最优分析一阶导数（\textit{fdao}）：一种估计包含随机自变量的非线性回归中不确定性的方法
First derivatives at the optimum analysis (\textit{fdao}): An approach to estimate the uncertainty in nonlinear regression involving stochastically independent variables
摘要：
优化分析的一个重要问题是当参数如$ \{θ_j\}_{j=1,\, \dots \,,k }$，确定一个函数$ y=f(x\given\{θ_j\}) $，必须从一组可观测量$ \{ x_i,y_i\}_{i=1,\, \dots \,,m} $中估计出来时。其中$ \{x_i\} $是假设为无不确定性的自变量。众所周知，如果$ y=f(x\givenθ_j) $是$ \{θ_{j=1,\, \dots \,,k} \}.$的线性组合，则解析解是可能的。这里提出，如果参数是\textit{stochastically independent}，则可以从最优的导数$ \tfrac{\partial f(x \given \{θ_j\})}{\partial θ_j} $来确定不是\textit{linearly independent}的参数的不确定性。
英文摘要：
An important problem of optimization analysis surges when parameters such as $ \{θ_j\}_{j=1,\, \dots \,,k }$, determining a function $ y=f(x\given\{θ_j\}) $, must be estimated from a set of observables $ \{ x_i,y_i\}_{i=1,\, \dots \,,m} $. Where $ \{x_i\} $ are independent variables assumed to be uncertainty-free. It is known that analytical solutions are possible if $ y=f(x\givenθ_j) $ is a linear combination of $ \{θ_{j=1,\, \dots \,,k} \}.$ Here it is proposed that determining the uncertainty of parameters that are not \textit{linearly independent} may be achieved from derivatives $ \tfrac{\partial f(x \given \{θ_j\})}{\partial θ_j} $ at an optimum, if the parameters are \textit{stochastically independent}.
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