Bayesian Estimation and Hierarchical Bayesian Estimation of Zero-failure Data

The zero_failure data research is a new field in the recent years, but it is required urgently in practical projects, so the work has more theory and practical values. In this paper, for zero_failure data (t i,n i) at moment t i , if the prior distribution of the failure probability p i=p{T【t i} is quasi_exponential distribution, the author gives the p i Bayesian estimation and hierarchical Bayesian estimation and the reliability under zero_failure date condition is also obtained.

Hierarchical Bayesian Calibration and On-line Updating Method for Influence Coefficient of Automatic Dynamic Balancing Machine

Measurement error of unbalance＇s vibration response plays a crucial role in calibration and on-line updating of influence coefficient（IC）. Focusing on the two problems that the moment estimator of data used in calibration process cannot fulfill the accuracy requirement under small sample and the disturbance of measurement error cannot be effectively suppressed in updating process, an IC calibration and on-line updating method based on hierarchical Bayesian method for automatic dynamic balancing machine was proposed. During calibration process, for the repeatedly-measured data obtained from experiments with different trial weights, according to the fact that measurement error of each sensor had the same statistical characteristics, the joint posterior distribution model for the true values of the vibration response under all trial weights and measurement error was established. During the updating process, information obtained from calibration was regarded as prior information, which was utilized to update the posterior distribution of IC combined with the real-time reference information to implement online updating. Moreover, Gibbs sampling method of Markov Chain Monte Carlo（MCMC） was adopted to obtain the maximum posterior estimation of parameters to be estimated. On the independent developed dynamic balancing testbed, prediction was carried out for multiple groups of data through the proposed method and the traditional method respectively, the result indicated that estimator of influence coefficient obtained through the proposed method had higher accuracy; the proposed updating method more effectively guaranteed the measurement accuracy during the whole producing process, and meantime more reasonably compromised between the sensitivity of IC change and suppression of randomness of vibration response.

Predicting Complex Word Emotions and Topics through a Hierarchical Bayesian Network

In this paper, we provide a Word Emotion Topic （WET） model to predict the complex word e- motion information from text, and discover the dis- trbution of emotions among different topics. A complex emotion is defined as the combination of one or more singular emotions from following 8 basic emotion categories： joy, love, expectation, sur- prise, anxiety, sorrow, anger and hate. We use a hi- erarchical Bayesian network to model the emotions and topics in the text. Both the complex emotions and topics are drawn from raw texts, without con- sidering any complicated language features. Our ex- periment shows promising results of word emotion prediction, which outperforms the traditional parsing methods such as the Hidden Markov Model and the Conditional Random Fields（CRFs） on raw text. We also explore the topic distribution by examining the emotion topic variation in an emotion topic diagram.

Local and regional flood frequency analysis based on hierarchical Bayesian model in Dongting Lake Basin,China

This study developed a hierarchical Bayesian(HB)model for local and regional flood frequency analysis in the Dongting Lake Basin,in China.The annual maximum daily flows from 15 streamflow-gauged sites in the study area were analyzed with the HB model.The generalized extreme value(GEV)distribution was selected as the extreme flood distribution,and the GEV distribution location and scale parameters were spatially modeled through a regression approach with the drainage area as a covariate.The Markov chain Monte Carlo(MCMC)method with Gibbs sampling was employed to calculate the posterior distribution in the HB model.The results showed that the proposed HB model provided satisfactory Bayesian credible intervals for flood quantiles,while the traditional delta method could not provide reliable uncertainty estimations for large flood quantiles,due to the fact that the lower confidence bounds tended to decrease as the return periods increased.Furthermore,the HB model for regional analysis allowed for a reduction in the value of some restrictive assumptions in the traditional index flood method,such as the homogeneity region assumption and the scale invariance assumption.The HB model can also provide an uncertainty band of flood quantile prediction at a poorly gauged or ungauged site,but the index flood method with L-moments does not demonstrate this uncertainty directly.Therefore,the HB model is an effective method of implementing the flexible local and regional frequency analysis scheme,and of quantifying the associated predictive uncertainty.

