According to the author of SciLua, Stefano Peluchetti:
Should be quite similar to your [Stan's] implementation with some differences in the adaptation strategy.
If you have time to have a look and give it a try I would appreciate your feedback. My website includes the LuaJIT binaries for 3 arches [Windows, Mac OS X, Linux], and the Xsys and Sci libraries needed to run NUTS.
I’ve also been working on a higher-level interface with some test models and datasets (the user can specify a simple script to describe the model, but it’s always Lua syntax, not a custom DSL).
Please notice that multi-pass forward automatic differentiation is used (I experimented with a single-pass, tape based, version but the speed-up was not big and for high-dimensional problems one wants to use reverse diff in any case, on my TODO).
For complex models you might want to increase loopunroll a little, and maybe callunroll as well. Feel free to ask any question.