Construction of a New Algebraic Statistical Theory for StatisticalCausal Inference

条件独立性在统计科学中具有根本的重要性。所有统计模型，如时间序列模型或贝叶斯模型，都是基于条件独立性的某些假设。统计条件独立性也描述了一组随机变量之间的因果关系。本研究的主要目的是用公理化方法研究条件独立性。为了研究统计因果推理，我们构造了一个新的统计代数系统cain。这个系统是基于概率密度函数的基本性质，这对于论证条件独立性是必不可少的。我们进一步建立了一个代数算法，用于导出一组关系，这些关系涉及某些条件独立于其他条件。

Conditional independence is of fundamental importance in statistical sciences. All statistical models, such as time series models or Bayesian models, are based on certain assumptions on conditional independence. Statistical conditional independence also characterizes the causal relations of a set of random variables. The main purpose of this research is to study the conditional independence using an axiomatic approach. We constructed a new statistical algebraic system called cain for studying statistical causal inference. This system is based on the basic properties of probability density functions which are essential for arguing for conditional independence. We further established an algebraic algorithm for deriving a set of relations concerning some conditional independence from other set of such conditions.