A Unified and Computationally Efficient Non-Gaussian Statistical Modeling Framework

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.