@paul.buerkner has provided the proof that evidence ratio for directed hypotheses, e.g., p(\theta>0)/p(\theta<0), is equivalent to a Bayes factor (https://github.com/paul-buerkner/brms/issues/311).
I wonder whether it is legitimate to interpret such kind of posterior ratios in a fashion similar to BF? For example, can one interpret a ratio of 5 as a “moderate” evidence or a ratio of 12 as a “strong” evidence favoring p(\theta>0)?
Could someone revive this topic? I have also been looking for a clear answer to the question of interpretation of evidence ratios. Which ER values would be considered weak, moderate and strong evidence?
My take is that, given that a directional Bayesian hypothesis test closely corresponds to frequentist p-values (see Fig 4 here Frontiers | Indices of Effect Existence and Significance in the Bayesian Framework | Psychology), it would be “safe” to say (assuming this is a one-directional hypothesis) that an evidence ratio of 19 (which is 0.95/0.05) is “strong”. If the directional hypothesis test is actually a two-directional test (by which I mean you would flip the direction of the test, > or <, in order to ensure an evidence ratio > 1), then the corresponding “strong” threshold would be 39 (which is 0.975/0.025). In the end, it’s all qualitative and subjective, but these seem like reasonable guidelines which more-or-less correspond to thresholds people are familiar with.