On smooth models for complex domains and distances

  • David Miller

Student thesis: Doctoral ThesisPhD


Spline smoothing is a popular technique for creating maps of a spatial phenomenon. Most smoothers use the Euclidean metric to measure the distancebetween data. This approach is flawed since the distances between points in thedomain as experienced by the objects within the domain are rarely Euclidean.For example, the movements of animals and people are subject to both physicaland political boundaries (respectively) which must be navigated. Measuringdistances between the objects using the incorrect (Euclidean) metric leads toincorrect inference. The first part of this thesis develops a finite area smootherwhich does not su↵er from this problem when the shape of the area is complex. It begins by rejecting the use of the Schwarz-Christo↵el transform as a method for morphing complex domains due to its squashing of space. From there a method based on preserving within-area distances using multidimensional scaling is developed. High dimensional projections of the data are necessary to avoid a loss of ordering in the points. To smooth reliably in high dimensions Duchon splines are used. The model developed rivals the current best finite area method in prediction error terms and fits easily into larger models. Finally, the utility of projection methods to smooth general distances is explored.The second part of the thesis concerns distance sampling, a widely used setof methods for estimating the abundance of biological populations. The workpresented here introduces mixture formulation for the detection function used tomodel the probability of detection. The use of mixture models leads to flexible but monotonic detection functions, avoiding the unrealistic shapes which conventional methods are prone to. These new models are then applied to several existing, problematic data sets.
Date of Award27 Apr 2012
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorSimon Wood (Supervisor)


  • statistics
  • smoothing
  • distance sampling

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