Ross L. Prentice received his B.Sc. from the University of Waterloo and his Ph.D. from the University of Toronto. He joined the University of Washington (UW) and the Fred Hutchinson Cancer Research Center (the Hutch) in 1974, and is currently Professor of Biostatistics at these institutions. He was Senior Vice President at the Hutch, and Director of its Public Health Sciences Division, for more than 25 years. Dr. Prentice’s expertise and research interests are in the fields of biostatistics, epidemiology, and disease prevention. He played a central role in the conception, design, and implementation of the Women’s Health Initiative. In statistical and medical literature he has over 500 scientific papers, including more than 40 with 500 or more citations. His substantial contributions to the theory of population and clinical research include the use of surrogate endpoints and case-cohort designs and other areas such as survival analysis, nutritional epidemiology, genetic epidemiology, biomarkers, and measurement error. Dr. Prentice is recognized for his mentoring of students and junior colleagues, and for his generous collaborations. Dr. Prentice has received numerous awards for his work, including an honorary doctorate in mathematics from the University of Waterloo, the Mantel Award for Lifetime Contributions to Statistics in Epidemiology from the American Statistical Association, the Mortimer Spiegelman Award from the American Public Health Association, the Committee of Presidents of Statistical Societies Presidents’ Award and RA Fisher Award, the Marvin Zelen Leadership Award for Outstanding Achievement in Statistical Science from Harvard University, the American Association of Cancer Research/American Cancer Society Award for Research Excellence in Cancer Epidemiology and Prevention, and the American Association for Cancer Research Team Science Award. He was elected to the Institute of Medicine/National Academy of Medicine in 1990. The Ross L. Prentice Endowed Professorship of Biostatistical Collaboration was created at the UW in 2005 and has been awarded every year since its inception. The interior space of the Public Health Sciences building at the Hutch has been named the Ross L. Prentice Atrium. In his spare time, Ross enjoys sports including water skiing, golf, running, and spending time with his wife, Didi, and with his daughters, sons-in-law, and grandchildren. He ran daily from when he was in his 20s until his knees objected about 10 years ago. This interview took place with Li Hsu and Charles Kooperberg via Zoom in December 2020.
Ross L.Prentice在滑铁卢大学获得理学学士学位，在多伦多大学获得博士学位。他于1974年加入华盛顿大学（UW）和弗雷德·哈钦森癌症研究中心（Hutch），目前是这些机构的生物统计学教授。他担任哈奇医院高级副院长兼公共卫生科学部主任超过25年。Prentice博士的专业知识和研究兴趣是生物统计学、流行病学和疾病预防领域。他在妇女健康倡议的构思、设计和实施中发挥了核心作用。在统计学和医学文献中，他有500多篇科学论文，其中40多篇引用次数达到或超过500次。他对人口和临床研究理论的重大贡献包括使用替代终点和病例队列设计，以及其他领域，如生存分析、营养流行病学、遗传流行病学、生物标志物和测量误差。普伦蒂斯博士因其对学生和初级同事的指导以及慷慨的合作而受到认可。普伦蒂斯博士的工作获得了许多奖项，包括滑铁卢大学的数学荣誉博士学位、美国统计协会的曼特尔流行病学统计终身贡献奖、美国公共卫生协会的莫蒂默·斯皮格尔曼奖、，统计学会主席委员会主席奖和RA Fisher奖、哈佛大学统计科学杰出成就马文·泽伦领导奖、美国癌症研究协会/美国癌症学会癌症流行病学和预防卓越研究奖、，以及美国癌症研究团队科学奖。1990年，他被选入美国国家医学院医学研究所。罗斯·L·普伦蒂斯授予的生物统计学协作教授职位于2005年在华盛顿大学设立，自成立以来每年都会颁发。哈奇公共卫生科学大楼的内部空间被命名为罗斯·L·普伦蒂斯中庭。在业余时间，罗斯喜欢运动，包括滑水、高尔夫、跑步，并与妻子迪迪、女儿、女婿和孙子孙女共度时光。从20多岁开始，他每天都在跑步，直到大约10年前膝盖出现问题。本次采访于2020年12月通过Zoom对李旭和查尔斯·库珀伯格进行。
