THE JOINT PROBLEM OF MODEL STRUCTURE DETERMINATION AND PARAMETER-ESTIMATION IN QUANTITATIVE IR SPECTROSCOPY

A method for automatically selecting the wave numbers best suited for quantitative analysis as well as for simultaneously estimating the par ameters in the emerging model is presented. As an indicator of the goo dness of the model, Akaike's information theoretic criterion (AIC) is used. Since this approach involves the maximum likelihood estimate of the parameters, the problem of how to scale the data prior to the calc ulations is eliminated. The method described in this paper is not rest ricted to Fourier transform infrared (FTIR) problems, but can be appli ed to other similar problems, where both the model structure and the p arameters should be determined. During the calibration stage, a mixed- integer nonlinear programming problem must be solved. It is demonstrat ed that the use of such modern optimization techniques makes it possib le to solve these types of problems without tremendous computational e ffort. During the prediction stage the obtained model is easy to use.