Clustering-based convergence diagnostic for multi-modal identification in parameter estimation of chromatography model with parallel MCMC

TL;DR

This paper introduces a clustering-based convergence diagnostic to improve the assessment of MCMC sampling convergence in multi-modal parameter estimation problems, specifically applied to chromatography models.

Contribution

It combines clustering methods with the traditional  diagnostic to better detect convergence issues in multi-modal distributions during parallel MCMC sampling.

Findings

Clustering-enhanced diagnostic better identifies multi-modal convergence.

Multi-modal distributions observed in binding and pore diffusion parameters.

Steric mass-action model may not fully capture ion-exchange effects under certain conditions.

Abstract

Uncertainties from experiments and models render multi-modal difficulties in model calibrations. Bayesian inference and \textsc{mcmc} algorithm have been applied to obtain posterior distributions of model parameters upon uncertainty. However, multi-modality leads to difficulty in convergence criterion of parallel \textsc{mcmc} sampling chains. The commonly applied $\widehat{R}$ diagnostic does not behave well when multiple sampling chains are evolving to different modes. Both partitional and hierarchical clustering methods has been combined to the traditional $\widehat{R}$ diagnostic to deal with sampling of target distributions that are rough and multi-modal. It is observed that the distributions of binding parameters and pore diffusion of particle parameters are multi-modal. Therefore, the steric mass-action model used to describe ion-exchange effects of the model protein, lysozyme, on the \textsc{sp} Sepharose \textsc{ff} stationary phase might not be fully capable in certain experimental conditions, as model uncertainty from steric mass-action would result in multi-modality.