A Type Theory for Probabilistic and Bayesian Reasoning
Paper i proceeding, 2018

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.

Probabilistic programming

Bayesian reasoning

effect module

probabilistic algorithm

type theory

Författare

Bart Jacobs

Radboud Universiteit

Robin Adams

Chalmers, Data- och informationsteknik, Datavetenskap

Leibniz International Proceedings in Informatics (LIPIcs)

1868-8969 (ISSN)

Vol. 69 1 1-34

21st International Conference on Types for Proofs and Programs, TYPES 2015
Talinn, Estonia,

Ämneskategorier

Algebra och logik

Sannolikhetsteori och statistik

Datavetenskap (datalogi)

Styrkeområden

Informations- och kommunikationsteknik

Fundament

Grundläggande vetenskaper

DOI

10.4230/lipics.types.2015.1

Mer information

Skapat

2018-08-19