Several high-dimensional numerical examples highlight the strengths and limitations of the method. We examine quantile estimators obtained using simulation with Latin hypercube sampling LHS, a variance-reduction technique that effic. Utilizing an LSS on the subspaces of a PSS provides a sampling strategy that reduces variance associated with both main effects and variable interactions and can be designed specially to minimize variance for a given problem. Quantiles are often used to measure risk of stochastic systems. The LSS method is equivalent to an Orthogonal Array based LHS under certain conditions but is easier to obtain. To overcome these challenges, the PSS method is coupled with a new method called Latinized stratified sampling (LSS) that produces sample sets that are simultaneously SS and LHS. Challenges associated with the use of PSS designs and their limitations are discussed.
It is widely used to generate samples that are known as controlled random samples and is often applied in Monte Carlo analysis because it can dramatically reduce the number of simulations needed to achieve accurate results. PSS designs are shown to reduce variance associated with variable interactions, whereas LHS reduces variance associated with main effects. Latin hypercube sampling is a method that can be used to sample random numbers in which samples are distributed evenly over a sample space. The variance of PSS estimates is derived along with some asymptotic properties. True SS and LHS are shown to represent the extremes of the PSS spectrum. Latin hypercube sampling (LHS) is generalized in terms of a spectrum of stratified sampling (SS) designs referred to as partially stratified sample (PSS) designs.
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