Spatial Modeling and Mapping of Tuberculosis Using Bayesian Hierarchical Approaches

Global spread of infectious disease threatens the well-being of human, domestic, and wildlife health. A proper understanding of global distribution of these diseases is an important part of disease management and policy making. However, data are subject to complexities by heterogeneity across host classes. The use of frequentist methods in biostatistics and epidemiology is common and is therefore extensively utilized in answering varied research questions. In this paper, we applied the hierarchical Bayesian approach to study the spatial distribution of tuberculosis in Kenya. The focus was to identify best fitting model for modeling TB relative risk in Kenya. The Markov Chain Monte Carlo (MCMC) method via WinBUGS and R packages was used for simulations. The Deviance Information Criterion (DIC) proposed by [1] was used for models comparison and selection. Among the models considered, unstructured heterogeneity model perfumes better in terms of modeling and mapping TB RR in Kenya. Variation in TB risk is observed among Kenya counties and clustering among counties with high TB Relative Risk (RR). HIV prevalence is identified as the dominant determinant of TB. We find clustering and heterogeneity of risk among high rate counties. Although the approaches are less than ideal, we hope that our formulations provide a useful stepping stone in the development of spatial methodology for the statistical analysis of risk from TB in Kenya.

Bayesian partial pooling to reduce uncertainty in overcoring rock stress estimation

The state of in situ stress is a crucial parameter in subsurface engineering,especially for critical projects like nuclear waste repository.As one of the two ISRM suggested methods,the overcoring(OC)method is widely used to estimate the full stress tensors in rocks by independent regression analysis of the data from each OC test.However,such customary independent analysis of individual OC tests,known as no pooling,is liable to yield unreliable test-specific stress estimates due to various uncertainty sources involved in the OC method.To address this problem,a practical and no-cost solution is considered by incorporating into OC data analysis additional information implied within adjacent OC tests,which are usually available in OC measurement campaigns.Hence,this paper presents a Bayesian partial pooling(hierarchical)model for combined analysis of adjacent OC tests.We performed five case studies using OC test data made at a nuclear waste repository research site of Sweden.The results demonstrate that partial pooling of adjacent OC tests indeed allows borrowing of information across adjacent tests,and yields improved stress tensor estimates with reduced uncertainties simultaneously for all individual tests than they are independently analysed as no pooling,particularly for those unreliable no pooling stress estimates.A further model comparison shows that the partial pooling model also gives better predictive performance,and thus confirms that the information borrowed across adjacent OC tests is relevant and effective.

Construct Validation by Hierarchical Bayesian Concept Maps: An Application to the Transaction Cost Economics Theory of the Firm

A concept map is a diagram depicting relationships among concepts which is used as a knowledge representation tool in many knowledge domains. In this paper, we build on the modeling framework of Hui et al. (2008) in order to develop a concept map suitable for testing the empirical evidence of theories. We identify a theory by a set of core tenets each asserting that one set of independent variables affects one dependent variable, moreover every variable can have several operational definitions. Data consist of a selected sample of scientific articles from the empirical literature on the theory under investigation. Our “tenet map” features a number of complexities more than the original version. First the links are two-layer: first-layer links connect variables which are related in the test of the theory at issue;second-layer links represent connections which are found statistically significant. Besides, either layer matrix of link-formation probabilities is block-symmetric. In addition to a form of censoring which resembles the Hui et al. pruning step, observed maps are subject to a further censoring related to second-layer links. Still, we perform a full Bayesian analysis instead of adopting the empirical Bayes approach. Lastly, we develop a three-stage model which accounts for dependence either of data or of parameters. The investigation of the empirical support and consensus degree of new economic theories of the firm motivated the proposed methodology. In this paper, the Transaction Cost Economics view is tested by a tenet map analysis. Both the two-stage and the multilevel models identify the same tenets as the most corroborated by empirical evidence though the latter provides a more comprehensive and complex insight of relationships between constructs.

Investigating Spatio-Temporal Pattern of Relative Risk of Tuberculosis in Kenya Using Bayesian Hierarchical Approaches

Proper understanding of global distribution of infectious diseases is an important part of disease management and policy making. However, data are subject to complexities caused by heterogeneities across host classes and space-time epidemic processes. This paper seeks to suggest or propose Bayesian spatio-temporal model for modeling and mapping tuberculosis relative risks in space and time as well identify risks factors associated with the tuberculosis and counties in Kenya with high tuberculosis relative risks. In this paper, we used spatio-temporal Bayesian hierarchical models to study the pattern of tuberculosis relative risks in Kenya. The Markov Chain Monte Carlo method via WinBUGS and R packages were used for simulations and estimation of the parameter estimates. The best fitting model is selected using the Deviance Information Criterion proposed by Spiegelhalter and colleagues. Among the spatio-temporal models used, the Knorr-Held model with space-time interaction type III and IV fit the data well but type IV appears better than type III. Variation in tuberculosis risk is observed among Kenya counties and clustering among counties with high tuberculosis relative risks. The prevalence of HIV is identified as the determinant of TB. We found clustering and heterogeneity of TB risk among high rate counties and the overall tuberculosis risk is slightly decreasing from 2002-2009. We proposed that the Knorr-Held model with interaction type IV should be used to model and map Kenyan tuberculosis relative risks. Interaction of TB relative risk in space and time increases among rural counties that share boundaries with urban counties with high tuberculosis risk. This is due to the ability of models to borrow strength from neighboring counties, such that nearby counties have similar risk. Although the approaches are less than ideal, we hope that our study provide a useful stepping stone in the development of spatial and spatio-temporal methodology for the statistical analysis of risk from tuberculosis in Kenya.

