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.