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A Brief History of Long Memory: Hurst, Mandelbrot and the Road to ARFIMA 《长记忆简史:赫斯特、曼德布洛和ARFIMA之路》
arXiv: Other Statistics Pub Date : 2017-05-26 DOI: 10.20944/PREPRINTS201705.0194.V1
T. Graves, R. Gramacy, N. Watkins, C. Franzke
{"title":"A Brief History of Long Memory: Hurst, Mandelbrot and the Road to ARFIMA","authors":"T. Graves, R. Gramacy, N. Watkins, C. Franzke","doi":"10.20944/PREPRINTS201705.0194.V1","DOIUrl":"https://doi.org/10.20944/PREPRINTS201705.0194.V1","url":null,"abstract":"Long memory plays an important role in many fields by determining the behaviour and predictability of systems; for instance, climate, hydrology, finance, networks and DNA sequencing. In particular, it is important to test if a process is exhibiting long memory since that impacts the accuracy and confidence with which one may predict future events on the basis of a small amount of historical data. A major force in the development and study of long memory was the late Benoit B. Mandelbrot. Here we discuss the original motivation of the development of long memory and Mandelbrot's influence on this fascinating field. We will also elucidate the sometimes contrasting approaches to long memory in different scientific communities","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121578148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 74
Curriculum Guidelines for Undergraduate Programs in Data Science 数据科学本科课程指南
arXiv: Other Statistics Pub Date : 2017-03-10 DOI: 10.1146/annurev-statistics-060116-053930
R. D. Veaux, Mahesh Agarwal, Maia Averett, Benjamin S. Baumer, Andrew Bray, T. Bressoud, Lance Bryant, Lei Cheng, Amanda Francis, R. Gould, Albert Y. Kim, Matt Kretchmar, Qin Lu, Ann Moskol, D. Nolan, Roberto Pelayo, Sean Raleigh, Ricky J. Sethi, Mutiara Sondjaja, Neelesh Tiruviluamala, P. Uhlig, Talitha M. Washington, Curtis L. Wesley, David L. White, Ping Ye
{"title":"Curriculum Guidelines for Undergraduate Programs in Data Science","authors":"R. D. Veaux, Mahesh Agarwal, Maia Averett, Benjamin S. Baumer, Andrew Bray, T. Bressoud, Lance Bryant, Lei Cheng, Amanda Francis, R. Gould, Albert Y. Kim, Matt Kretchmar, Qin Lu, Ann Moskol, D. Nolan, Roberto Pelayo, Sean Raleigh, Ricky J. Sethi, Mutiara Sondjaja, Neelesh Tiruviluamala, P. Uhlig, Talitha M. Washington, Curtis L. Wesley, David L. White, Ping Ye","doi":"10.1146/annurev-statistics-060116-053930","DOIUrl":"https://doi.org/10.1146/annurev-statistics-060116-053930","url":null,"abstract":"The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in Data Science. The group consisted of 25 undergraduate faculty from a variety of institutions in the U.S., primarily from the disciplines of mathematics, statistics and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in Data Science.","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132066225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 165
On $p$-values 在$ p $值
arXiv: Other Statistics Pub Date : 2016-11-18 DOI: 10.5705/SS.202016.0507
Laurie Davies
{"title":"On $p$-values","authors":"Laurie Davies","doi":"10.5705/SS.202016.0507","DOIUrl":"https://doi.org/10.5705/SS.202016.0507","url":null,"abstract":"Models are consistently treated as approximations and all procedures are consistent with this. They do not treat the model as being true. In this context $p$-values are one measure of approximation, a small $p$-value indicating a poor approximation. Approximation regions are defined and distinguished from confidence regions.","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132415306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Dynamic Data in the Statistics Classroom 统计课堂中的动态数据
arXiv: Other Statistics Pub Date : 2016-03-15 DOI: 10.5070/T5111031079
Johanna S. Hardin
{"title":"Dynamic Data in the Statistics Classroom","authors":"Johanna S. Hardin","doi":"10.5070/T5111031079","DOIUrl":"https://doi.org/10.5070/T5111031079","url":null,"abstract":"The call for using real data in the classroom has long meant using datasets which are culled, cleaned, and wrangled prior to any student working with the observations. However, an important part of teaching statistics should include actually retrieving data from the Internet. Nowadays, there are many different sources of data that are continually updated by the organization hosting the data website. The R tools to download such dynamic data have improved in such a way to make accessing the data possible even in an introductory statistics class. We provide five full analyses on dynamic data as well as an additional nine sources of dynamic data that can be brought into the classroom. The goal of our work is to demonstrate that using dynamic data can have a short learning curve, even for introductory students or faculty unfamiliar with the landscape. The examples provided are unlikely to create expert data scrapers, but they should help motivate students and faculty toward more engaged use of online data sources.","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131884960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Mandelbrot's 1/f fractional renewal models of 1963-67: The non-ergodic missing link between change points and long range dependence 曼德尔布罗特1963- 1967年的1/f分数更新模型:变化点与长期依赖之间的非遍历缺失环节
