 An approximation to peak detection power using Gaussian random field theoryYu Zhao, Dan Cheng and Armin Schwartzman Journal of Multivariate Analysis, 2024, vol. 204, issue C Abstract: We study power approximation formulas for peak detection using Gaussian random field theory. The approximation, based on the expected number of local maxima above the threshold u, E[Mu], is proved to work well under three asymptotic scenarios: small domain, large threshold, and sharp signal. An adjusted version of E[Mu] is also proposed to improve accuracy when the expected number of local maxima E[M−∞] exceeds 1. Cheng and Schwartzman (2018) developed explicit formulas for E[Mu] of smooth isotropic Gaussian random fields with zero mean. In this paper, these formulas are extended to allow for rotational symmetric mean functions, making them applicable not only for power calculations but also for other areas of application that involve non-centered Gaussian random fields. We also apply our formulas to 2D and 3D simulated datasets, and the 3D data is induced by a group analysis of fMRI data from the Human Connectome Project to measure performance in a realistic setting. Keywords: Gaussian random field; Image analysis; Peak detection; Power calculations (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:204:y:2024:i:c:s0047259x24000538 Ordering information: This journal article can be ordered from DOI: 10.1016/j.jmva.2024.105346 Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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