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I am just starting to look at Bayesian statistics and so far I am aware that Bayes factor summarizes some form of evidence of an alternative hypothesis against the null one.

As far as I know we can compare two competing models that use the same data, but is it not possible in any way to apply it to A/B testing?

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You can always think about your data as about a single set. In A/B testing it just happens that part of your dataset is related only to the method A and the other part is related only to the method B.

I'd suggest to take a look at: https://nbviewer.jupyter.org/github/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/blob/master/Chapter2_MorePyMC/Ch2_MorePyMC_PyMC3.ipynb#Example:-Bayesian-A/B-testing

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