Mapping the posterior mean relative risk as discussed previously does not make full use of the output of the Bayesian analysis that provides, for each area, samples from the whole posterior distribution of the relative risk. Mapping the probability that a relative risk is greater than a specified threshold of interest has been proposed by several authors [e.g., Clayton and Bernardinelli (1992)]. We carry this further and investigate the performance of decision rules for classifying an area Ai as having an increased risk based on how much of the posterior distribution of θi exceeds a reference threshold. Figure 4 presents an example of the posterior distribution of the relative risk for such an area. The shaded proportion corresponds to the posterior probability that θ > 1. To be precise, to classify any area as having an elevated risk, we define the decision rule D(c, R0), which depends on a cutoff probability c and a reference threshold R0 such that area Ai is classified as having an elevated risk according to D(c, R0) ↔ Prob(θi > R0) > c. The appropriate rules to investigate will depend on the shape of the posterior distribution of θi for the elevated areas. We first discuss rules adapted to the autoregressive BYM and L1-BYM models. For these two models we have seen that, in general, the mean of the posterior distribution of θi in the raised-risk areas is greater than 1 but rarely above 1.5 in many of the scenarios investigated. Thus, it seems sensible to take R0 = 1 as a reference threshold. We would also expect the bulk of the posterior distribution to be shifted above 1 for these areas, suggesting that cutoff probabilities well above 0.5 are indicated. In the first instance, we choose c = 0.8. Thus, for the BYM and L1-BYM models, we report results corresponding to the decision rule D(0.8, 1). See Appendix B for a detailed justification of this choice of value of c and the performance of different decision rules.