This article discusses the application of the method of approximation of experimental data by functional dependencies, which uses a probabilistic assessment of the deviation of the assumed dependence from experimental data. The application of this method involves the introduction of an independent parameter “scale of the error probability distribution function” and allows one to synthesize the deviation functions, forming spaces with a nonlinear metric, based on the existing assumptions about the sources of errors and noise. The existing method of regression analysis can be obtained from the considered method as a special case. The article examines examples of analysis of experimental data and shows the high resistance of the method to the appearance of single outliers in the sample under study. Since the introduction of an independent parameter increases the number of computations, for the practical application of the method in measuring and information systems, the architecture of a specialized computing device of the “system on a chip” class and practical approaches to its implementation based on programmable logic integrated circuits are considered.

中文翻译：

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使用多尺度概率分布函数确定功能依赖参数的数学方法

本文讨论了通过函数相关性近似实验数据的方法的应用，该方法对假设的相关性与实验数据之间的偏差进行了概率评估。该方法的应用包括引入独立参数“误差概率分布函数的标度”，并允许人们基于关于误差和噪声源的现有假设来合成偏差函数，形成具有非线性度量的空间。作为一种特殊情况，可以从考虑的方法中获得现有的回归分析方法。本文考察了实验数据分析的示例，并显示了该方法对所研究样品中单个异常值的出现具有很高的抵抗力。