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EDITED THIS IS INCORRECT Tecnically this is straightforward. You specify the equations $$ z_{ij}=\theta_i-\theta_j + \sigma_{ij} \epsilon_{ij} $$ and try to minimize the error with respect to $\theta$s $$ \sum_{ij}\epsilon_{ij}^2=\sum_{ij}\frac{1}{\sigma_{ij}^2}(z_{ij}-\theta_i+\theta_j)^2 $$ wit...