  We consider the problem of goodness-of-fit testing for a model that has at
least one unknown parameter that cannot be eliminated by transformation.
Examples of such problems can be as simple as testing whether a sample consists
of independent Gamma observations, or whether a sample consists of independent
Generalised Pareto observations given a threshold. Over time the approach to
determining the distribution of a test statistic for such a problem has moved
towards on-the-fly calculation post observing a sample. Modern approaches
include the parametric bootstrap and posterior predictive checks. We argue that
these approaches are merely approximations to integrating over the posterior
predictive distribution that flows naturally from a given model. Further, we
attempt to demonstrate that shortcomings which may be present in the parametric
bootstrap, especially in small samples, can be reduced through the use of
objective Bayes techniques, in order to more reliably produce a test with the
correct size.
