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題 名 | 最大化最小內點距離的拉丁超方陣=MaxMin MID Latin Hypercube |
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作 者 | 馬瀰嘉; 林共進; | 書刊名 | 中國統計學報 |
卷 期 | 37:1 1999.03[民88.03] |
頁 次 | 頁53-77 |
分類號 | 313.79 |
關鍵詞 | 計算機實驗; 拉丁超方陣; 最大化最小內點距離; Computer experiment; Latin hypercube; Maximum distance; |
語 文 | 中文(Chinese) |
英文摘要 | Computer experiments usually are used to instead of expensive physical experiment because it is more cheap and rapid. Because there is no random error in computer experiments, standard factorial designs are inadequate in the absence of certain main effects. The replication of standard factorial designs can not be used to estimate this error, but instead produces redundancy. Mckay, Beckman, and Conover (1979) use the latin hypercube in computer experiments. A n-point (n = k□) latin hypercube design matrix is constructed by randomly permuting the integers {1,…,n} for each factor and rescaling to the experimental region, so that the points project uniquely and equally-spaced to each dimension. Because of the unique projections, use of latin hypercubes allows for great flexibility in model fitting. This paper uses the difference of two point coordinates of minimum inter-point distance to find the maximum distance in d = 2 dimension space. The maximum distance design for n =k□ is the same as the k□-point rotated full factorial design of Beattie, Lin, and Morris (1997) by rotated standard k□ factorial design and the corresponding maximum distance is k□+ 1. If ones minimize the maximum interpoint distance, the design can not be unique and have no regularity. The maximum distance for n≠k□ are also not unique and have no regularity. Finally, if d=n, the coordinates of n. points of maximum distance design and the corresponding maximum distance are obtained. |
本系統中英文摘要資訊取自各篇刊載內容。