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

Statistical Theory and Related Fields 2022年第4期6卷 309-326页

作者： Cong Lin Dongchu Sun Chengyuan Song School of Statistics East China Normal UniversityShanghaiPeople's Republic of China Department of Statistics University of Nebraska-LincolnLincolnNEUSA Boehringer Ingelheim(China) ShanghaiPeople's Republic of China

Bayesian Hierarchical models has been widely used in modern statistical *** 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 *** 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 *** tackle this issue,[Berger,J,Sun,D.&Song,C.(2020b).An objective prior for hyperparameters in normal hierarchical *** of Multi-variate Analysis,178,***://***/10.1016/jmva.2020.104606]proposed a particular objective prior and investigated its properties *** propriety is important for the choice of priors to guarantee the convergence of MCMC *** 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,*** this paper,we complete this story and provide an user friendly *** 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 *** 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

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Bayesian analysis for the Lomax model using noninformative priors

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Statistical Theory and Related Fields 2023年第1期7卷 61-68页

作者： Daojiang He Dongchu Sun Qing Zhu Department of Statistics Anhui Normal UniversityWuhuPeople’s Republic of China Department of Statistics University of Nebraska-LincolnLincolnNEUSA

The Lomax distribution is an important member in the distribution *** this paper,we systematically develop an objective Bayesian analysis of data from a Lomax ***informative priors,including probability matching priors,the maximal data information(MDI)prior,Jeffreys prior and reference priors,are *** propriety of the posterior under each prior is subsequently *** is revealed that the MDI prior and one of the reference priors yield improper posteriors,and the other reference prior is a second-order probability matching prior.A simulation study is conducted to assess the frequentist performance of the proposed Bayesian ***,this approach along with the bootstrap method is applied to a real data set.

关键词： Lomax model probability matching priors MDI prior Jeffreys prior reference priors posterior propriety

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Bayesian analysis for quantile smoothing spline

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Statistical Theory and Related Fields 2021年第4期5卷 346-364页

作者： Zhongheng Cai Dongchu Sun Faculty of Economics and Management School of StatisticsEast China Normal UniversityShanghaiPeople's Republic of China Department of Statistics University of Nebraska-LincolnLincolnNEUSA

In Bayesian quantile smoothing spline[Thompson,P.,Cai,Y.,Moyeed,R.,Reeve,D.,&Stander,J.(2010).Bayesian nonparametric quantile regression using *** Statistics and Data Analysis,54,1138-1150.],a fixed-scale parameter in the asymmetric Laplace likelihood tends to result in misleading fitted *** solve this problem,we propose a new Bayesian quantile smoothing spline(NBQSS),which considers a random scale *** begin with,we justify its objective prior options by establishing one sufficient and one necessary condition of the posterior propriety under two classes of general priors including the invariant prior for the scale *** then develop partially collapsed Gibbs sampling to facilitate the *** of a practical concern,we extend the theoretical results to NBQSS with unobserved ***,simulation studies and two real data analyses reveal three main ***,NBQSS usually outperforms other competing curve fitting ***,NBQSS consid-ering unobserved knots behaves better than the NBQSS without unobserved knots in terms of estimation accuracy and ***,NBQSS is robust to possible outliers and could provide accurate estimation.

关键词： asymmetric Laplace likelihood objective Bayesian analysis posterior propriety quantile regression smoothing spline

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