Clustering Partition Models for Discrete Structures with Applications in Geographical Epidemiology

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.