{"title":"A Conversation with Ross Prentice","authors":"L. Hsu, C. Kooperberg","doi":"10.1214/21-sts829","DOIUrl":"https://doi.org/10.1214/21-sts829","url":null,"abstract":"Ross L. Prentice received his B.Sc. from the University of Waterloo and his Ph.D. from the University of Toronto. He joined the University of Washington (UW) and the Fred Hutchinson Cancer Research Center (the Hutch) in 1974, and is currently Professor of Biostatistics at these institutions. He was Senior Vice President at the Hutch, and Director of its Public Health Sciences Division, for more than 25 years. Dr. Prentice’s expertise and research interests are in the fields of biostatistics, epidemiology, and disease prevention. He played a central role in the conception, design, and implementation of the Women’s Health Initiative. In statistical and medical literature he has over 500 scientific papers, including more than 40 with 500 or more citations. His substantial contributions to the theory of population and clinical research include the use of surrogate endpoints and case-cohort designs and other areas such as survival analysis, nutritional epidemiology, genetic epidemiology, biomarkers, and measurement error. Dr. Prentice is recognized for his mentoring of students and junior colleagues, and for his generous collaborations. Dr. Prentice has received numerous awards for his work, including an honorary doctorate in mathematics from the University of Waterloo, the Mantel Award for Lifetime Contributions to Statistics in Epidemiology from the American Statistical Association, the Mortimer Spiegelman Award from the American Public Health Association, the Committee of Presidents of Statistical Societies Presidents’ Award and RA Fisher Award, the Marvin Zelen Leadership Award for Outstanding Achievement in Statistical Science from Harvard University, the American Association of Cancer Research/American Cancer Society Award for Research Excellence in Cancer Epidemiology and Prevention, and the American Association for Cancer Research Team Science Award. He was elected to the Institute of Medicine/National Academy of Medicine in 1990. The Ross L. Prentice Endowed Professorship of Biostatistical Collaboration was created at the UW in 2005 and has been awarded every year since its inception. The interior space of the Public Health Sciences building at the Hutch has been named the Ross L. Prentice Atrium. In his spare time, Ross enjoys sports including water skiing, golf, running, and spending time with his wife, Didi, and with his daughters, sons-in-law, and grandchildren. He ran daily from when he was in his 20s until his knees objected about 10 years ago. This interview took place with Li Hsu and Charles Kooperberg via Zoom in December 2020.","PeriodicalId":51172,"journal":{"name":"Statistical Science","volume":"1 1","pages":""},"PeriodicalIF":5.7,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41588952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Baddeley, Tilman M. Davies, S. Rakshit, Gopalan M. Nair, Greg McSwiggan
Traditional kernel methods for estimating the spatially-varying density of points in a spatial point pattern may exhibit unrealistic artefacts, in addition to the familiar problems of bias and overor undersmoothing. Performance can be improved by using diffusion smoothing, in which the smoothing kernel is the heat kernel on the spatial domain. This paper develops diffusion smoothing into a practical statistical methodology for two-dimensional spatial point pattern data. We clarify the advantages and disadvantages of diffusion smoothing over Gaussian kernel smoothing. Adaptive smoothing, where the smoothing bandwidth is spatially-varying, can be performed by adopting a spatiallyvarying diffusion rate: this avoids technical problems with adaptive Gaussian smoothing and has substantially better performance. We introduce a new form of adaptive smoothing using lagged arrival times, which has good performance and improved robustness. Applications in archaeology and epidemiology are demonstrated. The methods are implemented in open-source R code. AMS 2000 subject classifications: Primary 62G07; secondary 62M30.
