ISSN 0023-1584, Kinetics and Catalysis, 2006, Vol. 47, No. 4, pp. 537–548. © MAIK “Nauka /Interperiodica” (Russia), 2006. Original Russian Text © A.L. Pomerantsev, O.Ye. Rodionova, 2006, published in Kinetika i Kataliz, 2006, Vol. 47, No. 4, pp. 553–565. 537 Data analysis and mechanistic studies for complex chemical processes are the most important areas of chemical kinetics. Estimating kinetic parameters from experimental data or, in other words, solving the inverse problem of chemical kinetics was formed as an individ- ual area in the 1970s–1980s. Mathematicians [1, 2], as well as kineticians [3, 4], have taken part in the devel- opment of this area. Two main, fundamentally different approaches to the problem of kinetic data analysis can be distinguished. In the so-called soft approach [5–13], experimental data are described in terms of a linear multivariate model valid in a limited range of condi- tions. In this case, it is not necessary to know the mech- anism of the process. However, this approach does not always provide the desired accuracy. The other approach uses so-called hard physicochemical model- ing [4, 14], which is based on fundamental kinetic prin- ciples and allows parameters to be estimated with a high degree of accuracy. However this method is appli- cable only when a model of the process is known a pri- ori. Both approaches have strong and weak points, and both have advocates and opponents. Traditionally, Rus- sian researchers develop the hard approach [15], while Western researchers prefer soft methods [16]. The problem of data interpretation, model construc- tion, and prediction of unknown values (called calibra- tion for brevity) is among the oldest but still challeng- ing scientific problems. Since Gauss (1794), this prob- lem has been attacked using regression analysis. The basic principle of this method is minimizing the devia- tion of the model from experimental data (least-squares method) [17]. The development of this approach, including principal component analysis (1901) [18], the maximum likelihood method (1912) [19], ridge regression (1963) [20], and projection on latent struc- tures (PLS,1975) [21], has made it applicable to com- plex, ill-posed problems. However, all of these methods provide predictions as point estimates, whereas interval estimates taking into account the uncertainty of predic- tion are often required in practice. Constructing confi- dence intervals using conventional statistical methods is impossible because of the complexity of the problem [22], and employing simulation methods is impossible because of the long computational time required [23]. In 1962, Kantorovich [24] suggested another approach to the problem of linear calibration, which is to replace the objection function by a set of inequalities solvable by linear programming methods. In this case, the result of prediction appears immediately as an inter- val estimate. For this reason, this method was named simple interval calculation (SIC). Previously, this idea did not gain wide acceptance and was not developed because of inadequate computer performance. In the 1970s–1990s, this approach was taken in a series of interesting applied studies [25–32] but was not devel- oped into a standard method. The results of those inves- tigations were summed up in a monograph [33], where the main problem solved by the authors of the above- mentioned works is considered in detail. This problem includes the interval estimation of the model parameters and the immersion of the admitted region of these param- eters into a hypercube, parallelepiped, ellipsoid, etc. This problem formulation seems to be unprofitable and not very promising. This view is proved by the fact that no new works using this approach have been car- ried out in the last decade. At the same time, we believe that Kantorovich’s idea can provide interesting results when applied to the interval prediction of response. In Two Approaches to Kinetic Analysis Applied to the Prediction of Antioxidant Activity A. L. Pomerantsev and O. Ye. Rodionova Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, 117977 Russia e-mail: forecast@chph.ras.ru Received December 28, 2004 Abstract—Differential scanning calorimetry (DSC) followed by mathematical data processing can be used instead of the conventional method of long term thermal aging in predicting the activity of antioxidants in poly- olefins. In this method, a regression relationship is established between the oxidation initial temperatures mea- sured by DSC (X data) and the oxidation induction period values determined by thermal aging (Y data). Two approaches, called hard and soft, are employed in the construction of models. In the first case, nonlinear regres- sion analysis is used in combination with successive Bayesian estimation. The second approach combines par- tial least squares regression and simple interval calculation. Use of a common data set makes it possible to com- pare these approaches and to draw inferences as to the cases in which one or the other is preferable. DOI: 10.1134/S0023158406040094 This article is protected by the copyright law. You may copy and distribute this article for your personal use only. Other uses are only allowed with written permission by the copyright holder.