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Lévy-based modelling in brain imaging. (English) Zbl 1364.62261

Summary: 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.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
92C55 Biomedical imaging and signal processing
62M40 Random fields; image analysis
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