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

Abstract

• A rigorous analysis of high dimensional parameter sampling techniques. • New theoretical bounds for percentage coverage of parameter space by sampling. • Numerical simulations confirming bounds on percentage coverage of parameter space and applications of the coverage formula. • Results verifying t-way interactions coverage estimates in an experimental design setting depend on t not the total dimension. 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.