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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Citations
Optimized U-type designs on flexible regions
Dennis K. J. Lin,Chris Sharpe,P. Winker +2 more
TL;DR: The illustrative results for the two-dimensional case indicate that by using an optimization heuristic in combination with an appropriate discrepancy measure produces high-quality experimental designs on flexible regions.
A novel algorithm of maximin Latin hypercube design using successive local enumeration
TL;DR: A novel algorithm of maximin Latin hypercube design (LHD) using successive local enumeration (SLE) is proposed for generating arbitrary m points in n-dimensional space and results indicate that SLE is effective to generate sampling points with good space-filling and projective properties.
Sampling efficiency in Monte Carlo based uncertainty propagation strategies: Application in seawater intrusion simulations
TL;DR: It is illustrated that the use of optimized Latin hypercube sampling (OLHS) strategies instead of the widely employed simple random sampling (SRS) and Latin hyper cube sampling (L HS) strategies, can significantly improve sampling efficiency and hence decrease the simulation time of MCSs.
Time Series Simulation with Quasi Monte Carlo Methods
Jenny X. Li,Peter Winker +1 more
TL;DR: In this paper, the authors compare traditional and quasi Monte Carlo methods for time-series simulation in macro-econometrics, and show that traditional methods outperform traditional ones for all models investigated.
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