``高維度''一詞充斥在許多新的研究領域。以往該詞意指變數個數遠大過資料量。近來由於科技進步，數據常有資料量遠大過變數個數的情況，因此高維度可泛指前述任一情境。本計畫致力在高維度電腦實驗下，發展高品質的因子篩選設計，與準確的估計參數/預測反應曲面的方法，完整的理論結構與快速運行的程式套件將是本計畫執行重點之一。在計畫的第一部分，我們將發展當p>>n時，可快速篩選出重要因子之方法論。此方法論預計可容易執行，且不須太耗費硬體資源。在計畫的第二部分，我們將探討當n>>p時，利用混沌多項式來估計電腦實驗的模型參數與預測反應曲面。除了完整的理論價構外，有效率的演算法也是發展重點。本計畫的成果預計可改善傳統方法的效能，並期對社會產業有所貢獻。 ;With technological advances, the terminology “high-dimensional” is much more commonly seen nowadays than a few decades ago. It used to refer to “the number of variables are much greater than the sample size” (i.e., p>>n). Recently, there has been an exponential growth in the size of datasets. Therefore, high-dimensional data may also refer to those whose data sizes are much greater than the numbers of variables (i.e., n>>p). This project aims at developing an efficient screening methodology and highly accurate estimation/prediction techniques for high-dimensional computer experiments. In the first part, we plan to develop a new methodology that can effectively identify active factors, with linear/nonlinear effects, for the case of p>>n. This methodology is expected to perform well and easily implemented with little computational burden. In the second part, we study subdata selection through polynomial chaos expansions when n>>p. The proposed methods would cover several common scenarios. Theoretical properties and efficient algorithms are to be provided. To the best of our knowledge, all relevant research to date, for either p>>n or n>>p, has yet to be fully satisfactory. This project tries to fulfill these gaps and devotes to the theory and application that can be easily applied to real-world situations.
