A Unified and Computationally Efficient Non-Gaussian Statistical Modeling Framework

TL;DR

This paper introduces LLnGMs, a unified, efficient framework for modeling non-Gaussian data across various fields, extending latent Gaussian models with Bayesian inference and software implementation.

Contribution

It presents a novel, unified framework for non-Gaussian modeling that extends latent Gaussian models, with efficient Bayesian inference and an R package for practical use.

Findings

Framework unifies various non-Gaussian models.

Efficient Bayesian inference with theoretical guarantees.

Demonstrated applications in spatial and spatio-temporal modeling.

Abstract

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.