The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter estimation. The key idea is to consider the Bayes factor as a function of the parameter value under the null hypothesis. This 'Bayes factor function' is inverted to obtain point estimates ('maximum evidence estimates') and interval estimates ('support intervals'), similar to how P-value functions are inverted to obtain point estimates and confidence intervals. This provides data analysts with a unified inference framework as Bayes factors (for any tested parameter value), support intervals (at any level), and point estimates can be easily read off from a plot of the Bayes factor function. This approach shares similarities but is also distinct from conventional Bayesian and frequentist approaches: It uses the Bayesian evidence calculus, but without synthesizing data and prior, and it defines statistical evidence in terms of (integrated) likelihood ratios, but also includes a natural way for dealing with nuisance parameters. Applications to real-world examples illustrate how our framework is of practical value for making quantitative inferences.

翻译：贝叶斯因子作为数据驱动的先验概率与后验概率之比，是两个假设间统计证据的自然度量。我们展示了贝叶斯因子如何同时用于参数估计。关键思想是将贝叶斯因子视为原假设下参数值的函数，通过反转该"贝叶斯因子函数"获得点估计（"最大证据估计"）和区间估计（"支持区间"），这与p值函数反转获得点估计和置信区间的方法类似。这为数据分析师提供了统一的推断框架：通过贝叶斯因子函数图可同时读取贝叶斯因子（针对任意检验参数值）、支持区间（任意置信水平）和点估计。该方法与传统贝叶斯和频率学派方法既相似又不同：它采用贝叶斯证据演算，但无需综合数据与先验信息；它基于（整合）似然比定义统计证据，同时包含处理冗余参数的自然方式。实际案例应用表明该框架对定量推断具有实践价值。