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Maximum possible Bayes Factor

I've been doing bayesian repeated measures ANOVA, where I take a number of samples of 900.000 (as to have as little error as possible). I use the standard priors, as I want to include that I think all models are equally likely to explain the data. I have 3 levels for my RM Factor and another between-factor of 2 levels.
Calculating the Bayes Factors for all possible models compared to the null model, it shows me bayes factors of 50 million big? Is that possible?

Comments

  • If you have a large effect, or a small effect but with large sample size, BFs can be huge. Even with N=1, you can get a BF of infinity. Example: toss a coin; H0 says theta = 1 (i.e., coin has heads on both sides); throw the coin once and observe tails.

  • Alright, thanks, was a bit worried.
    So, would it be correct to say; if I have 2 experiments, one with a BF10 of 100 (very strong evidence for model 1) and then in another replication experiment, a BF10 of 1 million; that the replication experiment provides even much stronger evidence for model 1 than the original experiment?
    Because Jeffreys' rules only go to a value of 100, so was wondering how you distinguish the amount of evidence by a BF10 of 100 and a BF10 of 1 million for example. Or can you not really distinguish between such high values of a BF10 and do they all show an equal amount of 'very strong evidence'?
    I'm pretty new at BF so that's why the stupid questions.

  • Hi Caeline,
    Yes, that's correct. There are no verbal guidelines for BF10's of 1 million. You might invent your own category -- I usually call BF's in that range "overwhelming". In general though, the verbal labels are just heuristics, and the real value is in the numbers themselves.
    E.J.

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