Open Access
December 2017 Optimal design of fMRI experiments using circulant (almost-)orthogonal arrays
Yuan-Lung Lin, Frederick Kin Hing Phoa, Ming-Hung Kao
Ann. Statist. 45(6): 2483-2510 (December 2017). DOI: 10.1214/16-AOS1531


Functional magnetic resonance imaging (fMRI) is a pioneering technology for studying brain activity in response to mental stimuli. Although efficient designs on these fMRI experiments are important for rendering precise statistical inference on brain functions, they are not systematically constructed. Design with circulant property is crucial for estimating a hemodynamic response function (HRF) and discussing fMRI experimental optimality. In this paper, we develop a theory that not only successfully explains the structure of a circulant design, but also provides a method of constructing efficient fMRI designs systematically. We further provide a class of two-level circulant designs with good performance (statistically optimal), and they can be used to estimate the HRF of a stimulus type and study the comparison of two HRFs. Some efficient three- and four-levels circulant designs are also provided, and we proved the existence of a class of circulant orthogonal arrays.


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Yuan-Lung Lin. Frederick Kin Hing Phoa. Ming-Hung Kao. "Optimal design of fMRI experiments using circulant (almost-)orthogonal arrays." Ann. Statist. 45 (6) 2483 - 2510, December 2017.


Received: 1 January 2016; Revised: 1 November 2016; Published: December 2017
First available in Project Euclid: 15 December 2017

zbMATH: 06838140
MathSciNet: MR3737899
Digital Object Identifier: 10.1214/16-AOS1531

Primary: 05B10 , 05B15
Secondary: 62K15

Keywords: Circulant almost orthogonal arrays , complete difference system , design efficiency , hemodynamic response function

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 6 • December 2017
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