关于广义测度与泛函空间积分下随机变量Bayes公式的拓广

在讨论了可测空间（，），（Ｘ，）中条件数学期望Ｅ［ｇ（θ）ξ］的Ｂａｙｅｓ公式的基础上，进一步研究了广义测度Ｇ＝Ｇ（Ａ），Ａ∈下Ｅ［ｇ（θ）｜ξ］的Ｂａｙｅｓ公式的拓广以及将泛函空间积分代替按基本结局空间积分的Ｅ［ｇ（ξ，θ）｜］（ω）的Ｂａｙｅｓ公式的拓广，为进一步扩大Ｂａｙｅｓ估计的应用范围提供了可靠的理论依据与一种新的有价值的方法。     

设备诊断的Bayesian预测及其改进的SPRT方法

提出了设备诊断的Ｂａｙｅｓｉａｎ预测方法，并针对该方法中检测延迟的不足，给出了均值和方差都发生变化时改进的ＳＰＲＴ方法并且讨论了累积Ｂａｙｅｓｉａｎ因子的递推公式及其运行长度。     

测量不确定度表述讲座 第六讲 标准测量不确定度的B类评定

６ １什么叫不确定度的Ｂ类评定？测量不确定度的评定方法主要分成两大类。一类是用统计方法进行评定 ,称之为Ａ类评定（参阅１ ２）,而其他的非统计方法 ,统称之为Ｂ类评定 ,又称之为非统计方法的评定 ,由此评定出来的不确定度一般称为Ｂ类不确定度或称为Ｂ类标准不确定度。要注意的是ＩＮＣ—１（１９８０）（参阅１ ２）中以及《ＪＪＦ１０２７》中都曾规定Ａ类不确定度分量用符号ｓｉ,而Ｂ类不确定度分量用符号ｕｊ 表示 ,这一方式在《导则》以及《ＪＪＦ１０５９》中已作了更改 ,ｓ只是实验标准偏差的符号 ,当它作为不确定度时 ,则不论…     

A类不确定度评定时几点注意事项

不确定度的Ａ类评定 ,是用对被测量重复观测并根据测量数据进行统计分析的方法计算 ,用试验标准偏差表征。不确定度的Ｂ类评定 ,是用非统计方法计算 ,用资料、经验、常识以及假设的概率分布估计的标准偏差表征。这两类评定方法只是数值计算方法上不同 ,而不存在本质上的区别。按Ａ类评定的不确定度分量 ,若不做重复观测也可由资料、经验公式等计算出其数值 ,也可按Ｂ类评定。在不确定度的Ａ类评定中 ,需注意以下几点 :1 Ａ类不确定度的评定结果为多个不确定度分量的综合反映。由于Ａ类评定是由一系列对被测量独立重复的观测值按统计计算方法…     

椭球分布AR（p）序列的Bayes建模与预报

本文中，设ＡＲ（ｐ）序殊样本分布为椭球分布，ＡＲ（ｐ）序列的噪声为椭球白噪声。我们得到模型参数的Ｂａｙｅｓ估计，又得到Ｂａｙｅｓ预报。本文首次提出椭球白噪声概念。     

多项分布参数的经验Bayes估计

本文考虑了多项分布参数的经验Ｂａｙｅｓ估计问题。通过利用一种较特殊的样本结构，我们构造了参数向量的渐近最优的经验Ｂａｙｅｓ估计，并证明了对于参数向量的任何先验分布，该估计的收敛速度为Ｏ（ｎ－１）。     

平行度测量总不确定度的评估实例

本根据不确定度的新近概念，在平长计测量的Ａ类不确定度分量已定量结论的基础上，提出了相应Ｂ类不确定度分量的评估方法，并估算了平行度测量的总不确定度。     

三等量块比较测量不确定度的估算

测量结果的可靠性或测量结果的质量均是由其测量不确定度来表征的。本文拟以三等量块比较测量为例，依据《JJG146—94量块检定规程》，参照国际标准化组织（Ito）、国际法制计量组织（OIML）等共同颁布的《测量不确定度表征方法指南》进行测量不确定度分析估算。     

