Both the Bayes factor and the relative belief ratio satisfy the principle of evidence and so can be seen to be valid measures of statistical evidence. Certainly Bayes factors are regularly employed. The question then is: which of these measures of evidence is more appropriate? It is argued here that there are questions concerning the validity of a current commonly used definition of the Bayes factor based on a mixture prior and, when all is considered, the relative belief ratio has better properties as a measure of evidence. It is further shown that, when a natural restriction on the mixture prior is imposed, the Bayes factor equals the relative belief ratio obtained without using the mixture prior. Even with this restriction, this still leaves open the question of how the strength of evidence is to be measured. It is argued here that the current practice of using the size of the Bayes factor to measure strength is not correct and a solution to this issue is presented. Several general criticisms of these measures of evidence are also discussed and addressed.

翻译：贝叶斯因子和相对信念比均满足证据原则，因此可被视为有效的统计证据度量方法。贝叶斯因子无疑是常用的衡量标准。那么问题在于：哪种证据度量更合适？本文论证了当前基于混合先验的贝叶斯因子常用定义存在有效性问题，且综合考虑下，相对信念比作为证据度量具有更优性质。进一步研究表明，当对混合先验施加自然约束时，贝叶斯因子等于未使用混合先验获得的相对信念比。即使采用此约束，如何衡量证据强度的问题仍悬而未决。本文指出现行通过贝叶斯因子大小度量强度的做法并不正确，并提出了该问题的解决方案。此外，还讨论并回应了针对这些证据度量的若干普遍性质疑。