1,364 research outputs found
Validating Sample Average Approximation Solutions with Negatively Dependent Batches
Sample-average approximations (SAA) are a practical means of finding
approximate solutions of stochastic programming problems involving an extremely
large (or infinite) number of scenarios. SAA can also be used to find estimates
of a lower bound on the optimal objective value of the true problem which, when
coupled with an upper bound, provides confidence intervals for the true optimal
objective value and valuable information about the quality of the approximate
solutions. Specifically, the lower bound can be estimated by solving multiple
SAA problems (each obtained using a particular sampling method) and averaging
the obtained objective values. State-of-the-art methods for lower-bound
estimation generate batches of scenarios for the SAA problems independently. In
this paper, we describe sampling methods that produce negatively dependent
batches, thus reducing the variance of the sample-averaged lower bound
estimator and increasing its usefulness in defining a confidence interval for
the optimal objective value. We provide conditions under which the new sampling
methods can reduce the variance of the lower bound estimator, and present
computational results to verify that our scheme can reduce the variance
significantly, by comparison with the traditional Latin hypercube approach
Rotated sphere packing designs
We propose a new class of space-filling designs called rotated sphere packing
designs for computer experiments. The approach starts from the asymptotically
optimal positioning of identical balls that covers the unit cube. Properly
scaled, rotated, translated and extracted, such designs are excellent in
maximin distance criterion, low in discrepancy, good in projective uniformity
and thus useful in both prediction and numerical integration purposes. We
provide a fast algorithm to construct such designs for any numbers of
dimensions and points with R codes available online. Theoretical and numerical
results are also provided
Construction of nested space-filling designs
New types of designs called nested space-filling designs have been proposed
for conducting multiple computer experiments with different levels of accuracy.
In this article, we develop several approaches to constructing such designs.
The development of these methods also leads to the introduction of several new
discrete mathematics concepts, including nested orthogonal arrays and nested
difference matrices.Comment: Published in at http://dx.doi.org/10.1214/09-AOS690 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Design of Experiments for Screening
The aim of this paper is to review methods of designing screening
experiments, ranging from designs originally developed for physical experiments
to those especially tailored to experiments on numerical models. The strengths
and weaknesses of the various designs for screening variables in numerical
models are discussed. First, classes of factorial designs for experiments to
estimate main effects and interactions through a linear statistical model are
described, specifically regular and nonregular fractional factorial designs,
supersaturated designs and systematic fractional replicate designs. Generic
issues of aliasing, bias and cancellation of factorial effects are discussed.
Second, group screening experiments are considered including factorial group
screening and sequential bifurcation. Third, random sampling plans are
discussed including Latin hypercube sampling and sampling plans to estimate
elementary effects. Fourth, a variety of modelling methods commonly employed
with screening designs are briefly described. Finally, a novel study
demonstrates six screening methods on two frequently-used exemplars, and their
performances are compared
Entanglement and quantum combinatorial designs
We introduce several classes of quantum combinatorial designs, namely quantum
Latin squares, cubes, hypercubes and a notion of orthogonality between them. A
further introduced notion, quantum orthogonal arrays, generalizes all previous
classes of designs. We show that mutually orthogonal quantum Latin arrangements
can be entangled in the same way than quantum states are entangled.
Furthermore, we show that such designs naturally define a remarkable class of
genuinely multipartite highly entangled states called -uniform, i.e.
multipartite pure states such that every reduction to parties is maximally
mixed. We derive infinitely many classes of mutually orthogonal quantum Latin
arrangements and quantum orthogonal arrays having an arbitrary large number of
columns. The corresponding multipartite -uniform states exhibit a high
persistency of entanglement, which makes them ideal candidates to develop
multipartite quantum information protocols.Comment: 14 pages, 3 figures. Comments are very welcome
Second-order nearly orthogonal Latin hypercubes for exploring stochastic simulations
The article of record as published may be found at http://dx.doi.org/10.1057/jos.2016.8This paper presents new Latin hypercube designs with minimal correlations between all main, quadratic, and two-way interaction effects for a full second-order model. These new designs facilitate exploratory analysis of stochastic simulation models in which there is considerable a priori uncertainty about the forms of the responses. We focus on understanding the underlying complexities of simulated systems by exploring the input variables’effects on the behavior of simulation responses. These new designs allow us to determine the driving factors, detect interactions between input variables, identify points of diminishing or increasing rates of return, and find thresholds or change points in localized areas. Our proposed designs enable analysts to fit many diverse metamodels to multiple outputs with a single set of runs. Creating these designs is computationally intensive; therefore, several have been cataloged and made available online to experimenters.Office of Naval Research (N0001412WX20823
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