Graphical Models for Inference with Missing Data
We address inference problems associated with missing data using causal Bayesian networks to model the data generation process. We show that procedures based on graphical models can overcome limitations of conventional missing data methods and provide meaningful performance guarantees even when data are Missing Not At Random (MNAR). In particular, we identify conditions that guarantee consistent estimation of parameters of interest in broad categories of missing data problems, and derive procedures for implementing this estimation. We derive testable implications for missing data problems in both MAR (Missing At Random) and MNAR categories. Finally, we apply these techniques to develop a suite of algorithms for closed form estimation of Bayesian network parameters.