Multiple imputation has become viewed as a general solution to
missing data problems in statistics. However, in order to lead to
consistent asymptotically normal estimators, correct variance
estimators and valid tests, the imputations must be proper.
So far it seems that only Bayesian multiple imputation, i.e.\
using a Bayesian predictive distribution to generate the
imputations, or approximately Bayesian multiple imputations has
been shown to lead to proper imputations in some settings. In this
paper, we shall see that Bayesian multiple imputation does not
generally lead to proper multiple imputations. Furthermore, it
will be argued that for general statistical use, Bayesian multiple
imputation is inefficient even when it is proper.