Principles Of Simple Interval Calculations (pp. 43-64)
Authors: Rodionova, O. Ye.; Pomerantsev, A. L. (Institute of Chemical Physics, Moscow)
Abstract: Simple Interval Calculation (SIC) is proposed for linear modelling in general, and for the prediction of interval estimation in particular. The roots of the method, based on ideas of Kantorovich, are to apply linear programming to the data analysis. The SIC approach is based on a single assumption that the error is finite. For prediction modelling, this is shown to lead to results that can be represented in a convenient interval form, and that account for all uncertainties present (X measurement errors, Y measurement errors). The SIC-interval is opposed to the traditional confidence interval estimators based upon theoretical error distributional model assumptions, which rarely hold for practical data analysis of technological and natural systems. The SIC-approach is also used for object status classification, i.e. a relative position of each sample regarding the calibration set. Several important theorems are outlined which allow determination of object status for both the calibration set - as well as the test set samples To illustrate different issues of the method there is used a specially simulated example.