Bayes Wavelet Regression Approach to Solve Problems in Multivariable Calibration Modeling

Setiawan Setiawan, Sutikno Sutikno

Abstract


In the multiple regression modeling, a serious problems would arise if the independent variables are correlated among each other (the problem of ill conditioned) and the number of observations is much smaller than the number of independent variables (the problem of singularity). Bayes Regression (BR) is an approach that can be used to solve the problem of ill conditioned, but computing constraints will be experienced, so pre-processing methods will be necessary in the form of dimensional reduction of independent variables. The results of empirical studies and literature shows that the discrete wavelet transform (WT) gives estimation results of regression model which is better than the other preprocessing methods. This experiment will study a combination of BR with WT as pre-processing method to solve the problems ill conditioned and singularities. One application of calibration in the field of chemistry is relationship modeling between the concentration of active substance as measured by High Performance Liquid Chromatography (HPLC) with Fourier Transform Infrared (FTIR) absorbance spectrum. Spectrum pattern is expected to predict the value of the concentration of active substance. The exploration of Continuum Regression Wavelet Transform (CR-WT), and Partial Least Squares Regression Wavelet Transform (PLS-WT), and Bayes Regression Wavelet Transform (BR-WT) shows that the BR-WT has a good performance. BR-WT is superior than PLS-WT method, and relatively is as good as CR-WT method.

Keywords


Bayes; wavelet; ill conditioned; singularity

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DOI: http://dx.doi.org/10.12962/j20882033.v21i2.30

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