A Comparison of Hierarchical Bayesian Models for Small Area Estimation of Counts

Small area estimation (SAE) tackles the problem of providing reliable estimates for small areas, i.e., subsets of the population for which sample information is not sufficient to warrant the use of a direct estimator. Hierarchical Bayesian approach to SAE problems offers several advantages over traditional SAE models including the ability of appropriately accounting for the type of surveyed variable. In this paper, a number of model specifications for estimating small area counts are discussed and their relative merits are illustrated. We conducted a simulation study by reproducing in a simplified form the Italian Labour Force Survey and taking the Local Labor Markets as target areas. Simulated data were generated by assuming population characteristics of interest as well as survey sampling design as known. In one set of experiments, numbers of employment/unemployment from census data were utilized, in others population characteristics were varied. Results show persistent model failures for some standard Fay-Herriot specifications and for generalized linear Poisson models with (log-)normal sampling stage, whilst either unmatched or nonnormal sampling stage models get the best performance in terms of bias, accuracy and reliability. Though, the study also found that any model noticeably improves on its performance by letting sampling variances be stochastically determined rather than assumed as known as is the general practice. Moreover, we address the issue of model determination to point out limits and possible deceptions of commonly used criteria for model selection and checking in SAE context.

A Simulation Study of Hierarchical Bayesian Fusion Spatial Small Area Model for Binary Outcome under Spatial Misalignment

Simulation (stochastic) methods are based on obtaining random samples θ5 from the desired distribution p(θ) and estimating the expectation of any function h(θ). Simulation methods can be used for high-dimensional distributions, and there are general algorithms which work for a wide variety of models. Markov chain Monte Carlo (MCMC) methods have been important in making Bayesian inference practical for generic hierarchical models in small area estimation. Small area estimation is a method for producing reliable estimates for small areas. Model based Bayesian small area estimation methods are becoming popular for their ability to combine information from several sources as well as taking account of spatial prediction of spatial data. In this study, detailed simulation algorithm is given and the performance of a non-trivial extension of hierarchical Bayesian model for binary data under spatial misalignment is assessed. Both areal level and unit level latent processes were considered in modeling. The process models generated from the predictors were used to construct the basis so as to alleviate the problem of collinearity between the true predictor variables and the spatial random process. The performance of the proposed model was assessed using MCMC simulation studies. The performance was evaluated with respect to root mean square error (RMSE), Mean absolute error (MAE) and coverage probability of corresponding 95% CI of the estimate. The estimates from the proposed model perform better than the direct estimate.

Bayesian and hierarchical Bayesian analysis of response - time data with concomitant variables

This paper considers the Bayes and hierarchical Bayes approaches for analyzing clinical data on response times with available values for one or more concomitant variables. Response times are assumed to follow simple exponential distributions, with a different parameter for each patient. The analyses are carried out in case of progressive censoring assuming squared error loss function and gamma distribution as priors and hyperpriors. The possibilities of using the methodology in more general situations like dose- response modeling have also been explored. Bayesian estimators derived in this paper are applied to lung cancer data set with concomitant variables.

A Bayesian hierarchical model for the inference between metal grade with reduced variance:Case studies in porphyry Cu deposits