{"title":"Diffusion Smoothing for Spatial Point Patterns","authors":"A. Baddeley, Tilman M. Davies, S. Rakshit, Gopalan M. Nair, Greg McSwiggan","doi":"10.1214/21-sts825","DOIUrl":"https://doi.org/10.1214/21-sts825","url":null,"abstract":"Traditional kernel methods for estimating the spatially-varying density of points in a spatial point pattern may exhibit unrealistic artefacts, in addition to the familiar problems of bias and overor undersmoothing. Performance can be improved by using diffusion smoothing, in which the smoothing kernel is the heat kernel on the spatial domain. This paper develops diffusion smoothing into a practical statistical methodology for two-dimensional spatial point pattern data. We clarify the advantages and disadvantages of diffusion smoothing over Gaussian kernel smoothing. Adaptive smoothing, where the smoothing bandwidth is spatially-varying, can be performed by adopting a spatiallyvarying diffusion rate: this avoids technical problems with adaptive Gaussian smoothing and has substantially better performance. We introduce a new form of adaptive smoothing using lagged arrival times, which has good performance and improved robustness. Applications in archaeology and epidemiology are demonstrated. The methods are implemented in open-source R code. AMS 2000 subject classifications: Primary 62G07; secondary 62M30.","PeriodicalId":51172,"journal":{"name":"Statistical Science","volume":" ","pages":""},"PeriodicalIF":5.7,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47305929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pearson’s ρ is the most used measure of statistical dependence. It gives a complete characterization of dependence in the Gaussian case, and it also works well in some non-Gaussian situations. It is well known, however, that it has a number of shortcomings; in particular for heavy tailed distributions and in nonlinear situations, where it may produce misleading, and even disastrous results. In recent years a number of alternatives have been proposed. In this paper, we will survey these developments, especially results obtained in the last couple of decades. Among measures discussed are the copula, distribution-based measures, the distance covariance, the HSIC measure popular in machine learning, and finally the local Gaussian correlation, which is a local version of Pearson’s ρ. Throughout we put the emphasis on conceptual developments and a comparison of these. We point out relevant references to technical details as well as comparative empirical and simulated experiments. There is a broad selection of references under each topic treated.
{"title":"Statistical Dependence: Beyond Pearson’s ρ","authors":"D. Tjøstheim, Håkon Otneim, Bård Støve","doi":"10.1214/21-sts823","DOIUrl":"https://doi.org/10.1214/21-sts823","url":null,"abstract":"Pearson’s ρ is the most used measure of statistical dependence. It gives a complete characterization of dependence in the Gaussian case, and it also works well in some non-Gaussian situations. It is well known, however, that it has a number of shortcomings; in particular for heavy tailed distributions and in nonlinear situations, where it may produce misleading, and even disastrous results. In recent years a number of alternatives have been proposed. In this paper, we will survey these developments, especially results obtained in the last couple of decades. Among measures discussed are the copula, distribution-based measures, the distance covariance, the HSIC measure popular in machine learning, and finally the local Gaussian correlation, which is a local version of Pearson’s ρ. Throughout we put the emphasis on conceptual developments and a comparison of these. We point out relevant references to technical details as well as comparative empirical and simulated experiments. There is a broad selection of references under each topic treated.","PeriodicalId":51172,"journal":{"name":"Statistical Science","volume":" ","pages":""},"PeriodicalIF":5.7,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49302811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
With very large amounts of data, important aspects of statistical analysis may appear largely descriptive in that the role of probability sometimes seems limited or totally absent. The main emphasis of the present paper lies on contexts where formulation in terms of a probabilistic model is feasible and fruitful but to be at all realistic large numbers of unknown parameters need consideration. Then many of the standard approaches to statistical analysis, for instance direct application of the method of maximum likelihood, or the use of flat priors, often encounter difficulties. After a brief discussion of broad conceptual issues, we provide some new perspectives on aspects of high-dimensional statistical theory, emphasizing a number of open problems.
{"title":"Some Perspectives on Inference in High Dimensions","authors":"H. Battey, D. Cox","doi":"10.1214/21-sts824","DOIUrl":"https://doi.org/10.1214/21-sts824","url":null,"abstract":"With very large amounts of data, important aspects of statistical analysis may appear largely descriptive in that the role of probability sometimes seems limited or totally absent. The main emphasis of the present paper lies on contexts where formulation in terms of a probabilistic model is feasible and fruitful but to be at all realistic large numbers of unknown parameters need consideration. Then many of the standard approaches to statistical analysis, for instance direct application of the method of maximum likelihood, or the use of flat priors, often encounter difficulties. After a brief discussion of broad conceptual issues, we provide some new perspectives on aspects of high-dimensional statistical theory, emphasizing a number of open problems.","PeriodicalId":51172,"journal":{"name":"Statistical Science","volume":" ","pages":""},"PeriodicalIF":5.7,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46293804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Greenacre, E. Grunsky, J. Bacon-Shone, Ionas Erb, T. Quinn
The development of John Aitchison's approach to compositional data analysis is followed since his paper read to the Royal Statistical Society in 1982. Aitchison's logratio approach, which was proposed to solve the problematic aspects of working with data with a fixed sum constraint, is summarized and reappraised. It is maintained that the properties on which this approach was originally built, the main one being subcompositional coherence, are not required to be satisfied exactly -- quasi-coherence is sufficient, that is near enough to being coherent for all practical purposes. This opens up the field to using simpler data transformations, such as power transformations, that permit zero values in the data. The additional property of exact isometry, which was subsequently introduced and not in Aitchison's original conception, imposed the use of isometric logratio transformations, but these are complicated and problematic to interpret, involving ratios of geometric means. If this property is regarded as important in certain analytical contexts, for example unsupervised learning, it can be relaxed by showing that regular pairwise logratios, as well as the alternative quasi-coherent transformations, can also be quasi-isometric, meaning they are close enough to exact isometry for all practical purposes. It is concluded that the isometric and related logratio transformations such as pivot logratios are not a prerequisite for good practice, although many authors insist on their obligatory use. This conclusion is fully supported here by case studies in geochemistry and in genomics, where the good performance is demonstrated of pairwise logratios, as originally proposed by Aitchison, or Box-Cox power transforms of the original compositions where no zero replacements are necessary.
