Lévy-based Modelling in Brain Imaging

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

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review


A substantive problem in neuroscience is the lack of valid statistical methods for nonGaussian 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 Levy 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) Levy 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 Levy model
TidsskriftScandinavian Journal of Statistics
Udgave nummer3
Sider (fra-til)511-529
StatusUdgivet - 2013
Udgivet eksterntJa


  • Covariance
  • Cumulant
  • Gaussian random field
  • Matern covariance function
  • Non-Gaussian random field
  • Normal inverse Gaussian Levy basis


Jónsdóttir, K. Ý., Rønn-Nielsen, A., Mouridsen, K., & Jensen, E. B. V. (2013). Lévy-based Modelling in Brain Imaging. Scandinavian Journal of Statistics, 40(3), 511-529. https://doi.org/10.1002/sjos.12000