贝叶斯定理在合并样本方差估计中的应用

合并估计是计量学中的一种常见情况,<测量不确定度表示指南>(简称GUM)推荐了在此情况下估计测量不确定度的常规方法,但它的不足之处在于没有运用先前的测量信息.另一种被称为频率方法则充分利用了先前的测量信息,但在实际中却难以操作.而根据贝叶斯定理推导出的贝叶斯方法克服了上述方法的缺陷和不足,可以给出更可靠的测量结果,并且具有较好的可操作性.     

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。     

基于贝叶斯估计的结构固有频率不确定性分析

在结构振动测试中,由于测试环境影响、试验设备、操作人员以及模态分析过程中的简化,试验获取的结构模态参数中包含了不确定因素。为了正确的估计结构物理参数的统计特性,在贝叶斯估计方法中选择共轭先验分布,结合试验数据导出后验分布,得到了结构固有频率均值及方差的估计值。对一个4层钢筋混凝土框架结构模型进行了振动测试。试验结果表明:在不能获得大量样本信息时,充分利用先验信息,结合现场测试数据,对频率参数进行估计,能够有效地减小均值与方差的可信区间长度,具有工程实用参考价值。     

约束条件下的线性贝叶斯估计

本文提出等式约束下线性模型中回归参数的线性贝叶斯估计,证明其在均方误差矩阵准则下相对于约束最小二乘估计的优越性,并采用蒙特卡洛模拟和数值算例验证其优越性．     

基于贝叶斯频谱估计的行波测距算法研究

本文研究了贝叶斯频谱估计的基本理论和基本方法,并在此基础上提出了一种新的高频信号行波测距算法.该算法根据行波理论,在故障电缆测试端进行数据采集,再应用贝叶斯频谱估计算法对测得的数据进行分析,得出相位差,从而计算出故障点的位置.由于分析方法上的改进,在故障点的测量精度上获得了很好的效果.     

贝叶斯估计动态汽车衡分时段数据融合研究

数据融合是一个多级、多层面的数据处理过程,主要完成对来自多个信息源的数据进行自动检测、关联、相关、估计及组合等处理。该文通过分析动态汽车衡的称重原理,对两路称重传感器不同时段的输出数据进行分析,提出基于贝叶斯估计的数据融合方法。实验检定表明:采用这种融合方法的动态汽车衡称重误差小,克服了动态汽车衡由于车辆振动、路面不平和传感器灵敏度分散性、传感器线性度误差等因素对称量结果的影响,准确度高。     

基于贝叶斯估计的粘连颗粒尺寸检测方法

在高速流水线上对小视场物体大批量在线检测过程中,针对滚子、钢珠、卷烟爆珠等球形颗粒因体积过小、发生破裂、传输振动而引起的颗粒粘连,致使其尺寸无法精准检测的问题,采用机器视觉的检测手段,提出基于贝叶斯估计的尺寸视觉检测方法。首先,经图像采集系统获取粘连颗粒图像,对采集图像预处理去除干扰因素。之后,利用边缘检测方法进行轮廓坐标点提取,通过数据滤波选取有效轮廓点数据,代入到该文所提出的贝叶斯尺寸测量数学模型中,从而实现对粘连颗粒尺寸的精确测量。以卷烟爆珠为例进行试验验证,该方法测得的尺寸最小均方根误差为0.049 6 mm,测量误差均值最小为0.022 63 mm,验证所提方法的可靠性与稳定性,满足实际工业检测精度要求。该方法的提出可为高速流水线上小视场粘连颗粒测量研究提供基础。     

新型倾角传感器在伺服系统中的应用

本文介绍了一种新型的两轴倾角传感器在伺服系统中的应用,详述了其工作原理和工作方式,通过一个应用实例,简介使用该传感器后的伺服系统的组成,给出系统的应用电路图,包括一种数字输出和摸拟输出的接口电路及程序框图,对于在伺服系统中需要惯性空间位置信息的情况,本文提供了一个较为实用的设计方案.     

