ABSTRACT
Concepts for Bayesian inference for incomplete data began to be formalized in the mid1970s. Bayesian inference provides a powerful and appropriate framework for the analysis of incomplete data. Inherent in models and drawing inference in the presence of missing data is a lack of identifiability. Functionals of the distribution of the full data are generally not identifiable without uncheckable (from the data) assumptions. These can include parametric assumptions about the full data model and/or specific assumptions about the mechanism of missingness (discussed in considerable detail in Section 5.5). The Bayesian approach provides a principled way to account for uncertainty about the missingness and the lack of identifiability via prior distributions. Common approaches in the literature which result in identification of the full data response (e.g., parametric selection models) tend to ignore this uncertainty. Moment-based approaches (Scharfstein et al., 1999) vary parameters not identified by the data, but do not have a formal way to account for the underlying uncertainty of such parameters in the final inference. Given that we account for uncertainty in
by the data, it would seem unsatisfactory to allow for no uncertainty for parameters that are not identified by the data.
