Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Romero VJ, Burkardt JV, Gunzburger MD, Peterson JS (2006) Comparison of pure and “Latinized” centroidal Voronoi tessellation against various other statistical sampling methods. Metheron G (1963) Principles of geostatistics. Loh WL (1996) On Latin hypercube sampling. Locatelli M (2003) A note on the Griewank test function. Krykova I (2003) Evaluating of path-dependent securities with low discrepancy methods. J Chem Metal Mining Soc South Africa 52(6):119–139 Krige DG (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand. Jones DR (2001) A taxonomy of global optimization methods based on response surfaces. Husslage B, Rennen G, van Dam E, den Hertog D (2011) Space-filling Latin hypercube designs for computer experiments. Gunzburger MD, Burkardt JV (2004) Uniformity measures for point samples in hypercubes. High Perform Comput Computational Sci–VECPAR 4395:579–588 Gorissen D, Crombecq K, Hendrickx W, Dhaene T (2006) Adaptive distributed metamodeling. Goel T, Haftka RT, Shyy W, Watson LT (2008) Pitfalls of using a single criterion for selecting experimental designs. Eur J Oper Res 214:683–696ĭu Q, Faber V, Gunzburger M (1999) Centroidal Voronoi tessellations: applications and algorithms. Mh Math 101:261–278Ĭrombecq K, Laermans E, Dhaene T (2011) Efficient space-filling and non-collapsing sequential design strategies for simulation-based modeling. Geosci Model Dev 7:1247–1250Ĭlerck LD (1986) A method for exact calculation of the Star discrepancy of plane sets applied to the sequences of Hammersley. From the comparison results, we provided a guideline for selecting appropriate sampling methods for some systems of interest to be approximated.Ĭhai T, Draxler RR (2014) Root mean square error (RMSE) or mean absolute error (MAE)? – Arguments against avoiding RSME in the literature. We also compared the root mean square error (RMSE) values of Kriging meta-models generated using the five sampling methods to evaluate their prediction performance. In this research, we performed the comparison study among the popular sampling methods for computer experiments (CVT, OLHD, and three quasi-random sequences) with employing both space-filling properties and a projective property as performance measures to fairly compare them. Some literature on the CVT asserted that the performance of the CVT was better than that of the LHD, but this assertion seems unfair because those studies only employed space-filling performance measures in favor of the CVT. As such, a sampling method, the optimal Latin hypercube design (OLHD), has been popularly used, and quasi-random sequences and the centroidal Voronoi tessellation (CVT) have begun to be noticed recently. However, there is still no clear guideline for selecting an appropriate sampling method for computer experiments. Thus, it is very important to locate the sample points using a sampling method suitable for the system of interest to be approximated. It is well known that the sample points, in the design space located by a sampling method, determine the quality of the meta-model generated based on expensive computer experiment (or simulation) results obtained at sample (or training) points. This study compares the performance of popular sampling methods for computer experiments using various performance measures to compare them.
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