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Estimates of the coverage of parameter space by Latin Hypercube and Orthogonal Array-based sampling

2018    Donovan, D.; Burrage, K.; Burrage, P.; McCourt, T. A.; Thompson, B.; Yazici, E. S.

In this paper we use counting arguments to prove that the expected percentage coverage of a d dimensional parameter space of size n when performing k trials with either Latin Hypercube sampling or Orthogonal Array-based Latin Hypercube sampling is the same. We then extend these results to an experimental design setting by projecting onto a t < d dimensional subspace. These results are confirmed by simulations. The theory presented has both theoretical and practical significance in modelling and simulation science when sampling over high dimensional spaces. (C) 2017 Elsevier Inc. All rights reserved.