Causal effects of mathematics

The Mathematics of Causal Relations

These advances are central to the empirical sciences because the research questions that motivate most studies in the health, social, and behavioral sciences are not statistical but causal in nature. For example, what is the efficacy of a given drug in a given population? Can data prove an employer guilty of hiring discrimination? What fraction of past crimes could have been avoided by a given ...

The Mathematics of Causal Inference in Statistics

The \potential outcome," or Neyman-Rubin (NR) model through which statisticians were rst introduced to causal analysis suuers from two fundamental shortcomings: (1) It lacks formal underpinning and (2) it uses conceptually opaque language for expressing causal information. As a results, investigators nd it diicult to discern whether a set of formulae represents a faithful picture of one's knowl...

Testing Identifiability of Causal Effects

This paper concerns the probabilistic evalu­ ation of the effects of actions in the presence of unmeasured variables. We show that the identification of causal effect between a sin­ gleton variable X and a set of variables Y can be accomplished systematically, in time polynomial in the number of variables in the graph. When the causal effect is identifiable, a closed-form expression can be obta...

Bounding Causal Effects

Empirical researchers commonly use instrumental variable (IV) assumptions to identify treatment effects. However, the credibility of these assumptions are often questionable. In this paper, we consider what can be learned when the assumptions necessary for point identification are violated in two specific ways. First, we allow the data to be contaminated, meaning that the exclusion restrictions...

On Identifying Causal Effects