带有测量误差的Wiener退化模型的客观Bayes分析

本文研究了带有测量误差的Wiener退化模型的客观Bayes分析.对于该退化模型,利用重参数化导出了Jeffreys先验和reference先验,从理论上证明了其中两个reference先验所诱导的后验是正常的,而其它先验的后验均不正常.随机模拟研究了所提Bayes方法相对于最大似然估计的频率表现.最后,将所提方法应用到一个实际退化数据的分析中.     

突破性技术创新研发联盟伙伴选择研究

突破性技术创新研发联盟的研究已成为国内外学术界共同关注的重大理论和实践课题,而伙伴选择是研发联盟中一个十分重要的问题,伙伴挑选的成功与否直接关系到研发联盟的合作效果和成败.在分析Bernardo方法缺陷的基础上,提出改进的Bernardo方法,并将改进的Bernardo方法运用到突破性技术创新研发联盟的选择中,得到了候选伙伴的优劣排序.     

基于模糊不确定性理论的Bernardo方法

Bernardo方法是一种多属性群决策方法。针对Bernardo方法，本文结合模糊不确定性理论，提出“模糊Bernardo”方法；利用模糊变量表示决策者对多方案排序的模糊目标值，给出其Bernardo方法的模糊混合0-1规划模型和模糊机会约束混合0-1规划模型。该方法为群决策提供了一种多方案排序问题的实用且有效的理论依据和计算方法。最后通过实例对此方法予以验证。     

突破性创新研发联盟最优伙伴组合方案研究

突破性创新研发联盟的研究已成为国内外学术界共同关注的重大课题,而伙伴选择是研发联盟中一个十分重要的问题,伙伴挑选的成功与否直接关系到研发联盟的合作效果和成败.在分析Bernardo方法缺陷的基础上,提出改进的Bernardo方法,进而建立具有资源约束的伙伴选择的改进Bernardo模型,并将其应用到突破性创新研发联盟最优伙伴的选择中,不仅可以求得资源约束下候选伙伴的优劣排序,还能求得参与研发联盟的最优伙伴数量和最优伙伴组合方案.     

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本文主要讨论了变点的先验分布为beta-binomial分布 和Ibrahim等(2003)提出的幂型先验的条件下, 有一个变点的线性模型的贝叶斯统计推断问题, 并且我们假定变点两边的观测值的方差是相等的. 我们得到变点、回归系数、共同方差的后要分布的显示表达式. 本论文不仅把Ferrira(1975)论文从变点先验分布服从离散均匀分布推广到了更好描述变点 的形状的beta-binomial分布, 而且进一步将变点的先验分布推广到包含的历史信息的幂型先验. 当变点的先验分布为beta-binomial分布和幂型先验时, 模拟结果显示了贝叶斯方法具有更高的准确性.     

一些最大信息先验分布与广义最大熵先验分布

本文讨论了三种确定无信息先验分布的方法。利用熵不等式,简化了Zellnor(1984)关于最大数据信息先验分布的一条定理的证明,并得到了其唯一性。在此基础上提出了广义最大熵先验分布,它在某些方面改进了经典的最大熵原理,对于最大相关先验分布(即Lindley准则),我们得到了一个中间解,由此导出了许多常见分布族的最大相关先验分布。     

《统计决策论及贝叶斯分析》

书评 :《统计决策论及贝叶斯分析》是美国著名贝叶斯统计学家 J.O.Berger的一本专著 ,该书把 195 0年到 1985年间贝叶斯学派鼎盛时期的重要成果都包含在内 ,并按循育渐近的原则从引进二种非样本信息 (先验信息和后果信息 )开始逐步介绍贝叶斯分析与决策的基本思想、具体方法、只要具备微积分、概率与统计基本知识就可读懂全书 ,所以该书也是一本很好的专业课教材 ,一本贝叶斯统计的入门书 ,不少美国大学统计系都把该书前四章作为研究生教材使用 ,后四章让学生自己阅读并作专题研究。在我校我也多次试用这一方法 ,收效甚佳 ,学生得益匪浅。…     

