10.1 Inference engines

While conceptually simple, Bayesian methods can be mathematically and numerically challenging. The main reason is that the marginal likelihood, the denominator in Bayes’ theorem, usually takes the form of an intractable or computationally expensive integral to solve. For this reason, the posterior is usually estimated numerically using algorithms from the Markov Chain Monte Carlo (MCMC) family. These methods are sometimes called inference engines, because, at least in principle, they are capable of approximating the posterior distribution for any probabilistic model. Even though inference does not always work that well in practice, the existence of such methods has motivated the development of probabilistic programming languages such as PyMC.

The goal of probabilistic programming languages is to separate the model-building process from the inference process to facilitate the iterative steps of model-building, evaluation, and model modification/expansion...