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Bayesian calibration, process modeling and uncertainty quantification in biotechnology

Fig 8

Linear (top) and logistic (bottom) calibration model of glucose assay.

A calibration model comprising linear functions for both the location parameter μ_A365 and the scale parameter of a Student-t distribution was fitted to calibration data of glucose standard concentrations () and absorbance readouts by maximum likelihood estimation (A-C). The calibration data used to fit the linear model is the subset of standards that were spaced evenly on a log-scale up to (B, E). Likewise, a calibration model with a 5-parameter asymmetric logistic function for the μ parameter of the Student-t distribution was fitted to the full calibration dataset (D-E). In both models, the scale parameter was modeled as a 1st-order polynomial function of μ and the degree of freedom ν as a constant. The extended range of calibration standard concentrations up to reveals a saturation kinetic of the glucose assay (A, D) and depending on the glucose concentration, the residuals (C, F) with respect to the modeled location parameter are scattered by approximately 5%. Modeling the scale parameter of the distribution as a 1st-order polynomial function of μ describes the broadening of the distribution at higher concentrations (C).

doi: https://doi.org/10.1371/journal.pcbi.1009223.g008