基于贝叶斯估计的动载荷识别方法

为了降低测量误差等不确定性因素对识别结果的影响,建立基于贝叶斯估计理论的动力学系统载荷识别方法。首先,根据动力学系统运动方程,利用贝叶斯理论,推导载荷和误差参数的联合后验分布,进而得到载荷和误差参数的边缘概率分布;然后,采用马尔可夫蒙特卡罗方法,估计动力学系统所受的载荷,并利用仿真算例与基于奇异值分解的载荷识别方法进行对比;最后,利用实验数据,进一步验证本方法的有效性。结果表明,该方法在一定程度上减小了不确定性因素造成的识别误差,对于提高动载荷识别精度具有一定的参考意义。     

多批次小批量生产过程能力指数的贝叶斯估计

针对过程能力指数(PCIs)的传统计算方法应用于多批次小批量生产过程出现的失真问题,以多批次小批量生产过程的总体均值和总体方差分别服从共轭正态分布和共轭逆伽马分布,利用共轭贝叶斯估计理论提出了多批次小批量生产过程分布参数估计方法、过程能力指数计算方法及其通用表达式,这种贝叶斯估计方法减小仅用当前批小样本容量估计过程参数...     

Bayesian estimation of unavailability

This paper gives two Bayesian methods for estimating test-and-maintenance unavailability. Both unplanned and periodic maintenance are considered. One estimation method uses ‘detailed data,’ the individual outage times. The other method uses ‘summary data,’ totals of outage time and exposure time in various time periods such as calendar months. Either method can use either a noninformative or an informative prior distribution. Both methods are illustrated with an example data set, and the results are compared.     

Bayesian Weibull reliability estimation

The Weibull distribution is widely used as a failure model, particularly for mechanical components. This distribution is rich in shape and requires a fairly large sample size to produce accurate statistical estimators, particularly for the lower percentiles, as is usually required for a reliability analysis. In practice, sample sizes are almost always small and subjective judgement is applied, aided by a Weibull plot of the test data to determine the adequacy of the component design to meet reliability goals. The procedure is somewhat ad hoc, but apparently reasonably good results are obtained based on our experience with many past design and development programs and by comparison with actual field performance. We conjecture that the reason this procedure is successful is that test programs and methodology are standardized and quite well documented, from the standpoint of the physical test parameters. Test personnel have a wealth of experience in testing components, from one program to the next, and reliability judgements are made with regard to well-known points in the product's life. All of these factors tend to promote correct outcomes from the decision process even though sample sizes are small.

The Bayesian approach provides some structure for the application of subjective judgement to this decision process. To apply this approach, several complex decisions must be made. In this article, we have provided a structure for this decision process.     

Bayesian estimation of dose thresholds

An example is described of Bayesian estimation of radiation absorbed dose thresholds (subsequently simply referred to as dose thresholds) using a specific parametric model applied to a data set on mice exposed to 60Co gamma rays and fission neutrons. A Weibull based relative risk model with a dose threshold parameter was used to analyse, as an example, lung cancer mortality and determine the posterior density for the threshold dose after single exposures to 60Co gamma rays or fission neutrons from the JANUS reactor at Argonne National Laboratory. The data consisted of survival, censoring times and cause of death information for male B6CF1 unexposed and exposed mice. The 60Co gamma whole-body doses for the two exposed groups were 0.86 and 1.37 Gy. The neutron whole-body doses were 0.19 and 0.38 Gy. Marginal posterior densities for the dose thresholds for neutron and gamma radiation were calculated with numerical integration and found to have quite different shapes. The density of the threshold for 60Co is unimodal with a mode at about 0.50 Gy. The threshold density for fission neutrons declines monotonically from a maximum value at zero with increasing doses. The posterior densities for all other parameters were similar for the two radiation types.     

