Latent non-Gaussian models and efficient estimation using variational Bayes

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 from an LGM. These datasets require more general latent non-Gaussian models (LnGMs) that can handle these non-Gaussian features automatically. However, fast implementation and easy-to-use software are lacking, which prevent LnGMs from becoming widely applicable. In this seminar, I will present the generic class of LnGMs and variational Bayes algorithms for fast and scalable inference of LnGMs. The methods 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 have built the ngvb package, where LGMs implemented in R-INLA can be easily extended to LnGMs by adding a single line of code.

Paper: https://arxiv.org/abs/2211.11050

Package: https://github.com/rafaelcabral96/ngvb