共查询到19条相似文献,搜索用时 31 毫秒
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从设计到抽样 总被引:1,自引:1,他引:0
马长兴 《数学物理学报(A辑)》1999,19(2):149-153
张润楚,王兆军(1996)提出了均匀设计抽样,将均匀设计变成抽样.本文给出一种由设计到抽样的一般方法,它可以将任何一个有优良均匀性的设计点集变成所有样本都有同样优良均匀性的抽样。 相似文献
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偏差(Discrepancy)作为布点设计均匀性的一个重要度量准则,已被使用很长时间,但对它的性质还研究得很不够.该文从模平移的方面系统地研究了偏差的性质,给出了在超立方体中一个布点设计按整体、大格子、小格子各种模平移的偏差大样本性质,这些性质对于计算机试验引进有关的设计和抽样方法起着重要的作用. 相似文献
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均匀设计抽样及其优良性质 总被引:27,自引:4,他引:23
抽样和设计是计算机试验的一个重要研究课题。本文提出了一种新的抽样方法—均匀设计抽样,研究了它的一些基本性质,并将其应用于数值积分近似计算,这种抽样是王元和方开泰(1981)均匀设计思想的一个发展,也是对Latin Hypercube抽样的一个重要改进,通过与Monte Carlo方法,Latin Hypercube抽样(包括OA-Based Latin Hypercube抽样)和均匀设计的比较,表明了这种抽样的优越性,最后还讨论了在一般分布情形下如何应用这种抽样。 相似文献
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本文对LH型设计的偏差的计算问题进行了研究,给出了计算方法,并得到了部分LH型整体最优设计,改进了现有的均匀设计 相似文献
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本文给出了利用均匀设计和正交表构造低偏差OALH设计的方法,该方法构造的设计既有优良的均匀性具有正交设计的均衡性,一个更重要的优点是可以构造较大样本容量的设计点集,本文同时给出了某些参数的均匀设计表,这些设计优于现有的均匀设计,具有实用价值。 相似文献
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均匀设计抽样的应用 总被引:3,自引:0,他引:3
王兆军 《高校应用数学学报(A辑)》1997,(3):299-310
均匀设计抽样是张润楚和王兆军提出的,并且张润楚和王兆军从理论上证明了它的优良性质。本文考虑了均匀设计抽样在求函数的最大值,积分的近似计算,回归直线的拟合和极大似然估计的求取方面的应用。模拟的结果再次说明了均匀设计抽样的优良性。 相似文献
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“平均冒尖性”不能作为比较正交设计和均匀设计的准则 总被引:1,自引:1,他引:0
本文指出张里千〔3〕提出的“平均冒尖性”不能作为衡量试验设计方案好坏的标准,同时指出文献〔3〕〔4〕在计算方法上的不科学性。 相似文献
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Orthogonal array-based uniform Latin hypercube design(uniform OALHD) is a class of orthogonal array-based Latin hypercube designs to have the best uniformity. In this paper, we provide a less computational algorithm to construct uniform OALHD in 2-dimensional space from Bundschuh and Zhu(1993). And some uniform OALHDs are con- structed by using our method. 相似文献
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空间填充设计是有效的计算机试验设计,比如均匀设计、最大最小距离拉丁超立方体设计等.虽然这些设计在整个试验空间中有较好的均匀性,但其低维投影均匀性可能并不理想.对于因子是定量的计算机试验,已有文献构造了诸如最大投影设计、均匀投影设计等相适应的设计;而对于同时含有定性因子和定量因子的计算机试验,尚未有投影均匀设计的相关文献.文章提出了综合投影均匀准则,利用门限接受算法构造了投影均匀的分片拉丁超立方体设计.在新构造设计中,整体设计与每一片设计均具有良好的投影均匀性.模拟结果显示,与随机分片拉丁超立方体设计相比,利用新构造设计进行试验而拟合的高斯过程模型具有更小的均方根预测误差. 相似文献
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Latin Hypercube Sampling is a specific Monte Carlo estimator for numerical integration of functions on with respect to some product probability distribution function. Previous analysis established that Latin Hypercube Sampling is superior to independent sampling, at least asymptotically; especially, if the function to be integrated allows a good additive fit. We propose an explicit approach to Latin Hypercube Sampling, based on orthogonal projections in an appropriate Hilbert space, related to the ANOVA decomposition, which allows a rigorous error analysis. Moreover, we indicate why convergence cannot be uniformly superior to independent sampling on the class of square integrable functions. We establish a general condition under which uniformity can be achieved, thereby indicating the rôle of certain Sobolev spaces. 相似文献
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Shane S. Drew Tito Homem-de-Mello 《Methodology and Computing in Applied Probability》2012,14(2):203-232
Large deviations theory is a well-studied area which has shown to have numerous applications. Broadly speaking, the theory
