Uniform Design over General Input Domains with Applications to Target Region Estimation in Computer Experiments

Abstract

在這篇文章中，我們提供一些用以生成 Dirichlet 隨機向量的演算法，並根據以下標準來評估這些演算法的表現：（一）電腦生成時間；（二）敏感度；以及（三）適合度。 另外，我們特別檢驗一個基於 beta 變量轉換的演算法，並提供三個方針以減少此演算法的生成時間。模擬的結果顯示，除了所有（或大部分）的形狀變數都相當接近零的情況之外，基於我們所提出的方針整合而成的演算法顯著地在電腦生成時間上勝過其他的演算法。

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 cannot be adequately applied. In this study, we propose a new UD method that is suitable for any type of design area. For practical implementation, we develop an efficient algorithm to construct a so-called 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.