Abstract
The mathematical models used in predictive microbiology contain parameters that must be estimated based on experimental data. Due to experimental uncertainty and variability, they cannot be known exactly and must be reported with a measure of uncertainty (usually a standard deviation). In order to increase precision (i.e. reduce the standard deviation), it is usual to add extra sampling points. However, recent studies have shown that precision can also be increased without adding extra sampling points by using Optimal Experiment Design, which applies optimization and information theory to identify the most informative experiment under a set of constraints. Nevertheless, to date, there has been scarce contributions to know a priori whether an experimental design is likely to provide the desired precision in the parameter estimates. In this article, two complementary methodologies to predict the parameter precision for a given experimental design are proposed. Both approaches are based on in silico simulations, so they can be performed before any experimental work. The first one applies Monte Carlo simulations to estimate the standard deviation of the model parameters, whereas the second one applies the properties of the Fisher Information Matrix to estimate the volume of the confidence ellipsoids. The application of these methods to a case study of dynamic microbial inactivation, showing how they can be used to compare experimental designs and assess their precision, is illustrated. The results show that, as expected, the optimal experimental design is more accurate than the uniform design with the same number of data points. Furthermore, it is demonstrated that, for some heating profiles, the uniform design does not ensure that a higher number of sampling points increases precision. Therefore, optimal experimental designs are highly recommended in predictive microbiology.
Highlights
Predictive microbiology is nowadays a basic tool in food safety research [1]. It provides mathematical models whose applications include the prediction of the microbial response to environmental conditions, such as those encountered during storage or food processing [2,3,4]
Most of the mathematical models used in predictive microbiology are parametric models, with unknown parameter values that have to be estimated using experimental data
Accuracy is understood as model predictions being unbiased with respect to the actual values, whereas precision refers to their spread [9]
Summary
Predictive microbiology is nowadays a basic tool in food safety research [1] It provides mathematical models whose applications include the prediction of the microbial response to environmental conditions, such as those encountered during storage or food processing [2,3,4]. Another use of predictive models is inference, where the response to different bacteria is compared in order to, for instance, identify the most resistant bacterial strain to some treatment [5,6]. Precision can be quantified using some measure of uncertainty, for instance, the standard deviation of model parameters
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