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 make quantitative inferences.

翻译：贝叶斯因子作为先验概率比到后验概率比的基于数据的更新因子，是衡量一个假设相对于另一个假设统计证据的自然度量。我们展示了贝叶斯因子同样可用于参数估计。其核心思想是将贝叶斯因子视为原假设下参数值的函数。通过反转这一“贝叶斯因子函数”，可得到点估计（“最大证据估计”）和区间估计（“支持区间”），类似于通过反转P值函数获得点估计和置信区间的方法。这为数据分析人员提供了统一的推断框架：通过贝叶斯因子函数的图形即可直接读取（任何检验参数值的）贝叶斯因子、（任意水平的）支持区间和点估计。该方法与传统贝叶斯方法和频率学派方法既有相似性又有区别：它采用贝叶斯证据演算，但无需合成数据与先验信息；它以（综合）似然比定义统计证据，同时包含处理冗余参数的自然方式。实际应用案例展示了该框架在定量推断中的实践价值。