Ore sorting is a preconcentration technology and can dramatically reduce energy and water usage to improve the sustainability and profitability of a mining operation.In porphyry Cu deposits,Cu is the primary target,with ores usually containing secondary‘pay’metals such as Au,Mo and gangue elements such as Fe and As.Due to sensing technology limitations,secondary and deleterious materials vary in correlation type and strength with Cu but cannot be detected simultaneously via magnetic resonance(MR)ore sorting.Inferring the relationships between Cu and other elemental abundances is particularly critical for mineral processing.The variations in metal grade relationships occur due to the transition into different geological domains.This raises two questions-how to define these geological domains and how the metal grade relationship is influenced by these geological domains.In this paper,linear relationship is assumed between Cu grade and other metal grades.We applies a Bayesian hierarchical(partial-pooling)model to quantify the linear relationships between Cu,Au,and Fe grades from geochemical bore core data.The hierarchical model was compared with two other models-‘complete-pooling’model and‘nopooling’model.Mining blocks were split based on spatial domain to construct hierarchical model.Geochemical bore core data records metal grades measured from laboratory assay with spatial coordinates of sample location.Two case studies from different porphyry Cu deposits were used to evaluate the performance of the hierarchical model.Markov chain Monte Carlo(MCMC)was used to sample the posterior parameters.Our results show that the Bayesian hierarchical model dramatically reduced the posterior predictive variance for metal grades regression compared to the no-pooling model.In addition,the posterior inference in the hierarchical model is insensitive to the choice of prior.The data is wellrepresented in the posterior which indicates a robust model.The results show that the spatial domain can be successfully utilised for metal grade regression.Uncertainty in estimating the relationship between pay metals and both secondary and gangue elements is quantified and shown to be reduced with partial-pooling.Thus,the proposed Bayesian hierarchical model can offer a reliable and stable way to monitor the relationship between metal grades for ore sorting and other mineral processing options.

基于贝叶斯分层模型的液化侧移稳健的易损性分析方法

提出了一种基于贝叶斯分层模型的液化侧移稳健的易损性分析方法。采用贝叶斯分层模型量化不同增量动力分析(IDA)曲线间的差异,结合抽样方法预测潜在侧移的分布,建立液化侧移稳健的易损性曲线和超越概率曲线。以一处实际发生过液化侧移的场地为例,展示了稳健的易损性曲线及超越概率曲线的建立方法,并与相关方法进行比较。结果表明,所提出的方法可以较好地模拟IDA曲线的分布,较为准确地量化易损性曲线和超越概率曲线的不确定性。

Bayesian两变量层次模型及其在诊断试验系统评价中的应用

目的探讨Bayesian两变量层次模型的构建及其在诊断试验系统评价中的应用。方法将Bayesian两变量层次模型应用于传统Pap细胞学涂片诊断子宫颈癌准确性评价的历史Meta分析资料,估计相关的效应指标敏感度和特异度及筛查研究比随访研究的相对可信度。结果与经典综合受试者工作特征曲线方法相比,Bayesian两变量层次模型估计得到三个层次的效应指标,其中综合敏感度和特异度均数及95%可信区间分别为0.64(0.56,0.72)和0.74(0.67,0.80),预测敏感度和特异度均数及95%可信区间分别为0.61(0.12,0.96)和0.69(0.21,0.97),筛查研究比随访研究的相对可信度估计为1.3(0.59,2.48)。结论采用Bayesian两变量层次模型进行诊断试验Meta分析,更加灵活、有效,易于实现和解释,值得推广应用。

基于BHM-EcoFlow模型的汉江中下游河段水文-生态响应关系研究

河流水文-生态响应关系是确定生态流量阈值的科学基础。针对当前河流水文-生态响应关系研究中生态数据不足且生态建模难度大的问题,建立了基于贝叶斯层次分析法的BHM-EcoFlow(Bayesian hierarchical modelling-ecological flow)模型,该模型将河流不同河段及同一河段不同站点间的先验知识与实测数据相结合,可有效利用短系列数据,实现河流水文-生态响应关系的模拟。采用汉江中下游干流2011年的水文、生态数据,模拟了浮游植物细胞密度与流量、混合层温度间的关系,计算了不同流量条件下各河段的浮游植物密度。结果表明:BHM-EcoFlow模型提高了短系列数据的可用性,对汉江中下游干流的水文-生态响应关系具有良好的识别能力,为确定生态流量提供了科学依据。

基于层次结构与多模块的海洋生物分类算法

传统分类方法在海洋生物图像分类任务上视各类别相互独立,而生物间存在着明确的相互关系,常规方法忽略了其生物学关系。为了使分类网络充分利用数据间的关系,该文提出层次化贝叶斯信息准则(HBIC)探索分层结构,并结合预定义层次结构联合学习,共同辅助神经网络分类。此外,为更高效准确地提取数据全尺寸特征,设计了一种EAConv模块,并引入相对注意力机制,基于多模块与层次结构,进一步建立端到端联合优化的分层学习方法框架(EAHNet)。所有实验基于私有的南麂列岛潮间带大型海洋生物数据集进行,根据层次结构设计的常规卷积神经网络能够将分类准确率提高到86.16%,完整网络能够使准确率达到96.17%,同时能够保证准确率与参数量等网络性能的均衡。结果表明,所提出的多种层次结构辅助、卷积与注意力机制特异性结合的特征提取方法,有效加强了网络对于海洋生物关系信息与特征的捕获能力,从而在整体上取得非常有竞争力的结果。

