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Rejoinder: Let’s Be Imprecise in Order to Be Precise (About What We Don’t Know) 复辩状：为了准确，让我们变得不准确（关于我们不知道的事情）

IF 5.7 1区数学 Q1 STATISTICS & PROBABILITY

Statistical Science

Pub Date : 2021-04-01 DOI: 10.1214/21-STS765REJ

Ruobin Gong, X. Meng

Preparing a rejoinder is a typically rewarding, sometimes depressing, and occasionally frustrating experience. The rewarding part is self-evident, and the depression sets in when a discussant has much deeper and crisper insights about the authors’ thesis than authors themselves. Frustrations arise when the authors thought they made some points crystal clear, but the reflections from the discussants show a very different picture. We are deeply grateful to the editors of Statistical Science and the discussants for providing us an opportunity to maximize the first, sample the second, and minimize the third.

准备重新答辩通常是一种有益的、有时令人沮丧，有时也令人沮丧的经历。收获的部分是不言而喻的，当讨论者对作者的论文比作者自己有更深刻、更清晰的见解时，抑郁就会开始。当作者认为他们把一些观点说得非常清楚时，就会感到沮丧，但讨论者的反思显示了一幅截然不同的画面。我们非常感谢《统计科学》杂志的编辑和讨论者，他们为我们提供了一个最大化第一个、抽样第二个和最小化第三个的机会。

引用次数: 0

A Conversation with Dennis Cook 与丹尼斯·库克的对话

IF 5.7 1区数学 Q1 STATISTICS & PROBABILITY

Statistical Science

Pub Date : 2021-04-01 DOI: 10.1214/20-STS801

E. Bura, Bing Li, Lexin Li, C. Nachtsheim, D. Peña, C. Setodji, R. Weiss

Dennis Cook is a Full Professor, School of Statistics, at the University of Minnesota. He received his BS degree in Mathematics from Northern Montana College, and MS and PhD degrees in Statistics from Kansas State University. He has served as Chair of the Department of Applied Statistics, Director of the Statistical Center and Director of the School of Statistics, all at the University of Minnesota.His research areas include dimension reduction, linear and nonlinear regression, experimental design, statistical diagnostics, statistical graphics and population genetics. He has authored over 200 research articles and is author or co-author of two textbooks— An Introduction to Regression Graphics and Applied Regression Including Computing and Graphics—and three research monographs, Influence and Residuals in Regression, Regression Graphics: Ideas for Studying Regressions through Graphics and An Introduction to Envelopes: Dimension Reduction for Efficient Estimation in Multivariate Statistics.He has served as Associate Editor of the Journal of the American Statistical Association, The Journal of Quality Technology, Biometrika, Journal of the Royal Statistical Society and Statistica Sinica. He is a four-time recipient of the Jack Youden Prize for Best Expository Paper in Technometrics as well as the Frank Wilcoxon Award for Best Technical Paper. He received the 2005 COPSS Fisher Lecture and Award, and he is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics. The following conversation took place on March 22, 2019, following the banquet at the conference, “Cook’s Distance and Beyond: A Conference Celebrating the Contributions of R. Dennis Cook.” The interviewers were, Efstathia Bura (Effie), Bing Li, Lexin Li, Christopher Nachtsheim (Chris), Daniel Pena, Claude Messan Setodji and Robert Weiss (Rob).

丹尼斯·库克是明尼苏达大学统计学院的全职教授。他在北蒙大拿学院获得数学学士学位，在堪萨斯州立大学获得统计学硕士和博士学位。他曾担任明尼苏达大学应用统计系主任、统计中心主任和统计学院主任。他的研究领域包括降维、线性和非线性回归、实验设计、统计诊断、统计图形和群体遗传学。他撰写了200多篇研究论文，是两本教科书的作者或合著者-回归图形介绍和应用回归包括计算和图形-以及三本研究专著，回归中的影响和残差，回归图形:通过图形研究回归的想法和信封介绍:多维统计中有效估计的降维。他曾担任《美国统计协会杂志》、《质量技术杂志》、《生物计量学》、《皇家统计学会杂志》和《中国统计》的副主编。他曾四次获得Jack Youden技术计量学最佳说明性论文奖以及Frank Wilcoxon最佳技术论文奖。他获得了2005年COPSS费舍尔讲座和奖，他是美国统计协会和数学统计研究所的会员。以下对话发生在2019年3月22日，在会议宴会之后，“库克的距离和超越:庆祝r·丹尼斯·库克贡献的会议”。采访者分别是:Efstathia Bura(艾菲)、Bing Li、Lexin Li、Christopher Nachtsheim(克里斯)、Daniel Pena、Claude Messan Setodji和Robert Weiss(罗伯)。

