Estimation of low concentrations in the presence of high concentrations using Bayesian algorithms for interpretation of spectrophotometric data

Abstract

A Bayesian method for interpretation of spectral data, dedicated to the monitoring-type applications of mini-and micro-spectrometers, is addressed. The method generates estimates of the concentrations of the components of an analyzed substance on the basis of the data representative of its absorption spectrum, provided that both the normalized spectra of the components and statistical information on historical measurements of the monitored concentrations are available. The Bayesian method is systematically compared with the constrained least-squares method, under an assumption that the estimated concentrations differ considerably and the processed data are subject not only to random instrumental noise but also to some random disturbances introduced by the residual content of components of the analyzed substance being not identified. A study, performed using both synthetic and real-world spectrophotometric data, is aimed at the assessment of the robustness of the Bayesian method to the maximum-to-minimum ratio of concentrations and imprecision of a priori information.

Measurement Data Processing in Spectrophotometric Analysers of Food

“…When looking to the future, one should also mention the methods of measurement data processing, which are already in use, but whose potential of applicability seems to be far from being exhausted, viz. : methods of time-frequency analysis, including wavelet transforms [32,42,77,102,107,158,164,198,246], and Bayesian methods [180,[247][248][249] as means for preprocessing of spectral data and for calibration of spectrophotometric transducers.…”

Spectrophotometric applications of digital signal processing

“…The Bayesian method for the estimation of c using a realization ỹTr of ỹTr , described in the author's paper [166], is derived from the basic Bayes formula:…”

“…In general, the Bayesian estimation of concentrations may be based on the mean value or median or maximum value of the function defined by equation (7.7). The method described in the author's paper [166] is based on the following formula:…”