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I have run a series of Bayesian models with flat priors in which I obtain a posterior probability distribution for my coefficient of interest. The reviewer of my paper wishes us to classify these probability according to different strengths of evidences (strong, moderate, weak etc..). I have seen this done with Bayes factor, e.g., Lee and Wagenmakers' classification

I wish to avoid running the models with and without the coefficient. Instead, I thought I could compare the posterior and prior probability. However, I have uninformative priors so I think Bayes factor would not work(?). But I wonder whether I can still follow this classification, e.g., under the null prior, I expect 50% of the coefficient to be negative. While my posterior probability is 5%. From that, can I infer a Bayes factor of 10 (0.5/0.05), which would be strong evidence?

Or is there another classification scheme I could use?

Thanks for any help and especially any references?

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  • $\begingroup$ These formal wording schemes are problematic, in fact more for Bayesian inference than for p-values. The thing with the Bayes factor is that in general you can easily have a high Bayes factor for something that still has a low posterior (because it had a low prior to begin with, which in general may have been chosen based on good reliable information). Should you say "there's strong evidence for XXX" if it's posterior probability is, say, 0.08? I don't think so. $\endgroup$ Jan 9, 2020 at 14:45
  • $\begingroup$ I'd probably say that there's a strong indication (95%) that the coefficient is positive, and refuse to play the reviewer's evidence game, but of course this is risky; your call to make. $\endgroup$ Jan 9, 2020 at 14:46
  • $\begingroup$ I wonder if anyone has new thoughts/evidence on this? $\endgroup$
    – Jacob
    Aug 12, 2023 at 1:45

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