Have Stan developers considered HINTS ? I fell that it’s an overly-obscure algorithm that obeys detailed balance, is efficient at sampling the typical set and doesn’t require gradients. It’s therefore a potentially useful augmentation to Stan: motivated by the potential to do efficient inference where gradients are not readily calculated (eg for large discrete spaces), we are working to implement HINTS and will also add it as a sibling to NUTS in Stan in the hope that doing so would be useful.
See here for the paper:
I’ll be fascinated to understand Stan developers’ thoughts and comments.
 Malcolm Strens. “Efficient hierarchical MCMC for policy search.” Proceedings of the twenty-first international conference on Machine learning . ACM, 2004.