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

Controlling the flexibility of non-Gaussian processes through shrinkage priors