Sparse linear mixed model selection via streamlined variational Bayes

Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random from multiple sources of variability. In many situations, large number candidate is available it interest select parsimonious subset those being effectively relevant predicting the response variable. Variational approximations facilitate fast approximate Bayesian inference parameters variety models, including linear models. However, having high or effects, simple application standard variational principles does not lead algorithms, due size model design matrices inefficient treatment sparse matrix problems arising required approximating density updates. We illustrate how recently developed streamlined procedures can be generalized make accurate with nested global-local priors selection. Our algorithms achieve convergence same optima their implementations, although significantly lower computational effort, memory usage time, especially numbers effects. Using simulated real examples, we assess quality automated selection that free hyperparameters tuning only rely upon posterior approximations. Moreover, show accuracy against fitting via Markov Chain Monte Carlo sampling.