arXiv: Other Statistics Pub Date : 2016-02-29 DOI: 10.1007/978-3-319-55789-2_14
N. Watkins
{"title":"Mandelbrot's 1/f fractional renewal models of 1963-67: The non-ergodic missing link between change points and long range dependence","authors":"N. Watkins","doi":"10.1007/978-3-319-55789-2_14","DOIUrl":"https://doi.org/10.1007/978-3-319-55789-2_14","url":null,"abstract":"","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130368965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
What Teachers Should Know About the Bootstrap: Resampling in the Undergraduate Statistics Curriculum 关于本科统计学课程中的Bootstrap:重采样,教师应该知道什么
arXiv: Other Statistics Pub Date : 2016-02-11 DOI: 10.6084/M9.FIGSHARE.1569497.V3
C. Tim
{"title":"What Teachers Should Know About the Bootstrap: Resampling in the Undergraduate Statistics Curriculum","authors":"C. Tim","doi":"10.6084/M9.FIGSHARE.1569497.V3","DOIUrl":"https://doi.org/10.6084/M9.FIGSHARE.1569497.V3","url":null,"abstract":"I have three goals in this article: (1) To show the enormous potential of bootstrapping and permutation tests to help students understand statistical concepts including sampling distributions, standard errors, bias, confidence intervals, null distributions, and P-values. (2) To dig deeper, understand why these methods work and when they don't, things to watch out for, and how to deal with these issues when teaching. (3) To change statistical practice---by comparing these methods to common t tests and intervals, we see how inaccurate the latter are; we confirm this with asymptotics. n >= 30 isn't enough---think n >= 5000. Resampling provides diagnostics, and more accurate alternatives. Sadly, the common bootstrap percentile interval badly under-covers in small samples; there are better alternatives. The tone is informal, with a few stories and jokes.","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116019344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
J. B. S. Haldane's Contribution to the Bayes Factor Hypothesis Test J. B. S. Haldane对贝叶斯因子假设检验的贡献
arXiv: Other Statistics Pub Date : 2015-11-25 DOI: 10.1214/16-STS599
Alexander Etz, E. Wagenmakers
{"title":"J. B. S. Haldane's Contribution to the Bayes Factor Hypothesis Test","authors":"Alexander Etz, E. Wagenmakers","doi":"10.1214/16-STS599","DOIUrl":"https://doi.org/10.1214/16-STS599","url":null,"abstract":"This article brings attention to some historical developments that gave rise to the Bayes factor for testing a point null hypothesis against a composite alternative. In line with current thinking, we find that the conceptual innovation - to assign prior mass to a general law - is due to a series of three articles by Dorothy Wrinch and Sir Harold Jeffreys (1919, 1921, 1923). However, our historical investigation also suggests that in 1932 J. B. S. Haldane made an important contribution to the development of the Bayes factor by proposing the use of a mixture prior comprising a point mass and a continuous probability density. Jeffreys was aware of Haldane's work and it may have inspired him to pursue a more concrete statistical implementation for his conceptual ideas. It thus appears that Haldane may have played a much bigger role in the statistical development of the Bayes factor than has hitherto been assumed.","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133979068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 82
An Outline of the Bayesian Decision Theory 贝叶斯决策理论概述
arXiv: Other Statistics Pub Date : 2015-09-28 DOI: 10.1063/1.4959057
H. V. Erp, R. O. Linger, P. V. Gelder
{"title":"An Outline of the Bayesian Decision Theory","authors":"H. V. Erp, R. O. Linger, P. V. Gelder","doi":"10.1063/1.4959057","DOIUrl":"https://doi.org/10.1063/1.4959057","url":null,"abstract":"The Bayesian decision theory is neo-Bernoullian in that it proves, by way of a consistency derivation, that Bernoulli’s utility function is the only appropriate function by which to translate, for a given initial wealth, gains and losses to their corresponding utilities. But the Bayesian decision theory deviates from Bernoulli’s original expected utility theory in that it offers up an alternative for the traditional criterion of choice of expectation value maximization, as it proposes to choose that decision which has associated with it the utility probability distribution which maximizes the mean of the expectation value and the lower and upper confidence bounds.","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128684859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A Conversation with Alan Gelfand 《与艾伦·盖尔芬的对话
