A hierarchical bayesian model could be used to deduce whether there is the bias for coins from the same mint. One example model could be found here!
Suppose the HDI is (0.56, 0.58), and the ROPE is (0.49, 0.51), then we claim the mint is biased.
I am wondering whether it is beneficial to perform bootstrap and calculate the FDR afterwards. What I mean is that
- simulate the coins data
- redo the bayesian approach
- repeat the above two steps.
Then there will be a measurement of how many times the HDI is not interact with the ROPE, and hence the FDR could be calculated.
The posterior distribution of original data already captures the uncertainty in the data, so is it meaningful to do the bootstrap?