1	Find the estimate $\overline{\mathit{\alpha }}={\arg \min }_{\mathit{\alpha }}{\mathcal{L}}_1\left(\mathit{\alpha }\right)$, which is the optimal estimate at site 1;
2	Send $\overline{\mathit{\alpha }}$ to all sites and receive $\nabla {\mathcal{L}}_k\left(\mathit{\alpha }\right){\mid }_{\mathit{\alpha }=\overline{\mathit{\alpha }}}$ back;
3	Find ${\widehat{\mathit{\alpha }}}_{csl}={\arg \min }_{\mathit{\alpha }}\tilde{\mathcal{L}}\left(\mathit{\alpha }\right)$ and $\mathrm{Cov}\left({\widehat{\mathit{\alpha }}}_{csl}\right)=\frac{1}{N_c}{\nabla }^2{\mathcal{L}}_1{\left(\mathit{\alpha }\right)}^{-1}{\mid }_{\mathit{\alpha }={\widehat{\mathit{\alpha }}}_{csl}}$;
4	Sample α1, …, αM independently from $\mathcal{N}\left({\widehat{\mathit{\alpha }}}_{csl},\mathrm{Cov}\left({\widehat{\mathit{\alpha }}}_{csl}\right)\right)$;
5	Send α1, …, αM to all sites;
6	for m ← 1 to M do
7	for k ← 1 to K do Impute the missing data at site k based on αm;
8	Fit the analysis model and obtain ${\widehat{\mathit{\theta }}}_m$ and $\mathrm{Cov}\left({\widehat{\mathit{\theta }}}_m\right)$;
9	end
10	Combine the results by Rubin’s rule to obtain $\widehat{\mathit{\theta }}$ and $\mathrm{Cov}\left(\widehat{\mathit{\theta }}\right)$;