  Missing values in covariates due to censoring by signal interference or lack
of sensitivity in the measuring devices are common in industrial problems. We
propose a full Bayesian solution to the prediction problem with an efficient
Markov Chain Monte Carlo (MCMC) algorithm that updates all the censored
covariate values jointly in a random scan Gibbs sampler. We show that the joint
updating of missing covariate values can be at least two orders of magnitude
more efficient than univariate updating. This increased efficiency is shown to
be crucial for quickly learning the missing covariate values and their
uncertainty in a real-time decision making context, in particular when there is
substantial correlation in the posterior for the missing values. The approach
is evaluated on simulated data and on data from the telecom sector. Our results
show that the proposed Bayesian imputation gives substantially more accurate
predictions than na\"ive imputation, and that the use of auxiliary variables in
the imputation gives additional predictive power.
