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Lévy‐based Modelling in Brain Imaging
Author(s) -
JÓNSDÓTTIR KRISTJANA ÝR,
RØNNNIELSEN ANDERS,
MOURIDSEN KIM,
VEDEL JENSEN EVA B.
Publication year - 2013
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1002/sjos.12000
Subject(s) - gaussian , inverse gaussian distribution , gaussian random field , mathematics , random field , smoothing , statistical physics , gaussian function , kernel (algebra) , statistics , mathematical analysis , discrete mathematics , physics , distribution (mathematics) , quantum mechanics
. 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.