A model like that should run just fine on a cpu with nuts, if it is slow I’d look into the parametrization a bit. Your prior for sigma_w is a bit strange by the way, are you sure want to set beta to 100? If so, maybe normalize the data and set it so something like 2.5 instead.
You can also try the development version (or the soon to be released rc). We made some changes to the initialisation of nuts which might help here.