Independence for full conditional probabilities: Structure, factorization, non-uniqueness, and Bayesian networks

Fabio G. Cozman

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

This paper examines concepts of independence for full conditional probabilities; that is, for set-functions that encode conditional probabilities as primary objects, and that allow conditioning on events of probability zero. Full conditional probabilities have been used in economics, in philosophy, in statistics, in artificial intelligence. This paper characterizes the structure of full conditional probabilities under various concepts of independence; limitations of existing concepts are examined with respect to the theory of Bayesian networks. The concept of layer independence (factorization across layers) is introduced; this seems to be the first concept of independence for full conditional probabilities that satisfies the graphoid properties of Symmetry, Redundancy, Decomposition, Weak Union, and Contraction. A theory of Bayesian networks is proposed where full conditional probabilities are encoded using infinitesimals, with a brief discussion of hyperreal full conditional probabilities. © 2013 Elsevier Inc. All rights reserved.
Original languageAmerican English
Pages (from-to)1261-1278
Number of pages18
JournalInternational Journal of Approximate Reasoning
DOIs
StatePublished - 1 Nov 2013
Externally publishedYes

Fingerprint

Dive into the research topics of 'Independence for full conditional probabilities: Structure, factorization, non-uniqueness, and Bayesian networks'. Together they form a unique fingerprint.

Cite this