ABSTRACT
In the analysis of data over time or space, one often expects positive covariation between units that are close to each other in those domains, so that exchangeable priors are not necessarily appropriate. Consider health event counts for small geographical areas, or relatively rare diseases, when small event totals or small populations at risk lead to unstable estimates of rates or relative risks. One is then led to hierarchical methods for pooling strength over sets of areas to achieve more stable estimates (Riggan et al., 1991; Waller, 2002). An assumption of exchangeable random effects then implies global smoothing, with area rates or risks smoothed toward the overall mean. If there is spatial covariation (when contiguous areas have similar disease levels), a more appropriate smoothing mechanism would incorporate local smoothing toward the mean of adjacent areas (Clayton and Kaldor, 1987).
