  A general adaptive approach rooted in stratified sampling (SS) is proposed
for sample-based uncertainty quantification (UQ). To motivate its use in this
context the space-filling, orthogonality, and projective properties of SS are
compared with simple random sampling and Latin hypercube sampling (LHS). SS is
demonstrated to provide attractive properties for certain classes of problems.
The proposed approach, Refined Stratified Sampling (RSS), capitalizes on these
properties through an adaptive process that adds samples sequentially by
dividing the existing subspaces of a stratified design. RSS is proven to reduce
variance compared to traditional stratified sample extension methods while
providing comparable or enhanced variance reduction when compared to sample
size extension methods for LHS - which do not afford the same degree of
flexibility to facilitate a truly adaptive UQ process. An initial investigation
of optimal stratification is presented and motivates the potential for major
advances in variance reduction through optimally designed RSS. Potential paths
for extension of the method to high dimension are discussed. Two examples are
provided. The first involves UQ for a low dimensional function where
convergence is evaluated analytically. The second presents a study to asses the
response variability of a floating structure to an underwater shock.
