Using Quantile Regression in Cloud Transform Simulation

摘要

The cloud transform simulation is a technique used to generate realisations of correlated attributes.rnThe principle of this technique is to partition the scatter diagram between the input attributes intornseveral interval classes and derive for each class a cumulative distribution function (CDF) using onlyrnthe data pairs of the scatter diagram in that class. The simulation then proceeds like a traditionalrnMonte Carlo simulation but using the derived CDF in each class.rnThe cloud transform simulation has the advantage of being a simple and fast technique that isrnable to reproduce the uncertainty in the relationship between the two input attributes regardless ofrnwhether the relationship is linear or not. However, the technique has three major drawbacks. First,rnthe number of classes has an impact on fi nal simulated results and there is not a robust approach torndefi ne such number. Second, simulated results exhibit some saw tooth variations that are unrealisticrnand third the reproduction of the spatial continuity of the simulated attribute is not guaranteed.rnThis paper presents the use of the quantile regression approach in order to overcome the fi rst tworndisadvantages of the cloud transform simulation. Details of the technique and how it can be coupledrnwith the cloud transform simulation are presented along with a real case study.