Variational Approximations for Bayesian and Semi-Bayesian Inferences

Explore variational approximations for Bayesian and semi-Bayesian inferences in this comprehensive conference talk by Jun S. Liu at #ICBS2024. Begin with a review of basic frameworks for optimization and integration before delving into detailed formulations and challenges in two characteristic statistical problems. Examine Bayesian group-variable selection for linear regression and non-linear additive models, as well as the modeling and inference of heteroscedastic Gaussian processes and their extensions. Learn how latent structures are introduced to facilitate easier computations and discover the use of variational approximations for explicit marginalization of hidden functions, resulting in efficient parameter estimation and process forecasting. Gain insights into the advantages of these methods through simulations and real-data examples of regression, classification, and state-space models. This talk is based on joint work with Taehee Lee, Buyu Lin, and Changhao Ge, offering a deep dive into advanced statistical techniques and their practical applications.