ORTHOGONAL LATIN HYPERCUBE 抽樣方法在電腦實驗中之應用

Abstract

從1979年開始以Latin hypercube設計來建構電腦實驗（computer experiment）的研究便開始展開，自此研究的方向大致是以改善Latin hypercube設計含蓋整體空間性以及改善其最適性為主要。本研究報告是以探究Latin hypercube設計之架構以及其基本採樣精神為主，並比較Latin hypercube抽樣與隨機抽樣（random sampling）和分層隨機抽樣（stratified random sampling）之差異。本研究亦探究Latin hypercube抽樣在電腦實驗上之應用，並研究當模型為迴歸模型時Latin hypercube抽樣如何優於隨機抽樣。

Latin hypercube designs have been used in conducting computer experiments since 1979. After that, lots of efforts have been made to improve them either from a better-space filling perspective or form an optimality perspective. In this article we investigated thoroughly about the nature of Latin hypercube designs and compared Latin hypercube sampling with random sampling and stratified sampling. We also looked at the application of Latin hypercube sampling to computer experiments and found out that when a regression model is used, the regression may be more accurately estimated by Latin hypercube sampling than random sampling.