Date: December 3, 2019
Location: Rockefeller Hall 307
Title: Two criteria for prior choice in Bayesian two-sample testing
We propose two criteria for prior choice in two-sample testing which have a common starting point: a hypothetical situation where we attain perfect knowledge about one of the groups. The first criterion is based on a limiting argument where the sample size of one of the groups grows to infinity. The second criterion is based upon conditioning on the true value of the parameters for one of the groups.
In such scenarios, two-sample tests should arguably behave like one-sample tests where the distribution of one of the groups is known. In the context of testing equality of 2 normal means, we find explicit examples where two-sample tests don't behave like one-sample tests after obtaining perfect knowledge about one of the groups. We see this as evidence to "reject" certain prior specifications and favor others that don't exhibit this behavior.