An empirical multivariate log-normal distribution representing uncertainty of biokinetic parameters for 137Cs

A simplified biokinetic model for (137)Cs has six parameters representing transfer of material to and from various compartments. Using a Bayesian analysis, the joint probability distribution of these six parameters is determined empirically for two cases with quite a lot of bioassay data. The distribution is found to be a multivariate log-normal. Correlations between different parameters are obtained. The method utilises a fairly large number of pre-determined forward biokinetic calculations, whose results are stored in interpolation tables. Four different methods to sample the multidimensional parameter space with a limited number of samples are investigated: random, stratified, Latin Hypercube sampling with a uniform distribution of parameters and importance sampling using a lognormal distribution that approximates the posterior distribution. The importance sampling method gives much smaller sampling uncertainty. No sampling method-dependent differences are perceptible for the uniform distribution methods.     

Estimation of a normal mixture model through Gibbs sampling and Prior Feedback

Summary In this paper, we show how Gibbs sampling can provide a reliable approximation for Bayesian estimation of the parameters of a mixture distribution. Moreover, we deduce from the Bayesian approach an alternative derivation of maximum likelihood estimators in this setting, where standard nonin-formative approaches do not apply. Our method uses conjugate priors on each component of the mixture and is called Prior Feedback because the hyperparameters of these conjugate priors are iteratively replaced by the cor-responding posterior values until convergence is attained. We illustrate the appeal of this method through an astrophysical example, where the small sample size prohibits the use of standard maximum likelihood methods. A second example shows that Prior Feedback is also able to reject an unrealistic mixture model.     

Screening Strategies in the Presence of Interactions

Product and process improvement can involve a large number of factors that must be varied simultaneously. Understanding how factors interact is a key step in identifying those factors that have a substantial impact on the response. This article gives the first comprehensive assessment and comparison of screening strategies for interactions using two-level supersaturated designs, group screening, and a variety of data analysis methods including shrinkage regression and Bayesian methods. We develop novel methodology to allow application of Bayesian methods in two-stage group screening. Insights on using the strategies are provided through a variety of simulation scenarios and open issues are discussed. Supplementary materials are available online.     

Bayesian analysis with consideration of data uncertainty in a specific scenario

In this paper data uncertainty in a specific scenario is modeled with Berkson and Classical errors. With consideration of uncertainty three methods within Bayesian framework are presented to update the failure probability with Beta-Binomial model. It shows that the three methods have their posteriors in the same form of weighted Beta distributions, but the weights are different for each method. Approximation to the mixed posteriors has been proposed and demonstrated by computation results. Moreover, comparison and illustration of the three methods are made based on case study and analytical analysis, which suggest that the LO method with Classical error model be more appropriate in similar applications.     

Sensitivity estimations for Bayesian inference models solved by MCMC methods

The advent of Markov Chain Monte Carlo (MCMC) methods to simulate posterior distributions has virtually revolutionized the practice of Bayesian statistics. Unfortunately, sensitivity analysis in MCMC methods is a difficult task. In this paper, a computationally low-cost method to estimate local parametric sensitivities in Bayesian models is proposed. The sensitivity measure considered here is the gradient vector of a posterior quantity with respect to the parameter. The gradient vector components are estimated by using a result based on the integral/derivative interchange. The MCMC simulations used to estimate the posterior quantity can be re-used to estimate the sensitivity measures and their errors, avoiding the need for further sampling. The proposed method is easy to apply in practice as it is shown with an illustrative example.     

A Bayesian‐based Reliability Estimation Approach for Corrosion Fatigue Crack Growth Utilizing the Random Walk

Structural health monitoring enables corrosion fatigue damage for in‐service structures to be evaluated and prognosis health management to perform. In this paper, a Bayesian inference method using random walks is implemented to estimate the reliability of structures such as the pipelines subjected to repeated pressurization cycles and corrosive agents. The proposed method eliminates the intermediate step in updating process and computes the cumulative distribution function instead of calculating probability density function of individual parameters in conventional ones, which is affordable for a routine program, especially convenient for practical engineering use in the field. As taking all relevant random variables into account, this approach could significantly reduce uncertainties associated. For illustration and validation purpose, both numerical and practical examples are demonstrated in details. Copyright © 2016 John Wiley & Sons, Ltd.     