arXiv: Other Statistics Pub Date : 2015-09-10 DOI: 10.1214/15-STS521
B. Carlin, A. Herring
{"title":"A Conversation with Alan Gelfand","authors":"B. Carlin, A. Herring","doi":"10.1214/15-STS521","DOIUrl":"https://doi.org/10.1214/15-STS521","url":null,"abstract":"Alan E. Gelfand was born April 17, 1945, in the Bronx, New York. He attended public grade schools and did his undergraduate work at what was then called City College of New York (CCNY, now CUNY), excelling at mathematics. He then surprised and saddened his mother by going all the way across the country to Stanford to graduate school, where he completed his dissertation in 1969 under the direction of Professor Herbert Solomon, making him an academic grandson of Herman Rubin and Harold Hotelling. Alan then accepted a faculty position at the University of Connecticut (UConn) where he was promoted to tenured associate professor in 1975 and to full professor in 1980. A few years later he became interested in decision theory, then empirical Bayes, which eventually led to the publication of Gelfand and Smith [J. Amer. Statist. Assoc. 85 (1990) 398-409], the paper that introduced the Gibbs sampler to most statisticians and revolutionized Bayesian computing. In the mid-1990s, Alan's interests turned strongly to spatial statistics, leading to fundamental contributions in spatially-varying coefficient models, coregionalization, and spatial boundary analysis (wombling). He spent 33 years on the faculty at UConn, retiring in 2002 to become the James B. Duke Professor of Statistics and Decision Sciences at Duke University, serving as chair from 2007-2012. At Duke, he has continued his work in spatial methodology while increasing his impact in the environmental sciences. To date, he has published over 260 papers and 6 books; he has also supervised 36 Ph.D. dissertations and 10 postdocs. This interview was done just prior to a conference of his family, academic descendants, and colleagues to celebrate his 70th birthday and his contributions to statistics which took place on April 19-22, 2015 at Duke University.","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125415646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Le Her and Other Problems in Probability Discussed by Bernoulli, Montmort and Waldegrave 伯努利、蒙蒙特和瓦德格拉夫讨论的概率中的勒赫和其他问题
arXiv: Other Statistics Pub Date : 2015-02-01 DOI: 10.1214/14-STS469
D. Bellhouse, Nicolas Fillion
{"title":"Le Her and Other Problems in Probability Discussed by Bernoulli, Montmort and Waldegrave","authors":"D. Bellhouse, Nicolas Fillion","doi":"10.1214/14-STS469","DOIUrl":"https://doi.org/10.1214/14-STS469","url":null,"abstract":"Part V of the second edition of Pierre R'{e}mond de Montmort's Essay d'analyse sur les jeux de hazard published in 1713 contains correspondence on probability problems between Montmort and Nicolaus Bernoulli. This correspondence begins in 1710. The last published letter, dated November 15, 1713, is from Montmort to Nicolaus Bernoulli. There is some discussion of the strategy of play in the card game Le Her and a bit of news that Montmort's friend Waldegrave in Paris was going to take care of the printing of the book. From earlier correspondence between Bernoulli and Montmort, it is apparent that Waldegrave had also analyzed Le Her and had come up with a mixed strategy as a solution. He had also suggested working on the \"problem of the pool,\" or what is often called Waldegrave's problem. The Universit\"{a}tsbibliothek Basel contains an additional forty-two letters between Bernoulli and Montmort written after 1713, as well as two letters between Bernoulli and Waldegrave. The letters are all in French, and here we provide translations of key passages. The trio continued to discuss probability problems, particularly Le Her which was still under discussion when the Essay d'analyse went to print. We describe the probability content of this body of correspondence and put it in its historical context. We also provide a proper identification of Waldegrave based on manuscripts in the Archives nationales de France in Paris.","PeriodicalId":413623,"journal":{"name":"arXiv: Other Statistics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134057581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
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