Controlling the flexibility of non-Gaussian processes through shrinkage priors

TL;DR

This paper introduces priors that control the degree of non-Gaussianity in models driven by NIG and GAL distributions, promoting robustness and model simplicity while allowing for non-Gaussian features if supported by data.

Contribution

It proposes a new parameterization and priors for non-Gaussian models, enabling controlled flexibility and efficient implementation in Stan.

Findings

Priors lead to more robust estimation.

Preference for Gaussian models when appropriate.

Effective in spatial and time series models.

Abstract

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 Mat\'ern 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.