Posteriors derived from traditional likelihood analyses using a Gaussian likelihood with the true data covariance matrix, where the expectation ξ[π] is estimated from n_s simulations. The posterior samples are obtained from MCMC sampling the analytic posterior. The same prior used in the experiments for this work where the model for the expectation is fit to data alongside the parameters and the data covariance is known. This shows that the error contribution to the posterior from an unknown model is much less than that due to the data covariance being estimated from the same number of simulations.