2024/03/14 by Samuel Pawel, Pawel, Samuel
Engineering · #FOS: Computer and information sciences #Fault Detection and Control Systems #Methodology (stat.ME)
paper · pdf · doi:10.48550/arxiv.2403.09350
openalex publication_date 2024/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 `support curve' 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 support curve. 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 meta-analysis, replication studies, and logistic regression illustrate how our framework is of practical value for making quantitative inferences.