During the last few years, probabilistic programming frameworks (PPF), such as Stan, Pyro, and Turing, have become a new important tool for probabilistic machine learning and Bayesian statistics. Using PPFs, new and complex models can be freely specified and estimated using general inference algorithms such as Hamiltonian Monte Carlo (HMC) and variational inference. Although, there are still areas that limit the usability of PPF. This include (1) difficulties with the generality and efficiency of HMC, especially for models using discrete parameters, (2) the lack of tools and diagnostics to identify and remedy complex posterior geometries, and (3) efficient methods to evaluate the generality of new proposed general inference algorithms. This project will address these issues to further enable PPF as a tool for general statistical inference and probabilistic machine learning.