Some Limit Results for Efficiency in Stochastic fMRI Designs

Zarahn, Eric; Friston, Karl J.

doi:10.1002/1521-4036(200206)44:4<496::aid-bimj496>3.0.co;2-5

Cited by 4 publications

(6 citation statements)

References 22 publications

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“…Our results for the geometric distribution showed that an event occurrence probability of about p ¼ 0.5 was optimal. This probability is similar to previous results for estimation efficiency and detection power by Friston et al (1999), Birn et al (2002) and Zarahn and Friston (2002). For the uniform distribution, a smallest ISI of 2.5 s together with ISIs which were 5 s apart from each other, i.e., 2.5 s, 7.5 s, 12.5 s, 17.5 s, proved to be efficient, and the maximin design had ISIs 2.5 s, 7.5 s and 12.5 s for linearity as well as nonlinearity.…”

Section: Discussionsupporting

confidence: 89%

Optimal design for nonlinear estimation of the hemodynamic response function

Maus¹,

Goebel²,

Berger³

2011

Human Brain Mapping

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Subject-specific hemodynamic response functions (HRFs) have been recommended to capture variation in the form of the hemodynamic response between subjects (Aguirre et al., [ 1998]: Neuroimage 8:360-369). The purpose of this article is to find optimal designs for estimation of subject-specific parameters for the double gamma HRF. As the double gamma function is a nonlinear function of its parameters, optimal design theory for nonlinear models is employed in this article. The double gamma function is linearized by a Taylor approximation and the maximin criterion is used to handle dependency of the D-optimal design on the expansion point of the Taylor approximation. A realistic range of double gamma HRF parameters is used for the expansion point of the Taylor approximation. Furthermore, a genetic algorithm (GA) (Kao et al., [ 2009]: Neuroimage 44:849-856) is applied to find locally optimal designs for the different expansion points and the maximin design chosen from the locally optimal designs is compared to maximin designs obtained by m-sequences, blocked designs, designs with constant interstimulus interval (ISI) and random event-related designs. The maximin design obtained by the GA is most efficient. Random event-related designs chosen from several generated designs and m-sequences have a high efficiency, while blocked designs and designs with a constant ISI have a low efficiency compared to the maximin GA design.

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Section: Discussionsupporting

confidence: 89%

Optimal design for nonlinear estimation of the hemodynamic response function

Maus¹,

Goebel²,

Berger³

2011

Human Brain Mapping

View full text Add to dashboard Cite

show abstract

“…Our results for the geometric distribution showed that an event occurrence probability of about p = 0.5 was optimal. This probability is similar to previous results for estimation efficiency and detection power by Friston et al (1999), Birn et al (2002) and Zarahn & Friston (2002). For the uniform distribution, a smallest ISI of 2.5 s together with ISIs which were 5 s apart from each other, i.e., 2.5 s, 7.5 s, 12.5 s, 17.5 s, proved to be efficient, and the maximin design had ISIs 2.5 s, 7.5 s and 12.5 s for linearity as well as nonlinearity.…”

Section: Discussionsupporting

confidence: 89%

“…The design of Burock et al (1998) is an example of a possible way to characterize eventrelated designs. Rapid event-related designs can be described by the minimum possible SOA between trials (SOA min ) and the probability P of a stimulus type or a null event to be presented (stationary stochastic designs in Friston et al (1999) and Zarahn & Friston (2002)). For this characterization of a rapid-event related design the SOA min and the probability P are factors of optimization.…”

Section: Event-related Designsmentioning

confidence: 99%

“…The maximin approach has been applied in optimal design theory to construct designs which are robust against misspecification of parameters in various models, e.g., the linear mixed model (Berger & Tan, 2004;Ouwens et al, 2002) or exponential regression models (Dette et al, 2006). The effect of autocorrelation on optimal design has been studied before in the fMRI literature by assuming fixed parameter values in the error structure or by using real fMRI noise (Aguirre & D'Esposito, 1999;Smith et al, 2007;Wager & Nichols, 2003;Zarahn & Friston, 2002;Buračas & Boynton, 2002;Burock & Dale, 2000). As a result, the found optimal designs may not be robust against misspecification of these parameters.…”

Section: Introductionmentioning

confidence: 99%

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Optimal experimental designs for functional magnetic resonance imaging

Maus¹

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“…The maximin approach has been applied in optimal design theory to construct designs which are robust against misspecification of parameters in various models, e.g., the linear mixed model (Berger & Tan, 2004;Ouwens, Tan & Berger, 2002) or exponential regression models (Dette, Martinez Lopez, Ortiz Rodriguez & Pepelyshev, 2006). The effect of autocorrelation on optimal design has been studied before in the fMRI literature by assuming fixed parameter values in the error structure or by using real fMRI noise (Aguirre & D'Esposito, 1999;Smith et al, 2007;Wager & Nichols, 2003;Zarahn & Friston, 2002;Buračas & Boynton, 2002;Burock & Dale, 2000). As a result, the found optimal designs may not be robust against misspecification of these parameters.…”

Section: Introductionmentioning

confidence: 99%