Algorithm A1 Adjustment Sensitivity Algorithm

Initialize ${\mathsf{\Sigma }}_{ll}^0$, ${\mathit{l}}^0$  Compute ${\mathit{A}}_0$, ${\mathit{B}}_0$ from ${\mathit{l}}^0$, ${\mathit{x}}^0$  ${\mathsf{\Sigma }}_{\widehat{x}\widehat{x}}^0\leftarrow {\left({\mathit{A}}_0^T{\left({\mathit{B}}_0{\mathsf{\Sigma }}_{ll}^0{\mathit{B}}_0^T\right)}^{-1}{\mathit{A}}_0\right)}^{-1}$  Initialize $\mathit{I}$ with dimensions $\mathrm{len}\left({\mathcal{L}}_c\right)\times \mathrm{len}\left(\mathit{x}\right)$  for all $(\mathit{l},\mathrm{counter}i)\mathrm{in}{\mathcal{L}}_c$ do   ${\mathit{l}}_i\leftarrow {\left[\begin{array}{cc}{\mathit{l}}_0^T& {\mathit{l}}^T\end{array}\right]}^T$, ${\mathsf{\Sigma }}_{ll}^i\leftarrow \left[\begin{array}{cc}{\mathsf{\Sigma }}_{ll}^0& \mathbf{0}\\ \mathbf{0}& {\mathsf{\Sigma }}_{ll}\end{array}\right]$   Compute $\mathit{A}$, $\mathit{B}$ from ${\mathit{l}}_i$, ${\mathit{x}}^0$   ${\mathit{A}}_i\leftarrow {\left[\begin{array}{cc}{\mathit{A}}_0^T& {\mathit{A}}^T\end{array}\right]}^T$, ${\mathit{B}}_i\leftarrow \left[\begin{array}{cc}{\mathit{B}}_0& \mathbf{0}\\ \mathbf{0}& \mathit{B}\end{array}\right]$   ${\mathsf{\Sigma }}_{\widehat{x}\widehat{x}}^i\leftarrow {\left({\mathit{A}}_i^T{\left({\mathit{B}}_i{\mathsf{\Sigma }}_{ll}^i{\mathit{B}}_i^T\right)}^{-1}{\mathit{A}}_i\right)}^{-1}$   $\mathit{I}[i,:]\leftarrow 1-\frac{\mathrm{diag}\left({\mathsf{\Sigma }}_{xx}^i\right)}{\mathrm{diag}\left({\mathsf{\Sigma }}_{xx}^0\right)}$  end for