A Unified and Computationally Efficient Non-Gaussian Statistical Modeling Framework
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918359987126272 |
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| author | Bolin, David Jin, Xiaotian Simas, Alexandre B. Wallin, Jonas |
| author_facet | Bolin, David Jin, Xiaotian Simas, Alexandre B. Wallin, Jonas |
| contents | Datasets that exhibit non-Gaussian characteristics are common in many fields, while the current modeling framework and available software for non-Gaussian models is limited. We introduce Linear Latent Non-Gaussian Models (LLnGMs), a unified and computationally efficient statistical modeling framework that extends a class of latent Gaussian models to allow for latent non-Gaussian processes. The framework unifies several popular models, from simple temporal models to complex spatial-temporal and multivariate models, facilitating natural non-Gaussian extensions. Computationally efficient Bayesian inference, with theoretical guarantees, is developed based on stochastic gradient descent estimation. The R package \texttt{ngme2}, which implements the framework, is presented and demonstrated through a wide range of applications including novel non-Gaussian spatial and spatio-temporal models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23987 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Unified and Computationally Efficient Non-Gaussian Statistical Modeling Framework Bolin, David Jin, Xiaotian Simas, Alexandre B. Wallin, Jonas Methodology Datasets that exhibit non-Gaussian characteristics are common in many fields, while the current modeling framework and available software for non-Gaussian models is limited. We introduce Linear Latent Non-Gaussian Models (LLnGMs), a unified and computationally efficient statistical modeling framework that extends a class of latent Gaussian models to allow for latent non-Gaussian processes. The framework unifies several popular models, from simple temporal models to complex spatial-temporal and multivariate models, facilitating natural non-Gaussian extensions. Computationally efficient Bayesian inference, with theoretical guarantees, is developed based on stochastic gradient descent estimation. The R package \texttt{ngme2}, which implements the framework, is presented and demonstrated through a wide range of applications including novel non-Gaussian spatial and spatio-temporal models. |
| title | A Unified and Computationally Efficient Non-Gaussian Statistical Modeling Framework |
| topic | Methodology |
| url | https://arxiv.org/abs/2602.23987 |