A paper, essentially on using Stan for non-linear/non-Gaussian hierarchical models, is now online at:
The paper is very much in draft form, and any suggestions and comments are very much welcomed.
The paper aims to overcome problems with applying (Euclidian metric) HMC to hierarchical models. The methodology is easily implemented in Stan, and produces potentially large speedups / improved robustness for such models.
The idea is to introduce an explicitly (bijective) computable re-parameterization of the model, in such a manner that the re-parametererized model is easily sampled using Stan. The re-parameterization utilises both information from priors and observations in order to make the sampling problem as easy as possible. The method has similarities with a class of Riemann manifold HMC methods, but allows fully explicit, and thus computationally fast, sampling.