Is multiple imputation a Bayesian procedure?
Partly yes and partly no. When imputations are created under Bayesian arguments (and they usually are), MI has a natural interpretation as an approximate Bayesian inference for the quantities of interest based on the observed data. The validity of MI, however, does not require one to fully subscribe to the Bayesian paradigm. Rubin (1987) provides technical conditions under which MI leads to frequency-valid answers. An imputation method which satisfies these conditions is said to be ‘proper.’ Rubin’s definition of ‘proper’, like many frequentist criteria, are useful for evaluating the properties of a given method but provide little guidance for one seeking to create such a method in practice. For this reason, Rubin recommends that imputations be created through a Bayesian process: specify a parametric model for the complete data (and, if necessary, a model for the mechanism by which data become missing), apply a prior distribution to the unknown model parameters, and simulate m independ