双边定数截尾下Pareto分布的可靠性分析

基于双边定数截尾样本,选取未知参数的先验分布为无信息先验和Gamma分布,分别在平方损失和LINEX损失下,研究了Pareto分布的形状参数和可靠性指标(可靠度和失效率)的Bayes估计.为了研究估计的精度,采用Monte-Carlo模拟的方法给出了数值检验的例子.结果表明在LINEX损失下并选用Gamma先验分布时,参数的Bayes估计是最优的.     

在分子晶体中的一类广义非线性Schr(o)dinger方程组的初边值问题

研究了在分子晶体中的一类广义非线性Schr(o)dinger方程组的初边值问题.应用先验估计的方法,得到了整体解的存在性.     

基于维纳过程步进应力加速退化试验的客观贝叶斯分析

高可靠性产品在加速寿命试验中其失效数据经常比较少,利用步进应力加速退化试验来评估产品寿命分布是一种非常好的方法.本文基于维纳过程的步进应力加速退化试验模型利用客观贝叶斯方法获得了其模型参数的无信息先验(Jefferys先验和Reference先验).并证明了对应的后验分布都是正常的.对于Jefferys先验和Reference先验下的后验提出相应的Gibbs抽样算法.最后,我们模拟对比了客观贝叶斯估计、贝叶斯估计和极大似然估计,模拟结果揭示了客观贝叶斯方法的优良性.     

On the choice of a noninformative prior for Bayesian inference of discretized normal observations

We consider the task of Bayesian inference of the mean of normal observations when the available data have been discretized and when no prior knowledge about the mean and the variance exists. An application is presented which illustrates that the discretization of the data should not be ignored when their variability is of the order of the discretization step. We show that the standard (noninformative) prior for location-scale family distributions is no longer appropriate. We work out the reference prior of Berger and Bernardo, which leads to different and more reasonable results. However, for this prior the posterior also shows some non-desirable properties. We argue that this is due to the inherent difficulty of the considered problem, which also affects other methods of inference. We therefore complement our analysis by an empirical Bayes approach. While such proceeding overcomes the disadvantages of the standard and reference priors and appears to provide a reasonable inference, it may raise conceptual concerns. We conclude that it is difficult to provide a widely accepted prior for the considered problem.     

Bayesian inference using a noninformative prior for linear Gaussian random coefficient regression with inhomogeneous within-class variances

A Bayesian inference for a linear Gaussian random coefficient regression model with inhomogeneous within-class variances is presented. The model is motivated by an application in metrology, but it may well find interest in other fields. We consider the selection of a noninformative prior for the Bayesian inference to address applications where the available prior knowledge is either vague or shall be ignored. The noninformative prior is derived by applying the Berger and Bernardo reference prior principle with the means of the random coefficients forming the parameters of interest. We show that the resulting posterior is proper and specify conditions for the existence of first and second moments of the marginal posterior. Simulation results are presented which suggest good frequentist properties of the proposed inference. The calibration of sonic nozzle data is considered as an application from metrology. The proposed inference is applied to these data and the results are compared to those obtained by alternative approaches.     

Testing Hypotheses About the Power Law Process Under Failure Truncation Using Intrinsic Bayes Factors

Conventional Bayes factors for hypotheses testing cannot typically accommodate the use of standard noninformative priors, as such priors are defined only up to arbitrary constants which affect the values of the Bayes factors. To circumvent this problem, Berger and Pericchi (1996, J. Amer. Statist. Assoc., 19, 109-122) introduced a new criterion called the Intrinsic Bayes Factor (IBF). In this paper, we use their methodology to test several hypotheses regarding the shape parameter of the power law process. Assuming that we have data from the process according to the failure-truncation sampling scheme, we derive the arithmetic and geometric IBF's using the reference priors. We deduce a set of intrinsic priors that correspond to these IBF's, as the observed number of failures tends to infinity. We then use these results to analyze an actual data set on the failures of an aircraft generator.     

