物理定律统计建模的一般方法：非参数回归
A general approach to statistical modeling of physical laws: nonparametric regression
摘要：
实验物理定律的统计建模是基于测量变量的概率密度函数。它是通过核估计的实验数据表示。在实验装置标定过程中，通过数据的分散性客观地确定了核函数。通过条件平均估计量从实验数据中最优地提取与测量变量相关的物理定律。它直接来自核估计，对应于一般的非参数回归。所提出的方法证明了通过建模的返回映射的噪声混沌数据。在这个例子中，非参数回归被用来预测混沌时间序列的未来值。在预测质量的定义中使用了平均预测误差，而冗余度则用数据点之间的均方距离表示。这两种统计量都用于预测器成本函数的新定义中。从预测器成本函数的最小值，估计模型中的适当数量的数据。
英文摘要：
Statistical modeling of experimental physical laws is based on the probability density function of measured variables. It is expressed by experimental data via a kernel estimator. The kernel is determined objectively by the scattering of data during calibration of experimental setup. A physical law, which relates measured variables, is optimally extracted from experimental data by the conditional average estimator. It is derived directly from the kernel estimator and corresponds to a general nonparametric regression. The proposed method is demonstrated by the modeling of a return map of noisy chaotic data. In this example, the nonparametric regression is used to predict a future value of chaotic time series from the present one. The mean predictor error is used in the definition of predictor quality, while the redundancy is expressed by the mean square distance between data points. Both statistics are used in a new definition of predictor cost function. From the minimum of the predictor cost function, a proper number of data in the model is estimated.
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