By Arthur Berg and Vishal Midya (Penn State College of Medicine); Jason Liao (Penn State Cancer Institute)
Plenary speaker at this conference, John Kruschke, has strongly advocated the use of the "region of practical equivalence" (ROPE) for assessing null hypotheses in the Bayesian context. An alternative approach would be to calculate a Bayes factor. In his 2018 article on "The Bayesian New Statistics", Professor Kruschke highlights these two approaches in the context of a shifting emphasis from hypothesis testing (Bayes factor approach) to posterior estimation (ROPE approach). We establish a formal connection between these two approaches with two benefits. First, it helps to better understand and improve the ROPE procedure. Second, it leads to a simple and effective approach for computing the Bayes factor in a wide range of problems using draws from posterior distributions generated by standard Bayesian programs such as BUGS, JAGS and Stan.
Further details of our work have been published on arXiv: https://arxiv.org/abs/1903.03153.