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引用次数: 0

Confidence Intervals for Seroprevalence 血清流行率的置信区间

IF 5.7 1区数学 Q1 STATISTICS & PROBABILITY

Statistical Science

Pub Date : 2021-03-27 DOI: 10.1214/21-sts844

T. DiCiccio, D. Ritzwoller, Joseph P. Romano, A. Shaikh

This paper concerns the construction of confidence intervals in standard seroprevalence surveys. In particular, we discuss methods for constructing confidence intervals for the proportion of individuals in a population infected with a disease using a sample of antibody test results and measurements of the test’s false positive and false negative rates. We begin by documenting erratic behavior in the coverage probabilities of standard Wald and percentile bootstrap intervals when applied to this problem. We then consider two alternative sets of intervals constructed with test inversion. The first set of intervals are approximate, using either asymptotic or bootstrap approximation to the finite-sample distribution of a chosen test statistic. We consider several choices of test statistic, including maximum likelihood estimators and generalized likelihood ratio statistics. We show with simulation that, at empirically relevant parameter values and sample sizes, the coverage probabilities for these intervals are close to their nominal level and are approximately equi-tailed. The second set of intervals are shown to contain the true parameter value with probability at least equal to the nominal level, but can be conservative in finite samples. © Institute of Mathematical Statistics, 2022

本文讨论了标准血清患病率调查中置信区间的构建。特别是，我们讨论了使用抗体测试结果样本和测试的假阳性和假阴性率的测量来构建人群中感染某种疾病的个体比例的置信区间的方法。我们首先记录应用于该问题时标准Wald和百分位自举间隔的覆盖概率中的不稳定行为。然后，我们考虑用测试反演构造的两个可选区间集。第一组区间是近似的，使用对所选检验统计量的有限样本分布的渐近或自举近似。我们考虑了几种检验统计量的选择，包括极大似然估计量和广义似然比统计量。我们通过模拟表明，在经验相关的参数值和样本量下，这些区间的覆盖概率接近其名义水平，并且近似为等尾。第二组区间包含真实参数值，其概率至少等于标称水平，但在有限样本中可以是保守的。©中国数理统计研究所，2022

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引用次数: 4

Network Modeling in Biology: Statistical Methods for Gene and Brain Networks. 生物学中的网络建模：基因和大脑网络的统计方法》。

IF 3.9 1区数学 Q1 STATISTICS & PROBABILITY

Statistical Science

Pub Date : 2021-02-01 DOI: 10.1214/20-sts792

Y X Rachel Wang, Lexin Li, Jingyi Jessica Li, Haiyan Huang

The rise of network data in many different domains has offered researchers new insight into the problem of modeling complex systems and propelled the development of numerous innovative statistical methodologies and computational tools. In this paper, we primarily focus on two types of biological networks, gene networks and brain networks, where statistical network modeling has found both fruitful and challenging applications. Unlike other network examples such as social networks where network edges can be directly observed, both gene and brain networks require careful estimation of edges using covariates as a first step. We provide a discussion on existing statistical and computational methods for edge esitimation and subsequent statistical inference problems in these two types of biological networks.

网络数据在许多不同领域的兴起，为研究人员提供了对复杂系统建模问题的新见解，并推动了众多创新统计方法和计算工具的发展。在本文中，我们主要关注两类生物网络--基因网络和大脑网络，在这两类网络中，统计网络建模的应用既富有成果，又充满挑战。与社交网络等可以直接观察到网络边缘的其他网络实例不同，基因网络和大脑网络都需要首先使用协变量对边缘进行仔细估计。我们将讨论这两类生物网络中边缘估计和后续统计推断问题的现有统计和计算方法。

