The following is the HMC implemented in stan(.) if I choose to use “HMC” not “NUTS”

The above sampler is for the case of \theta that is assumed to be real (or vector of real numbers).

Interestingly, it seems that stan(.) can also easily sample from a parameter \theta which is, saying, supported on [a,\infty) for some a>0.

What stan do for this??

Certainly, the Gaussian proposal does not work here.

Do stan(.) transform the \theta, via logarithm, appropriately???