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Discussion of “Some statistical challenges in automated driving systems” “自动驾驶系统中的一些统计挑战”讨论
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-07-03 DOI: 10.1002/asmb.2797
David Banks, Yen-Chun Liu
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引用次数: 0
Discussion of “Specifying prior distributions in reliability applications”: Towards new formal rules for informative prior elicitation? “在可靠性应用中指定先验分布”的讨论:迈向信息先验启发的新形式化规则?
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-30 DOI: 10.1002/asmb.2794
Nicolas Bousquet

The article by Tian et al. (Appl. Stoch. Models Bus. Ind. 2023) takes an interesting look at the use of non-informative priors adapted to several censoring processes, which are common in reliability. It proposes a continuum of modelling approaches that go as far as defining weakly informative priors to overcome the well-known shortcomings of frequentist approaches to problems involving highly censored samples. In this commentary, I make some critical remarks and propose to link this work to a more generic vision of what could be a relevant Bayesian elicitation in reliability, taking advantage of recent theoretical and applied advances. Through tools like approximate posterior priors and prior equivalent sample sizes, and by illustrating them with simple reliability models, I suggest methodological avenues to formalize the elicitation of informative priors in a auditable, defensible way. By allowing a clear modulation of subjective information, this might respond to the authors' primary concern of constructing weakly informative priors and to a more general concern for precaution in Bayesian reliability.

Tian 等人的文章(Appl. Stoch.它提出了一系列建模方法,这些方法甚至定义了弱信息先验,以克服频数主义方法在涉及高删减样本问题上的众所周知的缺点。在这篇评论中,我提出了一些批评意见,并建议利用最近的理论和应用进展,将这项工作与可靠性领域相关贝叶斯征询方法的更普遍愿景联系起来。通过近似后验先验和先验等效样本量等工具,并用简单的可靠性模型加以说明,我提出了一些方法论途径,以一种可审计、可辩护的方式将信息先验的激发正规化。通过允许对主观信息的明确调节,这可能会回应作者对构建弱信息先验的主要关切,以及对贝叶斯可靠性中的预防措施的更普遍关切。
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引用次数: 0
Discussion of “Specifying prior distributions in reliability applications,” by Qinglong Tian, Colin Lewis-Beck, Jarad B. Niemi, and William Meeker 田庆龙、Colin Lewis‐Beck、Jarad B.Niemi和William Meeker关于“可靠性应用中指定先验分布”的讨论
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-30 DOI: 10.1002/asmb.2796
Necip Doganaksoy, Steven E. Rigdon
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引用次数: 0
A stochastic model for evaluating the peaks of commodities' returns 一个评估商品收益峰值的随机模型
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-26 DOI: 10.1002/asmb.2790
Roy Cerqueti, Raffaele Mattera, Alessandro Ramponi

This paper proposes a probabilistic model for the evaluation of the peak components of the return of a commodity. The ground of the study lies in the evidence that the spikes in the returns are due to the shocks occurring in the external environment. We follow an approach based on a particular class of point processes—the Spatial Mixed Poisson Processes—by exploiting an invariance property for such a class. The theoretical framework is used for presenting an estimation the procedure of the returns based on the available information. An empirical instance based on different commodities' returns and the abnormal returns of the volatility index as external shocks are presented to motivate our theoretical approach.

本文提出了一个用于评估商品收益峰值成分的概率模型。研究的基础在于有证据表明,回报的峰值是由外部环境的冲击造成的。我们采用的方法基于一类特殊的点过程--空间混合泊松过程--利用这类过程的不变量特性。该理论框架用于介绍基于可用信息的收益估算程序。为了激发我们的理论方法,我们介绍了一个基于不同商品回报率的经验实例,以及作为外部冲击的波动指数异常回报率。
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引用次数: 0
A Bayesian record linkage model incorporating relational data 一个包含关系数据的贝叶斯记录链接模型
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-26 DOI: 10.1002/asmb.2792
Juan Sosa, Abel Rodríguez

In this article, we introduce a novel Bayesian approach for linking multiple social networks in order to discover the same real world person having different accounts across networks. In particular, we develop a latent model that allows us to jointly characterize the network and linkage structures relying on both relational and profile data. In contrast to other existing approaches in the machine learning literature, our Bayesian implementation naturally provides uncertainty quantification via posterior probabilities for the linkage structure itself or any function of it. Our findings clearly suggest that our methodology can produce accurate point estimates of the linkage structure even in the absence of profile information, and also, in an identity resolution setting, our results confirm that including relational data into the matching process improves the linkage accuracy. We illustrate our methodology using real data from popular social networks such as Twitter, Facebook, and YouTube.

