Fig. 4

Left panel: an emulator for the simple 1D exponential model. The purple points show five evaluations D of the model at rate parameter locations x ^(j), which are the same as the 5 coloured points in Fig. 1. The blue line represents the emulator’s updated expectation E _D (f(x)), and the pair of red lines give the credible interval \(\mathrm {E}_{D}(f(x)) \pm 3 \sqrt {\text {Var}_{D}(f(x))}\), both as functions of x. This defines a region between the red lines that we believe is highly likely to contain the true function f(x). Note that evaluation of the emulator is extremely fast, as it only requires matrix multiplication. Right panel: an emulator for the more complex function given by Eq. (17). The true function f(x) is shown as the black line, which lies within the emulator credible intervals at all points