Poisson regression with spatially correlated random effects
 

Model descriptionOur data y_{i,j} are observed on a regular 10x10 grid of points: {i,j=1,...,10}. It is assumed that y_{i,j} ~ Poisson(l_{i,j}), wherelog(l_{i,j}) =
X_{i,j}b + e_{i,j}. Here, X_{i,j}b is a linear predictor and e_{i,j} are Gaussian random variables with covariance cov(e_{i1,j1},e_{i2,j2}) = s^{2} exp(a^{1} d), where d is the Euclidean distance. 