  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.
