关于贝叶斯估计的进一步讨论

文章则从绝对差损失函数与相对差损失函数出发 ,先导出两种新的贝叶斯解——中值估计和积分比估计 ;然后再对实际问题进行具体应用 ;在选定同类先验分布条件下将以上结果与传统的条件期望估计、最大后验估计相比较 ,探讨了各类贝叶斯解的优良性 .     

删失下的指数分布的贝叶斯估计

本文分别在Ⅱ型删失和随机删失下,表明了共轭先验下的指数分布的刻度参数的贝叶斯估计为具有如下形式的收缩估计(?)_(BE)=a■ bEθ,此处■为依赖样本θ的一个无偏估计且Eθ表示先验分布的期望。当采用平方损失函数时,a b=1;如果用加权平方损失函数,则a b＜1。     

略谈贝叶斯统计学派的假设检验

假设检验问题是统计推断和决策的基本形式之一，其核心是利用样本所提供的信息对总体的某个假设给出判断，接受假设或者拒绝假设。对于该问题经典统计和贝叶斯统计给出不同的检验方法和检验准则。本文浅谈贝叶斯统计在假设检验方面的优势及不足。     

伽玛分布形状参数的区间估计

国家标准GB80557-87给出了构造Γ分布形状参数的区间估计的方法,但是所得到的区间估计的水平仅近似地等于1-a,并且这个方法仅当形状参数大时适用.本文给出的构造形状参数区间估计的方法,其水平精确地等于1-a,并且关于形状参数没有任何限制。     

基于厚尾时间序列的贝叶斯单位根检验

本文运用贝叶斯因子和可信区间两种方法来研究厚尾时间序列中单位根检验问题．通过Monte Carlo模拟证实了这两种方法的有效性,并对两种方法进行对比和分析．然后,考察了先验信息和自由度对单位根检验结果的影响．最后,将这两种方法运用到检验美国失业率和居民消费物价指数时间序列中,发现这两列序列均存在单位根．     

扩散先验分布下Bayes线性假设检验方法的构造

首先讨论了扩散先验分布下多元线性回归模型Y=Xβ e，e～N(0，σ^2In)中参数β的边缘后验分布，然后根据该分布构造了R^m 1与其子集上的最大后验密度之比，据此检验回归系数β的线性假设，最后研究了部分系数同时为零这一特殊情况的Bayes检验方法。     

NA样本分布估计的一致强相合性

在NA相依样本下,研究经验分布函数估计和分布密度核估计的一致强相合性,获得了与独立情形一致的结论。     

非共轭先验分布下的贝叶斯统计质量控制研究

贝叶斯质量控制是企业小批量、多品种生产中质量控制的有效手段.在非共轭先验分布的条件下,利用基于马尔科夫链—蒙特卡罗(MCMC)的方法可以解决贝叶斯质量控制中的后验分布确定问题,并用WinBUGS软件执行.在方差未知的正态分布多元质量特性参数控制的模型中,对生产过程中控制图的控制界限进行了预测,在有限的信息条件下,实现对质量特性参数的控制.     

多元先验信息的融合问题

在多元先验信息条件下，运用Bayes理论讨论问题时，必然会遇到先验信息融合问题，文中提出了几种简化形式，并针对产品失效率的多个先验信息情形，结合实例与熵度量的拟合优度说明了该方法的合理性。     

条件密度递归双重核估计的渐近分布

本文引进了条件密度递归形式的双重核估计,并在适当的条件下证明了这种估计满足渐近正态性,本文还削减了文献[1]中定理的条件,其结果和该定理是一样的。     

Calculating a confidence interval on the sum of binned leakage

Calculating the expected number of misclassified outcomes is a standard problem of particular interest for rare-event searches. The Clopper-Pearson method allows calculation of classical confidence intervals on the amount of misclassification if data are all drawn from the same binomial probability distribution. However, data is often better described by breaking it up into several bins, each represented by a different binomial distribution. We describe and provide an algorithm for calculating a classical confidence interval on the expected total number of misclassified events from several bins, based on calibration data with the same probability of misclassification on a bin-by-bin basis. Our method avoids a computationally intensive multidimensional search by introducing a Lagrange multiplier and performing standard root finding. This method has only quadratic time complexity as the number of bins, and produces confidence intervals that are only slightly conservative.     

