  Posterior distributions on parameters computed from experimental data using
Bayesian techniques are only as accurate as the models used to construct them.
In many applications these models are incomplete, which both reduces the
prospects of detection and leads to a systematic error in the parameter
estimates. In the analysis of data from gravitational wave detectors, for
example, accurate waveform templates can be computed using numerical methods,
but the prohibitive cost of these simulations means this can only be done for a
small handful of parameters. In this work a novel method to fold model
uncertainties into data analysis is proposed; the waveform uncertainty is
analytically marginalised over using with a prior distribution constructed by
using Gaussian process regression to interpolate the waveform difference from a
small training set of accurate templates. The method is well motivated, easy to
implement, and no more computationally expensive than standard techniques. The
new method is shown to perform extremely well when applied to a toy problem.
While we use the application to gravitational wave data analysis to motivate
and illustrate the technique, it can be applied in any context where model
uncertainties exist.
