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URN: urn:nbn:de:0030-drops-84714
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A Type Theory for Probabilistic and Bayesian Reasoning

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Abstract

This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes our probabilistic type theory from quantum type theory, namely the bijective correspondence between predicates and side-effect free actions (called instrument, or assert, maps). The paper shows how suitable computation rules can be derived from this predicate-action correspondence, and uses these rules for calculating conditional probabilities in two well-known examples of Bayesian reasoning in (graphical) models. Our type theory may thus form the basis for a mechanisation of Bayesian inference.

BibTeX - Entry

@InProceedings{adams_et_al:LIPIcs:2018:8471,
  author =	{Robin Adams and Bart Jacobs},
  title =	{{A Type Theory for Probabilistic and Bayesian Reasoning}},
  booktitle =	{21st International Conference on Types for Proofs and Programs (TYPES 2015)},
  pages =	{1:1--1:34},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-030-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{69},
  editor =	{Tarmo Uustalu},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8471},
  URN =		{urn:nbn:de:0030-drops-84714},
  doi =		{10.4230/LIPIcs.TYPES.2015.1},
  annote =	{Keywords: Probabilistic programming, probabilistic algorithm, type theory, effect module, Bayesian reasoning}
}

Keywords: Probabilistic programming, probabilistic algorithm, type theory, effect module, Bayesian reasoning
Seminar: 21st International Conference on Types for Proofs and Programs (TYPES 2015)
Issue date: 2018
Date of publication: 15.03.2018


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