## The Annals of Statistics

### Optimal experimental designs for fMRI via circulant biased weighing designs

#### Abstract

Functional magnetic resonance imaging (fMRI) technology is popularly used in many fields for studying how the brain reacts to mental stimuli. The identification of optimal fMRI experimental designs is crucial for rendering precise statistical inference on brain functions, but research on this topic is very lacking. We develop a general theory to guide the selection of fMRI designs for estimating a hemodynamic response function (HRF) that models the effect over time of the mental stimulus, and for studying the comparison of two HRFs. We provide a useful connection between fMRI designs and circulant biased weighing designs, establish the statistical optimality of some well-known fMRI designs and identify several new classes of fMRI designs. Construction methods of high-quality fMRI designs are also given.

#### Article information

Source
Ann. Statist., Volume 43, Number 6 (2015), 2565-2587.

Dates
Revised: June 2015
First available in Project Euclid: 7 October 2015

https://projecteuclid.org/euclid.aos/1444222085

Digital Object Identifier
doi:10.1214/15-AOS1352

Mathematical Reviews number (MathSciNet)
MR3405604

Zentralblatt MATH identifier
1331.62381

Subjects
Primary: 62K05: Optimal designs

#### Citation

Cheng, Ching-Shui; Kao, Ming-Hung. Optimal experimental designs for fMRI via circulant biased weighing designs. Ann. Statist. 43 (2015), no. 6, 2565--2587. doi:10.1214/15-AOS1352. https://projecteuclid.org/euclid.aos/1444222085

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