This thesis is concerned with the analysis of data for a finite set of spatially structured units. For example, irregular structures, like political maps, are considered as well as regular lattices. The main field of application is geographical epidemiology.

In this thesis a prior model for the use within a hierarchical Bayesian framework is developed, and a theoretical basis is given. The proposed partition model combines the units under investigation to clusters, and allows for the estimation of parameters on the basis of local information. Special emphasis is on spatially adaptive smoothing of the data that retains possible edges in the estimated surface. Information about the existence of such edges is extracted from the data.

The investigation of different data types supports the suitability of the model for a wide range of applications. The model seems to be very flexible and shows the desired smoothing behavior. In comparison to commonly used Markov random field models the proposed model has some advantages. With respect to the quality of the data, either both models yield similar results, or the proposed model provides more clear structure in the estimates and simplifies the interpretation of the results.