Comparing and generating Latin Hypercube designs in Kriging models

Abstract

Computer experiments, Latin hypercube, Mean square prediction error, Gaussian linear prediction,

Application of metamodeling to the valuation of large variable annuity portfolios

“…From the figure we see that there is only one sample point in each row and each column. For more information about LHS, readers are referred to (McKay, Beckman, and Conover 1979), (Liefvendahl and Stocki 2006), (Minasny and McBratney 2006), (Pistone and Vicario 2010), (Petelet, Iooss, Asserin, and Loredo 2010), and (Viana 2013).…”

“…In this paper, we apply a metamodeling approach to address the computational problem mentioned above. In particular, we adopt a metamodel by using a Latin hypercube sampling method (McKay, Beckman, and Conover 1979, Pistone and Vicario 2010, Petelet, Iooss, Asserin, and Loredo 2010, Viana 2013 and the ordinary kriging model (Isaaks and Srivastava 1990).…”

Computer experiments: a review

“…Additional construction methods leading to orthogonal or nearly orthogonal LHDs were given by Bingham et al (2009) and by Lin et al (2009). 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.…”

Modelling of a thermomechanically coupled forming process based on functional outputs from a finite element analysis and from experimental measurements

“…The LHDs were optimised in order to maximise the information for the estimation of the parameters in the correlation function (3), using the entropy criterion as the objective in the algorithm of Jin et al (2005). This heuristic algorithm was chosen because the size of the design is too large to perform the symbolic calculation of optimal designs (Pistone and Vicario 2010). In addition, the observations at the 16 corner points of the four-dimensional factor space were considered since LHDs tend to cover the inside of the factor space.…”