摘要在本文中,我们介绍了一种新的贝叶斯方法,用于连接多个社交网络,以发现同一个现实世界中的人在网络中拥有不同的帐户。特别是,我们开发了一个潜在的模型,使我们能够共同表征依赖关系数据和配置文件数据的网络和链接结构。与机器学习文献中的其他现有方法相比,我们的贝叶斯实现自然地通过连杆结构本身或其任何函数的后验概率提供了不确定性量化。我们的研究结果清楚地表明,即使在没有轮廓信息的情况下,我们的方法也可以对连杆结构产生准确的点估计,在身份解析设置中,我们的结果证实,在匹配过程中包含关系数据可以提高链接的准确性。我们使用Twitter、Facebook和YouTube等流行社交网络的真实数据来说明我们的方法。
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引用次数: 0
Discussion of: Specifying prior distributions in reliability applications 讨论:在可靠性应用中指定先验分布
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-20 DOI: 10.1002/asmb.2791
Richard Arnold
<p>This interesting paper by Tian et al. presents a comprehensive investigation of non-informative and weakly informative priors for two parameter (log-location and scale) failure distributions. They provide helpful and practical advice to the Bayesian analyst on the selection of appropriate priors and specifically on the avoidance of posterior estimates that are unrealistic, particularly where data are sparse.</p><p>The motivating examples provide challenging settings where the information provided by the data is extremely slight. These settings are typical of systems engineered to be very high reliable, where failure data are minimal by design, but where inferences about failure risk are critical. These are also precisely the settings where default choices for noninformative priors may be unexpectedly influential,<span><sup>1</sup></span> leading either to improper posteriors, or to posteriors which place significant mass in regions which are implausible. The authors' fundamental principle (§5.4) of ensuring that the priors always be constructed to avoid this consequence is very well stated, and one which will bear much repetition in other forums.</p><p>We have only one main point to make. It relates to their statement in the abstract that ‘for Bayesian inference, there is only one method of constructing equal-tailed credible intervals—but it is necesssary to provide a prior distribution to full specify the model.’ We agree, but our view is that the statement is incomplete: the <b>model</b> must have been chosen to begin with. Although this is not the main point of the paper, the consequences of model choice can be considerable, particularly when all of the inferential action is being carried out on the tails of the distribution, where only a few percent of failures may ever be observed to occur.</p><p>In this spirit we have reproduced in our Figure 1 the authors' Weibull probability plot (their Figure 1) of the Bearing Cage failure data.<span><sup>2</sup></span> The estimated parameters of the original Weibull fit are <math> <semantics> <mrow> <mo>(</mo> <mover> <mrow> <mi>β</mi> </mrow> <mo>^</mo> </mover> <mo>,</mo> <mover> <mrow> <mi>η</mi> </mrow> <mo>^</mo> </mover> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>2</mn> <mo>.</mo> <mn>035</mn> <mo>,</mo> <mn>11792</mn> <mo>)</mo> </mrow> <annotation>$$ left(hat{beta},hat{eta}right)=left(2.035,11792right) $$</annotation>
我们还展示了对数正态分布和伽马分布的累积分布,它们的匹配值为 ( t p , λ q ) $$ left({t}_p,{lambda}_qright) $$。当然,它们的尾部形状有些不同,对数正态分布的尾部形状最为明显。尽管如此,我们还是提出了这样一个问题:如果重点主要放在分布的低尾部,那么在单一假定可能性的基础上选择一个合适的先验值,是否能够像在模型空间上选择先验值一样,完成一些繁重的工作?此外,关于 ( t p , λ q ) $$ left({t}_p,{lambda}_qright) $$ 的先验值可能会在诱导中产生进一步的优势--考虑到大尺度参数 σ $$ sigma $$ 可能比第二量级 q $$ q $$ 更难描述。总之,我们感谢作者们对先验规范问题的全面处理,以及他们提供的实际指导。
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引用次数: 0
Deep partial least squares for instrumental variable regression 工具变量回归的深度偏最小二乘
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-19 DOI: 10.1002/asmb.2787
Maria Nareklishvili, Nicholas Polson, Vadim Sokolov

In this paper, we propose deep partial least squares for the estimation of high-dimensional nonlinear instrumental variable regression. As a precursor to a flexible deep neural network architecture, our methodology uses partial least squares for dimension reduction and feature selection from the set of instruments and covariates. A central theoretical result, due to Brillinger (2012) Selected Works of Daving Brillinger. 589-606, shows that the feature selection provided by partial least squares is consistent and the weights are estimated up to a proportionality constant. We illustrate our methodology with synthetic datasets with a sparse and correlated network structure and draw applications to the effect of childbearing on the mother's labor supply based on classic data of Chernozhukov et al. Ann Rev Econ. (2015b):649–688. The results on synthetic data as well as applications show that the deep partial least squares method significantly outperforms other related methods. Finally, we conclude with directions for future research.

