Use of horseshoe prior under complete separation

I am interested in fitting a logistic model with a horseshoe prior as done in the paper “Sparsity information and regularization in the horseshoe and other shrinkage priors” ( I have the following concern, however.

When p > n, there is an issue of complete separation and a posterior will be as heavy-tailed as a prior in some directions. Since a horseshoe prior has a Cauchy-like tail (Carvalho, 2008), it seems to me that posterior means of regression coefficients may not be well-defined.

Let me know if this is an issue and, if not, why that’s the case.

The regularized horseshoe introduced in that paper solves the separation problem. The regularized horseshoe changes the shape of the tail. See more in the paper.


Thank you. It turns out I was reading another 2017 paper of yours (“On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior”). The regularized horseshoe indeed solves the issue.