This PR: [WIP] Add givens argument to DensityDist by OriolAbril · Pull Request #4433 · pymc-devs/pymc3 · GitHub will probably be interesting to people following this thread. I have not used DensityDist much so feedback will be appreciated.
Also, if someone is able to run the original blackbox likelihood notebook with the cython code, their help will be welcome at GitHub - pymc-devs/pymc-examples: Examples of PyMC3 models, including a library of Jupyter notebooks.