模糊Bayes检验

本文对原假设和备择假设中参数是模糊子集的假设检验问题，引入了模糊Ｂａｙｅｓ检验的概念，对简单模糊假设，给出了求模糊Ｂａｙｅｓ检验的方法，讨论了它的性质，并针对一类特殊的隶属函数，得出了检验的具体公式。最后，通过几个数值实例，表明了模糊Ｂａｙｅｓ检验的优良性。     

序进应力加速寿命试验的Bayes推断

本文将根据序进应力加速寿命试验的数据，利用Ｂａｙｅｓ方法，探讨对有关参数，和剩余寿命分布的统计推断。     

一类单边截断型分布族参数的经验Bayes检验

讨论一类单边截断型分布族位置参数的经验Ｂａｙｅｓ检验问题，文中构造了经验Ｂａｙｅｓ判决函数，证明了它具有渐近最优的性质，并且获得了收敛速度。     

Bayes局部影响分析

本文从Ｂａｙｅｓ观点出发，利用Ｋｕｌｌｂａｃｋ－Ｌｅｉｂｌｅｒ距离和微分几何方法，系统地讨论了微小扰对于Ｂａｙｅｓ统计推断的局部影响，给出了Ｂａｙｅｓ局部影响分析的一般公式，作为应用，具体讨论了线性回归模型的Ｂａｙｅｓ估计和Ｂａｙｅｓ预测的局部影响问题，数值计算的结果表明，本文的方法是比较有效的。     

计数型最小样本量截尾值的序贯检验

对具有"高成本、破坏性"计数型产品的可靠性验收试验,序贯检验方案的样本量截尾值对试验的成本预算起着决定性作用.为降低试验的成本预算,本文对最小样本量截尾值序贯检验(minimum truncated sample size sequential test, MTST)进行研究,给出MTST的定义、性质及求解方法.通过与目前广泛采用的国际标准IEC1123及序贯网图检验进行比较,结果表明MTST显著地减少了样本量截尾值.为进一步减少序贯检验的样本量截尾值,当已知产品质量的先验信息时,本文研究了Bayes最小样本量截尾值序贯检验方案(Bayesian minimum truncated sample size sequential test, BMTST),与MTST的比较表明, BMTST极大地减少了序贯检验的样本量截尾值及平均试验次数,能更好地缩减"高成本、破坏性"产品的试验成本预算及平均试验费用.     

指数型产品失效率鉴定试验的Bayes方案

本文用可靠性增长方法给出了产品鉴定试验的一种Ｂａｙｅｓ方法,这种鉴定试验方法了产品研制过程中的先验信息,在确保产品质量的前提下,与传统的鉴定试验方案相比,将大大节省试验时间。     

基于Koopman-Darmois分布族的序贯网图检验方法

通常高成本、破坏性的抽样检验需采用具有最大样本量限制的序贯检验方法．立足于设计出最大样本量尽量小的序贯检验方案,本文基于Koopman-Darmois分布族建立了序贯网图检验方法．与目前广泛采用的截尾序贯概率比检验方法相比,序贯网图检验方案具有更小的样本量上界,更适合高成本、破坏性的抽样检验．     

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．     

二项分布可靠度的Bayes,多层Bayes估计

本文给出了二项分布可靠度的Ｂａｙｅｓ估计、多层Ｂａｙｅｓ估计，并对一些结果进行了比较。     

系统树中的近似Bayes方法

本文利用近似Ｂａｙｅｓ方法对一个具有树形结构的成败型系统的可靠性进行估计．本文证明了利用近似Ｂａｙｅｓ方法对系统的可靠性参数的估计，具点估计在Ｆｉｓｈｅｒ意义下是渐近有效的，其相应的置信下限也是Ｆｉｓｈｅｒ意义下渐近有效的．     

A stopping rule for a compound poisson random variable

An optimal empirical Bayesian stopping rule for the Poisson compounded with the geometric distribution is developed and applied to the problem of the sequential testing of computer software. For each checkpoint in time, either the software satisfies a desired economic criterion, or else the software testing is continued.     

The Wiener Sequential Testing Problem with Finite Horizon

We present a solution of the Bayesian problem of sequential testing of two simple hypotheses about the mean value of an observed Wiener process on the time interval with finite horizon. The method of proof is based on reducing the initial optimal stopping problem to a parabolic free-boundary problem where the continuation region is determined by two continuous curved boundaries. By means of the change-of-variable formula containing the local time of a diffusion process on curves we show that the optimal boundaries can be characterized as a unique solution of the coupled system of two nonlinear integral equations.     

An innovative Bayesian sequential censored sampling inspection method and application to test design

This paper proposes an innovative Bayesian sequential censored sampling inspection method to improve the inspection level and reduce the sample size in acceptance test plans for continuous lots. A mathematical model of Bayesian sequential censored sampling is built, where a new inspection parameter is created and two types of risk are modified. As the core of Bayesian risk formulas, a new structure method of the prior distribution is presented by combining the empirical distribution with the uncertainty of the estimation. To improve the fitting accuracy of parameter estimation, an adaptive genetic algorithm is applied and compared with different parameter estimation methods. In the prior distribution, a prior estimator is introduced to design a sampling plan for continuous lots. Then, three types of producer's and consumer's risks are derived and compared. The simulation results indicate that the modified Bayesian sampling method performs well, with the lowest risks and the smallest sample size. Finally, a new sequential censored sampling plan for continuous lots is designed for the accuracy acceptance test of an aircraft. The test results show that compared with the traditional single sampling plan, the sample size is reduced by 66.7%, saving a vast amount of test costs.     

