A recently developed Centroidal Voronoi Tessellation (CVT) sampling method is investigated here to assess its suitability for use in response surface generation. CVT is an unstructured sampling method that can generate nearly uniform point spacing over arbitrarily shaped Mdimensional parameter spaces. For rectangular parameter spaces (hypercubes), CVT appears to extend to higher dimensions more...

Latin hypercube designs have been found very useful for designing computer experiments. In recent years, several methods of constructing orthogonal Latin hypercube designs have been proposed in the literature. In this article, we report some more results on Latin hypercube designs, including several new designs.

Stochastic linear programs can be solved approximately by drawing a subset of all possible random scenarios and solving the problem based on this subset, an approach known as sample path optimization. The value of the optimal solution to the sampled problem provides an estimate of the true objective function value. This estimator is known to be optimistically biased; the expected optimal object...

We provide probabilistic lower bounds for the star discrepancy of Latin hypercube samples. These bounds are sharp in the sense that they match the recent probabilistic upper bounds for the star discrepancy of Latin hypercube samples proved in [M. Gnewuch, N. Hebbinghaus. Discrepancy bounds for a class of negatively dependent random points including Latin hypercube samples. Preprint 2016.]. Toge...

 The use of optimal orthogonal array latin hypercube designs is proposed. Orthogonal arrays were proposed for constructing latin hypercube designs by Tang (1993). Such designs generally have better space filling properties than random latin hypercube designs. Even so, these designs do not necessarily fill the space particularly well. As a result, we consider orthogonal-array-based latin...

In this chapter we explain variance reduction techniques from the Hilbert space standpoint, in the terminating simulation context. We use projection ideas to explain how variance is reduced, and to link different variance reduction techniques. Our focus is on the methods of control variates, conditional Monte Carlo, weighted Monte Carlo, stratification, and Latin hypercube sampling.