Limitations of estimating prediction variances using linearization. In this figure, the gray dots indicate model predictions corresponding to simulations of the nonlinear model. On the prediction side, the black distribution is based on linearly projecting the parameter uncertainties onto the predictions, while the gray distribution is based on the non-linear model. Shown on the left is the case with small uncertainty, where the linear parameter sensitivities provide an adequate description for projecting the parameter uncertainty onto the predictions as can be seen from the overlapping black and gray lines. On the right, the case with large parameter uncertainty, where the non-linearity of the model results in a poor estimate of the predictive distribution when it is estimated via linear projection i.e. the black and gray lines do not overlap.