Graphical Models for Inference with Missing Data

We address the problem of recoverability i.e. deciding whether there exists a con-sistent estimator of a given relation Q, when data are missing not at random. We employ a formal representation called ‘Missingness Graphs ’ to explicitly portray the causal mechanisms responsible for missingness and to encode dependencies between these mechanisms and the variables being measured. Using this represen-tation, we derive conditions that the graph should satisfy to ensure recoverability and devise algorithms to detect the presence of these conditions in the graph.