wlandau
commented
1 year ago I will start by adding an optional l_tau hyper parameter to control the lower bound of the uniform prior on tau. Then different versions of the hierarchical model can be compared by setting different hyperparameters. Pooling should happen when l_tau is 0 and s_tau is close to 0, and borrowing should mostly disappear when l_tau and s_tau are very high. By using hbl_mcmc_hierarchical() with these hyperparameters instead of hbl_mcmc_pool() or hbl_mcmc_independent(), we will hopefully achieve a more direct apples-to-apples comparison because the dimensionality of the 3 models will agree.
On some datasets, the hierarchical model marginal posteriors are sometimes not strictly between those of the independent and pooled models. I think there may be a refactor which makes all these models more directly comparable.