引用次数: 0

Introduction to the Special Section 专题介绍

IF 5.7 1区数学 Q1 STATISTICS & PROBABILITY

Statistical Science

Pub Date : 2021-02-01 DOI: 10.1214/20-sts361ed

Yihong Wu, Harrison H. Zhou

引用次数: 0

Bipartite Causal Inference with Interference. 具有干扰的二部因果推理。

IF 5.7 1区数学 Q1 STATISTICS & PROBABILITY

Statistical Science

Pub Date : 2021-02-01 Epub Date: 2020-12-21 DOI: 10.1214/19-sts749

Corwin M Zigler, Georgia Papadogeorgou

Statistical methods to evaluate the effectiveness of interventions are increasingly challenged by the inherent interconnectedness of units. Specifically, a recent flurry of methods research has addressed the problem of interference between observations, which arises when one observational unit's outcome depends not only on its treatment but also the treatment assigned to other units. We introduce the setting of bipartite causal inference with interference, which arises when 1) treatments are defined on observational units that are distinct from those at which outcomes are measured and 2) there is interference between units in the sense that outcomes for some units depend on the treatments assigned to many other units. The focus of this work is to formulate definitions and several possible causal estimands for this setting, highlighting similarities and differences with more commonly considered settings of causal inference with interference. Towards an empirical illustration, an inverse probability of treatment weighted estimator is adapted from existing literature to estimate a subset of simplified, but interesting, estimands. The estimators are deployed to evaluate how interventions to reduce air pollution from 473 power plants in the U.S. causally affect cardiovascular hospitalization among Medicare beneficiaries residing at 18,807 zip code locations.

评估干预措施有效性的统计方法越来越受到单位内在相互联系的挑战。具体来说，最近一系列的方法研究已经解决了观察之间的干扰问题，当一个观察单位的结果不仅取决于它的治疗，还取决于分配给其他单位的治疗时，就会出现这种问题。我们引入了带有干扰的双部因果推理的设置，当1)治疗是在与测量结果不同的观察单位上定义的，2)在某些单位的结果依赖于分配给许多其他单位的治疗的意义上，单位之间存在干扰。这项工作的重点是为这种设置制定定义和几个可能的因果估计，突出与更常见的干扰因果推理设置的相似性和差异性。对于经验说明，从现有文献中改编了一个逆处理概率加权估计器，以估计简化但有趣的估计子集。这些估算器用于评估减少美国473家发电厂空气污染的干预措施如何对居住在18807个邮政编码地区的医疗保险受益人的心血管住院治疗产生因果影响。

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引用次数: 49

A Conversation with Tze Leung Lai 与Tze Leung Lai的对话

IF 5.7 1区数学 Q1 STATISTICS & PROBABILITY

Statistical Science

Pub Date : 2021-02-01 DOI: 10.1214/20-sts775

Ying Lu, Dylan S. Small, Z. Ying

This conversation began in June 2015 in the Department of Statistics at Columbia University during Lai’s visit to his alma mater where he celebrated his seventieth birthday. It continued in the subsequent years at Columbia and Stanford. Lai was born on June 28, 1945, in Hong Kong, where he grew up and attended The University of Hong Kong, receiving his B.A. degree (First Class Honors) in Mathematics in 1967. He went to Columbia University in 1968 for graduate study in statistics and received his Ph.D. degree in 1971. He stayed on the faculty at Columbia and was appointed Higgins Professor of Mathematical Statistics in 1986. A year later he moved to Stanford, where he is currently Ray Lyman Wilbur Professor of Statistics, and by courtesy, also of Biomedical Data Science and Computational and Mathematical Engineering. He is a fellow of the Institute of Mathematical Statistics, the American Statistical Association and an elected member of Academia Sinica in Taiwan. He was the third recipient of the COPSS Award which he won in 1983. He has been married to Letitia Chow since 1975, and they have two sons and two grandchildren.

这段对话始于2015年6月，在赖访问母校庆祝70岁生日期间，在哥伦比亚大学统计系开始。在随后的几年里，它在哥伦比亚大学和斯坦福大学继续着。赖1945年6月28日出生于香港，在那里长大，就读于香港大学，1967年获得数学学士学位（一级荣誉）。1968年，他前往哥伦比亚大学攻读统计学研究生，1971年获得博士学位。他留在哥伦比亚大学任教，1986年被任命为希金斯数理统计教授。一年后，他搬到了斯坦福大学，目前是雷·莱曼·威尔伯统计学教授，同时也是生物医学数据科学和计算与数学工程教授。他是美国统计协会数理统计研究所研究员，台湾中央研究院当选委员。他是1983年获得的COPSS奖的第三位获得者。自1975年起，他与周结婚，育有两子两孙。

引用次数: 0

Comparison of Two Frameworks for Analyzing Longitudinal Data 两种纵向数据分析框架的比较

IF 5.7 1区数学 Q1 STATISTICS & PROBABILITY

Statistical Science

Pub Date : 2021-01-01 DOI: 10.1214/20-sts813

Jie Zhou, Xiao Zhou, Liuquan Sun

Under the random design of longitudinal data, observation times are irregular, and there are mainly two frameworks for analyzing such kind of longitudinal data. One is the clustered data framework and the other is the counting process framework. In this paper, we give a thorough comparison of these two frameworks in terms of data structure, model assumptions and estimation procedures. We find that modeling the observation times in the counting process framework will not gain any efficiency when the observation times are correlated with covariates but independent of the longitudinal response given covariates. Some simulation studies are conducted to compare the finite sample behaviors of the related estimators, and a real data analysis of the Alzheimer’s disease study is implemented for further comparison.

