A weighted grid prior for the spatial correlation coefficient in spatial lag and error models can be specified (Lesage, 1997) as

\[\pi(\lambda) \propto(s+1) \lambda^{s} I_{(0,1)}(\lambda)\]

where the positive coefficient \(s\) is preset, and \(I_{(0,1)}(\lambda)\) indicates that \(\lambda\) is constrained between 0 and 1 . The value \(s=0\) leads to a uniform (equal probability) prior over different \(\lambda_{g}\) values in the grid \(g=1, \ldots, G\), while higher integer values for \(s\) (e.g. \(s=5\) ) give higher weight to high correlations. Apply a prior with \(s=2\) to the pure spatial autoregression model (without predictors) for the London TB data, and compare the estimated \(\lambda\) and LPML with those obtained under a uniform grid prior.