Lévy-based Modelling in Brain Imaging
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Lévy-based Modelling in Brain Imaging. / Jónsdóttir, Kristjana Ýr; Rønn-Nielsen, Anders; Mouridsen, Kim; Jensen, Eva B. Vedel.
In: Scandinavian Journal of Statistics, Vol. 40, No. 3, 09.2013, p. 511-529.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
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
VL - 40
SP - 511
EP - 529
JO - Scandinavian Journal of Statistics
JF - Scandinavian Journal of Statistics
SN - 0303-6898
IS - 3
ER -
ID: 92322951