Fitting Latent Non-Gaussian Models Using Variational Bayes and Laplace Approximations

• 成果类型: Article
• 署名作者: Cabral, Rafael; Bolin, David; Rue, Havard
• 署名单位: King Abdullah University of Science & Technology
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2296704
• 发表日期: 2024
• 页码: 2983-2995
• 关键词: inference; distributions; inla; car

摘要

Latent Gaussian models (LGMs) are perhaps the most commonly used class of models in statistical applications. Nevertheless, in areas ranging from longitudinal studies in biostatistics to geostatistics, it is easy to find datasets that contain inherently non-Gaussian features, such as sudden jumps or spikes, that adversely affect the inferences and predictions made using an LGM. These datasets require more general latent non-Gaussian models (LnGMs) that can handle automatically these non-Gaussian features. However, fast implementation and easy-to-use software are lacking, preventing the broad applicability of LnGMs. In this article, we derive variational Bayes algorithms for fast and scalable inference of LnGMs. The approximation leads to an LGM that downweights extreme events in the latent process, reducing their influence and leading to more robust inferences. It can be applied to a wide range of models, such as autoregressive processes for time series, simultaneous autoregressive models for areal data, and spatial Matern models. To facilitate Bayesian inference, we introduce the ngvb package, where LGMs implemented in R-INLA can be easily extended to LnGMs by adding a single line of code. Supplementary materials for this article are available online.