Application of conditional robust calibration to ordinary differential equations models in computational systems biology: a comparison of two sampling strategies

Mathematical modelling is a widely used technique for describing the temporal behaviour of biological systems. One of the most challenging topics in computational systems biology is the calibration of non‐linear models; i.e. the estimation of their unknown parameters. The state‐of‐the‐art methods in this field are the frequentist and Bayesian approaches. For both of them, the performance and accuracy of results greatly depend on the sampling technique employed. Here, the authors test a novel Bayesian procedure for parameter estimation, called conditional robust calibration (CRC), comparing two different sampling techniques: uniform and logarithmic Latin hypercube sampling. CRC is an iterative algorithm based on parameter space sampling and on the estimation of parameter density functions. They apply CRC with both sampling strategies to the three ordinary differential equations (ODEs) models of increasing complexity. They obtain a more precise and reliable solution through logarithmically spaced samples.Inspec keywords: sampling methods, parameter estimation, Bayes methods, differential equations, iterative methodsOther keywords: CRC, parameter space sampling, parameter density functions, sampling strategies, ordinary differential equations models, logarithmically spaced samples, computational systems biology, mathematical modelling, temporal behaviour, biological systems, challenging topics, nonlinear models, unknown parameters, frequentist approaches, Bayesian approaches, sampling technique, novel Bayesian procedure, parameter estimation, called conditional robust calibration, different sampling techniques     

Sensibility of Bayesian inference methods for reliability prediction of ageing systems,case of Diesel locomotives

This paper addresses the problem of reliability analysis of in-service identical systems when a limited number of lifetime data is available compared to censored ones. Lifetime (resp. censored) data characterise the life of failed (resp. non-failed) systems in the sample. Because, censored data induce biassed estimators of reliability model parameters, a methodology approach is proposed to overcome this inconvenience and improve the accuracy of the parameter estimation based on Bayesian inference methods. These methods combine, in an effective way, system’s life data and expert opinions learned from failure diagnosis of similar systems. Three Bayesian inference methods are considered: Classical Bayesian, Extended Bayesian and Bayesian Restoration Maximisation methods. Given a sample of lifetime data, simulated according to prior opinions of maintenance expert, a sensibility analysis of each Bayesian method is performed. Reliability analysis of critical subsystems of Diesel locomotives is established under the proposed methodology approach. The relevance of each Bayesian inference methods with respect to collected reliability data of critical subsystems and expert opinions is discussed.     

A Bayesian evaluation of simulation models of multiple-site fatigue cracks

The rivet holes along the longitudinal top row of the outer skin of the fuselage over a two-bay length are considered as the independent structural unit for the simulated multiple-site fatigue cracks. Models of multiple-site fatigue cracks are proposed. The models are divided into several phases with some uncertain parameters. These phases are incorporated sequentially into a computer code with the Monte Carlo simulation method. The Bayesian estimation of uncertain parameters in the model can be identified on visual inspections by the Bayesian procedure from in-service inspection data measuring crack lengths of each rivet hole. In summary, this study evaluates effects of differences in the simulation models for the crack coalescence and failure phase for the distribution of inspection data measuring crack lengths with the Bayesian estimation of uncertain parameters from simulated in-service inspection data.     

Finite element model updating using Hamiltonian Monte Carlo techniques

Bayesian techniques have been widely used in finite element model (FEM) updating. The attraction of these techniques is their ability to quantify and characterize the uncertainties associated with dynamic systems. In order to update an FEM, the Bayesian formulation requires the evaluation of the posterior distribution function. For large systems, this function is difficult to solve analytically. In such cases, the use of sampling techniques often provides a good approximation of this posterior distribution function. The hybrid Monte Carlo (HMC) method is a classic sampling method used to approximate high-dimensional complex problems. However, the acceptance rate of HMC is sensitive to the system size, as well as to the time step used to evaluate the molecular dynamics trajectory. The shadow HMC technique (SHMC), which is a modified version of the HMC method, was developed to improve sampling for large system sizes by drawing from a modified shadow Hamiltonian function. However, the SHMC algorithm performance is limited by the use of a non-separable modified Hamiltonian function. Moreover, two additional parameters are required for the sampling procedure, which could be computationally expensive. To overcome these weaknesses, the separable shadow HMC (S2HMC) method has been introduced. This method uses a transformation to a different parameter space to generate samples. In this paper, we analyse the application and performance of these algorithms, including the parameters used in each algorithm, their limitations and the effects on model updating. The accuracy and the efficiency of the algorithms are demonstrated by updating the finite element models of two real mechanical structures. It is observed that the S2HMC algorithm has a number of advantages over the other algorithms; for example, the S2HMC algorithm is able to efficiently sample at larger time steps while using fewer parameters than the other algorithms.     

