廣泛區域之均勻設計與電腦實驗之運用

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莊世鐘(Shih-Chung Chuang) 查詢紙本館藏

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統計研究所

論文名稱

廣泛區域之均勻設計與電腦實驗之運用
(Uniform Design over General Input Domains with Applications to Computer Experiments)

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摘要(中)

近年來，均勻設計在電腦實驗上廣被應用。在傳統均勻設計的發展中，其重心為單位超立方體區域上之均勻佈點。然而，最近我們發現在許多電腦的模擬當中，會面臨需在非矩形區域上做均勻設計的問題。因此在本研究當中，我們改進傳統均勻設計的方法，使其適用在更廣泛的區域上做佈點設計。此外，本論文同時提供一套具高效率的演算法來降低均勻設計時所需耗費的時間，同時也會藉由實例來驗證此演算法的有效性。接著，在應用當中，我們亦提出一套目標區域估計的演算法，此演算法主要是利用逐步均勻設計加上適當的迴歸模型來提高對目標區域偵測的效率。文末，我們也會以一些實際的例子來評估以上演算法效用；在這些例子當中，我們固定電腦模擬可進行的次數，然後比較各種不同方法對目標區域偵測的結果，從中可以發現，本論文所提之演算法所得到的估計結果均優於其它現有方法。

摘要(英)

The power of uniform design (UD) has received great attention in the area of computer experiments over the last two decades. However, when conducting a typical computer experiment, one finds many non-rectangular types of input domains on which traditional UD methods can not be adequately applied. In this study, we propose a new UD method that is suitable for any types of design area. For practical implementation, we develop an efficient algorithm to construct a socalled nearly uniform design (NUD) and show that it approximates very well the UD solution for small sizes of experiment. By utilizing the proposed UD method, we also develop a methodology for estimating the target region of computer experiments. The methodology is sequential and aims to (i) provide adaptive models that predict well the output measures related to the experimental target; and (ii) minimize the number of experimental trials. Finally, we illustrate the developed methodology on various examples and show that, given the same experimental budget, it outperforms other approaches in estimating the prespecified target region of computer experiments.

關鍵字(中)

★ 目標區域
★ 電腦實驗
★ 均勻設計
★ 廣泛區域

關鍵字(英)

★ target detection
★ computer experiment
★ uniform design

論文目次

1 Introduction and Motivating Examples 1
2 Uniform Design over General Input Domains 6
2.1 Introduction to Uniform Design . . . . . . . . . . . . . . . . . . 6
2.2 A New Measure of Uniformity: Central Composite Discrepancy . 8
2.3 The Weighted Uniform Design . . . . . . . . . . . . . . . . . . . 10
2.4 Construction of Nearly Uniform Designs . . . . . . . . . . . . . . 11
2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Methodology for Target Region Estimation 17
3.1 Choosing the Weight Function f(x) for UD . . . . . . . . . . . . 18
3.2 Fitting Response Models . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Sequential Weighted Uniform Design for Target Region Estimation 22
4 Performance Assessment 25
5 Concluding Remarks 35
Bibliography 37

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指導教授

樊采虹、洪英超
(Tsai-Hung Fan、Ying-Chao Hung)

審核日期

2009-10-2

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