A gradient field approach to modelling fibre-generated spatial point processes
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, Vol.2011 (No.18).
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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
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|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
Dryden IL, Koloydenko A, Zhou D (2009), \Non-Euclidean statistics for covariance matrices, with applications
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