{"title":"Aitchison’s Compositional Data Analysis 40 Years on: A Reappraisal","authors":"M. Greenacre, E. Grunsky, J. Bacon-Shone, Ionas Erb, T. Quinn","doi":"10.1214/22-sts880","DOIUrl":"https://doi.org/10.1214/22-sts880","url":null,"abstract":"The development of John Aitchison's approach to compositional data analysis is followed since his paper read to the Royal Statistical Society in 1982. Aitchison's logratio approach, which was proposed to solve the problematic aspects of working with data with a fixed sum constraint, is summarized and reappraised. It is maintained that the properties on which this approach was originally built, the main one being subcompositional coherence, are not required to be satisfied exactly -- quasi-coherence is sufficient, that is near enough to being coherent for all practical purposes. This opens up the field to using simpler data transformations, such as power transformations, that permit zero values in the data. The additional property of exact isometry, which was subsequently introduced and not in Aitchison's original conception, imposed the use of isometric logratio transformations, but these are complicated and problematic to interpret, involving ratios of geometric means. If this property is regarded as important in certain analytical contexts, for example unsupervised learning, it can be relaxed by showing that regular pairwise logratios, as well as the alternative quasi-coherent transformations, can also be quasi-isometric, meaning they are close enough to exact isometry for all practical purposes. It is concluded that the isometric and related logratio transformations such as pivot logratios are not a prerequisite for good practice, although many authors insist on their obligatory use. This conclusion is fully supported here by case studies in geochemistry and in genomics, where the good performance is demonstrated of pairwise logratios, as originally proposed by Aitchison, or Box-Cox power transforms of the original compositions where no zero replacements are necessary.","PeriodicalId":51172,"journal":{"name":"Statistical Science","volume":" ","pages":""},"PeriodicalIF":5.7,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47827621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. The two of us have shared a fascination with James Victor Uspensky’s 1937 textbook Introduction to Mathematical Probability ever since our graduate student days: it contains many interesting results not found in other books on the same subject in the English language, together with many non-trivial examples, all clearly stated with careful proofs. We present some of Uspensky’s gems to a modern audience hoping to tempt others to read Uspensky for themselves, as well as report on a few of the other mathematical topics he also wrote about (for example, his book on number theory contains early results about perfect shuffles). Uspensky led an interesting life: a member of the Russian Academy of Sciences, he spoke at the 1924 International Congress of Mathematicians in Toronto before leaving Russia in 1929 and coming to the US and Stanford. Comparatively little has been written about him in English; the second half of this paper attempts to remedy this.