测量不确定度计算中的一点注意事项

在测量不确定度的计算中 ,按Ａ类评定法评定的不确定度分量 ,其标准不确定度 ,可用ｎ次测量所得数据列算术平均值的标准偏差表征 ,即 :ｓ( ｘ) =1ｎ(ｎ -1 ) ∑ｎｉ=1(ｘｉ- ｘ) 2 ;也可用单次测量的标准偏差表征 ,即 :ｓ(ｘ) =1ｎ -1 ∑ｎｉ=1(ｘｉ- ｘ) 2 。其区别在于测量结果是用ｎ次测量平均值还是单次测量值表示。而在具体的测量设备 (或测量方法 )的不确定度评定中 ,则与测量设备的使用状态有关。例如 :对一测量设备进行测量不确定度评定 ,在重复测量条件下 ,对某量进行ｎ次测量 ,得测量列ｘ1 、ｘ2 、…、ｘｎ。其它误差源忽略不计 …     

不确定度的B类评定方法

在不确定度评定中，Ｂ类评定十分重要．本文讨论不确定度Ｂ类评定方法．给出应用实例，以便有关人员在无法用Ａ类评定不确定度时，按被测量可能变化的信息，作出Ｂ类评定．     

GUM与基于观测方程的测量不确定度评估

比较了GUM系列文件与贝叶斯方法评估不确定度的过程,说明GUM是以测量方程为基础的前向分析方法,而贝叶斯分析是以观测方程为基础、以数据分析为主的一种后向不确定度评估方法。运用概率模型的描述方法对上述两种分析过程进行了分析与比较,说明了两种方法在线性测量模型的条件下,不考虑被测量先验分布时两种结果基本一致,对于非线性的测量模型,GUM S1得到的结果与一定先验分布条件下的贝叶斯分析的结果也基本一致。最后通过实例说明了该结论。     

Calculation of Measurement Uncertainty Using Prior Information

We describe the use of Bayesian inference to include prior information about the value of the measurand in the calculation of measurement uncertainty. Typical examples show this can, in effect, reduce the expanded uncertainty by up to 85 %. The application of the Bayesian approach to proving workpiece conformance to specification (as given by international standard ISO 14253-1) is presented and a procedure for increasing the conformance zone by modifying the expanded uncertainty guard bands is discussed.     

Bayesian decision threshold, detection limit and confidence limits in ionising-radiation measurement

Based on Bayesian statistics and the Bayesian theory of measurement uncertainty, characteristic limits such as the decision threshold, detection limit and limits of a confidence interval can be calculated taking into account all sources of uncertainty. This approach consists of the complete evaluation of a measurement according to the ISO Guide to the Expression of Uncertainty in Measurement (GUM) and the successive determination of the characteristic limits by using the standard uncertainty obtained from the evaluation. This procedure is elaborated here for several particular models of evaluation. It is, however, so general that it allows for a large variety of applications to similar measurements. It is proposed for the revision of those parts of DIN 25482 and ISO 11929 that are still based on conventional statistics and, therefore, do not allow to take completely into account all the components of measurement uncertainty in the calculation of the characteristic limits.     

A Bayesian approach to diagnosis and prognosis using built-in test

Accounting for the effects of test uncertainty is a significant problem in test and diagnosis, especially within the context of built-in test. Of interest here, how does one assess the level of uncertainty and then utilize that assessment to improve diagnostics? One approach, based on measurement science, is to treat the probability of a false indication [e.g., built-in-test (BIT) false alarm or missed detection] as the measure of uncertainty. Given the ability to determine such probabilities, a Bayesian approach to diagnosis, and by extension, prognosis suggests itself. In the following, we present a mathematical derivation for false indication and apply it to the specification of Bayesian diagnosis. We draw from measurement science, reliability theory, signal detection theory, and Bayesian decision theory to provide an end-to-end probabilistic treatment of the fault diagnosis and prognosis problem.     

