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Orthogonal arrays for computer experiments, integration and visualization. (English) Zbl 0822.62064
Summary: This paper uses orthogonal arrays to define generalizations of Latin hypercube sampling and of lattice sampling in the $$d$$-dimensional unit cube. These are proposed as suitable designs for computer experiments, numerical integration and visualization. The orthogonal array based designs extend to $$t$$-dimensional margins the univariate stratification properties of Latin hypercube and lattice sampling. As a consequence, the variance reduction property of Latin hypercube and lattice sampling also extends to orthogonal array based samples. We give a sample based estimate of the error variance in the case of bivariate stratification.

##### MSC:
 62K99 Design of statistical experiments 05B15 Orthogonal arrays, Latin squares, Room squares 65C05 Monte Carlo methods