Graphoid properties of concepts of independence for sets of probabilities

Fabio Gagliardi Cozman

Research output: Contribution to journalArticlepeer-review

Abstract

We examine several concepts of independence associated with (1) credal sets, understood as sets of probability measures, (2) sets of full conditional probabilities, (3) sets of lexicographic probabilities, and (4) sets of desirable gambles. Concepts of independence are evaluated with respect to the graphoid properties they satisfy, as these properties capture important abstract features of “independence”. We emphasize the analysis of sets of probability measures as this is a popular formalism, looking at versions of epistemic, confirmational, and type-5 independence that are based on regular conditioning, as well as complete and strong independence. We then examine analogous concepts of independence for sets of full conditional probabilities, sets of lexicographic probabilities, and sets of desirable gambles.

Original languageEnglish
Pages (from-to)56-79
Number of pages24
JournalInternational Journal of Approximate Reasoning
Volume131
DOIs
StatePublished - Apr 2021
Externally publishedYes

Keywords

  • Credal sets
  • Epistemic irrelevance and independence
  • Graphoid properties
  • Lexicographic probabilities
  • Sets of desirable gambles

Fingerprint

Dive into the research topics of 'Graphoid properties of concepts of independence for sets of probabilities'. Together they form a unique fingerprint.

Cite this