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.
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