  When using incorrect or inaccurate signal models to perform parameter
estimation on a gravitational wave signal, biased parameter estimates will in
general be obtained. For a single event this bias may be consistent with the
posterior, but when considering a population of events this bias becomes
evident as a sag below the expected diagonal line of the P-P plot showing the
fraction of signals found within a certain significance level versus that
significance level. It would be hoped that recently proposed techniques for
accounting for model uncertainties in parameter estimation would, to some
extent, alleviate this problem. Here we demonstrate that this is indeed the
case. We derive an analytic approximation to the P-P plot obtained when using
an incorrect signal model to perform parameter estimation. This approximation
is valid in the limit of high signal-to-noise ratio and nearly correct waveform
models. We show how the P-P plot changes if a Gaussian process likelihood that
allows for model errors is used to analyse the data. We demonstrate
analytically and using numerical simulations that the bias is always reduced in
this way. These results provide a way to quantify bias in inference on
populations and demonstrate the importance of utilising methods to mitigate
this bias.
