For the second assumption one can check its validity for the present situation by inspecting figure . The assumptions requires that the model can be linearised around the true value within the errors. It is evident from figure that this requirement is very well satisfied. For the model at hand only relative errors of well above 20% would cause the assumption to break down. If one wants to drop either assumption (or both) the only proper way out would be to design a Bayesian hierarchical forward model by sampling directly from the distribution f 2 and F 2 . One could another step back and sample directly on the observables of the experiment with some assumed error distribution. This would captures the non-linearity at each stage but we would argue that the gain should be marginal as discussed above.