Bayesian Boosting for Linear Mixed Models
This addresses the need for precise uncertainty estimates and covariate selection in high-dimensional data analysis for fields like neurophysiology, representing an incremental improvement by integrating existing techniques.
The paper tackled the problem of uncertainty estimation in boosting methods for linear mixed models by proposing BayesBoost, which combines boosting and Bayesian inference to enable uncertainty estimation for random effects and improve covariate selection, with effectiveness demonstrated through simulation and a neurophysiology data example.
Boosting methods are widely used in statistical learning to deal with high-dimensional data due to their variable selection feature. However, those methods lack straightforward ways to construct estimators for the precision of the parameters such as variance or confidence interval, which can be achieved by conventional statistical methods like Bayesian inference. In this paper, we propose a new inference method "BayesBoost" that combines boosting and Bayesian for linear mixed models to make the uncertainty estimation for the random effects possible on the one hand. On the other hand, the new method overcomes the shortcomings of Bayesian inference in giving precise and unambiguous guidelines for the selection of covariates by benefiting from boosting techniques. The implementation of Bayesian inference leads to the randomness of model selection criteria like the conditional AIC (cAIC), so we also propose a cAIC-based model selection criteria that focus on the stabilized regions instead of the global minimum. The effectiveness of the new approach can be observed via simulation and in a data example from the field of neurophysiology focussing on the mechanisms in the brain while listening to unpleasant sounds.