Peil J, Schmerling S
Institut für Anatomie des Bereichs Medizin, Martin-Luther-Universität Halle-Wittenberg.
Gegenbaurs Morphol Jahrb. 1989;135(5):659-71.
Measurements of endocrinological and pharmacological processes often yield courses of time series with exponentially saturated increasing first part followed by an exponentially decreasing part. Such measured courses may be mathematically modelled by the so-called BATEMAN function type, an expression consisting of 2 e-function terms. In this paper, the method of locally adjusted functional approximation for model-free quantitative evaluation of measured time series is sketched. By means of 2 real examples of measured data, it will be demonstrated how the results of the model-free evaluation may serve for internal regression to estimate starting parameter values for an iterative fitting of a BATEMAN function to measured data courses. Furthermore, it is shown that the model-free approach of data evaluation may give substantial hints for the mathematical model building process and for model verification.
对内分泌和药理过程的测量常常会产生时间序列曲线，其起始部分呈指数饱和增长，随后是指数下降部分。这样的测量曲线可以用所谓的贝特曼函数类型进行数学建模，该表达式由两个指数函数项组成。本文概述了用于对测量时间序列进行无模型定量评估的局部调整函数逼近方法。通过两个实测数据的实例，将展示无模型评估的结果如何用于内部回归，以估计将贝特曼函数迭代拟合到测量数据曲线时的初始参数值。此外，还表明数据评估的无模型方法可以为数学模型构建过程和模型验证提供重要提示。
