On the pros and cons of Bayesian kinetic modeling in food science. (May 2020) - van Boekel, M.A.J.S.
Abstract: Background: Kinetics is an important part of food science and statistics is a necessary key element in modeling. Ordinary least-squares (OLS) regression is mostly used to obtain parameter estimates and their uncertainties; this is done within the frequentist framework. Scope and approach: This article introduces Bayesian statistics as an alternative to OLS. The background of Bayesian statistics is briefly explained, emphasizing the difference with the frequentist approach. Basically, frequentists go for the probability of data given a hypothesis, resulting in point estimates, while Bayesians go for the probability of a hypothesis given the data, resulting in probability distributions for parameters. This study shows how to apply the Bayesian approach to kinetic problems using freely available R packages. To focus on the Bayesian approach, the kinetic problem presented is a trivial zero-order reaction concerning the formation of furan in a soy sauce. Key findings and conclusions: The main result is numerical and graphical output showing probability distributions of parameters. Interpretation of regression results is shown leading to the conclusion that the Bayesian approach yields a more intuitive result with richer information than the conventional OLS approach. The pros and cons of the Bayesian approach are highlighted, the major pro being the intuitive and informative result and the major con that one has to learn and apply a programming language like R or Python. The Bayesian approach is very general and the outline shown here can be applied easily to much more complicated kinetic models. Highlights: It is shown how to deal rigorously with uncertainty in regression problems applied to kinetics. Ordinary least squares regression is compared with Bayesian regression. The pros and cons of Bayesian regression are discussed. The advantages of Bayesian regression are illustrated.