Statistical Error Propagation
Statistical Error Propagation
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统计误差传播
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
J. Tellinghuisen
中科院分区：
文献类型：
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作者：
J. Tellinghuisen
通过对 104−4 × 105 等效数据集进行蒙特卡洛计算，对来自线性和非线性最小二乘 (LS) 拟合的参数的许多线性和非线性函数进行测试，这个简单但经常被忽视的相关变量函数中统计误差传播方程。测试示例包括多项式和指数表示以及带分析模型。对于线性 LS 参数的线性函数，误差传播方程是精确的。非线性参数和函数产生非正态分布，但误差传播方程仍然可以很好地预测它们的离散度。通常，可以通过重新定义最小二乘模型来绕过误差计算，以将感兴趣的数量作为可调整参数包含在内，在这种情况下，其方差直接在方差-协方差矩阵中返回。这种方法在形式上被证明与误差传播方法等效。
The simple but often neglected equation for the propagation of statistical errors in functions of correlated variables is tested on a number of linear and nonlinear functions of parameters from linear and nonlinear least-squares (LS) fits, through Monte Carlo calculations on 104−4 × 105 equivalent data sets. The test examples include polynomial and exponential representations and a band analysis model. For linear functions of linear LS parameters, the error propagation equation is exact. Nonlinear parameters and functions yield nonnormal distributions, but their dispersion is still well predicted by the propagation-of-error equation. Often the error computation can be bypassed by a redefinition of the least-squares model to include the quantity of interest as an adjustable parameter, in which case its variance is returned directly in the variance-covariance matrix. This approach is shown formally to be equivalent to the error propagation method.