**统计与管理学院****2017****年学术报告第****11****期**【主 题】

**Nearly column-orthogonal designs based on leave-one-out good lattice point sets**【报告人】 袁茹, Ph.D. Candidate

南开大学

【时 间】 2017年03月20日（星期一）11:30－12:30

【地 点】 上海财经大学统计与管理学院大楼1208室

【摘 要】Computer experiments are becoming increasingly prevalent as a useful tool for study of uncertainty quantification. In designing a computer experiment, it is crucial to spread the design points throughout the experimental region as evenly as possible. Due to the curse of dimensionality, it is rather difficult for design points to cover a large portion of a high dimensional design region. Thus, it is more reasonable to consider designs that are space- filling in lower dimensional projections of the input space.

Besides space-filling, orthogonality is another useful criterion for designing computer experiments. Orthogonality is of importance when polynomial modeling is considered. For the first-order polynomial model, orthogonal designs ensure the orthogonality among all main effects. When second-order effects are present, however, it is desirable to have orthogonal designs that are able to estimate the linear effects without being correlated with the second- order effects. Thus designs with the following two properties are desirable: (a) all the columns are orthogonal to each other; and (b) the sum of the elementwise product of any three columns is zero. Property (b) is an important property that ensures the estimates of the linear effects being uncorrelated with that of the second-order effects.

Good lattice point sets have good space-filling properties, and many designs with large L1- distance can be obtained by the leave-one-out good lattice point method (Zhou and Xu, 2015). However, there are negatively fully correlated columns in such designs. This is undesirable in the modeling of computer experiments. To overcome such a deficiency, we propose a class of designs based on the leave-one-out good lattice point method, whose columns can be divided into two groups, such that any two columns are column-orthogonal when they are from different groups and nearly column-orthogonal when they are in the same group. The new designs satisfy property (b), thus they can also estimate the linear effects without being correlated with the second-order effects. Moreover, they have good stratification properties and their L1-distances are comparable with the corresponding designs in Zhou and Xu (2015).

【邀请人】 冯兴东