  This paper proposes a flexible Bayesian approach to multiple imputation using
conditional Gaussian mixtures. We introduce novel shrinkage priors for
covariate-dependent mixing proportions in the mixture models to automatically
select the suitable number of components used in the imputation step. We
develop an efficient sampling algorithm for posterior computation and multiple
imputation via Markov Chain Monte Carlo methods. The proposed method can be
easily extended to the situation where the data contains not only continuous
variables but also discrete variables such as binary and count values. We also
propose approximate Bayesian inference for parameters defined by loss functions
based on posterior predictive distributing of missing observations, by
extending bootstrap-based Bayesian inference for complete data. The proposed
method is demonstrated through numerical studies using simulated and real data.
