The dataset was gathered to investigate the impact of changes in spatial scale on model outcome for a set of spatial structures and to evaluate the performance of various Bayesian spatial smoothness priors for spatial dependence, namely an intrinsic Gaussian Markov random field (IGMRF), a second-order random walk (RW2D) on a lattice, and a Gaussian field with Matérn correlation function.

The cases in dataset X4 were generated from an inhomogeneous Thomas process with parameters and and a simple trend function for the intensity of parent points given by , on the unit square. The cases were then superimposed with controls generated from an inhomogeneous Poisson process with trend function . The average intensity of the cases and the controls was 648 points per unit square.

Presented are the estimated precision parameters of the MATERN2D model at various spatial scales for dataset X4.