Latin hypercube sampling (LHS) is generalized in terms of a spectrum of
stratified sampling (SS) designs referred to as partially stratified sample
(PSS) designs. True SS and LHS are shown to represent the extremes of the PSS
spectrum. The variance of PSS estimates is derived along with some asymptotic
properties. PSS designs are shown to reduce variance associated with variable
interactions, whereas LHS reduces variance associated with main effects.
Challenges associated with the use of PSS designs and their limitations are
discussed. 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. The LSS method is equivalent to an
Orthogonal Array based LHS under certain conditions but is easier to obtain.
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. Several
high-dimensional numerical examples highlight the strengths and limitations of
the method. The Latinized partially stratified sampling method is then applied
to identify the best sample strategy for uncertainty quantification on a plate
buckling problem.

本文介绍了部分分层样本设计，扩展了拉丁超立方抽样（Latin hypercube sampling，LHS）。该方法利用拉丁超立方抽样和分层抽样的优势减少了误差方差，且可以专门设计降低给定问题方差。通过在薄板屈曲问题上的应用，使其成为不确定性量化的最佳样本策略。