Posterior propriety of an objective prior for generalized hierarchical normal linear models  

作　　者：Cong Lin Dongchu Sun Chengyuan Song 

机构地区：[1]School of Statistics,East China Normal University,Shanghai,People's Republic of China [2]Department of Statistics,University of Nebraska-Lincoln,Lincoln,NE,USA [3]Boehringer Ingelheim(China),Shanghai,People's Republic of China

出　　处：《Statistical Theory and Related Fields》2022年第4期309-326,共18页统计理论及其应用（英文）

基　　金：The research was supported by the National Natural Science Foundation of China[grant number 11671146].

摘　　要：Bayesian Hierarchical models has been widely used in modern statistical application.To deal with the data having complex structures,we propose a generalized hierarchical normal linear(GHNL)model which accommodates arbitrarily many levels,usual design matrices and'vanilla'covari-ance matrices.Objective hyperpriors can be employed for the GHNL model to express ignorance or match frequentist properties,yet the common objective Bayesian approaches are infeasible or fraught with danger in hierarchical modelling.To tackle this issue,[Berger,J,Sun,D.&Song,C.(2020b).An objective prior for hyperparameters in normal hierarchical models.Journal of Multi-variate Analysis,178,104606.https://doi.org/10.1016/jmva.2020.104606]proposed a particular objective prior and investigated its properties comprehensively.Posterior propriety is important for the choice of priors to guarantee the convergence of MCMC samplers.James Berger conjec-tured that the resulting posterior is proper for a hierarchical normal model with arbitrarily many levels,a rigorous proof of which was not given,however.In this paper,we complete this story and provide an user friendly guidance.One main contribution of this paper is to propose a new technique for deriving an elaborate upper bound on the integrated likelihood but also one uni-fied approach to checking the posterior propriety for linear models.An eficient Gibbs sampling method is also introduced and outperforms other sampling approaches considerably.

关 键 词：Hierarchical linear model linear mixed-effect model objective Bayesian analysis posterior propriety Gibbs sampling 

分 类 号：O17[理学—数学]