  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.
