< Back to Article

Bayesian calibration, process modeling and uncertainty quantification in biotechnology

Fig 13

Comparison of Monod model fit with linear error model.

Two Monod kinetic process models were fitted to the same observations from culture well D06 utilizing either a linear calibration model for the biomass/backscatter relationship (orange in A, calibration in D) or the previously established logistic model (blue in A). In A the posterior distribution of backscatter observations (density bands) is overlaid with actual backscatter observations. A linear calibration (D) model with fixed intercept (Section 3.1.5) was fitted to the subset of calibration data points up to such that it covers the range of biomass concentrations expected in the experiment. Residual plots of the observations compared to the posterior predictive distribution of backscatter observations (B, C) show that the fit obtained with the logistic calibration model (blue) has much less lack-of-fit compared to the one with the linear model (orange). Note that the backscatter residuals of ±1% are small compared to the amplitude of the absolute values going from close to 0 to approximately 20. The discrepancy between the two models is also evident from the 90% HDI of the maximum growth rate μ_max of [0.414, 0.423] h⁻¹ in the logistic and [0.480, 0.530] h⁻¹ in the linear case.

doi: https://doi.org/10.1371/journal.pcbi.1009223.g013