Lévy-based Modelling in Brain Imaging

Kristjana Ýr Jónsdóttir; Anders Rønn-Nielsen; Kim Mouridsen; Eva B. Vedel Jensen

doi:10.1002/sjos.12000

Lévy-based Modelling in Brain Imaging

Kristjana Ýr Jónsdóttir, Anders Rønn-Nielsen, Kim Mouridsen, Eva B. Vedel Jensen

Institut for Matematiske Fag

16 Citationer (Scopus)

Abstract

A substantive problem in neuroscience is the lack of valid statistical methods for non-Gaussian random fields. In the present study, we develop a flexible, yet tractable model for a random field based on kernel smoothing of a so-called Lévy basis. The resulting field may be Gaussian, but there are many other possibilities, including random fields based on Gamma, inverse Gaussian and normal inverse Gaussian (NIG) Lévy bases. It is easy to estimate the parameters of the model and accordingly to assess by simulation the quantiles of test statistics commonly used in neuroscience. We give a concrete example of magnetic resonance imaging scans that are non-Gaussian. For these data, simulations under the fitted models show that traditional methods based on Gaussian random field theory may leave small, but significant changes in signal level undetected, while these changes are detectable under a non-Gaussian Lévy model.

Originalsprog	Engelsk
Tidsskrift	Scandinavian Journal of Statistics
Vol/bind	40
Udgave nummer	3
Sider (fra-til)	511-529
ISSN	0303-6898
DOI	https://doi.org/10.1002/sjos.12000
Status	Udgivet - sep. 2013

Adgang til dokumentet

10.1002/sjos.12000

Citationsformater

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title = "L{\'e}vy-based Modelling in Brain Imaging",

abstract = "A substantive problem in neuroscience is the lack of valid statistical methods for non-Gaussian random fields. In the present study, we develop a flexible, yet tractable model for a random field based on kernel smoothing of a so-called L{\'e}vy basis. The resulting field may be Gaussian, but there are many other possibilities, including random fields based on Gamma, inverse Gaussian and normal inverse Gaussian (NIG) L{\'e}vy bases. It is easy to estimate the parameters of the model and accordingly to assess by simulation the quantiles of test statistics commonly used in neuroscience. We give a concrete example of magnetic resonance imaging scans that are non-Gaussian. For these data, simulations under the fitted models show that traditional methods based on Gaussian random field theory may leave small, but significant changes in signal level undetected, while these changes are detectable under a non-Gaussian L{\'e}vy model.",

author = "J{\'o}nsd{\'o}ttir, {Kristjana {\'Y}r} and Anders R{\o}nn-Nielsen and Kim Mouridsen and Jensen, {Eva B. Vedel}",

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T1 - Lévy-based Modelling in Brain Imaging

AU - Jónsdóttir, Kristjana Ýr

AU - Rønn-Nielsen, Anders

AU - Mouridsen, Kim

AU - Jensen, Eva B. Vedel

PY - 2013/9

Y1 - 2013/9

N2 - A substantive problem in neuroscience is the lack of valid statistical methods for non-Gaussian random fields. In the present study, we develop a flexible, yet tractable model for a random field based on kernel smoothing of a so-called Lévy basis. The resulting field may be Gaussian, but there are many other possibilities, including random fields based on Gamma, inverse Gaussian and normal inverse Gaussian (NIG) Lévy bases. It is easy to estimate the parameters of the model and accordingly to assess by simulation the quantiles of test statistics commonly used in neuroscience. We give a concrete example of magnetic resonance imaging scans that are non-Gaussian. For these data, simulations under the fitted models show that traditional methods based on Gaussian random field theory may leave small, but significant changes in signal level undetected, while these changes are detectable under a non-Gaussian Lévy model.

AB - A substantive problem in neuroscience is the lack of valid statistical methods for non-Gaussian random fields. In the present study, we develop a flexible, yet tractable model for a random field based on kernel smoothing of a so-called Lévy basis. The resulting field may be Gaussian, but there are many other possibilities, including random fields based on Gamma, inverse Gaussian and normal inverse Gaussian (NIG) Lévy bases. It is easy to estimate the parameters of the model and accordingly to assess by simulation the quantiles of test statistics commonly used in neuroscience. We give a concrete example of magnetic resonance imaging scans that are non-Gaussian. For these data, simulations under the fitted models show that traditional methods based on Gaussian random field theory may leave small, but significant changes in signal level undetected, while these changes are detectable under a non-Gaussian Lévy model.

U2 - 10.1002/sjos.12000

DO - 10.1002/sjos.12000

M3 - Journal article

SN - 0303-6898

VL - 40

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EP - 529

JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

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