Ordinary least squares

Bayesian probability

Bayes factor

Statistics

Bayesian linear regression

Frequentist inference

Bayesian statistics

Computer science

Mathematics

Econometrics

Bayesian inference

Trends in Food Science & Technology

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. 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. 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.

On the pros and cons of Bayesian kinetic modeling in food science