  Missing data is a pervasive problem in data analyses, resulting in datasets
that contain censored realizations of a target distribution. Many approaches to
inference on the target distribution using censored observed data, rely on
missing data models represented as a factorization with respect to a directed
acyclic graph. In this paper we consider the identifiability of the target
distribution within this class of models, and show that the most general
identification strategies proposed so far retain a significant gap in that they
fail to identify a wide class of identifiable distributions. To address this
gap, we propose a new algorithm that significantly generalizes the types of
manipulations used in the ID algorithm, developed in the context of causal
inference, in order to obtain identification.
