Block bootstrap methods for the estimation of the intensity of a spatial point process with confidence bounds
Journal article, 2013

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.

variance

intensity

patterns

statistical-analysis

point process

capillaries

Bootstrap

sample reuse methods

sections

pathology

dependent data

dependent data

computer-intensive methods

Author

T. Mattfeldt

University of Ulm

Henrike Häbel

Chalmers, Mathematical Sciences, Mathematical Statistics

University of Gothenburg

SuMo Biomaterials

F. Fleischer

Boehringer Ingelheim Pharma GmbH & Co. KG

Journal of Microscopy

0022-2720 (ISSN) 1365-2818 (eISSN)

Vol. 251 1 84-98

Subject Categories

Other Engineering and Technologies

Cell and Molecular Biology

Probability Theory and Statistics

Areas of Advance

Life Science Engineering (2010-2018)

DOI

10.1111/jmi.12048

More information

Latest update

2/28/2018