Selecting scale factor of Bayesian multi-fidelity surrogate by minimizing posterior variance

The Bayesian Multi-Fidelity Surrogate(MFS) proposed by Kennedy and O’Hagan(KOH model) has been widely employed in engineering design, which builds the approximation by decomposing the high-fidelity function into a scaled low-fidelity model plus a discrepancy function. The scale factor before the low-fidelity function, ρ, plays a crucial role in the KOH model. This scale factor is always tuned by the Maximum Likelihood Estimation(MLE). However, recent studies reported that the MLE may sometimes r...