Centered L 2 -discrepancy of random sampling and Latin hypercube design, and construction of uniform designs
TL;DR: In this paper properties and construction of designs under a centered version of the L2-discrepancy are analyzed and optimization is performed using the threshold accepting heuristic which produces low discrepancy designs compared to theoretic expectation and variance.
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Abstract: In this paper properties and construction of designs under a centered version of the L2-discrepancy are analyzed. The theoretic expectation and variance of this discrepancy are derived for random designs and Latin hypercube designs. The expectation and variance of Latin hypercube designs are significantly lower than that of random designs. While in dimension one the unique uniform design is also a set of equidistant points, low-discrepancy designs in higher dimension have to be generated by explicit optimization. Optimization is performed using the threshold accepting heuristic which produces low discrepancy designs compared to theoretic expectation and variance.
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Improvement of random LHD for high dimensions
TL;DR: Fast algorithm of construction of good Latin hypercube designs is developed and designs of experiments for multivariate case are reviewed.
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LHD: An R package for efficient Latin hypercube designs with flexible sizes
Hongzhi Wang,Qian Xiao,Abhyuday Mandal +2 more
- 19 Oct 2020
TL;DR: The R package LHD is developed that integrates and improves various algebraic and searching methods to construct efficient LHDs with flexible design sizes and many of the designs found in this paper are better than the existing ones.
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Audze-eglājs criterion for orthogonal and regular triangular grids
Magdalena Šmídová,Václav Sadílek,Jan Eliáš,Miroslav Vořechovský +3 more
- 01 Jan 2015
TL;DR: In this article, the authors describe two deterministic designs that optimally fill a unit hypercube, based on the lower bound of the Audze-Eglājs (AE) criterion.
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A New Method for Constructing Optimal Design of Computer Experiments
Hong Wu,Wei Ping Wang,Feng Yang +2 more
TL;DR: A new method for constructing optimal experimental design (SOEDM) is developed, which is good in terms of both the correlation and distance criteria, the new method can be used in other experimental designs besides Latin hypercube design and the new algorithm is fast.
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