The Beta-Bernoulli process and algebraic effects

In this paper we analyze the Beta-Bernoulli process from Bayesian nonparametrics using the framework of algebraic effects from programming language theory. Our analysis reveals the importance of abstract data types, and two types of program equations, called commutativity and discardability, in the study of the Beta-Bernoulli process. We develop an equational theory of terms that use the Beta-Bernoulli process, and show that the theory is complete with respect to the measure-theoretic semantics, and also in the syntactic sense of Post. Our analysis has a potential for being generalized to other Bayesian nonparametric models and helping understand these models from the perspective of programming. Digital Object Identifier 10.4230/LIPIcs..2018.