The Wiener process as a degradation model plays an important role in the degradation analysis.In this paper, we propose an objective Bayesian analysis for an acceleration degradation Wienermodel which is subjected to ...The Wiener process as a degradation model plays an important role in the degradation analysis.In this paper, we propose an objective Bayesian analysis for an acceleration degradation Wienermodel which is subjected to measurement errors. The Jeffreys prior and reference priors underdifferent group orderings are first derived, the propriety of the posteriors is then validated. It isshown that two of the reference priors can yield proper posteriors while the others cannot. A simulation study is carried out to investigate the frequentist performance of the approach comparedto the maximum likelihood method. Finally, the approach is applied to analyse a real data.展开更多
In Bayesian quantile smoothing spline[Thompson,P.,Cai,Y.,Moyeed,R.,Reeve,D.,&Stander,J.(2010).Bayesian nonparametric quantile regression using splines.Computational Statistics and Data Analysis,54,1138-1150.],a fi...In Bayesian quantile smoothing spline[Thompson,P.,Cai,Y.,Moyeed,R.,Reeve,D.,&Stander,J.(2010).Bayesian nonparametric quantile regression using splines.Computational Statistics and Data Analysis,54,1138-1150.],a fixed-scale parameter in the asymmetric Laplace likelihood tends to result in misleading fitted curves.To solve this problem,we propose a new Bayesian quantile smoothing spline(NBQSS),which considers a random scale parameter.To 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 component.We then develop partially collapsed Gibbs sampling to facilitate the compu-tation.Out of a practical concern,we extend the theoretical results to NBQSS with unobserved knots.Finally,simulation studies and two real data analyses reveal three main findings.Firstly,NBQSS usually outperforms other competing curve fitting methods.Secondly,NBQSS consid-ering unobserved knots behaves better than the NBQSS without unobserved knots in terms of estimation accuracy and precision.Thirdly,NBQSS is robust to possible outliers and could provide accurate estimation.展开更多
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 arb...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.展开更多
基金The work is supported by the Humanities and Social Sciences Foundation of Ministry of Education,China(Grant No.17YJC910003).
文摘The Wiener process as a degradation model plays an important role in the degradation analysis.In this paper, we propose an objective Bayesian analysis for an acceleration degradation Wienermodel which is subjected to measurement errors. The Jeffreys prior and reference priors underdifferent group orderings are first derived, the propriety of the posteriors is then validated. It isshown that two of the reference priors can yield proper posteriors while the others cannot. A simulation study is carried out to investigate the frequentist performance of the approach comparedto the maximum likelihood method. Finally, the approach is applied to analyse a real data.
基金The project was supported by the National Natural Science Foundation of China[Grant Number 11671146].
文摘In Bayesian quantile smoothing spline[Thompson,P.,Cai,Y.,Moyeed,R.,Reeve,D.,&Stander,J.(2010).Bayesian nonparametric quantile regression using splines.Computational Statistics and Data Analysis,54,1138-1150.],a fixed-scale parameter in the asymmetric Laplace likelihood tends to result in misleading fitted curves.To solve this problem,we propose a new Bayesian quantile smoothing spline(NBQSS),which considers a random scale parameter.To 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 component.We then develop partially collapsed Gibbs sampling to facilitate the compu-tation.Out of a practical concern,we extend the theoretical results to NBQSS with unobserved knots.Finally,simulation studies and two real data analyses reveal three main findings.Firstly,NBQSS usually outperforms other competing curve fitting methods.Secondly,NBQSS consid-ering unobserved knots behaves better than the NBQSS without unobserved knots in terms of estimation accuracy and precision.Thirdly,NBQSS is robust to possible outliers and could provide accurate estimation.
基金The research was supported by the National Natural Science Foundation of China[grant number 11671146].
文摘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.
