  This work focuses on the design of experiments of multi-fidelity computer
experiments. We consider the autoregressive Gaussian process model proposed by
Kennedy and O'Hagan (2000) and the optimal nested design that maximizes the
prediction accuracy subject to a budget constraint. An approximate solution is
identified through the idea of multi-level approximation and recent error
bounds of Gaussian process regression. The proposed (approximately) optimal
designs admit a simple analytical form. We prove that, to achieve the same
prediction accuracy, the proposed optimal multi-fidelity design requires much
lower computational cost than any single-fidelity design in the asymptotic
sense. Numerical studies confirm this theoretical assertion.
