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	Disease Mapping	Besag-York-Mollie Model
Field	Spatial Epidemiology	Spatial Epidemiology
Family	Process / pipeline	Regression model
Year of origin	1987	1991
Originator	David Clayton & Jack Kaldor (empirical Bayes); Andrew Lawson (Bayesian hierarchical synthesis)	Julian Besag, Jeremy York & Annie Mollie (BYM2 by Riebler, Sorbye, Simpson & Rue)
Type	Pipeline for estimating and smoothing small-area disease relative risk from counts	Hierarchical Bayesian Poisson model with structured and unstructured spatial random effects
Seminal source	Clayton, D., & Kaldor, J. (1987). Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics, 43(3), 671-681.	Besag, J., York, J., & Mollie, A. (1991). Bayesian image restoration, with two applications in spatial statistics. Annals of the Institute of Statistical Mathematics, 43(1), 1-20.
Aliases	Small-Area Risk Mapping, Relative-Risk Smoothing, Empirical Bayes Disease Mapping, Spatial Risk Estimation	BYM Model, Convolution Prior Model, CAR Convolution Model, BYM2 Reparameterization
Related	4	4
Summary	Disease mapping is the set of model-based methods for estimating and displaying the geographic distribution of disease risk across small areas. Its central problem is that raw area-level rates, especially standardized mortality or incidence ratios, are statistically unstable where populations are small: a handful of cases can produce wildly high or low rates that reflect chance rather than true risk. Clayton and Kaldor's 1987 empirical-Bayes paper showed how to stabilize these estimates by shrinking each area's rate toward an overall mean using a Poisson-gamma (or log-normal) hierarchical model, and the approach was developed into the fully Bayesian, spatially smoothed hierarchical framework synthesized in Lawson's textbook. As a pipeline, disease mapping computes expected counts, places the counts in a hierarchical risk model, borrows strength globally and across neighbors to smooth the estimates, and produces a risk map with quantified uncertainty, including probabilities that risk exceeds a threshold.	The Besag-York-Mollie (BYM) model is the workhorse hierarchical Bayesian model for small-area disease mapping. Proposed by Julian Besag, Jeremy York, and Annie Mollie (1991), it models area-level disease counts with a Poisson likelihood whose log relative risk is the sum of two random effects: a spatially structured component, given an intrinsic conditional autoregressive (ICAR) prior that borrows strength from neighboring areas, and an unstructured component capturing area-specific heterogeneity that is not spatially patterned. This convolution of structured and unstructured effects lets the model smooth noisy small-area rates toward local and global means while distinguishing genuine spatial trend from independent overdispersion. Because the original parameterization makes the two variance components hard to interpret and depends on the graph, Riebler, Sorbye, Simpson, and Rue (2016) introduced the scaled BYM2 reparameterization, which mixes a scaled spatial effect and an unstructured effect through a single interpretable mixing parameter and a total-variance parameter, improving prior specification and identifiability.