Bayesian analysis of band-broadening models used in high performance liquid chromatography

Extensive studies into band-broadening of high performance liquid chromatography (HPLC) data have seen numerous models being proposed to account for the underlying physical and chemical processes responsible for the broadening. The experimental analysis of these models requires high quality data, i.e. duplicated data sets (∼3) which have a low noise level (≲ 3%), and a large number of data points (and ≳ 20). Given the many models and the number of parameters which define them, it is sometimes difficult to determine the most plausible model for a particular data set and instrumental settings. Bayesian analysis is proposed as an alternative to orthodox statistical techniques for quantifying the parameter values in the band-broadening models, as well as testing the statistical plausibility of competing models, which enables the models to be ranked in an ordered manner. Systematic studies using simulation data have demonstrated that Bayesian analysis consistently predicts the correct model for data with up to ∼6% noise level, while the conventional statistical approaches, including the weighted sum of square residuals (WSSR), Akaikes Information Criterion (AIC) and Schwartz Information Criterion (SIC), produce inconsistencies. Bayesian analysis is also applied to experimental HPLC band-broadened data obtained in the separation of propylparaben. The probability density functions (pdfs) for the parameters and the a posteriori probabilities for all competing models are determined from the data. Recommendations arising from the studies regarding the data collection and analysis are made.