Controlling the Flexibility of Non-Gaussian Processes Through Shrinkage Priors

Rafael Cabral∗, David Bolin, Håvard Rue

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The normal inverse Gaussian (NIG) and generalized asymmetric Laplace (GAL) distributions can be seen as skewed and semi-heavy-tailed extensions of the Gaussian distribution. Models driven by these more flexible noise distributions are then regarded as flexible extensions of simpler Gaussian models. Inferential procedures tend to overestimate the degree of non-Gaussianity in the data and therefore we propose controlling the flexibility of these non-Gaussian models by adding sensible priors in the inferential framework that contract the model towards Gaussianity. In our venture to derive sensible priors, we also propose a new intuitive parameterization of the non-Gaussian models and discuss how to implement them efficiently in Stan. The methods are derived for a generic class of non-Gaussian models that include spatial Matérn fields, autoregressive models for time series, and simultaneous autoregressive models for aerial data. The results are illustrated with a simulation study and geostatistics application, where priors that penalize model complexity were shown to lead to more robust estimation and give preference to the Gaussian model, while at the same time allowing for non-Gaussianity if there is sufficient evidence in the data.

Original languageEnglish (US)
Pages (from-to)1223-1246
Number of pages24
Issue number4
StatePublished - 2023

Bibliographical note

Publisher Copyright:
© (2023) International Society for Bayesian Analysis


  • Bayesian
  • generalized asymmetric Laplace
  • Matérn covariance
  • non-Gaussian
  • normal inverse Gaussian
  • penalized complexity
  • priors
  • SPDE

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics


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