  Common cluster models for multi-type point processes model the aggregation of
points of the same type. In complete contrast, in the study of Anglo-Saxon
settlements it is hypothesized that administrative clusters involving
complementary names tend to appear. We investigate the evidence for such an
hypothesis by developing a Bayesian Random Partition Model based on clusters
formed by points of different types (complementary clustering).
  As a result we obtain an intractable posterior distribution on the space of
matchings contained in a k-partite hypergraph. We apply the Metropolis-Hastings
(MH) algorithm to sample from this posterior. We consider the problem of
choosing an efficient MH proposal distribution and we obtain consistent mixing
improvements compared to the choices found in the literature. Simulated
Tempering techniques can be used to overcome multimodality and a multiple
proposal scheme is developed to allow for parallel programming. Finally, we
discuss results arising from the careful use of convergence diagnostic
techniques.
  This allows us to study a dataset including locations and placenames of 1316
Anglo-Saxon settlements dated approximately around 750-850 AD. Without strong
prior knowledge, the model allows for explicit estimation of the number of
clusters, the average intra-cluster dispersion and the level of interaction
among placenames. The results support the hypothesis of organization of
settlements into administrative clusters based on complementary names.
