Efficient Nearly Orthogonal and Space-Filling Latin Hypercubes

By Thomas M. Cioppa, Thomas W. Lucas. Technometrics, 2007

416 citations recorded by the source corpus.

This article presents an algorithm for constructing orthogonal Latin hypercubes, given a fixed sample size, in more dimensions than previous approaches. In addition, we detail a method that dramatically improves the space-filling properties of the resultant Latin hypercubes at the expense of inducing small correlations between the columns in the design matrix. Although the designs are applicable to many situations, they were developed to provide Department of Defense analysts flexibility in fitting models when exploring high-dimensional computer simulations where there is considerable a priori uncertainty about the forms of the response surfaces.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5a8450bedc62d7dbb9624f1bbf6f96eaccde14a1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

The effects of Labour Market Reforms upon Unemployment and Income Inequalities: an agent based model (2018, positive): “25 The meta-model is estimated from a set of observations (from the original model) carefully picked using a high-efﬁciency, nearly orthogonal Latin hypercube design of experiments (Cioppa and Lucas, 2007).”
An algorithm for fast optimal Latin hypercube design of experiments (2010, background): “Cioppa and Lucas [31] presented an algorithm that improves the space-filling properties of LHD at the expense of inducing small correlations between the columns in the design matrix.”
Selecting random Latin hypercube dimensions and designs through estimation of maximum absolute pairwise correlation (2012, background): “Secondly, analysts can set a threshold map ρ to select acceptable designs.”
Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence (2013, neutral): “Several other disciplines also use Monte-Carlo based uncertainty analysis [11]: selected evocative examples are health care optimisation [12], economic risk evaluation [13], and defence scenario comparison [14].”
Optimal maximin $L_{1}$-distance Latin hypercube designs based on good lattice point designs (2018, background): “Many researchers have constructed orthogonal or nearly orthogonal LHDs; see, among others, Ye (1998), Steinberg and Lin (2006), Cioppa and Lucas (2007), Lin, Mukerjee and Tang (2009), Sun, Liu and Lin (2009), Yang and Liu (2012), Georgiou and Efthimiou (2014), Lin and Tang (2015) and Sun and Tang (2”
The generalization of Latin hypercube sampling (2015, background): “The widespread popularity of LHS has led to the invention of numerous variants meant to improve space-filling [5, 6, 7, 8, 9, 10, 11], optimize projective properties [12], minimize least square error and maximize entropy [13], and reduce spurious correlations [14, 15, 16, 17, 7, 9, 18].”