Disease Mapping

Disease mapping is the broad task and pipeline, taking small-area counts and producing stabilized, uncertainty-aware relative-risk estimates and maps, while Besag-York-Mollie is one specific model used within that pipeline for the spatial-smoothing step. You can do disease mapping with a simple global empirical-Bayes (Poisson-gamma) model that has no spatial structure, with a CAR model, with BYM or BYM2, or with more elaborate space-time and covariate models. So Besag-York-Mollie is a particular, very common choice of prior for the smoothing component of disease mapping, not a synonym for the whole enterprise.

Because raw standardized ratios are statistically unstable wherever expected counts are small, which is exactly the rural, sparsely populated areas that often dominate a map's visual extremes. A single chance case can produce a ratio that looks dramatically high or low but carries almost no real information. Mapping these raw values invites chasing artifacts and missing genuine patterns. Disease mapping replaces them with model-based estimates that shrink unreliable small-area values toward a local or global mean in proportion to how little their own data say, yielding a map that distinguishes true elevated risk from small-number noise and attaches uncertainty to each estimate.

An exceedance probability is the posterior probability that an area's relative risk exceeds a chosen threshold, such as a risk of 1 (above average) or 2 (double the average). Because disease mapping is a full probability model, this quantity falls out naturally. It is more useful for surveillance than a point estimate because it directly answers the decision-relevant question, 'how confident are we that this area is genuinely elevated?', rather than just 'what is its estimated risk?'. Mapping exceedance probabilities highlights areas that are probably, not merely apparently, high-risk, helping to prioritize limited investigation and intervention resources.