Dear Johannes,
I just came across a paper by Bhattarai, Lee and Park “Policy regimes, policy shifts, and U.S. business cycles” in the ReStat. They write in footnote 24:
“Moreover, note that although we estimate the model conditional on one policy regime at a time, it is possible to construct an unconditional posterior distribution of the parameters across all three policy regimes. This requires specifying a prior distribution over the policy regimes and then sampling from the posterior distribution of the parameters conditional on each policy regime, according to the posterior distribution over the policy regimes.”
I am not sure that I understand their procedure fully, especially how they computed the marginal likelihoods in table 2. But I also do not understand it wrt to your above answer. Different policy regimes are just different priors, that is at least what I think they do, using different priors. Could you maybe put your remark in context or give a brief idea why Bhattarai don’t simply compare the log data density?
Thanks so much!