1	for k ← 1 to K do
2	Fit the imputation model at site k to find ${\widehat{\mathit{\alpha }}}^{\left(k\right)}$ and $\mathrm{Cov}\left({\widehat{\mathit{\alpha }}}^{\left(k\right)}\right)$;
3	Sample ${\mathit{\alpha }}_1^{\left(k\right)},\dots ,{\mathit{\alpha }}_M^{\left(k\right)}$ independently from $\mathcal{N}\left({\widehat{\mathit{\alpha }}}^{\left(k\right)},\mathrm{Cov}\left({\widehat{\mathit{\alpha }}}^{\left(k\right)}\right)\right)$;
4	end
5	for m ← 1 to M do
6	for k ← 1 to K do Impute the missing data at site k based on ${\mathit{\alpha }}_m^{\left(k\right)}$
7	Fit the analysis model and obtain ${\widehat{\mathit{\theta }}}_m$ and $\mathrm{Cov}\left({\widehat{\mathit{\theta }}}_m\right)$;
8	end
9	Combine the results by Rubin’s rule to obtain $\widehat{\mathit{\theta }}$ and $\mathrm{Cov}\left(\widehat{\mathit{\theta }}\right)$;