考虑参数更新的大跨桥梁温差极值分布估计方法研究

为了建立可靠的大跨桥梁全寿命温差极值分布模型,提出采用广义帕累托分布（Generalized Pareto Distribution,GPD）对超阈值温差的统计特征进行描述,并给出了超阈值温差样本相关性的去除方法和最优阈值的确定方法。为了融合温差分布的先期经验信息和不断递增的温差监测样本,建立了考虑参数更新的贝叶斯估计方法,利用Gibbs抽样对贝叶斯后验分布进行计算,进而得到准确的基于广义帕累托分布的温差极值分布模型。最后利用九堡大桥长期监测温差数据进行了验证。研究结果表明,广义帕累托分布能够对超阈值温差样本的尾部统计特征进行准确描述,提出的考虑参数更新的温差极值分布贝叶斯估计方法能够对广义帕累托分布的参数进行可靠估计,估计的统计模型比极大似然估计计算的结果更接近真实情况。研究结果可为大跨桥梁温差特性分析提供参考。     

Objective Bayesian methods for one-sided testing

The one-sided testing problem can be naturally formulated as the comparison between two nonnested models. In an objective Bayesian setting, that is, when subjective prior information is not available, no general method exists either for deriving proper prior distributions on parameters or for computing Bayes factor and model posterior probabilities. The encompassing approach solves this difficulty by converting the problem into a nested model comparison for which standard methods can be applied to derive proper priors. We argue that the usual way of encompassing does not have a Bayesian justification. and propose a variant of this method that provides an objective Bayesian solution. The solution proposed here is further extended to the case where nuisance parameters are present and where the hypotheses to be tested are separated by an interval. Some illustrative examples are given for regular and non-regular sampling distributions. This paper has been supported by Ministerio de Ciencia y Tecnología under grant BEC20001-2982     

Advances in Sequential Bayesian Work Sampling

Sequential Bayesian work sampling has been previously shown to be both more efficient and more adaptable than traditional methods of work sampling. However, a few deficiencies of the Bayesian approach remained. The advances to that methodology shown here greatly reduce or eliminate those deficiencies. These advances include beta parameter maps, confidence subinterval estimation in closed form, preposterior analysis, estimation methods for remaining sample sizes, and other aids to the management of Bayesian work-sampling studies.     

神经网络和贝叶斯网络在汉语词义消歧上的对比研究

神经网络和贝叶斯网络是两种经典的机器学习方法。本文通过实验考察了这两种网络模型在汉语词义消歧上的应用效果。实验对象是通过特定规则构造的6个伪词。使用伪词可以避免有指导的词义消歧方法中的数据稀疏问题,充分验证词义分类器的实验效果。贝叶斯网络用于词义分类简单高效,模型容易构造,而神经网络的结构则相对复杂,用于词义消歧需要先解决输入问题。实验中采用词间互信息成功构造了神经网络的输入模型,实验效果较为理想。实验数据表明贝叶斯网络比神经网络更适合解决汉语词义消歧问题。但贝叶斯网络的抗噪声能力却明显逊色于神经网络。     

基于DR-BN的冷水机组故障检测

在冷水机组现场的故障数据通常难以获得,这是导致基于多分类算法的故障检测方法未被广泛现场应用的主要障碍之一。本文将距离拒绝(DR)机制融入贝叶斯网络(BN)中,将冷水机组故障检测转化为一类划分问题,提出一种基于DR-BN的冷水机组故障检测方法,该方法仅使用正常数据训练模型,从而有效克服上述障碍。本文通过使用ASHRAE RP-1043的故障实验数据对提出方法的性能进行验证,并与传统方法的性能进行了对比,可知基于DR-BN的模型具有更高的故障检测性能,尤其对低劣化等级下的故障,故障检测正确率最高时可高出94%。     