Bayesian sequential testing for Lévy processes with diffusion and jump components

We study the Bayesian problem of sequential testing of two simple hypotheses about the Lévy-Khintchine triplet of a Lévy process, having diffusion component, represented by a Brownian motion with drift, and jump component of finite variation. The method of proof consists of reducing the original optimal stopping problem to a free-boundary problem. We show it is characterized by a second order integro-differential equation, that the unknown value function solves on the continuation region, and by the smooth fit principle, which holds at the unknown boundary points. Several examples are presented.     

Weibull分布恒定应力加速寿命试验的Bayes估计

对定时和定数截尾样本情形CE模型下Weibull分布场合恒定应力加速寿命试验进行了Bayes统计分析,利用Laplace方法给出了该模型的近似Bayes估计.最后通过模拟实例表明该Bayes估计是有效的.     

Asymptotically optimal Bayesian sequential change detection and identification rules

We study the joint problem of sequential change detection and multiple hypothesis testing. Suppose that the common distribution of a sequence of i.i.d. random variables changes suddenly at some unobservable time to one of finitely many distinct alternatives, and one needs to both detect and identify the change at the earliest possible time. We propose computationally efficient sequential decision rules that are asymptotically either Bayes-optimal or optimal in a Bayesian fixed-error-probability formulation, as the unit detection delay cost or the misdiagnosis and false alarm probabilities go to zero, respectively. Numerical examples are provided to verify the asymptotic optimality and the speed of convergence.     

A Gridding Method for Bayesian Sequential Decision Problems

This article introduces a numerical method for finding optimal or approximately optimal decision rules and corresponding expected losses in Bayesian sequential decision problems. The method, based on the classical backward induction method, constructs a grid approximation to the expected loss at each decision time, viewed as a function of certain statistics of the posterior distribution of the parameter of interest. In contrast with most existing techniques, this method has a computation time which is linear in the number of stages in the sequential problem. It can also be applied to problems with insufficient statistics for the parameters of interest. Furthermore, it is well-suited to be implemented using parallel processors.     

APPLICATION OF BAYESIAN STATISTICAL INFERENCE AND DECISION THEORY TO A FUNDAMENTAL PROBLEM IN NATURAL RESOURCE SCIENCE: THE ADAPTIVE MANAGEMENT OF AN ENDANGERED SPECIES

Abstract A fundamental problem of interest to contemporary natural resource scientists is that of assessing whether a critical population parameter such as population proportion p has been maintained above (or below) a specified critical threshold level p_c. This problem has been traditionally analyzed using frequentist estimation of parameters with confidence intervals or frequentist hypothesis testing. Bayesian statistical analysis provides an alternative approach that has many advantages. It has a more intuitive interpretation, providing probability assessments of parameters. It provides the Bayesian logic of “if (data), then probability (parameters)” rather than the frequentist logic of “if (parameters), then probability (data).” It provides a sequential, cumulative, scientific approach to analysis, using prior information and reassessing the probability distribution of parameters for adaptive management decision making. It has been integrated with decision theory and provides estimates of risk. Natural resource scientists have the opportunity of using Bayesian statistical analysis to their advantage now that this alternative approach to statistical inference has become practical and accessible.     

逐步区间删失Weibull分布的Bayesian稳健设计

逐步区间删失是获取高可靠性产品相关信息的一种重要方法.文章研究了产品寿命服从Weibull分布,带有随机移除逐步区间删失寿命试验的最优设计问题.采用极大似然方法获取模型参数的估计及其信息矩阵.利用Bayesian方法处理模型参数未知情况下设计准则对模型参数的依赖问题,获得了模型参数估计的Bayesian稳健设计准则.在考虑试验费用有限制的条件下,给出了获得最优稳健设计非线性混合整数算法.同时对先验选取及约束参数设定的敏感性做了分析.数值结果表明文章提出的方法是有效可行的.     

Multiple change-points detection by empirical Bayesian information criteria and Gibbs sampling induced stochastic search

Uncovering hidden change-points in an observed signal sequence is challenging both mathematically and computationally. We tackle this by developing an innovative methodology based on Markov chain Monte Carlo and statistical information theory. It consists of an empirical Bayesian information criterion (emBIC) to assess the fitness and virtue of candidate configurations of change-points, and a stochastic search algorithm induced from Gibbs sampling to find the optimal change-points configuration. Our emBIC is derived by treating the unknown change-point locations as latent data rather than parameters as is in traditional BIC, resulting in significant improvement over the latter which is known to mostly over-detect change-points. The use of the Gibbs sampler induced search enables one to quickly find the optimal change-points configuration with high probability and without going through computationally infeasible enumeration. We also integrate the Gibbs sampler induced search with a current BIC-based change-points sequential testing method, significantly improving the method’s performance and computing feasibility. We further develop two comprehensive 3-step computing procedures to implement the proposed methodology for practical use. Finally, simulation studies and real examples analyzing business and genetic data are presented to illustrate and assess the procedures.