A Gradient Field Approach to Modelling Fibre-Generated Spatial Point Processes
Bryony Hill, Wilfrid S. Kendall, Elke Thoennes
Department of Statistics, University of Warwick, Coventry, United Kingdom

A new non-parametric model is introduced for point processes that are clustered along curves or “fibres”, with additional background noise. The model identifies random curves as integral lines of a gradient field. In principle this enables the inclusion of all possible non-intersecting curves with one underlying smoothness constraint. Markov chain Monte Carlo is combined with Empirical Bayes to provide a practical estimation procedure for properties of the underlying fibre distribution, based on the observed point pattern data. Comparisons are made with other techniques in the literature. Illustrations of the methodology include applications to fingerprints, earthquakes and galaxies.

Keywords: Markov chain Monte Carlo; Stochastic geometry; Random fibres

Biography: Wilfrid Kendall is Professor of Statistics at the Department of Statistics, University of Warwick. He has a variety of scientific interests centering around the interactions of probability, statistics, and geometry. Amongst other professional service, he has been Scientific Secretary for the Bernoulli Society (1996-2000), Chief Editor of Electronic Communications in Probability (1999-2002), Scientific Programme Chair for the 2004 Bernoulli/IMS World Congress, and co-Director of the UK Academy for PhD Training in Statistics (2007-date).