Fig. 2

Left panel: the unrealistic case when both the observation error e and model discrepancy ε are ignored. The model f(x) is given by the purple line, the observed data z by the horizontal black line. Here only one value of x can be viewed as acceptable (coloured green) while all others are unacceptable (red), however a repeat of the experiment would yield a slightly different z and hence x. Right panel: the more realistic situation where we include both observation error e (the black dashed lines represent z±3σ _e ) and model discrepancy ε (the purple dashed lines show f(x)±3σ _ε ). There is now a range of acceptable values for x (green points) with borderline/unacceptable points in yellow/red. It now may be possible to simultaneously match multiple outputs