Hill, Bryony, Kendall, Wilfrid S. and Thönnes, Elke (2011) A gradient field approach to modelling fibre-generated spatial point processes. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers).

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Abstract

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-self-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.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Point processes -- Mathematical models
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2011
Volume:	Vol.2011
Number:	No.18
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
References:	Dryden IL, Koloydenko A, Zhou D (2009), \Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging". Annals of Applied Statistics;3(3):1102{1123. Hastie T, Stuetzle W (1989), \Principal curves". Journal of the American Statistical Association;84(406):502{ 516. Stanford DC, Raftery AE (2000), \Finding curvilinear features in spatial point patterns: principal curve clustering with noise". IEEE Transactions on Pattern Analysis and Machine Intelligence;22(6):601{609. Stoica RS, Martinez VJ, Saar E (2007), \A three-dimensional object point process for detection of cosmic filaments". Journal of the Royal Statistical Society: Series C (Applied Statistics);56(4):459{477. Su J (2009), A Tensor Approach to Fingerprint Analysis, PhD Thesis, University of Warwick. Su J, Hill B, Kendall WS, Thonnes E (2008), \Inference for point processes with unobserved, one-dimensional reference structure". University of Warwick Department of Statistics CRiSM Working Paper No.8{10. Watson, C (2001), NIST Special Database 30: Dual Resolution Images from Paired Fingerprint Cards. National Institute of Standards and Technology, Gaithersburg, Md, USA. 2001.
URI:	http://wrap.warwick.ac.uk/id/eprint/35064

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