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Block bootstrap methods for the estimation of the intensity of a spatial point process with confidence bounds

Artikel i vetenskaplig tidskrift
Författare T. Mattfeldt
Henrike Häbel
F. Fleischer
Publicerad i Journal of Microscopy
Volym 251
Nummer/häfte 1
Sidor 84-98
ISSN 0022-2720
Publiceringsår 2013
Publicerad vid Institutionen för matematiska vetenskaper, matematisk statistik
Sidor 84-98
Språk en
Länkar dx.doi.org/10.1111/jmi.12048
Ämnesord Bootstrap, computer-intensive methods, dependent data, intensity, pathology, point process, sample reuse methods, statistical-analysis, dependent data, patterns, capillaries, variance, sections
Ämneskategorier Patologi, Teknisk fysik, Matematisk statistik

Sammanfattning

This paper deals with the estimation of the intensity of a planar point process on the basis of a single point pattern, observed in a rectangular window. If the model assumptions of stationarity and isotropy hold, the method of block bootstrapping can be used to estimate the intensity of the process with confidence bounds. The results of two variants of block bootstrapping are compared with a parametric approximation based on the assumption of a Gaussian distribution of the numbers of points in deterministic subwindows of the original pattern. The studies were performed on patterns obtained by simulation of well-known point process models (Poisson process, two Matern cluster processes, Matern hardcore process, Strauss hardcore process). They were also performed on real histopathological data (point patterns of capillary profiles of 12 cases of prostatic cancer). The methods are presented as worked examples on two cases, where we illustrate their use as a check on stationarity (homogeneity) of a point process with respect to different fields of vision. The paper concludes with various methodological discussions and suggests possible extensions of the block bootstrap approach to other fields of spatial statistics.

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