License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2018.141
URN: urn:nbn:de:0030-drops-91456
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9145/
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Staton, Sam ; Stein, Dario ; Yang, Hongseok ; Ackerman, Nathanael L. ; Freer, Cameron E. ; Roy, Daniel M.

The Beta-Bernoulli process and algebraic effects

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Abstract

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.

BibTeX - Entry

@InProceedings{staton_et_al:LIPIcs:2018:9145,
  author =	{Sam Staton and Dario Stein and Hongseok Yang and Nathanael L. Ackerman and Cameron E. Freer and Daniel M. Roy},
  title =	{{The Beta-Bernoulli process and algebraic effects}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{141:1--141:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9145},
  URN =		{urn:nbn:de:0030-drops-91456},
  doi =		{10.4230/LIPIcs.ICALP.2018.141},
  annote =	{Keywords: Beta-Bernoulli process, Algebraic effects, Probabilistic programming, Exchangeability}
}

Keywords: Beta-Bernoulli process, Algebraic effects, Probabilistic programming, Exchangeability
Collection: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue Date: 2018
Date of publication: 04.07.2018

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