Lévy-based Modelling in Brain Imaging

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

Research output: Contribution to journalJournal articlepeer-review

Abstract

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.
Original languageEnglish
JournalScandinavian Journal of Statistics
Volume40
Issue number3
Pages (from-to)511-529
ISSN0303-6898
DOIs
Publication statusPublished - 2013
Externally publishedYes

Keywords

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

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