A Bayesian procedure for process capability assessment

The usual practice of judging process capability by evaluating point estimates of some process capability indices has a flaw that there is no assessment on the error distributions of these estimates. However, the distributions of these estimates are usually so complicated that it is very difficult to obtain good interval estimates. In this paper we adopt a Bayesian approach to obtain an interval estimation, particularly for the index C_pm. The posterior probability p that the process under investigation is capable is derived; then the credible interval, a Bayesian analogue of the classical confidence interval, can be obtained. We claim that the process is capable if all the points in the credible interval are greater than the pre‐specified capability level ω, say 1.33. To make this Bayesian procedure very easy for practitioners to implement on manufacturing floors, we tabulate the minimum values of Ĉ_pm/ω, for which the posterior probability p reaches the desirable level, say 95%. For the special cases where the process mean equals the target value for C_pm and equals the midpoint of the two specification limits for C_pk, the procedure is even simpler; only chi‐square tables are needed. Copyright © 1999 John Wiley & Sons, Ltd.     

Bayesian estimation of the 3-parameter inverse gaussian distribution

The three-parameter inverse Gaussian distribution is used as an alternative model for the three parameter lognormal, gamma and Weibull distributions for reliability problems. In this paper Bayes estimates of the parameters and reliability function of a three parameter inverse Gaussian distribution are obtained. Posterior variance estimates are compared with the variance of their maximum likelihood counterparts. Numerical examples are given.     

Bayesian reliability: Combining information

ABSTRACT

One of the most powerful features of Bayesian analyses is the ability to combine multiple sources of information in a principled way to perform inference. This feature can be particularly valuable in assessing the reliability of systems where testing is limited. At their most basic, Bayesian methods for reliability develop informative prior distributions using expert judgment or similar systems. Appropriate models allow the incorporation of many other sources of information, including historical data, information from similar systems, and computer models. We introduce the Bayesian approach to reliability using several examples and point to open problems and areas for future work.     

On Bayesian EWMA control charts under different loss functions

The motivation for this study is to analyze Bayesian exponentially weighted moving average (EWMA) control chart under 3 loss functions namely, SELF, LLF, and PLF. Informative priors (normal and mixture of normal) and non‐informative priors (Uniform and Jefferys) are considered for the analysis. The performance of Bayesian EWMA control chart using posterior and posterior predictive distribution scheme has been evaluated using average run length (ARL) and standard deviation run length (SDRL) as performance measures. Monte Carlo simulations are used to compute the performance measures for different values of smoothing constant. An illustrative example is also presented for practical considerations of Bayesian EWMA control chart.     

Confidence Interval Estimation for the Weibull and Extreme Value Distributions

This paper reviews methods of constructing confidence intervals for parameters or other characteristics of the Weibull or extreme value distribution. The conditional method of obtaining confidence intervals is stressed, with emphasis on the flexibility of the method, and on the computations which are necessary to use it.     

Noninformative bayesian estimation for the optimum in a single factor quadratic response model

The estimation of the location and magnitude of the optimum has long been considered as an important problem in the realm of response surface methodology. In this paper, we consider the Bayes estimates in a single factor quadratic response function, after a reparametrization from the linear model, using noninformative priors. The usual constant noninformative prior for the reparametrized model does not yield a proper posterior, thus it is desirable to consider other noninformative priors such as the Jeffreys prior and reference priors. Comparisons will be made based on the resulting posterior means, variances and credible intervals by examples and simulations. This work has been supported by the National Science Council, Grants NSC88-2118-M008-009, in Taiwan.