Including experimental uncertainty on the independent variables when modelling microbial dynamics: The combined effect of pH and acetic acid on the growth rate of E. coli K12

Modelling methods applied in predictive microbiology generally neglect the importance of uncertainty on the measurement of the independent variables. The Ordinary Least Squares (OLS) method that is commonly applied in predictive microbiology is only applicable if the experimental error on the inputs of the model are insignificant. However, this does not apply for many types of experimental measurements of the independent variables. Therefore, a parameter estimation method was adapted in this research for the estimation of the parameters of secondary models, taking into account uncertainty on the measurement of the influencing food characteristics. This parameter estimation method was based on the work of Stortelder (1996) and is referred to as the Weighted Total Least Squares method (WTLS). The method is formulised as an extension of the commonly used OLS method. Consequently the current WTLS method (i) is easily implemented using similar numerical methods, (ii) reduces to an OLS method when the measurement error on the model inputs is negligible and (iii) enables the evaluation of the accuracy of the model parameter estimates based on the same approximations.