Estimate the spatial error model for the Columbus crime data retaining the grid prior and special likelihood approach, but with Student \(t\) distributed disturbances \(u_{i}\). The precision for the \(i\) th neighbourhood is

\[\kappa_{i} / \sigma_{u}^{2}\]

where \(\kappa_{i} \sim G a(v / 2, v / 2)\) and \(v\) is an unknown. Compare the LPML to that obtained under the homoscedastic model.