{"title":"In Praise (and Search) of J. V. Uspensky","authors":"P. Diaconis, S. Zabell","doi":"10.1214/22-sts866","DOIUrl":"https://doi.org/10.1214/22-sts866","url":null,"abstract":". The two of us have shared a fascination with James Victor Uspensky’s 1937 textbook Introduction to Mathematical Probability ever since our graduate student days: it contains many interesting results not found in other books on the same subject in the English language, together with many non-trivial examples, all clearly stated with careful proofs. We present some of Uspensky’s gems to a modern audience hoping to tempt others to read Uspensky for themselves, as well as report on a few of the other mathematical topics he also wrote about (for example, his book on number theory contains early results about perfect shuffles). Uspensky led an interesting life: a member of the Russian Academy of Sciences, he spoke at the 1924 International Congress of Mathematicians in Toronto before leaving Russia in 1929 and coming to the US and Stanford. Comparatively little has been written about him in English; the second half of this paper attempts to remedy this.","PeriodicalId":51172,"journal":{"name":"Statistical Science","volume":" ","pages":""},"PeriodicalIF":5.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45991960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bayesian adaptive designs formalize the use of previous knowledge at the planning stage of an experiment, permitting recursive updating of the prior information. They often make use of utility functions, while also allowing for randomization. We review frequentist and Bayesian adaptive design methods and show that some of the frequentist adaptive design methodology can also be employed in a Bayesian context. We use compound utility functions for the Bayesian designs, that are a trade-off between an optimal design information criterion, that represents the acquisition of scientific knowledge, and some ethical or utilitarian gain. We focus on binary response models on two groups with independent Beta prior distributions on the success probabilities. The treatment allocation is shown to converge to the allocation that produces the maximum utility. Special cases are the Bayesian Randomized (simply) Adaptive Compound (BRAC) design, an extension of the frequentist Sequential Maximum Likelihood (SML) design and the Bayesian Randomized (doubly) Adaptive Compound Efficient (BRACE) design, a generalization of the Efficient Randomized Adaptive DEsign (ERADE). Numerical simulation studies compare BRAC with BRACE when D-optimality is the information criterion chosen. In analogy with the frequentist theory, the BRACE-D design appears more efficient than the BRAC-D design.
{"title":"Bayesian Adaptive Randomization with Compound Utility Functions","authors":"A. Giovagnoli, I. Verdinelli","doi":"10.1214/21-sts848","DOIUrl":"https://doi.org/10.1214/21-sts848","url":null,"abstract":"Bayesian adaptive designs formalize the use of previous knowledge at the planning stage of an experiment, permitting recursive updating of the prior information. They often make use of utility functions, while also allowing for randomization. We review frequentist and Bayesian adaptive design methods and show that some of the frequentist adaptive design methodology can also be employed in a Bayesian context. We use compound utility functions for the Bayesian designs, that are a trade-off between an optimal design information criterion, that represents the acquisition of scientific knowledge, and some ethical or utilitarian gain. We focus on binary response models on two groups with independent Beta prior distributions on the success probabilities. The treatment allocation is shown to converge to the allocation that produces the maximum utility. Special cases are the Bayesian Randomized (simply) Adaptive Compound (BRAC) design, an extension of the frequentist Sequential Maximum Likelihood (SML) design and the Bayesian Randomized (doubly) Adaptive Compound Efficient (BRACE) design, a generalization of the Efficient Randomized Adaptive DEsign (ERADE). Numerical simulation studies compare BRAC with BRACE when D-optimality is the information criterion chosen. In analogy with the frequentist theory, the BRACE-D design appears more efficient than the BRAC-D design.","PeriodicalId":51172,"journal":{"name":"Statistical Science","volume":" ","pages":""},"PeriodicalIF":5.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46839550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We showcase some unexplored connections between saddlepoint approximations, measure transportation, and some key topics in information theory. To bridge these different areas, we review selectively the fundamental results available in the literature and we draw the connections between them. First, for a generic random variable we explain how the Esscher’s tilting (which is a result rooted in information theory and lies at the heart of saddlepoint approximations) is connected to the solution of the dual Kantorovich problem (which lies at the heart of measure transportation theory) via the Legendre transform of the cumulant generating function. Then, we turn to statistics: we illustrate the connections when the random variable we work with is the sample mean or a statistic with known (either exact or approximate) cumulant generating function. The unveiled connections offer the possibility to look at the saddlepoint approximations from different angles, putting under the spotlight the links to convex analysis (via the notion of duality) or differential geometry (via the notion of geodesic). We feel these possibilities can trigger a knowledge transfer between statistics and other disciplines, like mathematics and machine learning. A discussion on some topics for future research concludes the paper.
