An interesting epidemiological problem is the analysis of geographical vari
ation in rates of disease incidence or mortality. One goal of such an analy
sis is to detect clusters of elevated (or lowered) risk in order to identif
y unknown risk factors regarding the disease. We propose a nonparametric Ba
yesian approach for the detection of such clusters based on Green's (1995,
Biometrika 82, 711-732) reversible jump MCMC methodology. The prior model a
ssumes that geographical regions can be combined in clusters with constant
relative risk within a cluster. The number of clusters, the location of the
clusters, and the risk within each cluster is unknown. This specification
can be seen as a change-point problem of variable dimension in irregular, d
iscrete space. We illustrate our method through an analysis of oral cavity
cancer mortality rates in Germany and compare the results with those obtain
ed by the commonly used Bayesian disease mapping method of Besag, York, and
Mollie (1991, Annals of the Institute of Statistical Mathematics, 43, 1-59
).