数据扩充下0-1膨胀几何分布的客观贝叶斯分析及应用

在交通安全、公共卫生、风险管理等实际应用领域,经常会遇到0观测值、1观测值出现较多的样本数据。为了更深入地研究这类数据集,本文提出了0-1膨胀几何分布模型,通过设计数据扩充策略和构造完全似然函数,得到了Jeffreys先验和reference先验。设置不同的样本容量和参数真值,对不同的客观先验进行数值仿真和比较分析。最后,利用0-1膨胀几何分布模型对底特律城市交通事故死亡数据集进行了分析。研究表明,采用客观贝叶斯方法比主观贝叶斯方法能够实现更佳的拟合效果。     

Investigating different approaches to develop informative priors in hierarchical Bayesian safety performance functions

The Bayesian inference method has been frequently adopted to develop safety performance functions. One advantage of the Bayesian inference is that prior information for the independent variables can be included in the inference procedures. However, there are few studies that discussed how to formulate informative priors for the independent variables and evaluated the effects of incorporating informative priors in developing safety performance functions. This paper addresses this deficiency by introducing four approaches of developing informative priors for the independent variables based on historical data and expert experience. Merits of these informative priors have been tested along with two types of Bayesian hierarchical models (Poisson-gamma and Poisson-lognormal models). Deviance information criterion (DIC), R-square values, and coefficients of variance for the estimations were utilized as evaluation measures to select the best model(s). Comparison across the models indicated that the Poisson-gamma model is superior with a better model fit and it is much more robust with the informative priors. Moreover, the two-stage Bayesian updating informative priors provided the best goodness-of-fit and coefficient estimation accuracies. Furthermore, informative priors for the inverse dispersion parameter have also been introduced and tested. Different types of informative priors’ effects on the model estimations and goodness-of-fit have been compared and concluded. Finally, based on the results, recommendations for future research topics and study applications have been made.     

A Bayesian Semiparametric Analysis of the Reliability and Maintenance of Machine Tools

A Bayesian semiparametric proportional hazards model is presented to describe the failure behavior of machine tools. The semiparametric setup is introduced using a mixture of Dirichlet processes prior. A Bayesian analysis is performed on real machine tool failure data using the semiparametric setup, and development of optimal replacement strategies are discussed. The results of the semiparametric analysis and the replacement policies are compared with those under a parametric model.     

Markov Chains: Gibbs Fields,Monte Carlo Simulation,and Queues

In this work we will provide a monitoring scheme for the mean of an autocorrelated process which can experience bidirectional jumps of random size and occurrence and has a steady state. Our interest focuses in the start up phase and short-run scenarios, where traditional SPC techniques fail to provide formal testing. Furthermore, we will provide a framework where prior information regarding the process can be employed. These will be achieved by adopting a Bayesian sequentially updated scheme that will allow inference in an online fashion. The performance of the proposed model will be compared against other methods which can be applied in similar settings. A simulation study along with a real data application from the dairy business will conclude this work. Supplemental files are available online, with technical details and the code for applying the proposed methodology in R.     

Component reliability assessment using quantitative and qualitative data

The estimation of a component failure rate depends on the availability of plant specific numerical data. The purpose of this study was development of a new method that explicitly includes numerical and linguistic information into the assessment of a specific failure rate. The basis of the method is the Bayesian updating approach. A prior distribution is selected from a generic database, whereas likelihood is assessed using the principles of fuzzy set theory. The influence of component operating conditions on component failure rate is modeled using a fuzzy inference system. Results of fuzzy reasoning are then used for building an appropriate likelihood function for the Bayesian inference.The method was applied on a high voltage transformer. Results show that with the proposed method, one can estimate the specific failure rate and analyze possible measures to improve component reliability. The method can be used for specific applications including components for which there is not enough numerical data for specific evaluation.     

基于TV-泊松奇异积分联合先验模型的图像重构

目的针对当前图像重构算法容易产生过渡平滑图像纹理区域,使复原图像丢失大量纹理,降低重构图像视觉质量等缺陷,提出TV-泊松奇异积分联合先验模型耦合贝叶斯推理的图像重构算法。方法引入配分函数,结合TV函数,构造TV图像先验。定义泊松奇异积分先验,并将其嵌入到TV先验中,设计一种联合先验模型,控制图像纹理平滑度。基于高阶统计量技术,完善图像退化模型,并耦合先验模型,生成重构图像的最大后验估计MAP。引入优化最小原则,求解MAP,完成贝叶斯推理,获取重构图像。对文中算法复原图像纹理的关键参数进行优化,并研究分析该算法的用户响应。结果与当前图像重构算法相比,文中算法的复原视觉质量更高,能够较好地平衡噪声与纹理。在图像退化程度较大时,文中算法具有良好的用户响应。结论文中算法能够较好地同步保持图像边缘与纹理。     

Bayesian analysis of nonlinear regression with equicorrelated elliptical errors

For a nonlinear regression model with an intercept, it is shown that, under diffuse priors of the intercept and of the error precision, the assumption of equicorrelated and jointly elliptical errors (instead of uncorrelated Normal ones) has no new consequences on posterior inference about the (nonlinear) regression parameters (except for the constant term) and on predictive inference. Support from the Polish Committee for Scientific Research (KBN, grant no. 1-H02B-015-11) is gratefully acknowledged.