Abstract:
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.
