I have a question concerning tests between a large control cohort and a smaller number of cases in a simple comparison. In particular I was wondering about the differences of baysian and frequentists approaches. The question is partly inspired by this recent question.
So lets say I have $n_a=10000$ and $n_b=10$ with $p$ variables and I suspect that difference between $n_b$ and $n_a$ is quite large.
As far as I know power, under the frequentist framework, is limited by the "strength" of the smallest sample size. So I would assume that, even with a relative large effect, I might be still unable to observe a significant p-value.
But what is the effect in a bayesian framework? How does my prior relate to sample size under this situation?
