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The size of the connected components of excursion sets of χ2, t and F fields

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

J. Cao
J. Cao*
Affiliation:
Bell Laboratories
*
∗ Postal address: Bell Laboratories, Lucent Technologies, 700 Mountain Avenue, Room 2C-260, Murray Hill, NJ 07974-2070, USA. Email address: cao@research.bell-labs.com
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Abstract

The distribution of the size of one connected component and the largest connected component of the excursion set is derived for stationary χ2, t and F fields, in the limit of high or low thresholds. This extends previous results for stationary Gaussian fields (Nosko 1969, Adler 1981) and for χ2 fields in one and two dimensions (Aronowich and Adler 1986, 1988). An application of this is to detect regional changes in positron emission tomography (PET) images of blood flow in human brain, using the size of the largest connected component of the excursion set as a test statistic.

Keywords

Excursion setrandom fieldsimage analysis

MSC classification

Primary: 60G15: Gaussian processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 31 , Issue 3 , September 1999 , pp. 579 - 595
Copyright
Copyright © Applied Probability Trust 1999 

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