在纵向数据随机设计下，观测时间是不规则的，分析这类纵向数据主要有两种框架。一种是聚类数据框架，另一种是计数过程框架。在本文中，我们在数据结构、模型假设和估计过程方面对这两种框架进行了全面的比较。我们发现，当观测次数与协变量相关而与给定协变量的纵向响应无关时，在计数过程框架中对观测次数建模将不会获得任何效率。进行了仿真研究，比较了相关估计器的有限样本行为，并对阿尔茨海默病研究的真实数据进行了分析，进一步进行了比较。

引用次数: 0

Confidence as Likelihood 信心即可能性

IF 5.7 1区数学 Q1 STATISTICS & PROBABILITY

Statistical Science

Pub Date : 2021-01-01 DOI: 10.1214/20-sts811

Y. Pawitan, Youngjo Lee

Confidence and likelihood are fundamental statistical concepts with distinct technical interpretation and usage. Confidence is a meaningful concept of uncertainty within the context of confidence-interval procedure, while likelihood has been used predominantly as a tool for statistical modelling and inference given observed data. Here we show that confidence is in fact an extended likelihood, thus giving a much closer correspondence between the two concepts. This result gives the confidence concept an external meaning outside the confidence-interval context, and vice versa, it gives the confidence interpretation to the likelihood. In addition to the obvious interpretation purposes, this connection suggests two-way transfers of technical information. For example, the extended likelihood theory gives a clear way to update or combine confidence information. On the other hand, the confidence connection gives the extended likelihood direct access to the frequentist probability, an objective certification not directly available to the classical likelihood. This implies that intervals derived from the extended likelihood have the same logical status as confidence intervals, thus simplifying the terminology in the inference of random parameters.

置信度和似然度是具有不同技术解释和用法的基本统计概念。在置信区间过程中，置信度是一个有意义的不确定性概念，而似然主要被用作统计建模和给定观测数据推断的工具。在这里，我们表明信心实际上是一种扩展的可能性，从而在两个概念之间给出了更紧密的对应关系。这一结果使置信概念在置信区间上下文之外具有外部意义，反之亦然，它为似然提供了置信解释。除了明显的解释目的之外，这种联系表明技术信息的双向转移。例如，扩展似然理论提供了一种更新或组合置信度信息的清晰方法。另一方面，置信度连接使扩展似然直接获得频率概率，这是经典似然无法直接获得的客观证明。这意味着由扩展似然导出的区间与置信区间具有相同的逻辑状态，从而简化了随机参数推理中的术语。

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引用次数: 9

Gambler’s Ruin and the ICM 赌徒的毁灭和ICM

IF 5.7 1区数学 Q1 STATISTICS & PROBABILITY

Statistical Science

Pub Date : 2020-11-15 DOI: 10.1214/21-sts826

P. Diaconis, S. Ethier

Consider gambler's ruin with three players, 1, 2, and 3, having initial capitals $A$, $B$, and $C$. At each round a pair of players is chosen (uniformly at random) and a fair coin flip is made resulting in the transfer of one unit between these two players. Eventually, one of the players is eliminated and the game continues with the remaining two. Let $sigmain S_3$ be the elimination order (e.g., $sigma=132$ means player 1 is eliminated first, player 3 is eliminated second, and player 2 is left with $A+B+C$). We seek approximations (and exact formulas) for the probabilities $P_{A,B,C}(sigma)$. One frequently used approximation, the independent chip model (ICM), is shown to be inadequate. A regression adjustment is proposed, which seems to give good approximations to the players' elimination order probabilities.

以赌徒的破产为例，有三个玩家，1、2和3，初始资本分别为$A$、$B$和$C$。在每一轮比赛中，都会选择一对选手（随机统一），并进行公平的硬币翻转，从而在这两名选手之间转移一个单位。最终，其中一名选手被淘汰，剩下的两名选手继续比赛。设S_3$中的$sigma为淘汰顺序（例如，$sigma=132$意味着玩家1首先被淘汰，玩家3第二被淘汰，并且玩家2剩下$A+B+C$）。我们寻求概率$P_{A，B，C}（西格玛）$的近似（和精确公式）。一个经常使用的近似，独立芯片模型（ICM），被证明是不够的。提出了一种回归调整，它似乎能很好地近似玩家的淘汰顺序概率。

引用次数: 6

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