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 a 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 use the Metropolis-Hastings (MH) algorithm to sample from such a distribution. We consider the problem of what is the optimal, informed MH proposal distribution given a fixed set of allowed moves. To answer such a question we de ne the notion of balanced proposals and we prove that, under some assumptions, such proposals are maximal in the Peskun sense. Using such ideas we obtain substantial mixing improvements compared to other 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 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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:682972 |
| Date | January 2015 |
| Creators | Zanella, Giacomo |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/78043/ |
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