截尾试验下指数分布的贝叶斯估计

在指数分布场合，定数或定时截尾试验，文［１］给出了参数λ在先验分布为Γ（α，β）分布的假设下的Ｂａｙｅｓ估计．文［３］给出了在平方损失下的Ｂａｙｅｓ估计．本文讨论先验分布为Ｂ（ａ，ｂ）分布时，参数λ的Ｂａｙｅｓ估计．     

错误先验假定下回归系数Bayes估计的小样本性质

本在于错误指定的先验假定获得了回归系数的Ｂａｙｅｓ估计（ＢＥ）,并在均方误差矩阵准则下对其与最小二乘（ＬＳ）估计进行了比较,导出了它们的相对效率的界、讨论了在后验ＰｉｔｍａｎＣｌｏｓｅｎｅｓｓ准则下ＢＥ相对于ＬＳ估计的优良性。     

无失效数据失效率的综合多层Bayes估计

文章对指数分布无失效数据的失效率,在先验分布为Ｇａｍｍａ分布时,在引进失效信息后,给出了多层Ｂａｙｅｓ估计以及综合多层Ｂａｙｅｓ估计,并给出了可靠度的综合估计。最后,结合实际问题进行了计算     

导弹最大射程Bayesw估计的分析和改进

本文用验前数据的质量因子及估计的相对方程差分析了导弹最大射程的一类Ｂａｙｅｓ估计的性能。对不同的质量因子，给出了最佳验前数据量的一种近似公式，针对这类Ｂａｙｅｓ估计的冒进问题，本文对它们进行了改进并得到了一类新的估计，最后，通过ＭｏｎｔｅＣａｒｌｏ法比较了这些估计的相对均方误差，验证了新估计的优良性。     

导弹最大射程Bayes估计的分析和改进

本文用验前数据的质量因子及估计的相对均方误差分析了导弹最大射程的一类Ｂａｙｅｓ估计的性能，对不同的质量因子，给出了最佳验前数据量的一种近似公式。针对这类Ｂａｙｅｓ估计的冒进问题，本文对它们进行了改进并得到了一类新的估计。最后，通过ＭｏｎｔｅＣａｒｌｏ法比较了这些估计的相对均方误差，验证了新估计的优良性。     

无失效数据情形失效率的估计及其应用

该文对指数分布的无失效数据,在失效率　的先验密度的核为　ａ－１时,给出了失效率　的Ｂａｙｅｓ估计和多层Ｂａｙｅｓ估计．并对某液压电动机,在寿命眼从指数分布时,给出了该液压电动机无失效数据情形可靠度的估计．     

无失效数据失效率的估计

对指数分布无失效数据（ｔｉ,ｎｉ）的失效率λ,在λ的先验密度的核为ｅｘｐ（－λ）时,给出了λ的Ｂａｙｅｓ估计和多层Ｂａｙｅｓ估计,从而可以得到可靠度的估计,最后,给合实际问题进行了计算。     

二项分布参数N的一种Bayes估计

本文给出了模糊先验分布下二项分布参数Ｎ的Ｂａｙｅｓ点估计和ＨＰＤ置信域。这些Ｂａｙｅｓ估计不但具有较简单的计算公式，通过大量的模拟计算，表明它们也具有较合理的性质。最后本文给出了两个实例。     

指数分布无失效数据的多层Bayes分析

韩明等．指数分布无失效数据的多层Ｂａｙｅｓ分析．数理统计与管理，１９９８，１７（４），２４～２７．本文对指数分布无失效数据的失效率，在先验分布为Ｇａｍｍａ分布时，给出了多层Ｂａｙｅｓ估计。最后，结合实际问题进行了计算     

正态──正态结构串联系统可靠度的Bayes估计

本文利用Ｂａｙｅｓ方法讨论了正态——正态结构串联系统可靠度θ＝Ｐ_ｒ０（Ｘ＞Ｙ）的估计问题，把θ的后验均值作为它的点估计，在特殊情况下，还得到了θ的Ｂａｙｅｓ置信限。     

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or the variance parameter of the normal distribution with a normal-inverse-gamma prior, we analytically calculate the Bayes posterior estimator with respect to a conjugate normal-inverse-gamma prior distribution under Stein's loss function. This estimator minimizes the Posterior Expected Stein's Loss (PESL). We also analytically calculate the Bayes posterior estimator and the PESL under the squared error loss function. The numerical simulations exemplify our theoretical studies that the PESLs do not depend on the sample, and that the Bayes posterior estimator and the PESL under the squared error loss function are unanimously larger than those under Stein's loss function. Finally, we calculate the Bayes posterior estimators and the PESLs of the monthly simple returns of the SSE Composite Index.     

