| Summary: | Classically, spatial smoothing methods such as kriging estimate smooth interpolating fields for features measured at well-located points. In this thesis, we make a simultaneous reconstruction of interpolating spatial fields and measurement locations. We give models, and sample-based Bayesian inference, for estimating locations of dialect samples on a map of England. The method exploits dialect-based spellings to locate these samples. The data are feature vectors extracted from written dialect samples. Just a fraction of the feature vectors ('anchors') have an associated spatial location. When coupled to a prior for the smoothly varying feature field, and the anchor texts, the unlocated feature vectors are jointly informative of their own location and the feature fields. The dataset is large, but sparse, since a given word has a large number of variant spellings which may appear in just a few documents. We report an analysis including Bayesian model fitting and validation on a large and representative subset of the data. The thesis has two main aims - to provide statistical tools for the linguists who collected the data, and to meet the computational and inferential challenge of simultaneously locating large numbers of feature vectors. The results presented in this thesis show that we have largely succeeded in meeting these challenges.
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