Nonlinear calculation of three-dimensional static magnetic fields

We present here the principle and structure of a method to calculate the three-dimensional (3-D) static magnetic fields which have already permitted us to study hybrid magnets for magnetic resonance imaging and ion confinement. Field sources can be issued from resistive or superconducting coils, permanent magnets, and other magnetic bodies such as soft iron. It can be extended to very low-frequency fields calculation as long as eddy current effects do not intervene. We call this method CALMAG3D     

Bayesian estimation of mixed Weibull distributions

Estimation of mixed Weibull distribution by maximum likelihood estimation and other methods is frequently difficult due to unstable estimates arising from limited data. Bayesian techniques can stabilize these estimates through the priors, but there is no closed-form conjugate family for the Weibull distribution. This paper reduces the number of numeric integrations required for using Bayesian estimation on mixed Weibull situations from five to two, thus making it a more feasible approach to the typical user. It also examines the robustness of the Bayesian estimates under a variety of different prior distributions. It is found that Bayesian estimation can improve accuracy over the MLE for situations with low mixture ratios so long as the prior on the weak subpopulation's characteristic life has an expected value less than or equal to the true characteristic life.     

Bayesian estimation of location parameters in life distributions

For some distributions commonly used in reliability analysis the likelihood function has a singularity at the smallest observation. The use of grouped likelihood in Bayesian inference is discussed. It is shown that the product of spacings can be used in place of the likelihood. Similarities with and differences from a standard Bayesian approach are illustrated by means of examples. In particular some computational advantages are pointed out.     

Fast Bayesian approach for parameter estimation

This paper presents two techniques, i.e. the proper orthogonal decomposition (POD) and the stochastic collocation method (SCM), for constructing surrogate models to accelerate the Bayesian inference approach for parameter estimation problems associated with partial differential equations. POD is a model reduction technique that derives reduced‐order models using an optimal problem‐adapted basis to effect significant reduction of the problem size and hence computational cost. SCM is an uncertainty propagation technique that approximates the parameterized solution and reduces further forward solves to function evaluations. The utility of the techniques is assessed on the non‐linear inverse problem of probabilistically calibrating scalar Robin coefficients from boundary measurements arising in the quenching process and non‐destructive evaluation. A hierarchical Bayesian model that handles flexibly the regularization parameter and the noise level is employed, and the posterior state space is explored by the Markov chain Monte Carlo. The numerical results indicate that significant computational gains can be realized without sacrificing the accuracy. Copyright © 2008 John Wiley & Sons, Ltd.     

Introducing two hyperparameters in Bayesian estimation of wave spectra

An estimate of the on-site wave spectrum can be obtained from measured ship responses by use of Bayesian modelling, which means that the wave spectrum is found as the optimum solution from a probabilistic viewpoint. The paper describes the introduction of two hyperparameters into Bayesian modelling so that the prior information included in the modelling is based on two constraints: the wave spectrum must be smooth directional-wise as well as frequency-wise. Traditionally, only one hyperparameter has been used to control the amount of smoothing applied in both the frequency and directional ranges. From numerical simulations of stochastic response measurements, it is shown that the optimal hyperparameters, determined by use of ABIC (a Bayesian Information Criterion), correspond to the best estimate of the wave spectrum, which is not always the case when only one hyperparameter is included in the Bayesian modelling. The paper includes also an analysis of full-scale motion measurements where wave spectra estimated by the Bayesian modelling are compared with results from ocean surface measurements by satellite and from a wave radar. The agreement is found to be reasonable.     

Bayesian transformed models for small area estimation

Sample surveys are usually designed and analyzed to produce estimates for larger areas. However, sample sizes are often not large enough to give adequate precision for small area estimates of interest. To overcome such difficulties,borrowing strength from related small areas via modeling becomes an appropriate approach. In line with this, we propose hierarchical models with power transformations for improving the precision of small area predictions. The proposed methods are applied to satellite data in conjunction with survey data to estimate mean acreage under a specified crop for counties in Iowa.     

Bayesian Poisson rate estimation using parameter maps

This paper presents a procedure for the sequential estimation of the rate parameter for a Poisson process. The procedure is based on Bayes' rule for combining new sample data with a prior estimate to obtain a posterior estimate. The procedure is facilitated by the use of a parameter map for monitoring the sequence of estimates and by a stationarity test for verifying the appropriateness of some of the assumptions.