Fitting Latent Non-Gaussian Models Using Variational Bayes and Laplace Approximations
针对潜在非高斯模型缺乏快速实现和易用软件的问题，本文推导了变分贝叶斯算法，并开发了ngvb包，只需一行代码即可将R-INLA中的潜在高斯模型扩展为非高斯模型，适用于时间序列、区域数据和空间模型。
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 Matérn 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.