DETECTING SPARSE CONE ALTERNATIVES FOR GAUSSIAN RANDOM FIELDS, WITH AN APPLICATION TO fMRI

被引：4

作者：

Taylor, Jonathan E. ^{[1
]}

Worsley, Keith J. ^{[2
,3
]}

机构：

[1] Stanford Univ, Dept Stat, Stanford, CA 94305 USA

[2] Univ Chicago, Chicago, IL 60637 USA

[3] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada

来源：

STATISTICA SINICA | 2013年 / 23卷 / 04期

关键词：

Euler characteristic; kinematic formulae; multivariate one-sided hypotheses; non-negative least squares; order-restricted inference; random fields; volumes of tubes expansion; EXCURSION SETS; UNKNOWN LOCATION; CONFIDENCE BANDS; MAXIMA; SIGNALS; GEOMETRY; LATENCY; SMOOTH; CHI(2); VOLUME;

D O I：

10.5705/ss.2012-218s

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Our problem is to find a good approximation to the P-value of the maximum of a random field of test statistics for a cone alternative at each point in a sample of Gaussian random fields. These test statistics have been proposed in the neuroscience literature for the analysis of fMRI data allowing for unknown delay in the hemodynamic response. However the null distribution of the maximum of this 3D random field of test statistics, and hence the threshold used to detect brain activation, was unsolved. To find a solution, we approximate the P-value by the expected Euler characteristic (EC) of the excursion set of the test statistic random field. Our main result is the required EC density, derived using the Gaussian Kinematic Formula.

引用

页码：1629 / 1656

页数：28

共 50 条

[1] Detecting sparse signals in random fields, with an application to brain mapping
Taylor, Jonathan E.
Worsley, Keith J.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2007, 102 (479) : 913 - 928
[2] Mixed Membership Sparse Gaussian Conditional Random Fields
Yang, Jie
Leung, Henry C. M.
Yiu, S. M.
Chin, Francis Y. L.
ADVANCED DATA MINING AND APPLICATIONS, ADMA 2017, 2017, 10604 : 287 - 302
[3] An approximation to cluster size distribution of two Gaussian random fields conjunction with application to FMRI data
Alodat, M. T.
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2011, 141 (07) : 2331 - 2347
[4] ONLINE LEARNING OF SPARSE GAUSSIAN CONDITIONAL RANDOM FIELDS WITH APPLICATION TO PREDICTION OF ENERGY CONSUMERS BEHAVIOR
Soltani, Nasim Yahya
2021 IEEE STATISTICAL SIGNAL PROCESSING WORKSHOP (SSP), 2021, : 486 - 490
[5] Rotation space random fields with an application to fMRI data
Shafie, K
Sigal, B
Siegmund, D
Worsley, KJ
ANNALS OF STATISTICS, 2003, 31 (06): : 1732 - 1771
[6] Sparse Gaussian Conditional Random Fields on Top of Recurrent Neural Networks
Wang, Xishun
Zhang, Minjie
Ren, Fenghui
THIRTY-SECOND AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE / THIRTIETH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE / EIGHTH AAAI SYMPOSIUM ON EDUCATIONAL ADVANCES IN ARTIFICIAL INTELLIGENCE, 2018, : 4219 - 4226
[7] Multiscale Gaussian random fields and their application to cosmological simulations
Bertschinger, E
ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES, 2001, 137 (01): : 1 - 20
[8] Efficient methods for Gaussian Markov random fields under sparse linear constraints
Bolin, David
Wallin, Jonas
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 34 (NEURIPS 2021), 2021, 34
[9] Fast Sparse Gaussian Markov Random Fields Learning Based on Cholesky Factorization
Stojkovic, Ivan
Jelisavcic, Vladisav
Milutinovic, Veljko
Obradovic, Zoran
PROCEEDINGS OF THE TWENTY-SIXTH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE, 2017, : 2758 - 2764
[10] Wireless Channel Quality Prediction using Sparse Gaussian Conditional Random Fields
Raj, Raushan
Kulkarni, Adita
Seetharam, Anand
Ramesh, Arti
2021 IEEE 18TH ANNUAL CONSUMER COMMUNICATIONS & NETWORKING CONFERENCE (CCNC), 2021,

← 1 2 3 4 5 →