School of Physics and Astronomy, Queen Mary University of London, London, E1 4NS, UK.
Sci Rep. 2022 Jan 19;12(1):993. doi: 10.1038/s41598-021-04694-7.
The Bayes factor is the gold-standard figure of merit for comparing fits of models to data, for hypothesis selection and parameter estimation. However, it is little-used because it has been considered to be subjective, and to be computationally very intensive. A simple computational method has been known for at least 30 years, but has been dismissed as an approximation. We show here that all three criticisms are misplaced. The method should be used to complement and augment all least-squares fitting, because it can give very different, and better outcomes than classical methods. It can discriminate between models with equal numbers of parameters and equally good fits to data. It quantifies the Occam's Razor injunction against over-fitting, and it demands that physically-meaningful parameters rejected by classical significance testing be included in the fitting, to avoid spurious precision and incorrect values for the other parameters. It strongly discourages the use of physically-meaningless parameters, thereby satisfying the Occam's Razor injunction to use existing entities for explanation rather than multiplying new ones. More generally, as a relative probability, the Bayes factor combines naturally with other quantitative information to guide action in the absence of certain knowledge.
贝叶斯因子是比较模型与数据拟合度、假设选择和参数估计的黄金标准衡量标准。然而，由于它被认为是主观的，并且计算量非常大，因此很少被使用。至少 30 年来，人们已经知道一种简单的计算方法，但它被认为是一种近似值而被摒弃。我们在这里表明，所有这三个批评都是没有根据的。该方法应该用于补充和增强所有最小二乘拟合，因为它可以提供比经典方法更好的、截然不同的结果。它可以区分具有相同参数数量和对数据具有相同良好拟合度的模型。它量化了奥卡姆剃刀的禁止过度拟合的原则，并要求将经典显著性检验拒绝的具有物理意义的参数包含在拟合中，以避免虚假精度和其他参数的不正确值。它强烈反对使用没有物理意义的参数，从而满足奥卡姆剃刀的原则，即用现有的实体进行解释，而不是增加新的实体。更一般地说，作为一个相对概率，贝叶斯因子与其他定量信息自然结合，在缺乏确定性知识的情况下指导行动。
