Graphoid properties of epistemic irrelevance and independence

DOI10.1007/s10472-005-9004-zzbMath1097.68128OpenAlexW2073989874MaRDI QIDQ819940

Fabio G. Cozman, Peter Walley

Publication date: 4 April 2006

Published in: Annals of Mathematics and Artificial Intelligence (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10472-005-9004-z

zbMATH Keywords

conditional independenceimprecise probabilityepistemic independencelower previsioncredal setgraphoid axioms

Mathematics Subject Classification ID

Logics of knowledge and belief (including belief change) (03B42) Probability and inductive logic (03B48) Reasoning under uncertainty in the context of artificial intelligence (68T37) Graph theory (05C99) Axioms; other general questions in probability (60A05)

Related Items (23)

Epistemic irrelevance on sets of desirable gambles ⋮ DAG representation of asymmetric independence models arising in coherent conditional possibility theory ⋮ An Algorithm to Find a Perfect Map for Graphoid Structures ⋮ Bruno de Finetti and imprecision: imprecise probability does not exist! ⋮ Probabilistic logic with independence ⋮ Graphical models for imprecise probabilities ⋮ Credal networks under epistemic irrelevance ⋮ Computing lower and upper expectations under epistemic independence ⋮ Sets of probability distributions, independence, and convexity ⋮ On extreme points of p-boxes and belief functions ⋮ Epistemic irrelevance in credal nets: the case of imprecise Markov trees ⋮ Acyclic directed graphs representing independence models ⋮ Subjective causal networks and indeterminate suppositional credences ⋮ Independent natural extension ⋮ Robust optimization approximation for ambiguous P-model and its application ⋮ Credal networks under epistemic irrelevance: the sets of desirable gambles approach ⋮ Independent products in infinite spaces ⋮ Graphoid properties of concepts of independence for sets of probabilities ⋮ Conditional independence structure and its closure: inferential rules and algorithms ⋮ Coherent choice functions under uncertainty ⋮ Probability logic, logical probability, and inductive support ⋮ A survey of the theory of coherent lower previsions ⋮ Asymmetric decomposability and persegram representation in coherent conditional probability theory

Uses Software

• Separoids
• TETRAD

Cites Work

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• Probabilistic logic
• Axioms of causal relevance
• Towards a frequentist theory of upper and lower probability
• Dilation for sets of probabilities
• Semigraphoids and structures of probabilistic conditional independence
• Credal networks
• Epistemic independence for imprecise probabilities
• Direct algorithms for checking consistency and making inferences from conditional probability assessments
• On two pseudo-paradoxes in Bayesian analysis
• Separoids: a mathematical framework for conditional independence and irrelevance
• Fundamental concepts of qualitative probabilistic networks
• Identifying independence in bayesian networks

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