A universal algebraic approach for conditional independence

作者：Wang Jinfang^*

来源：Annals of the Institute of Statistical Mathematics, 2010, 62(4): 747-773.

DOI：10.1007/s10463-010-0278-5

• Cain
• Conditional independence
• Graphical model
• Graphoid
• Probability density function
• Separoid

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.

• 出版日期2010-8