A Dirichlet process functional approach to heteroscedastic-consistent covariance estimation

The mixture of Dirichlet process (MDP) defines a flexible prior distribution on the space of probability measures. This study shows that ordinary least-squares (OLS) estimator, as a functional of the MDP posterior distribution, has posterior mean given by weighted least-squares (WLS), and has posterior covariance matrix given by the (weighted) heteroscedastic-consistent sandwich estimator. This is according to a pairs bootstrap distribution approximation of the posterior, using a Pólya urn scheme. Also, when the MDP prior baseline distribution is specified as a product of independent probability measures, this WLS solution provides a new type of generalized ridge regression estimator. Such an estimator can handle multicollinear or singular design matrices even when the number of covariates exceeds the sample size, and can shrink the coefficient estimates of irrelevant covariates towards zero, which makes it useful for nonlinear regressions via basis expansions. Also, this MDP/OLS functional methodology can be extended to methods for analyzing the sensitivity of the heteroscedasticity-consistent causal effect size over a range of hidden biases, due to missing covariates omitted from the regression; and more generally, can be extended to a Vibration of Effects analysis. The methodology is illustrated through the analysis of simulated and real data sets. Overall, this study establishes new connections between Dirichlet process functional inference, the bootstrap, consistent sandwich covariance estimation, ridge shrinkage regression, WLS, and sensitivity analysis, to provide regression methodology useful for inferences of the mean dependent response.     

产品失效率的验前分布稳健性分析

研究Bayes统计分析中利用验前信息的稳健性.首先,用一般方法研究了指数寿命型分布中失效率的验前分布的稳健性.然后利用Gamma分布函数的典型性质,并以平方损失下的后验期望损失为判别准则,讨论了失效率的最优Bayes稳健区间.给出了失效率的最优Bayes稳健点估计.     

Minimax Bayes estimators of a multivariate normal mean

In three or more dimensions it is well known that the usual point estimator for the mean of a multivariate normal distribution is minimax but not admissible with respect to squared Euclidean distance loss. This paper gives sufficient conditions on the prior distribution under which the Bayes estimator has strictly lower risk than the usual estimator. Examples are given for which the posterior density is useful in the formation of confidence sets.     

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.     

基于Kullback信息融合方法的串联系统可靠性评估

讨论了串联系统在具有多源验前信息的情形下的可靠性评估问题,运用K u llback信息作为分布之间距离的度量,在K u llback信息的融合准则下对多个先验分布进行融合.并以融合后的先验分布作为系统的最终验前分布,对串联系统的可靠性指标进行Bayes估计.最后进行的计算机随机模拟结果表明,文中所提出的方法合理且便于应用.     

Targeting Bayes factors with direct-path non-equilibrium thermodynamic integration

Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a comparatively small number of parameters, intrinsic errors from sampling fluctuations may outweigh the differences in the log marginal likelihood estimates. In the present article, we propose a TI scheme that directly targets the log Bayes factor. The method is based on a modified annealing path between the posterior distributions of the two models compared, which systematically avoids the high variance prior regime. We combine this scheme with the concept of non-equilibrium TI to minimise discretisation errors from numerical integration. Results obtained on Bayesian regression models applied to standard benchmark data, and a complex hierarchical model applied to biopathway inference, demonstrate a significant reduction in estimator variance over state-of-the-art TI methods.     

多源验前信息之下Bayes可靠性估计

本文考虑存在多源验前信息的情况，以二项分布为例，首先把各种验前信息化成不同的约束条件，并运用最大熵准则推导出各种验前信息所对应的验前分布，然后将这些分布综合成最终的验前分布，最后根据系统的寿命试验数据得出可靠性参数的验后分布并进行了Ｂａｙｅｓ推断，文中给出了仿真实例以说明方法的有效性。     

An efficient estimator for the expectation of a bounded function under the residual distribution of an autoregressive process

Consider a stationary first-order autoregressive process, with i.i.d. residuals following an unknown mean zero distribution. The customary estimator for the expectation of a bounded function under the residual distribution is the empirical estimator based on the estimated residuals. We show that this estimator is not efficient, and construct a simple efficient estimator. It is adaptive with respect to the autoregression parameter.     

Weibull分布场合无失效数据的可靠性验证试验

对于Weibull分布的无失效数据问题,利用Bayes方法给出了产品寿命服从Weibull分布,形状参数的先验分布为U(0,1),尺度参数为1,假定产品的可靠性指标达到某个给定的值的情况下,无失效数据的可靠性验证试验,并利用相同的分析方法给出形状参数的Bayes估计.