The accuracy of indirect measurements and model calibration by falsification
Scientific measurements should deliver quantitative values and error specifications. This requirement is also valid for indirect measurements, were model parameters are deduced from direct measurements. The regression (fitting) of parameters should include a specification of their accuracies. This is difficult for the case of two or more parameters. An individual direct measurement can be quantified by a numerical interval. It represents all available information in the frequent case of a predominating systematic error. For models with more than one parameter it is not constructive to quantify the parameters by intervals as these enclose parameter sets not supported by the measurements. One has to determine the region of possible parameters by a special kind of membership function. The model falsification indicator function (MFIF) F determines the region of possible parameters not falsified by a given set of measurements. Alternatively it provides a measure for the fraction of outliers in the experimental data set. The MFIF can be used for model identification and calibration (regression analysis). Being a positive realization of Popper's falsification approach, it is useful for the determination of structural and practical parameter identifiability, model sloppiness, outlier detection and the discussion of model validation questions. The MFIF is applicable to any model and scientific discipline. It is exemplified and visualized for the simplest possible (linear) case and an easily reproducible nonlinear example. Being simple to implement, this new mathematical tool demands the attention of all scientists.
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