在本文中,我们提出了用于估计高维非线性工具变量回归的深度偏最小二乘。作为灵活的深度神经网络架构的先驱,我们的方法使用偏最小二乘法从一组仪器和协变量中进行降维和特征选择。Brillinger(2012)的一个核心理论结果表明,偏最小二乘法提供的特征选择是一致的,并且权重被估计到比例常数。我们用具有稀疏和相关网络结构的合成数据集来说明我们的方法,并基于Angrist和Evans(1996)的经典数据,绘制了生育对母亲劳动力供应影响的应用程序。合成数据和应用结果表明,深度偏最小二乘法显著优于其他相关方法。最后,我们总结了未来研究的方向。
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引用次数: 1
Comments on “specifying prior distributions in reliability applications” by Tian, Lewis-Beck, Niemi, and Meeker Tian、Lewis‐Beck、Niemi和Meeker关于“在可靠性应用中指定先验分布”的评论
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-19 DOI: 10.1002/asmb.2789
Jie Min, Zhengzhi Lin, Yili Hong
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引用次数: 0
Discussion of specifying prior distributions in reliability applications—Applications for Bayesian estimation software design 确定先验分布在可靠性应用中的讨论——在贝叶斯估计软件设计中的应用
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-17 DOI: 10.1002/asmb.2786
Peng Liu

It is a great pleasure to have the opportunity to write a discussion on “Specifying Prior Distributions in Reliability Applications” by Tian et al. Appl Stochast Models Bus Ind, (2023). One coauthor of the paper, Dr Meeker, has conducted Bayesian methodology research on reliability data analysis for many years, and I have followed his work on the subject for quite some time. The work by Dr Meeker helped us develop Bayesian estimation products which are both powerful and easy to use. This time, I learned something new as usual. In this discussion, I will focus on the great value of the paper for developing user friendly Bayesian estimation software.

很高兴有机会就 Tian 等人的论文 "在可靠性应用中指定先验分布"(Specifying Prior Distributions in Reliability Applications)撰写一篇讨论文章。 Appl Stochast Models Bus Ind, (2023)。该论文的合著者之一 Meeker 博士多年来一直从事可靠性数据分析方面的贝叶斯方法研究,我关注他在这方面的工作也有一段时间了。米克博士的工作帮助我们开发出了贝叶斯估算产品,这些产品功能强大且易于使用。这次,我像往常一样学到了一些新东西。在本次讨论中,我将重点讨论这篇论文对于开发用户友好型贝叶斯估计软件的巨大价值。
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引用次数: 0
On relevation transform involved with statistical dependence between two component lifetimes 涉及两组分寿命统计相关性的关联变换
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-06-14 DOI: 10.1002/asmb.2785
Rui Fang, Chen Li, Xiaohu Li

Krakowski (Rev Fr Autom Inform Rech Opèr. 1973;7:107–120.) introduced the relevation transform for component and active redundancy with independent lifetimes, and except for Johnson and Kotz (Am J Math Manag Sci. 1981;1:155–165; Nav Res Logist. 1983;30:163–169.) most subsequent researches were conducted under this framework. However, it is not uncommon that a component and its active redundancy bear some common stresses due to the environment and thus they have dependent lifetimes. In this note, we equip the involved lifetimes with a survival copula and then clarify the potential difference between the new and classical versions through making stochastic comparison. Moreover, by ordering the lifetime of system with relevation redundancy we also study the way of allocating a relevation redundancy at component level to ultimately improve the system reliability. The present results on series and parallel systems serve as a generalization of the corresponding ones of Belzunce et al. (Appl Stoch Models Bus Ind. 2019;35:492–503.). Several numerical examples are presented to illustrate these findings as well.

克拉科夫斯基(自动通知技术操作牧师)(1973; 7:107-120)提出了具有独立生命周期的组件和主动冗余的关联变换,除了Johnson和Kotz (Am J Math management Sci. 1981; 1:155-165;Nav Res ologist . 1983; 30:163-169 .)之后的大多数研究都是在这个框架下进行的。然而,组件及其主动冗余由于环境而承受一些共同的压力,因此它们具有依赖的生命周期,这并不罕见。在本文中,我们为所涉及的寿命配备了一个生存联结,然后通过随机比较来澄清新版本和经典版本之间的潜在差异。此外,通过对具有关联冗余的系统进行寿命排序,研究了在组件级分配关联冗余的方法,最终提高了系统的可靠性。目前关于串联和并联系统的结果是对Belzunce等人的相应结果的概括(apple Stoch Models Bus Ind. 2019; 35:492-503)。并给出了几个数值例子来说明这些发现。
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引用次数: 0
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Applied Stochastic Models in Business and Industry
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