  Multifidelity Monte Carlo methods rely on a hierarchy of possibly less
accurate but statistically correlated simplified or reduced models, in order to
accelerate the estimation of statistics of high-fidelity models without
compromising the accuracy of the estimates. This approach has recently gained
widespread attention in uncertainty quantification. This is partly due to the
availability of optimal strategies for the estimation of the expectation of
scalar quantities-of-interest. In practice, the optimal strategy for the
expectation is also used for the estimation of variance and sensitivity
indices. However, a general strategy is still lacking for vector-valued
problems, nonlinearly statistically-dependent models, and estimators for which
a closed-form expression of the error is unavailable. The focus of the present
work is to generalize the standard multifidelity estimators to the above cases.
The proposed generalized estimators lead to an optimization problem that can be
solved analytically and whose coefficients can be estimated numerically with
few runs of the high- and low-fidelity models. We analyze the performance of
the proposed approach on a selected number of experiments, with a particular
focus on cardiac electrophysiology, where a hierarchy of physics-based
low-fidelity models is readily available.
