Subjective Restoration of Mathematical Models for a Research Object, Its Measurements, and Measurement-Data Interpretation

Abstract

The problems of empirical reconstruction of the subjective model of a research object (RO), the subjective model of its measurements, their subjective analysis, and subjective interpretation of the measurement data are considered. To solve these problems, we use the mathematical formalism for subjective modeling (MFSM), subjective judgments made by the researcher–modeler (r.–m.) concerning the mathematical model of the RO and its measurements and based on his scientific experience and intuition. The subjective models of measurements of the RO and measurement-data interpretation are defined by the r.–m. as elements of a parametric family of smoothing splines. It is shown that the maximum posterior accuracy of the subjective interpretation of the measurement-experiment data, which is “observed” in the solution process for the problems of restoring the subjective models of the RO and its measurements, analysis, and measurement-data interpretation, can serve as a criterion for the truth of the subjective models of the measurement experiment and interpretation of the obtained measurement data, since the criterion for the accuracy of measurement-data interpretation is not used in the reconstruction of the above models. The paper suggests the principle of the maximum posterior accuracy of the subjective interpretation of measurement-experiment data as a criterion for the adequacy of subjectively reconstructed models of measurement experiments and interpretation of measurement data.