Confidence Intervals for Discrete Approximations to Ill-Posed Problems
Confidence Intervals for Discrete Approximations to Ill-Posed Problems
复制标题
不适定问题的离散近似的置信区间
DOI：
10.1080/10618600.1994.10474631
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发表时间：
1994
影响因子：
2.4
通讯作者：
D. O’Leary
中科院分区：
文献类型：
--
作者：
B. Rust;D. O’Leary
摘要：我们考虑线性模型 Y = Xβ + e，该模型是通过对描述一组物理测量的第一类积分方程组进行离散化而获得的。 n 向量 β 表示所需量，m x n 矩阵 X 表示仪器响应函数，m 向量 Y 包含实际获得的测量值。这些测量结果被从具有零均值向量和已知方差矩阵的分布中得出的随机测量误差 e 破坏。第一类积分方程的解是一个不适定问题，因此上述模型的最小二乘解是测量值的高度不稳定函数，并且该解的经典置信区间太宽而无用。通常可以通过施加物理驱动的非负约束来稳定该解决方案。在上一篇文章（O'Leary 和 Rust 1986）中，我们开发了一种计算非负约束同时置信区间集的方法。在本文中，我们简要回顾了...
Abstract We consider the linear model Y = Xβ + e that is obtained by discretizing a system of first-kind integral equations describing a set of physical measurements. The n vector β represents the desired quantities, the m x n matrix X represents the instrument response functions, and the m vector Y contains the measurements actually obtained. These measurements are corrupted by random measuring errors e drawn from a distribution with zero mean vector and known variance matrix. Solution of first-kind integral equations is an ill-posed problem, so the least squares solution for the above model is a highly unstable function of the measurements, and the classical confidence intervals for the solution are too wide to be useful. The solution can often be stabilized by imposing physically motivated nonnegativity constraints. In a previous article (O'Leary and Rust 1986) we developed a method for computing sets of nonnegatively constrained simultaneous confidence intervals. In this article we briefly review the ...