deals with analytical approximations of probabilities of certain types of rare events. Moreover, the theory has recently proven
instrumental in the study of complexity of methods that solve stochastic optimization problems by replacing expectations with
sample averages (such an approach is called sample average approximation in the literature). The typical results, however, assume that the underlying random variables are either i.i.d. or exhibit
some form of Markovian dependence. Our interest in this paper is to study the application of large deviations results in the
context of estimators built with Latin Hypercube sampling, a well-known sampling technique for variance reduction. We show that a large deviation principle holds for Latin Hypercube
sampling for functions in one dimension and for separable multi-dimensional functions. Moreover, the upper bound of the probability
of a large deviation in these cases is no higher under Latin Hypercube sampling than it is under Monte Carlo sampling. We
extend the latter property to functions that are monotone in each argument. Numerical experiments illustrate the theoretical
results presented in the paper. 相似文献
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For comparing random designs and Latin hypercube designs, this paper con- siders a wrap-around version of the L2-discrepancy (WD). The theoretical expectation and variance of this discrepancy are derived for these two designs. The expectation and variance of Latin hypercube designs are significantly lower than those of the corresponding random designs. We also study construction of the uniform design under the WD and show that one-dimensional uniform design under this discrepancy can be any set of equidistant points. For high dimensional uniform designs we apply the threshold accepting heuristic for finding low discrepancy designs. We also show that the conjecture proposed by K. T. Fang, D. K. J. Lin, P. Winker, and Y. Zhang (2000, Technometrics) is true under the WD when the design is complete. 相似文献
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Latin hypercube designs have been found very useful for designing computer experiments. In recent years, several methods of constructing orthogonal Latin hypercube designs have been proposed in the literature. In this article, we report some more results on the construction of orthogonal Latin hypercubes which result in several new designs. 相似文献
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In this paper we use counting arguments to prove that the expected percentage coverage of a d dimensional parameter space of size n when performing k trials with either Latin Hypercube sampling or Orthogonal Array-based Latin Hypercube sampling is the same. We then extend these results to an experimental design setting by projecting onto a t < d dimensional subspace. These results are confirmed by simulations. The theory presented has both theoretical and practical significance in modelling and simulation science when sampling over high dimensional spaces. 相似文献
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基于模型对称分解的对称全局敏感性分析在高维复杂模型的推断中起着重要作用.Wang和Chen (2017)提出了一种对称设计来获得对称灵敏度指标的估计,此设计具有较高的抽样效率且不需要得到对称分解项的解析表达.然而,给定试验次数,对称设计的生成具有较强的随机性,导致某些设计的空间填充性较差且在低维投影出现塌陷.文章提出了一种对称拉丁超立方体,使对称设计同时具有拉丁超立方体结构,从而在保持设计对称性的基础上最大化一维投影的均匀性.通过剖析设计的结构得到了对称拉丁超立方体的构造方法.同时,进一步提出最优化算法,得到具有最优中心化L2偏差的对称拉丁超立方体设计.通过一个构造算例,验证了所得设计的优良性. 相似文献