  Probabilistic graphical models are a powerful concept for modeling
high-dimensional distributions. Besides modeling distributions, probabilistic
graphical models also provide an elegant framework for performing statistical
inference; because of the high-dimensional nature, however, one must often use
approximate methods for this purpose. Belief propagation performs approximate
inference, is efficient, and looks back on a long success-story. Yet, in most
cases, belief propagation lacks any performance and convergence guarantees.
Many realistic problems are presented by graphical models with loops, however,
in which case belief propagation is neither guaranteed to provide accurate
estimates nor that it converges at all. This thesis investigates how the model
parameters influence the performance of belief propagation. We are particularly
interested in their influence on (i) the number of fixed points, (ii) the
convergence properties, and (iii) the approximation quality.
