A tutorial on uncertainty propagation techniques for predictive microbiology models: A critical analysis of state-of-the-art techniques

Building mathematical models in predictive microbiology is a data driven science. As such, the experimental data (and its uncertainty) has an influence on the final predictions and even on the calculation of the model prediction uncertainty. Therefore, the current research studies the influence of both the parameter estimation and uncertainty propagation method on the calculation of the model prediction uncertainty. The study is intended as well as a tutorial to uncertainty propagation techniques for researchers in (predictive) microbiology. To this end, an in silico case study was applied in which the effect of temperature on the microbial growth rate was modelled and used to make simulations for a temperature profile that is characterised by variability. The comparison of the parameter estimation methods demonstrated that the one-step method yields more accurate and precise calculations of the model prediction uncertainty than the two-step method. Four uncertainty propagation methods were assessed. The current work assesses the applicability of these techniques by considering the effect of experimental uncertainty and model input uncertainty. The linear approximation was demonstrated not always to provide reliable results. The Monte Carlo method was computationally very intensive, compared to its competitors. Polynomial chaos expansion was computationally efficient and accurate but is relatively complex to implement. Finally, the sigma point method was preferred as it is (i) computationally efficient, (ii) robust with respect to experimental uncertainty and (iii) easily implemented.