Background

Kinetics is an important part of food science and statistics is a necessary key element in modelling. 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.

中文翻译：

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食品科学中贝叶斯动力学建模的利弊

背景

动力学是食品科学的重要组成部分，而统计学是建模的必要关键要素。普通最小二乘（OLS）回归通常用于获取参数估计值及其不确定性。这是在常客框架内完成的。

范围和方法

本文介绍了贝叶斯统计量作为OLS的替代方法。简要解释了贝叶斯统计的背景，并强调了与频偏方法的区别。基本上，常客使用给定假设的数据概率，从而得出点估计值，而贝叶斯主义者则求出给定数据的假设概率，从而得出参数的概率分布。这项研究显示了如何使用免费提供的R包将贝叶斯方法应用于动力学问题。为了关注贝叶斯方法，提出的动力学问题是一个与酱油中呋喃的形成有关的零级琐碎反应。

主要发现和结论

主要结果是数值和图形输出，显示了参数的概率分布。显示了对回归结果的解释，得出的结论是，与传统的OLS方法相比，贝叶斯方法具有更直观的结果，并且具有更丰富的信息。强调了贝叶斯方法的优缺点，主要优点是直观和有益的结果，而主要缺点是必须学习和应用R或Python等编程语言。贝叶斯方法非常笼统，此处显示的轮廓可以轻松地应用于更为复杂的动力学模型。