Variational Inference of Bayesian Quantile Regression in Linear Mixed Effect Model
Bayesian quantile regression can well estimate the parameters in the lin-ear mixed effect model.Gibbs sampling is commonly used in Bayesian parameter estimation.In order to obtain accurate estimation results,Gibbs sampling method requires multiple sampling.When the model parameter dimension is high,the Gibbs sampling will be very time-consuming.Therefore,we use variational inference to ap-proximate the posterior distribution of parameters.Variational inference uses uncon-ditional distribution to approximate the conditional distribution obtained by Gibbs method,thus making the calculation more efficient.In this paper,a priori assumption of the parameters of the model is normal distribution,and the variation inference of the parameters of the unpunished linear mixed effect model is carried out.Considering the high dimensional situation,we assume the prior distribution of the model param-eters as Laplace distribution,and make variational inference for the parameters of the double penalty linear mixed effect model.From the simulation results,although the accuracy of variational inference for model parameter estimation is slightly less than that of Gibbs sampling,it runs faster.In the case of high dimension,the improvement of operation efficiency is more obvious.In the era of big data,the consumption of time and resources is the first factor we need to consider.Therefore,the method proposed in this paper can be applied to the high-dimensional linear mixed effect model.
万方数据
维普
