Recovering from Selection Bias in Causal and Statistical Inference
Elias Bareinboim, Jin Tian, Judea Pearl
Abstract
Selection bias is caused by preferential exclusion of units from the samples and represents a major obstacle to valid causal and statistical inferences; it cannot be removed by randomized experiments and can rarely be detected in ei-ther experimental or observational studies. In this paper, we provide complete graphical and algorithmic conditions for recovering conditional probabilities from selection biased data. We also provide graphical conditions for recoverabil-ity when unbiased data is available over a subset of the vari-ables. Finally, we provide a graphical condition that gener-alizes the backdoor criterion and serves to recover causal ef-fects when the data is collected under preferential selection.