Separoids: A Mathematical Framework for Conditional Independence and Irrelevance. We introduce an axiomatic definition of a mathematical structure that we term a separoid. We develop some general mathematical properties of separoids and related axiom systems, as well as connections with other mathematical structures, such as distributive lattices, Hilbert spaces, and graphs. And we show, by means of a detailed account of a number of models of the separoid axioms, how the concept of separoid unifies a variety of notions of ‘irrelevance’ arising out of different formalisms for representing uncertainty in Probability, Statistics, Artificial Intelligence, and other fields.

References in zbMATH (referenced in 21 articles )

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  1. Córdoba, Irene; Bielza, Concha; Larrañaga, Pedro: A review of Gaussian Markov models for conditional independence (2020)
  2. Fritz, Tobias: A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics (2020)
  3. Mogensen, Søren Wengel; Hansen, Niels Richard: Markov equivalence of marginalized local independence graphs (2020)
  4. Studený, Milan: Contribution of František Matúš to the research on conditional independence. (2020)
  5. Cho, Kenta; Jacobs, Bart: Disintegration and Bayesian inversion via string diagrams (2019)
  6. Oates, Chris J.; Smith, Jim Q.; Mukherjee, Sach: Estimating causal structure using conditional DAG models (2016)
  7. Byrne, Simon; Dawid, A. Philip: Structural Markov graph laws for Bayesian model uncertainty (2015)
  8. Lopatatzidis, Stavros; van der Gaag, Linda C.: Computing concise representations of semi-graphoid independency models (2015)
  9. Li, Benchong; Cai, Shoufeng; Guo, Jianhua: A computational algebraic-geometry method for conditional-independence inference (2013)
  10. Cozman, Fabio G.: Sets of probability distributions, independence, and convexity (2012)
  11. Baioletti, Marco; Busanello, Giuseppe; Vantaggi, Barbara: Exploiting independencies to compute semigraphoid and graphoid structures (2011)
  12. Wang, Jinfang: Computation of conditional independence using cain polynomials (2011)
  13. Dawid, A. Philip; Didelez, Vanessa: Identifying the consequences of dynamic treatment strategies: a decision-theoretic overview (2010)
  14. Smith, Jim Q.: Bayesian decision analysis. Principles and practice. (2010)
  15. Wang, Jinfang: A universal algebraic approach for conditional independence (2010)
  16. Baioletti, Marco; Busanello, Giuseppe; Vantaggi, Barbara: Conditional independence structure and its closure: inferential rules and algorithms (2009)
  17. Cozman, Fabio G.; Walley, Peter: Graphoid properties of epistemic irrelevance and independence (2006)
  18. Zaffalon, Marco (ed.); de Cooman, Gert (ed.): Special issue: Imprecise probability perspectives on artificial intelligence. Selected papers based on the presentation at the 2nd international symposium on imprecise probabilities and their applications (ISIPTA ’01), Ithaca, NY, USA, June 26--29, 2001 (2006)
  19. Ben Yaghlane, Boutheina; Smets, Philippe; Mellouli, Khaled: Belief function independence. II: The conditional case. (2002)
  20. Studený, Milan: On stochastic conditional independence: The problems of characterization and description (2002)

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