The Gibbs sampler for the horseshoe prior does not work on the conditional distributions found in the model, but on the conditional distributions of a transformed version of the model.
In particular, it exploits the fact that a half-Cauchy distribution can be intepreted as a mixture of inverse-gamma distributions, and that if $Z \sim \operatorname{InvGamma}(1, a)$ then $Z \sim 1 / \operatorname{Exp}(a)$.
We should instead implement these relations and update construct_samplers so it finds this structure and builds the sampling steps for each variable in the original model expression.
The Gibbs sampler for the horseshoe prior does not work on the conditional distributions found in the model, but on the conditional distributions of a transformed version of the model.
In particular, it exploits the fact that a half-Cauchy distribution can be intepreted as a mixture of inverse-gamma distributions, and that if $Z \sim \operatorname{InvGamma}(1, a)$ then $Z \sim 1 / \operatorname{Exp}(a)$.
We should instead implement these relations and update
construct_samplersso it finds this structure and builds the sampling steps for each variable in the original model expression.Related to #46, #65