Latin hypercube sampling with inequality constraints

Abstract

Computer experiment, Latin hypercube sampling, Design of experiments, Uncertainty analysis, Dependence,

Comparing and generating Latin Hypercube designs in Kriging models

“…The present paper is aimed to discuss a specific algebraic methodology to assess the properties of each LHD. See also the discussion by (Jourdan and Franco 2010) and (Petelet et al 2010) in this Issue. The computation of a BLUP from an LHD requires the inversion of a sub-matrix of Γ d defined in (6).…”

Computer experiments: a review

“…Pistone and Vicario (2010) examine the behaviour of several LHDs in the context of the Gaussian process model. Petelet et al (2010) propose an algorithm that constructs LHDs that are able to uphold certain inequality constraints between the sample variables. Jourdan and Franco (2010) build a new class of LHDs, using the Kullback-Leibler information as a criterion to ensure that the design gives effective coverage of the factor space.…”

Weighted space-filling designs

“…In the literature, a variety of approaches have been taken to finding constrained spacefilling designs under deterministic constraints, see Iman and Conover (1982), Stinstra et al (2003), Petelet et al (2010) and Draguljić et al (2012) for examples. In this paper, we develop, apply and investigate space-filling designs that take account of probabilistic prior information and, particularly, relationships between input variables.…”