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Inhomogeneous spatial point processes with hidden second-order stationarity

Publikation: Working paperForskning

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Inhomogeneous spatial point processes with hidden second-order stationarity. / Hahn, Ute; Jensen, Eva B. Vedel.

Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University, 2013.

Publikation: Working paperForskning

Harvard

APA

Hahn, U., & Jensen, E. B. V. (2013). Inhomogeneous spatial point processes with hidden second-order stationarity. Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University. CSGB Research Reports Bind 2013 Nr. 07 http://math.au.dk/publs?publid=985

CBE

Hahn U, Jensen EBV. 2013. Inhomogeneous spatial point processes with hidden second-order stationarity. Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University.

MLA

Hahn, Ute og Eva B. Vedel Jensen Inhomogeneous spatial point processes with hidden second-order stationarity. Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University. (CSGB Research Reports; Journal nr. 07, Bind 2013). 2013., 33 s.

Vancouver

Hahn U, Jensen EBV. Inhomogeneous spatial point processes with hidden second-order stationarity. Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University. 2013.

Author

Hahn, Ute ; Jensen, Eva B. Vedel. / Inhomogeneous spatial point processes with hidden second-order stationarity. Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University, 2013. (CSGB Research Reports; Nr. 07, Bind 2013).

Bibtex

@techreport{1ac056e9f9c248e292dba284bc5bce32,
title = "Inhomogeneous spatial point processes with hidden second-order stationarity",
abstract = "Modelling of inhomogeneous spatial point patterns is a challenging research area with numerous applications in diverse areas of science. In recent years, the focus has mainly been on the class of reweighted second-order stationary point processes that is characterized by the mathematically attractive property of a translation invariant pair correlation function. Motivated by examples where this model class is not adequate, we extend the class of reweighted second-order stationary processes. The extended class consists of hidden second-order stationary point processes for which the pair correlation function g(u, v) is a function of u −˘ v, where −˘ is a generalized subtraction operator. For the reweighted second-order stationary processes, the subtraction operator is simply u −˘ v = u − v. The processes in the extended class are called hidden second-order stationary because, in many cases, they may be derived from second-order stationary template processes. We review and discuss different types of hidden second-order stationarity. Alternatives to reweighted second-order stationarity are retransformed and locally rescaled second-order stationarity. Permutation tests for the different types of hidden second-order stationarity are developed. A test for local anisotropy is also derived. We illustrate our approach by a detailed analysis of three point patterns.",
keywords = " Inhomogeneity, Intensity reweighted stationarity, Local scaling , Second-order stationarity, ; Spatial point processes, Transformation",
author = "Ute Hahn and Jensen, {Eva B. Vedel}",
year = "2013",
language = "English",
series = "CSGB Research Reports",
number = "07",
publisher = "Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University",
type = "WorkingPaper",
institution = "Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University",

}

RIS

TY - UNPB

T1 - Inhomogeneous spatial point processes with hidden second-order stationarity

AU - Hahn, Ute

AU - Jensen, Eva B. Vedel

PY - 2013

Y1 - 2013

N2 - Modelling of inhomogeneous spatial point patterns is a challenging research area with numerous applications in diverse areas of science. In recent years, the focus has mainly been on the class of reweighted second-order stationary point processes that is characterized by the mathematically attractive property of a translation invariant pair correlation function. Motivated by examples where this model class is not adequate, we extend the class of reweighted second-order stationary processes. The extended class consists of hidden second-order stationary point processes for which the pair correlation function g(u, v) is a function of u −˘ v, where −˘ is a generalized subtraction operator. For the reweighted second-order stationary processes, the subtraction operator is simply u −˘ v = u − v. The processes in the extended class are called hidden second-order stationary because, in many cases, they may be derived from second-order stationary template processes. We review and discuss different types of hidden second-order stationarity. Alternatives to reweighted second-order stationarity are retransformed and locally rescaled second-order stationarity. Permutation tests for the different types of hidden second-order stationarity are developed. A test for local anisotropy is also derived. We illustrate our approach by a detailed analysis of three point patterns.

AB - Modelling of inhomogeneous spatial point patterns is a challenging research area with numerous applications in diverse areas of science. In recent years, the focus has mainly been on the class of reweighted second-order stationary point processes that is characterized by the mathematically attractive property of a translation invariant pair correlation function. Motivated by examples where this model class is not adequate, we extend the class of reweighted second-order stationary processes. The extended class consists of hidden second-order stationary point processes for which the pair correlation function g(u, v) is a function of u −˘ v, where −˘ is a generalized subtraction operator. For the reweighted second-order stationary processes, the subtraction operator is simply u −˘ v = u − v. The processes in the extended class are called hidden second-order stationary because, in many cases, they may be derived from second-order stationary template processes. We review and discuss different types of hidden second-order stationarity. Alternatives to reweighted second-order stationarity are retransformed and locally rescaled second-order stationarity. Permutation tests for the different types of hidden second-order stationarity are developed. A test for local anisotropy is also derived. We illustrate our approach by a detailed analysis of three point patterns.

KW - Inhomogeneity

KW - Intensity reweighted stationarity

KW - Local scaling

KW - Second-order stationarity

KW - ; Spatial point processes

KW - Transformation

M3 - Working paper

T3 - CSGB Research Reports

BT - Inhomogeneous spatial point processes with hidden second-order stationarity

PB - Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University

ER -