A unified study on brain connectivity using statistical methods

概率条件独立性是建立统计因果模型的关键，我们建立了一个处理概率条件独立性的代数框架，称为凯恩代数。结果表明，Cain代数与梯形群和分离群都是一致的。此外，我们定义了一种称为该隐多项式的新类型的多项式，并证明了用该隐多项式定义的统计模型可以用该凯恩多项式的工具来推导。

Probabilistic conditional independence (PCI) is a key for building statistical causal models, and we established an algebraic framework called the cain algebra for dealing with PCI. It is shown that the cain algebra is consistent with both the graphoid and the separoid. Further, we defined a new type of polynomials called the cain polynomials and showed that statistical models defined in terms of cain polynomials may be derived using tools of the cain polynomials.