Sampling low-fidelity outputs for estimation of high-fidelity density and its tails

In a multifidelity setting, data are available under the same conditions from two (or more) sources, e.g. computer codes, one being lower-fidelity but computationally cheaper, and the other higher-fidelity and more expensive. This work studies for which low-fidelity outputs, one should obtain high-fidelity outputs, if the goal is to estimate the probability density function of the latter, especially when it comes to the distribution tails and extremes. It is suggested to approach this problem from the perspective of the importance sampling of low-fidelity outputs according to some proposal distribution, combined with special considerations for the distribution tails based on extreme value theory. The notion of an optimal proposal distribution is introduced and investigated, in both theory and simulations. The approach is motivated and illustrated with an application to estimate the probability density function of record extremes of ship motions, obtained through two computer codes of different fidelities.