L log L criterion for a class of multitype superdiffusions with non-local branching mechanisms

In this paper, we provide a pathwise spine decomposition for multitype superdiffusions with nonlocal branching mechanisms under a martingale change of measure. As an application of this decomposition,we obtain a necessary and sufficient condition(called the L log L criterion) for the limit of the fundamental martingale to be non-degenerate. This result complements the related results obtained in Kyprianou et al.(2012),Kyprianou and Murillo-Salas(2013) and Liu et al.(2009) for superprocesses with purely local branching mechanisms and in Kyprianou and Palau(2018) for super Markov chains.     

行m-NSD随机变量阵列的完全收敛性

本文研究了行m-NSD随机变量阵列的完全收敛性问题.主要利用m-NSD随机变量的Kolmogorov型指数不等式,获得了行m-NSD随机变量阵列的完全收敛性定理,将Hu等（1998）andSung等（2005）的结果从独立情形推广到了m-NSD随机变量阵列.本文的结论同样推广了Chen等（2008）,Hu等（2009）,Qiu等（2011）和Wang等（2014）的结果.     

多重响应的非参数预测的渐近贝叶斯设计

本文研究在单位方体上多重响应预测的试验设计问题.将多重响应函数视作相互独立的无限维随机过程的实现,因此我们采用非参数贝叶斯方法及渐近技术建立渐近贝叶斯设计准则.在一定条件下,我们证明单位方体上的均匀设计测度是最优渐近贝叶斯设计.     

Convergence analysis of a modified inexact implicit method for general mixed monotone variational inequalities

We consider a useful modification of the inexact implicit method with a variable parameter in Wang et al. J Optim Theory 111: 431–443 (2001) for generalized mixed monotone variational inequalities. One of the contributions of the proposed method in this paper is that the restrictions imposed on the variable parameter are weaker than the ones in Wang et al. J Optim Theory 111: 431–443 (2001). Another contribution is that we establish a sufficient and necessary condition for the convergence of the proposed method to a solution of the general mixed monotone variational inequality.     

On minimaxity and admissibility of hierarchical Bayes estimators

This paper obtains conditions for minimaxity of hierarchical Bayes estimators in the estimation of a mean vector of a multivariate normal distribution. Hierarchical prior distributions with three types of second stage priors are treated. Conditions for admissibility and inadmissibility of the hierarchical Bayes estimators are also derived using the arguments in Berger and Strawderman [Choice of hierarchical priors: admissibility in estimation of normal means, Ann. Statist. 24 (1996) 931-951]. Combining these results yields admissible and minimax hierarchical Bayes estimators.     

嵌入全球金融因子的中国广义灵活动态金融状况指数构建及应用--基于MI-TVP-SV-SFAVAR模型的实证分析

借鉴Thompson等(2013)[1]嵌入全球金融因子的做法,在周德才等(2015)[2]的基础上,从利率、信贷、货币供给、房价、股价和全球金融6类共30个金融指标中分别提取6个结构公因子,使用新建的MI-TVP-SV-SFAVAR模型,提出并測度了中国广义灵活动态金融状况指数(BFDFCI),进而分析其与通胀的关系,并与不包含全球金融因子的NFDFCI进行比较。结果表明:与NFDFCI相比,BFDFCI是通胀更优的领先性、相关性、因果性和预测指标,并明显优于FCI的已有研究;BFDFCI的权重是灵活时变的,其中全球金融因子的权重在世界金融危机后一直居于首位。     

倒向随机微分方程Lp解的性质

2003年Briand et al等在很一般的假设下建立了倒向随机微分方程（BSDEs）L^p解的存在唯一性定理.本文在此基础上得到了这种假设下一维BSDEs的L^p解的几个连续性质.