multiple coins, one mint, bayesian model and bootstrap

Question

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?

Answer 1

I think that in a certain sense it is meaningful. The FDR is a frequentist achievment of a test (relating to the fact that 95% of the confidence intervals will contain the true value). The procedure you mention in your question is a Bayesian one and in general has no reason to provide this property simply because in general the Bayesian credibility interval (or HDI in your question) has no reason to come with the above mentioned frequentist coverage (see From a Bayesian probability perspective, why doesn't a 95% confidence interval contain the true parameter with 95% probability? fore details). So by making the test you mention, you can see in what extend a given Bayesian model has this, sometimes attractive, property.

Notice that there exists the so-called "matching prior" that are priors ensuring the coverage property of Bayesian credibility interval of the associated model.