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.TYPES.2015.1
URN: urn:nbn:de:0030-drops-84714
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8471/
Adams, Robin ;
Jacobs, Bart
A Type Theory for Probabilistic and Bayesian Reasoning
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 |
Collection: |
|
21st International Conference on Types for Proofs and Programs (TYPES 2015) |
Issue Date: |
|
2018 |
Date of publication: |
|
15.03.2018 |