares two Bayesian model checking procedures using a test problem, showing that a global goodness-of-fit p-value closely matches the posterior predictive p-value, offering a computationally simpler alternative.

Contribution

It demonstrates that a global goodness-of-fit p-value can effectively replace the more complex posterior predictive p-value in Bayesian model checking.

Findings

Global p-values agree with posterior predictive p-values across a wide range of scenarios.

Global p-values can serve as efficient proxies for posterior predictive checks.

The methods are validated on a test problem based on the local Hubble expansion.

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.