  Determining the adsorption isotherms is an issue of significant importance in
preparative chromatography. A modern technique for estimating adsorption
isotherms is to solve an inverse problem so that the simulated batch separation
coincides with actual experimental results. However, due to the ill-posedness,
the high non-linearity, and the uncertainty quantification of the corresponding
physical model, the existing deterministic inversion methods are usually
inefficient in real-world applications. To overcome these difficulties and
study the uncertainties of the adsorption-isotherm parameters, in this work,
based on the Bayesian sampling framework, we propose a statistical approach for
estimating the adsorption isotherms in various chromatography systems. Two
modified Markov chain Monte Carlo algorithms are developed for a numerical
realization of our statistical approach. Numerical experiments with both
synthetic and real data are conducted and described to show the efficiency of
the proposed new method.
