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.

翻译：在许多领域中，呈现非高斯特性的数据集十分常见，而当前针对非高斯模型的建模框架和可用软件却相当有限。我们提出了线性潜变量非高斯模型，这是一个统一且计算高效的统计建模框架，它将一类潜变量高斯模型扩展至允许潜变量非高斯过程。该框架统一了从简单的时间模型到复杂的时空及多元模型在内的多种流行模型，从而促进了自然的非高斯扩展。基于随机梯度下降估计，我们开发了具有理论保证的计算高效的贝叶斯推断方法。实现了该框架的R包 \texttt{ngme2} 被提出，并通过包括新颖的非高斯空间与时空模型在内的广泛应用进行了演示。