{#subsec3.2}
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So far, the population distribution of the incomplete covariate that is used to derive the calibrated-$\delta$ adjustment is assumed to be obtained from a population census or equivalent. In other words, it is assumed that there is no uncertainty associated with estimating the reference distribution, and hence, the adjustment. In calibrated-$\delta$ adjustment MI, we believe that the extra uncertainty in estimating the calibrated-$\delta$ adjustment should be ignored when the population distribution of the incomplete covariate is assumed to be invariant, unless the reference population is not a census or equivalent. Since MI is a Bayesian procedure in which all sources of uncertainty are modelled, this explains why, if there is uncertainty about the population distribution of the incomplete covariate, this uncertainty needs to be accounted for in the derivation of the calibrated-$\delta$ adjustment across imputations.

When the population distribution of the incomplete covariate is not ‘known’ and is estimated, a natural approach for incorporating this extra uncertainty would be to draw values of the population proportions from their distribution and calculate the calibrated-$\delta$ adjustment using these draws, so that this uncertainty is reflected in the MI variance estimation. This additional step is expected to have an effect on 