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Missing data has the potential to affect analyses conducted in all fields ofscientific study, including healthcare, economics, and the social sciences.Several approaches to unbiased inference in the presence of non-ignorablemissingness rely on the specification of the target distribution and itsmissingness process as a probability distribution that factorizes with respectto a directed acyclic graph. In this paper, we address the longstandingquestion of the characterization of models that are identifiable within thisclass of missing data distributions. We provide the first completeness resultin this field of study -- necessary and sufficient graphical conditions underwhich, the full data distribution can be recovered from the observed datadistribution. We then simultaneously address issues that may arise due to thepresence of both missing data and unmeasured confounding, by extending thesegraphical conditions and proofs of completeness, to settings where somevariables are not just missing, but completely unobserved.

Full Law Identification In Graphical Models Of Missing Data: Completeness Results