基于近端算子PHMC的机载雷达高度表参数估计

传统雷达高度表参数估计算法在面对参数的高维特性时会出现过拟合情况,导致参数估计精确度降低。为此,提出一种新颖的基于近端算子修正的哈密顿蒙特卡洛(PHMC)算法,通过统计学的手段估计高程参数。首先假设高程参数具有稀疏特性,并使用拉普拉斯分布对其进行表征,这种稀疏先验可表征高程突变的地形场景。稀疏先验与似然函数之间为非共轭关系,使用分层贝叶斯的方法获得后验分布函数的闭合解,采用哈密顿蒙特卡洛(HMC)方法通过采样的方式解决贝叶斯推论中的参数估计问题,引入近端算子提供次梯度完成参数估计。仿真数据验证了所提PHMC算法优于其他传统算法。

基于贝叶斯层级模型的用户异常行为检测研究

大多数操作系统的安全防护主要依赖基于签名或基于规则的方法,因此现有大多数的异常检测方法精度较低。因此,利用贝叶斯模型为同类群体建模,并结合时间效应与分层原则,为用户实体行为分析(User and Entity Behavior Analytics,UEBA)研究提供精度更高的数据集。然后,将基于实际记录的用户行为数据与贝叶斯层级图模型推测出的数据进行比较,降低模型中的误报率。该方法主要分为两个阶段:在第1阶段,基于数据驱动的方法形成用户行为聚类,定义用户的个人身份验证模式;在第2阶段,同时考虑到周期性因素和分层原则,并通过泊松分布建模。研究表明,数据驱动的聚类方法在减少误报方面能够取得更好的结果,并减轻网络安全管理的负担,进一步减少误报数量。

可信推断近场稀疏综合阵列三维毫米波成像

考虑到主动式电扫描毫米波成像系统在实际应用中成像场景要求大,分辨率要求高,但毫米波的波长短,继而造成满足奈奎斯特采样定理的均匀阵列规模及馈电网络复杂度过高,面临着成像精度、成像速度和系统成本之间的矛盾。针对以上问题,该文提出了可信推断近场稀疏综合阵列算法(CBI-SAS),在全贝叶斯学习框架下,该算法基于贝叶斯推断对复激励权值进行稀疏优化,得到复激励权值的完全统计后验概率密度函数,从而利用其高阶统计信息得到复激励权值的最优值及其置信区间和置信度。在贝叶斯推断中,为了实现较少数量的阵元合成期望波束方向图,可通过对复值激励权值引入重尾的拉普拉斯稀疏先验。然而,由于先验概率模型与参考方向图数据模型非共轭,因此需对先验模型进行分层贝叶斯建模,从而保证得到的复激励权值完全后验分布具有闭合解析解。为了避免求解完全后验分布的高维积分,采用变分贝叶斯期望最大化方法计算复激励权值后验概率密度函数,实现复激励权值的可信推断。仿真模拟实验结果显示,相较于传统稀疏阵列合成方法,所提方法阵元稀疏度更低、归一化均方误差更小、匹配方向图精度更好。此外,基于设计的稀疏阵列采集近场一维电扫和二维平面全电扫实测回波数据后,利用改进三维时域算法进行三维重建,验证了所提CBI-SAS算法在保证成像结果的同时降低了系统复杂性的优势。

基于有偏误辅助变量的分层贝叶斯小域估计方法研究

抽样调查中的小域估计问题指的是,根据较少样本量进行一定精度下子总体估计的现实问题。与基于设计的方法不同,基于模型的方法不依赖大样本理论,能在估计过程中借助其他域的样本信息,更加适用于小域估计问题。然而,现实中测量误差无法完全避免,当模型协变量有偏误时,小域估计结果失效。对此,采用测量误差模型校正辅助变量误差,基于单元层次的分层贝叶斯模型进行小域估计,并在贝叶斯框架下估计辅助变量偏误机制。鉴于实际调查中为方便数据编码与统计、控制无回答误差,调查结果以分类型数据居多,本文重点讨论了更适用于小域估计问题的模型方法,针对分类型辅助变量存在测量误差的情形,给出了方法合理性的证明,同时通过模拟和实证对其估计效果进行验证与实践。本文模拟六种实践中常见的情形,除仅有分类型变量存在测量误差的情形之外,还考虑了存在测量误差的变量既有分类型又有连续型的情形等。数值模拟与实证结果一致表明,本文方法不仅能充分纳入与推断相关的不确定性因素,克服样本量受限的问题,还具有广泛的适用性,相较于传统方法,估计结果在提升准确度的同时更为稳健。