  Here we present a Bayesian formalism for the goodness-of-fit that is the
evidence for a fixed functional form over the evidence for all functions that
are a general perturbation about this form. This is done under the assumption
that the statistical properties of the data can be modelled by a multivariate
Gaussian distribution. We use this to show how one can optimise an experiment
to find evidence for a fixed function over perturbations about this function.
We apply this formalism to an illustrative problem of measuring perturbations
in the dark energy equation of state about a cosmological constant.
