2.1 Probabilistic programming

Bayesian statistics is conceptually very simple. We have the knowns and the unknowns, and we use Bayes’ theorem to condition the latter on the former. If we are lucky, this process will reduce the uncertainty about the unknowns. Generally, we refer to the knowns as data and treat it like constants, and the unknowns as parameters and treat them as random variables.

Although conceptually simple, fully probabilistic models often lead to analytically intractable expressions. For many years, this was a real problem and one of the main issues that hindered the adoption of Bayesian methods beyond some niche applications. The arrival of the computational era and the development of numerical methods that, at least in principle, can be used to solve any inference problem, have dramatically transformed the Bayesian data analysis practice. We can think of these numerical methods as universal inference engines. The possibility of automating the inference process...