The sensitivity of estimates of regression to the mean

Estimations of the effectiveness of remedial treatments in road safety analysis are frequently bedevilled by the problem of regression to the mean (RTM). The number of accidents x observed at a site in the “before” period is a “noisy” quantity: x is Poisson distributed about an (unknown) true mean m for that site, so that x = m + e. Sites selected for treatment tend to have a positive random error component e, which will on average be zero in the “after” period, even if no treatment is applied.Methods for estimating RTM usually require some assumption about the underlying (prior) between-site distribution of the true means f₀(m): for example, in the empirical Bayes method, a gamma distribution is assumed. The paper considers the impact of different assumptions for this distribution and, indeed, whether any distributional form needs to be assumed. Using Markov Chain Monte Carlo methods, a variety of distributional forms are assumed for f₀(m) and applied to each of a number of real data sets, including that from a major study on the effectiveness of speed cameras. It is shown that, in some cases, the size of the estimated RTM effect can be quite sensitive to the choice of distribution.     

数据缺失条件下AR（p）模型参数不确定性研究

在数据缺失条件下,探讨贝叶斯推断法在AR（p）模型参数不确定性研究中的应用。根据Bayesian理论与Markov chain Monte Carlo（简称MCMC）法,在WinBUGS软件中搜索一个或更多数据缺失时AR（p）模型参数的后验状态空间。计算结果表明,贝叶斯推断法既能充分利用现有资料信息,又能考虑参数的不确定性,是一种AR（p）模型参数估计的有效方法。     

基于贝叶斯算法的220kV变压器故障检修成本模型分析

针对电力网络中220kV变压器运行现状和其所处的故障检修阶段,根据全寿命周期成本管理理念,基于贝叶斯计量经济学理论和计量经济学软件WinBUGS,建立了220kV变压器的失效故障维修成本优化模型．该模型充分考虑到电气设备经济成本活动的不确定性和特殊性,能够较为合理地反映出变压器寿命周期内的检修故障阶段所对应的费用．并结合福建某变电站220kV变压器的运行情况,验证了该模型的可行性与适用性．     

Optimal batting orders in one-day cricket

This paper concerns the search for optimal or nearly optimal batting orders in one-day cricket. A search is conducted over the space of permutations of batting orders where simulated annealing is used to explore the space. A non-standard aspect of the optimization is that the objective function (which is the mean number of runs per innings) is unavailable and is approximated via simulation. The simulation component generates runs ball by ball during an innings taking into account the state of the match and estimated characteristics of individual batsmen. The methods developed in the paper are applied to the national team of India based on their performance in one-day international cricket matches.     

应用分层模型进行核电站设备可靠性参数估计

目前国内对于从多个核电站统计的设备失效数据进行各特定核电站设备可靠性参数估计的方法研究尚少。本文研究了用于可靠性参数估计的分层模型以及实现分层模型的两种方法:带Kass-Steffey修正的参数经验贝叶斯方法和马氏链蒙特卡洛方法。以设备需求失效的稀少失效数据样本为例,推导了带Kass-Steffey修正的Beta-Binomial模型原理并编程求解,研究了马氏链蒙特卡罗方法及软件计算,对比了核电站后验失效概率的计算结果。计算表明:两种方法得到的部分失效概率后验估计的均值相差0~25%;95分位值相差5%~15%,两种方法都可用于稀少数据的样本估计。     

基于层次贝叶斯法的沙门氏菌食品污染率统计分析

为系统性研究我国大陆范围内食品中沙门氏菌污染状况,基于贝叶斯估计方法,利用文献挖掘(Literature mining)所得的数据,建立层次贝叶斯模型(Hierarchical Bayesian model),对我国市售食品中沙门氏菌污染率进行可靠统计。结果表明,我国大陆地区市售食品的沙门氏菌平均污染率,2004～2018年为5.91%(95%置信区间为4.69%～7.27%),在2.02%～8.29%范围内波动;市售食品中污染率最高的是肉与肉制品,污染率为8.45%;黑龙江省、上海市和四川省是食品沙门氏菌污染严重地区,食品污染率分别为12.05%、11.53%和10.68%;肠道沙门氏菌亚群Ⅰ,以及既可感染人又可感染动物的沙门氏菌种群是主要的病原菌类型;肠炎沙门氏菌(Salmonella enteritidis)、德尔卑沙门氏菌(Salmonella derby)和鼠伤寒沙门氏菌(Salmonella typhimurium)是主要的食品污染菌种类型,食品污染率分别为22.10%、15.23%和12.54%。因此,卫生和市场监管部门应加强肉与肉制品的监管,注重因地制宜,针对主要病原菌类型和优势菌种制定防范策略,以保障食品卫生安全。     

Validation of a Full Bayes methodology for observational before-after road safety studies and application to evaluation of rural signal conversions

The objective of the study on which the paper is based was to explore the application of fully Bayesian methods for before-after road safety studies. Several variations of the methodology were evaluated with a simulated dataset in which hypothetical treatments with no safety effect were randomly assigned to high accident locations to mimic the common site selection process in road jurisdictions. It was confirmed that the fully Bayesian method by estimating no safety effect can account for the regression-to-the-mean that results from this biased site selection process. The fully Bayesian method was then applied to California rural intersection data to evaluate the safety effect of conversion from stop to signalized control. The results were then compared with those from the empirical Bayesian method, currently the accepted approach for conducting unbiased before-after evaluations. This comparison was generally favorable in that FB can provide similar results as EB.     

Calibration, Error Analysis, and Ongoing Measurement Process Monitoring for Mass Spectrometry

We consider problems of quantifying and monitoring accuracy and precision of measurement in mass spectrometry, particularly in contexts where there is unavoidable day-to-day/period-to-period changes in instrument sensitivity. First, we consider the issue of estimating instrument sensitivity based on data from a typical calibration study. Simple method-of-moments methods, likelihood-based methods, and Bayes methods based on the one-way random effects model are illustrated. Then, we consider subsequently assessing the precision of an estimate of a mole fraction of a gas of interest in an unknown. Finally, we turn to the problem of ongoing measurement process monitoring and illustrate appropriate setup of Shewhart control charts in this application.     

Using Degradation Data to Assess Reliability

For highly reliable products, little information about reliability is provided by lifetests using a practical test duration in which few or no failures are typically observed. In this article, we illustrate the advantages of using degradation data to assess reliability. We use a Bayesian approach for analyzing the degradation data because of its advantages. The uncertainty of reliability and lifetime distribution quantile estimates can be determined in a straightforward manner. Moreover, calculating for a specified time the reliability of a population of units with varying ages is easily done. We illustrate these advantages by a laser degradation example.