A Bayesian framework for uncertainty quantification of perturbed gamma process based on simulated likelihood

The perturbed gamma process (PGP) has recently been widely used in modeling the noisy degradation data collected from engineering structures and components since it can simultaneously consider the temporal variability of degradation and measurement uncertainty. As a result of the sampling and inspection uncertainty in engineering practice, it is necessary to account for the resulting parameter uncertainty. Meanwhile, the flexibility of the form of measurement error motivates a potential demand for quantifying the model uncertainty and selecting the most fitting error model for the given inspection data. The Bayesian approach is well-suited to quantity the parameter uncertainty induced by imperfect inspection and limited inspection data, but its practical implementation is extremely challenging due to the intractable likelihood function of PGP. In the paper, a novel Bayesian framework for quantifying parameter and model uncertainty of PGP is presented, where the simulated likelihood that is an unbiased estimator generated by Sequential Monte Carlo (SMC) is introduced to overcome the intractable likelihood of PGP. More specifically, an Adaptive Particle Markov chain Monte Carlo (APMCMC) is proposed to perform the Bayesian sampling from the posterior distributions of parameters, achieving the requirement for the quantification of parameter uncertainty. By utilizing the posterior samples from APMCMC, a model selection method based on the Bayes factor is employed to determine the most fitting one from some alternative error models. Finally, two simulation examples are presented to illustrate the efficiency and accuracy of the proposed framework and its applicability is confirmed by a practical case involving the corrosion modeling of a group of pipelines.     

Variability and uncertainty of biokinetic model parameters: the discrete empirical Bayes approximation

In the Bayesian approach to internal dosimetry, uncertainty and variability of biokinetic model parameters need to be taken into account. The discrete empirical Bayes approximation replaces integration over biokinetic model parameters by discrete summation in the evaluation of Bayesian posterior averages using Bayes theorem. The discrete choices of parameters are taken as best-fit point determinations of model parameters for a study subpopulation with extensive data. A simple heuristic model is constructed to numerically and theoretically study this approximation. The heuristic example is the measurement of heights of a group of people, say from a photograph where measurement uncertainty is significant. A comparison is made of posterior mean and standard deviation of height after a measurement, (i) using the exact prior describing the distribution of true height in the population and (ii) using the approximate discrete empirical Bayes prior obtained from measurements of some study subpopulation.     

基于贝叶斯理论的热电偶合格判定风险

民用航空用易耗型廉金属热电偶的指标要求远高于其他行业,但在进行计量确认时,一般忽略了测量不确定度的影响,带来了较大的质量风险。本文基于贝叶斯理论,对测量过程和测量不确定度对易耗型廉金属热电偶符合性判断的特定消费者风险和全局消费者风险进行分析。探究不同测量过程和不确定度下的决策错误率风险,并提出了降低风险的方法,为易耗型廉金属热电偶的计量确认提供了参考。     

基于贝叶斯理论的测量不确定度A类评定

文章介绍了贝叶斯理论，并利用此理论对测量不确定度A类评定进行分析，与基于经典统计方法的不确定度A类评定相比，该方法能充分利用历史测量数据所提供的信息，因此评定时信息量大，使评定更加合理。最后通过实例分析说明了基于贝叶斯理论的不确定度A类评定的合理性和优越性。     

NPUA: A new approach for the analysis of computer experiments

An important problem in the analysis of computer experiments is the specification of the uncertainty of the prediction according to a meta-model. The Bayesian approach, developed for the uncertainty analysis of deterministic computer models, expresses uncertainty by the use of a Gaussian process. There are several versions of the Bayesian approach, which are different in many regards but all of them lead to time consuming computations for large data sets.In the present paper we introduce a new approach in which the distribution of uncertainty is obtained in a general nonparametric form. The proposed approach is called non-parametric uncertainty analysis (NPUA), which is computationally simple since it combines generic sampling and regression techniques. We compare NPUA with the Bayesian and Kriging approaches and show the advantages of NPUA for finding points for the next runs by reanalyzing the ASET model.