Rotation space random fields with an application to fMRI data
type: Item
instance of: scholarly article
title: Rotation space random fields with an application to fMRI data
zbMATH Open document ID: 1043.92019
published in: The Annals of Statistics
publication date: 2004-05-27T00:00:00Z
review text: The problem of testing for a signal with unknown location and scale in a Gaussian random field defined on \(R^2\) is investigated. The test statistic is the maximum over all filter's rotations and scales of the rotation space field. The Euler characteristic and the tubes approaches are presented. The obtained results are applied to the problem of searching for activation in brain images.
Mathematics Subject Classification ID: 92C55
Mathematics Subject Classification ID: 62M40
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 52A22
zbMATH DE Number: 2067666
zbMATH Keywords: random fields
zbMATH Keywords: Euler characteristic
zbMATH Keywords: differential topology
zbMATH Keywords: integral geometry
zbMATH Keywords: image analysis
zbMATH Keywords: nonstationary Gaussian
author: K. Shafie
author: Belle M. Sigal
author: David Siegmund
author: Keith J. Worsley
reviewed by: Andriy Olenko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1074290326
OpenAlex ID: W2015369872
cites work: Q5558293
cites work: Q3935962
cites work: On excursion sets, tube formulas and maxima of random fields.
cites work: Level crossings for random fields
cites work: Ten Lectures on Wavelets
cites work: Tubes and Spheres in n-Spaces, and a Class of Statistical Problems
cites work: On Hotelling's Approach to Testing for a Nonlinear Parameter in Regression
cites work: Q4282636
cites work: Q3860459
cites work: Volumes of tubular neighborhoods of spherical polyhedra and statistical inference
cites work: Q4494142
cites work: Q3218902
cites work: Testing for a signal with unknown location and scale in a stationary Gaussian random field
cites work: The expected number of local maxima of a random field and the volume of tubes
cites work: Tail probabilities of the maxima of Gaussian random fields
cites work: On the equivalence of the tube and Euler characteristic methods for the distribution of the maximum of Gaussian fields over piecewise smooth domains
cites work: On the Volume of Tubes
cites work: Q3258642
cites work: Local Maxima and the Expected Euler Characteristic of Excursion Sets of χ 2, F and t Fields
cites work: Testing for signals with unknown location and scale in a χ2random field, with an application to fMRI
DOI: 10.1214/AOS/1074290326
Recommended article: A Stochastic Geometry Model for Functional Magnetic Resonance Images
Recommended article: Detecting sparse cone alternatives for Gaussian random fields, with an application to fMRI
Recommended article: Q3172377
Recommended article: Q4425373
Recommended article: Riemannian geometry for the statistical analysis of diffusion tensor data
Recommended article: A spatiotemporal nonparametric Bayesian model of multi-subject fMRI data
description: scientific article; zbMATH DE number 2067666