Theory and Applications of Simple Interval Calculation

Oxana Ye. Rodionova

Polycert, Institute of Chemical Physics, 4, Kosygin St, Moscow, 117977,

Russia, Email: rcs@chph.ras.ru

Simple Interval Calculation (SIC) is proposed for linear modeling in general, for prediction of interval estimation in particular. It does not employ the conventional regression approach but is based on the single assumption that the experimental error is finite. The roots of the method, based on ideas of Kantorovich, are to be applied linear programming to the data analysis.

SIC is also used for construction of sample status classification. This classification considers the status, i.e. relative position of each sample regarding the calibration set, for which it is shown that only boundary samples are important for prediction. The following additional object status categories are introduced: insiders that lie close to the model, outsiders that are far from the model, and outliers that contradict the model. SIC-leverage and SIC-residual concepts are defined.

For X-matrix rank deficiency, SIC employs traditional bilinear projections (PCR, PLS).

The SIC-method

·       gives the result of prediction directly in the interval form,

·       calculates the prediction interval irrespective of sample position regarding the model,

·       summarizes and processes all errors involved in bi-linear modeling all together and estimates the Maximum Error Deviation for the model,

·       provides wide possibilities for sample classification and outlier detection.

The feasibility of SIC- approach is demonstrated on simulated and real-world data. All SIC-calculations were made with the specially implemented software which includes the following base algorithms: NIPALS algorithm for the pertinent matrix decompositions, a standard Simplex algorithm or optimization, as well as special procedures for preliminary data analysis that reduces initial problems to a form suitable for efficient application of the simplex procedure.