Function space view of a GP. For our problem of searching a fixed pool of COFs, we are only interested in the joint distribution of the random variables listed in Y in eqn. 22. However, an alternative view of the GP in eqn. 5 is that it specifies a (prior and posterior) distribution over functions f (x, ) that aim to approximate the blackbox input (COF x, fidelity ) -output (simulated Xe/Kr selectivity, y ( ) ) relationship under-lurking the simulations-the black-box function f (x, ) in eqn. 26. This perspective is illustrated in the middle panel of Fig. , where the dark line shows the posterior mean function µ [n] (x, ) and the bands show a posterior credible region for these functions, µ [n] (x, ) ± σ [n] (x, ).