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A universal algebraic approach for conditional independence

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Abstract

In this paper we show that elementary properties of joint probability density functions naturally induce a universal algebraic structure suitable for studying probabilistic conditional independence (PCI) relations. We call this algebraic system the cain. In the cain algebra, PCI relations are represented in equational forms. In particular, we show that the cain satisfies the axioms of the graphoid of Pearl and Paz (Advances in artificial intelligence. North-Holland, Amsterdam, 1987) and the separoid of Dawid (Ann. Math. Artif. Intell. 32:335–372, 2001), these axiomatic systems being useful for general probabilistic reasoning.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Graduate School of Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, 263-8522, Japan

    Jinfang Wang

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  1. Jinfang Wang
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Correspondence to Jinfang Wang.

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This article was submitted to “Special Section on Algebraic Methods in Computational Statistics”.

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Wang, J. A universal algebraic approach for conditional independence. Ann Inst Stat Math 62, 747–773 (2010). https://doi.org/10.1007/s10463-010-0278-5

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  • DOI: https://doi.org/10.1007/s10463-010-0278-5

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