Stan MCMC is what you should be using to do your analysis. It is robust, fast, and relatively easy to use. It has interfaces with R, Python, Matlab, and Stata. But come on, get with it, you should be using R or Python.
Jim Savage's blog. Includes a lot of nice posts that use Stan in modelling issues in economics, statistics and machine learning applications.
Betancourt is one of the developers of Stan, and he gives good talks explaining what is going on behind the scenes. Spoiler: it involves some 3-d advanced donut geometry