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Estimates of the coverage of parameter space by Latin Hypercube and Orthogonal Array-based sampling |
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| Affiliation: | 1. School of Mathematics and Physics, The University of Queensland, Queensland, 4072, Australia;2. Department of Computer Science, University of Oxford, UK;3. ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology (QUT), Australia;4. Department of Mathematics and Statistics, Plymouth University, Plymouth, UK;5. Department of Mathematics, Koç University, Sarıyer, İstanbul 34450, Turkey |
| Abstract: | 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. |
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