Controlling the flexibility of non-Gaussian processes through shrinkage priors

dc.contributor.authorCabral, Rafael
dc.contributor.authorBolin, David
dc.contributor.authorRue, H˚avard
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.contributor.departmentStatistics Program
dc.date.accessioned2022-11-08T09:19:15Z
dc.date.available2022-05-16T08:35:07Z
dc.date.available2022-11-08T09:19:15Z
dc.date.issued2022-10-29
dc.description.abstractThe 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 nonGaussian 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.
dc.eprint.versionPost-print
dc.identifier.arxivid2203.05510
dc.identifier.journalBayesian Analysis
dc.identifier.urihttps://repository.kaust.edu.sa/handle/10754/677946.2
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2203.05510.pdf
dc.rightsThis is an accepted manuscript version of a paper before final publisher editing and formatting. The version of record is available from Bayesian Analysis.
dc.titleControlling the flexibility of non-Gaussian processes through shrinkage priors
dc.typeArticle
display.details.left<span><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Cabral, Rafael,equals">Cabral, Rafael</a><br><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0003-2361-5465&spc.sf=dc.date.issued&spc.sd=DESC">Bolin, David</a> <a href="https://orcid.org/0000-0003-2361-5465" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0002-0222-1881&spc.sf=dc.date.issued&spc.sd=DESC">Rue, H˚avard</a> <a href="https://orcid.org/0000-0002-0222-1881" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><br><h5>KAUST Department</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division,equals">Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Statistics Program,equals">Statistics Program</a><br><br><h5>Date</h5>2022-10-29</span>
display.details.right<span><h5>Abstract</h5>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 nonGaussian 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.<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=arXiv,equals">arXiv</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=Bayesian Analysis,equals">Bayesian Analysis</a><br><br><h5>arXiv</h5><a href="https://arxiv.org/abs/2203.05510">2203.05510</a><br><br><h5>Additional Links</h5>https://arxiv.org/pdf/2203.05510.pdf</span>
kaust.personCabral, Rafael
kaust.personBolin, David
kaust.personRue, H˚avard
orcid.authorCabral, Rafael
orcid.authorBolin, David::0000-0003-2361-5465
orcid.authorRue, H˚avard::0000-0002-0222-1881
orcid.id0000-0002-0222-1881
orcid.id0000-0003-2361-5465
refterms.dateFOA2022-05-16T08:35:58Z
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