Nested Lattice Sampling: A New Sampling Scheme Derived by Randomizing Nested Orthogonal Arrays

A nested orthogonal array is an orthogonal array that contains a smaller orthogonal array as a subarray. We construct a new sampling scheme, called nested lattice sampling, by randomizing nested orthogonal arrays with nested permutations. For a pair of nested lattice samples associated with a nested orthogonal array of strength t, the points in both samples achieve uniformity in t or lower dimensions. Some statistical properties of nested lattice samples based on strength two nested orthogonal arrays are derived. The proposed sampling scheme is useful for running multifidelity computer experiments, sequential evaluation of computer models, and calibration and validation of computer models. This article has supplementary material online.