Controlling the flexibility of non-Gaussian processes through shrinkage priors
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The normal inverse Gaussian (NIG) and generalized asymmetric Laplace (GAL) distributions can be seen as skewed and heavy-tailed extensions of the Gaussian distribution. Models driven by these more flexible noise distributions are then regarded as generalizations of simpler Gaussian models. Inferential procedures tend to overestimate the degree of non-Gaussianity in the data and in this paper we propose controlling the flexibility of these non-Gaussian models by adding sensible priors in the inferential framework that contract the model towards Gaussianity. The methods are derived for a generic class of non-Gaussian models that include non-Gaussian spatial Matérn fields, autoregressive models for time series, and simultaneous autoregressive models for aerial data. The results are illustrated with a simulation study, 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 of asymmetry and leptokurtosis in the data. We also propose a new method for assessing if there is enough support in the data for choosing the non-Gaussian model over the simpler Gaussian model and show how to determine at which time points or regions in space the Gaussian model lacks flexibility.
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