结合近似贝叶斯计算和改进群体蒙特卡洛抽样的结构损伤识别

为避免陷入低概率区抽样并提高抽样效率,改进了群体蒙特卡洛(PMC)抽样算法,再结合近似贝叶斯计算(ABC)和随机响应面(SRS)提出一种概率损伤识别方法。首先将ABC和改进PMC算法进行嵌套,利用每个迭代步的样本方差来搅动粒子群和求取自适应权重系数,再构造衡量仿真和实测样本间相似度的误差函数,用于替代似然函数;然后使用SRS建立结构随机响应的显式表达式,大幅提高响应统计特征值的计算效率;最后将求得的参数后验概率分布统计特征值作为损伤指标,根据损伤前后指标值的变化来判断损伤位置和程度。对试验钢筋混凝土梁的单、多工况损伤进行了识别,验证了所提出方法在保证参数后验分布估计精度的条件下,可以有效提高贝叶斯推断过程的计算效率。     

An efficient analytical Bayesian method for reliability and system response updating based on Laplace and inverse first-order reliability computations

This paper presents an efficient analytical Bayesian method for reliability and system response updating without using simulations. The method includes additional information such as measurement data via Bayesian modeling to reduce estimation uncertainties. Laplace approximation method is used to evaluate Bayesian posterior distributions analytically. An efficient algorithm based on inverse first-order reliability method is developed to evaluate system responses given a reliability index or confidence interval. Since the proposed method involves no simulations such as Monte Carlo or Markov chain Monte Carlo simulations, the overall computational efficiency improves significantly, particularly for problems with complicated performance functions. A practical fatigue crack propagation problem with experimental data, and a structural scale example are presented for methodology demonstration. The accuracy and computational efficiency of the proposed method are compared with traditional simulation-based methods.     

Reliability demonstration test for a finite population

In many situations, we want to accept or reject a population with small or finite population size. In this paper, we will describe Bayesian and non‐Bayesian approaches for the reliability demonstration test based on the samples from a finite population. The Bayesian method is an approach that combines prior experience with newer test data in the application of statistical tools for reliability quantification. When test time and/or sample quantity is limited, the Bayesian approach should be considered. In this paper, a non‐Bayesian reliability demonstration test is considered for both finite and large population cases. The Bayesian approach with ‘uniform’ prior distributions, Polya prior distributions, and sequential sampling is also presented. Copyright © 2001 John Wiley & Sons, Ltd.     

基于Mindlin理论的Winkler地基参数动态Bayes识别

基于Bayes理论,提出了Winkler地基参数的动态识别方法。引入Mindlin理论,并利用考虑横向剪切效应板的基本方程,推导了Winkler地基上Mindlin板的控制微分方程。应用Fourier变换技术,推求了Winkler地基上简支板的Fourier闭式解。首次建立了Winkler地基参数的动态Bayes误差函数,推导了地基参数的动态Bayes均值和方差表达式,提出步长的一维自动寻优方案后,并结合共轭梯度法给出了Winkler地基参数的动态Bayes识别步骤。研究表明:动态Bayes识别方法能有效地动态识别Winkler地基参数;Winkler地基参数的收敛性依赖于地基参数先验信息的准确性和考察点位移实测资料的准确性;动态Bayes方法也可用于其它地基模型地基参数的动态识别。     

A method for determining the fatigue critical plane for biaxial random vibration in the frequency domain

This paper provides a direct method to determine the critical plane orientation for biaxial random vibration. The critical plane is obtained by finding the direction that maximizes the normal stress variance. It is found that the shear stress is uncorrelated with the normal stress in this orientation. Furthermore, the direction of maximal normal stress is shown to coincide with the principal direction in the case of proportional stress components. Spectral fatigue damage methods proposed in recent literature involve a Monte Carlo enumeration step to find the critical plane orientation. By using the proposed technique, computationally expensive enumeration methods are avoided and greater accuracy in the fatigue damage estimate may result.