[PyMC3] Make SMC-ABC faster and more flexible

PyMC3 provides state-of-the-art tools to specify rich mathematical probabilistic models and algorithms to efficiently approximate the posterior distribution of such models conditioned on observed data. One such algorithm is the Sequential Monte Carlo (SMC) sampler which is capable of drawing samples from complex posterior distributions (e.g., multimodal distributions).

In addition to traditional Bayesian inference, SMC can also be used to perform Approximate Bayesian Computation (ABC), which allows one to define models without a pure mathematical likelihood term, which is difficult to derive in many complex real world problems. To achieve this, SMC-ABC makes use of a “Simulator” function that is capable of returning simulated observed data given different unobserved parameters.

This project seeks to extend the documentation, performance and flexibility of SMC and SMC-ABC sampling in PyMC3, to make it competitive with specialized libraries while remaining accessible to the large user-base of the PyMC3 library.