The Beta-Bernoulli process and algebraic effects

Authors Sam Staton, Dario Stein, Hongseok Yang, Nathanael L. Ackerman, Cameron E. Freer, Daniel M. Roy

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Author Details

Sam Staton
  • Univ. Oxford
Dario Stein
  • Univ. Oxford
Hongseok Yang
Nathanael L. Ackerman
  • Harvard Univ.
Cameron E. Freer
  • Borelian
Daniel M. Roy
  • Univ. Toronto

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Sam Staton, Dario Stein, Hongseok Yang, Nathanael L. Ackerman, Cameron E. Freer, and Daniel M. Roy. The Beta-Bernoulli process and algebraic effects. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 141:1-141:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


In this paper we use the framework of algebraic effects from programming language theory to analyze the Beta-Bernoulli process, a standard building block in Bayesian models. Our analysis reveals the importance of abstract data types, and two types of program equations, called commutativity and discardability. 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 stochastic processes relevant to Bayesian modelling, yielding new understanding of these processes from the perspective of programming.

Subject Classification

ACM Subject Classification
  • Theory of computation → Probabilistic computation
  • Beta-Bernoulli process
  • Algebraic effects
  • Probabilistic programming
  • Exchangeability


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