NONPARAMETRIC DENSITY ESTIMATION FOR RANDOMLY PERTURBED ELLIPTIC PROBLEMS I: COMPUTATIONAL METHODS, A POSTERIORI ANALYSIS, AND ADAPTIVE ERROR CONTROL
NONPARAMETRIC DENSITY ESTIMATION FOR RANDOMLY PERTURBED ELLIPTIC PROBLEMS I: COMPUTATIONAL METHODS, A POSTERIORI ANALYSIS, AND ADAPTIVE ERROR CONTROL
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DOI：
10.1137/080731670
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发表时间：
2009-01-01
影响因子：
3.1
通讯作者：
Tavener, S.
中科院分区：
文献类型：
--
作者：
Estep, D.;Malqvist, A.;Tavener, S.
我们考虑的非参数密度估计问题的一个感兴趣的数量计算的椭圆型偏微分方程的随机扰动系数和数据的解决方案。我们特别感兴趣的问题，其中有限的知识的随机扰动是已知的。我们推导出一个有效的方法来计算样本，并产生一个近似的概率分布的基础上狮子的区域分解方法和诺依曼级数。然后，我们得出一个后验误差估计的计算概率分布反映了所有来源的确定性和统计误差。最后，我们提出了一种基于后验估计的自适应误差控制算法。
We consider the nonparametric density estimation problem for a quantity of interest computed from solutions of an elliptic partial differential equation with randomly perturbed coefficients and data. Our particular interest are problems for which limited knowledge of the random perturbations are known. We derive an efficient method for computing samples and generating an approximate probability distribution based on Lion's domain decomposition method and the Neumann series. We then derive an a posteriori error estimate for the computed probability distribution reflecting all sources of deterministic and statistical errors. Finally, we develop an adaptive error control algorithm based on the a posteriori estimate.