I am trying to understand how Bayesian inference works, so this might be a very simple question. I have an experiment where I test two hypotheses predicting opposite results. Let’s say, hypothesis 1 (H1) predicts that x > 0, and hypothesis 2 (H2) predicts that x < 0.
I calculated Bayes factor with informed priors (positive and negative half-normals for H1 and H2 respectively) for two hypotheses. BF10 for the H1 was 0.04, and BF10 for the H2 was 0.13. In other words, both results indicate that I have to believe more in H0 than in any of two alternative hypotheses.
However, if I still want to make some inference on H1 and H2, can I just
divide BF10(for H2) by BF10(for H1)? This ratio (it will Bayes Factor too, right?) will be
0.13 / 0.04 = 3.25. Does this result tell me that I have to increase my belief in H2 compared to H1?