Maximum possible Bayes Factor

Caeline

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?

EJ

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.

Caeline

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.

EJ

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.