I can surely try. However this is not clear to me, but that’s probably because I focused on understanding the standard Metropolis-Hasting algorithm with a random walk proposal until now and I haven’t take the time to fully understand Gibbs sampling.
I’m going to take sometime to read some references on Gibbs and on NUTS and will come back to you either if I still don’t understand or if I am confident enough in my understanding to write a doc.
Thanks for your answer!