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Objective Bayesian Analysis of Degradation Model with Respect to a Wiener Process

Journal of Systems Science & Complexity 2016年第6期29卷 1737-1751页

作者： HE Lei HE Daojiang CAO Mingxiang Department of Statistics Anhui Normal University

This paper proposes an objective Bayesian method to study the degradation model with respect to a Wiener *** jeffreys prior and reference prior for the parameters are derived,and the propriety of the posteriors under these priors is *** sampling algorithms are introduced to compute the posteriors.A simulation study is conducted to investigate the performance of the objective Bayesian ***,the authors apply the approach to a degradation data.

关键词： Degradation model jeffreys prior objective Bayes reference prior.

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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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Objective Bayesian analysis for the accelerated degradation model usingWiener process with measurement errors

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Statistical Theory and Related Fields 2018年第1期2卷 27-36页

作者： Daojiang He Yunpeng Wang Mingxiang Cao Department of Statistics Anhui Normal UniversityWuhu 241003China

The Wiener process as a degradation model plays an important role in the degradation *** 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.

关键词： Accelerated degradation model objective Bayesian analysis Wiener process measurement errors jeffreys prior reference prior

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Learning Gaussian mixture with automatic model selection:A comparative study on three Bayesian related approaches

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Frontiers of Electrical and Electronic Engineering in China 2011年第2期6卷 215-244页

作者： Lei SHI Shikui TU Lei XU Department of Computer Science and Engineering The Chinese University of Hong KongHong KongChina

Three Bayesian related approaches,namely,variational Bayesian(VB),minimum message length(MML)and Bayesian Ying-Yang(BYY)harmony learning,have been applied to automatically determining an appropriate number of components during learning Gaussian mixture model(GMM).This paper aims to provide a comparative investigation on these approaches with not only a jeffreys prior but also a conjugate Dirichlet-Normal-Wishart(DNW)prior on *** addition to adopting the existing algorithms either directly or with some modifications,the algorithm for VB with jeffreys prior and the algorithm for BYY with DNW prior are developed in this paper to fill the missing *** performances of automatic model selection are evaluated through extensive experiments,with several empirical findings:1)Considering priors merely on the mixing weights,each of three approaches makes biased mistakes,while considering priors on all the parameters of GMM makes each approach reduce its bias and also improve its performance.2)As jeffreys prior is replaced by the DNW prior,all the three approaches improve their ***,jeffreys prior makes MML slightly better than VB,while the DNW prior makes VB better than MML.3)As the hyperparameters of DNW prior are further optimized by each of its own learning principle,BYY improves its performances while VB and MML deteriorate their performances when there are too many free ***,VB and MML lack a good guide for optimizing the hyper-parameters of DNW prior.4)BYY considerably outperforms both VB and MML for any type of priors and whether hyper-parameters are *** different from VB and MML that rely on appropriate priors to perform model selection,BYY does not highly depend on the type of *** has model selection ability even without priors and performs already very well with jeffreys prior,and incrementally improves as jeffreys prior is replaced by the DNW ***,all algorithms are applied on the Berkeley segment

关键词： Bayesian Ying-Yang(BYY)harmony learning variational Bayesian(VB) minimum message length(MML) empirical comparison Gaussian mixture model(GMM) automatic model selection jeffreys prior Dirichlet joint Normal-Wishart(NW) conjugate distributions marginalized student’s T-distribution

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