{"title":"On Some Connections Between Esscher’s Tilting, Saddlepoint Approximations, and Optimal Transportation: A Statistical Perspective","authors":"D. La Vecchia, E. Ronchetti, A. Ilievski","doi":"10.1214/21-sts847","DOIUrl":"https://doi.org/10.1214/21-sts847","url":null,"abstract":"We showcase some unexplored connections between saddlepoint approximations, measure transportation, and some key topics in information theory. To bridge these different areas, we review selectively the fundamental results available in the literature and we draw the connections between them. First, for a generic random variable we explain how the Esscher’s tilting (which is a result rooted in information theory and lies at the heart of saddlepoint approximations) is connected to the solution of the dual Kantorovich problem (which lies at the heart of measure transportation theory) via the Legendre transform of the cumulant generating function. Then, we turn to statistics: we illustrate the connections when the random variable we work with is the sample mean or a statistic with known (either exact or approximate) cumulant generating function. The unveiled connections offer the possibility to look at the saddlepoint approximations from different angles, putting under the spotlight the links to convex analysis (via the notion of duality) or differential geometry (via the notion of geodesic). We feel these possibilities can trigger a knowledge transfer between statistics and other disciplines, like mathematics and machine learning. A discussion on some topics for future research concludes the paper.","PeriodicalId":51172,"journal":{"name":"Statistical Science","volume":" ","pages":""},"PeriodicalIF":5.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43550808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The 21st century has seen an enormous growth in the development and use of approximate Bayesian methods. Such methods produce computational solutions to certain intractable statistical problems that challenge exact methods like Markov chain Monte Carlo: for instance, models with unavailable likelihoods, high-dimensional models, and models featuring large data sets. These approximate methods are the subject of this review. The aim is to help new researchers in particular -- and more generally those interested in adopting a Bayesian approach to empirical work -- distinguish between different approximate techniques; understand the sense in which they are approximate; appreciate when and why particular methods are useful; and see the ways in which they can can be combined.
{"title":"Approximating Bayes in the 21st Century","authors":"G. Martin, David T. Frazier, C. Robert","doi":"10.1214/22-STS875","DOIUrl":"https://doi.org/10.1214/22-STS875","url":null,"abstract":"The 21st century has seen an enormous growth in the development and use of approximate Bayesian methods. Such methods produce computational solutions to certain intractable statistical problems that challenge exact methods like Markov chain Monte Carlo: for instance, models with unavailable likelihoods, high-dimensional models, and models featuring large data sets. These approximate methods are the subject of this review. The aim is to help new researchers in particular -- and more generally those interested in adopting a Bayesian approach to empirical work -- distinguish between different approximate techniques; understand the sense in which they are approximate; appreciate when and why particular methods are useful; and see the ways in which they can can be combined.","PeriodicalId":51172,"journal":{"name":"Statistical Science","volume":" ","pages":""},"PeriodicalIF":5.7,"publicationDate":"2021-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44404322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose, implement, and evaluate a method to estimate the daily number of new symptomatic COVID-19 infections, at the level of individual U.S. counties, by deconvolving daily reported COVID-19 case counts using an estimated symptom-onset-to-case-report delay distribution. Importantly, we focus on estimating infections in real-time (rather than retrospectively), which poses numerous challenges. To address these, we develop new methodology for both the distribution estimation and deconvolution steps, and we employ a sensor fusion layer (which fuses together predictions from models that are trained to track infections based on auxiliary surveillance streams) in order to improve accuracy and stability.
{"title":"Real-Time Estimation of COVID-19 Infections: Deconvolution and Sensor Fusion","authors":"M. Jahja, Andrew Chin, R. Tibshirani","doi":"10.1214/22-sts856","DOIUrl":"https://doi.org/10.1214/22-sts856","url":null,"abstract":"We propose, implement, and evaluate a method to estimate the daily number of new symptomatic COVID-19 infections, at the level of individual U.S. counties, by deconvolving daily reported COVID-19 case counts using an estimated symptom-onset-to-case-report delay distribution. Importantly, we focus on estimating infections in real-time (rather than retrospectively), which poses numerous challenges. To address these, we develop new methodology for both the distribution estimation and deconvolution steps, and we employ a sensor fusion layer (which fuses together predictions from models that are trained to track infections based on auxiliary surveillance streams) in order to improve accuracy and stability.","PeriodicalId":51172,"journal":{"name":"Statistical Science","volume":" ","pages":""},"PeriodicalIF":5.7,"publicationDate":"2021-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43138722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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