| Causality is very common relation existed in reality. In statistics, we focus on correlation in many situations. But with the emergence of Simpson paradox, the shortcoming of correlation began to be recognized. In our paper, three different methods will be used to estimate the causal effect.In causal-diagram, variables have effects on response variable. And we choose to make the variance of response variable under controlling different variables to be minimum. We introduce causal-diagram, some corresponding notion and the linear structural equation. Under normal assumption we eval-uate mean and variance of the causal-effect. But in reality, we only have the observed data and lack of the real value. We calculate the asymptotic variance of the variance estimator under large sample, and use it as our selection of vari-able criterion.Afterwards, we change our discussion of covariable selection under dis-crete distribution. Here, the assumption is multinomial distribution. Under controlling confounder, some variable become non-confounder. Then we prove that the controlling of non-confounder will increase the variance of the causal-effect.Then we discuss the effect of experiment about random trial. We use Bayesian model. For convenience, we introduce that principle stratification, then the complicated posterior distribution will be simplified and obtain the es-timator of the average causal-effect and the corresponding variance or Interval estimation of this estimation. |
