BRADLEY EFRON Professor of Statistics and Biostatistics
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The Meaning of Probability
CHAPTER 2 THE MEANING OF PROBABILITY INTRODUCTION by Glenn Shafer The meaning of probability has been debated since the mathematical theory of probability was formulated in the late 1600s. The five articles in this section have been selected to provide perspective on the history and present state of this debate. Mathematical statistics provided the main arena for debating the meaning of probability during the nineteenth and early twentieth centuries. The debate was conducted mainly between two camps, the subjectivists and the frequentists. The subjectivists contended that the probability of an event is the degree to which someone believes it, as indicated by their willingness to bet or take other actions. The frequentists contended that probability of an event is the frequency with which it occurs. Leonard J. Savage (1917-1971), the author of our first article, was an influential subjectivist. Bradley Efron, the author of our second article, is a leading contemporary frequentist. A newer debate, dating only from the 1950s and conducted more by psychologists and economists than by statisticians, has been concerned with whether the rules of probability are descriptive of human behavior or instead normative for human and machine reasoning. This debate has inspired empirical studies of the ways people violate the rules. In our third article, Amos Tversky and Daniel Kahneman report on some of the results of these studies. In our fourth article, Amos Tversky and I propose that we resolve both debates by formalizing a constructive interpretation of probability. According to this interpretation, probabilities are degrees of belief deliberately constructed and adopted on the basis of evidence, and frequencies are only one among many types of evidence. -
THE HISTORY and DEVELOPMENT of STATISTICS in BELGIUM by Dr
THE HISTORY AND DEVELOPMENT OF STATISTICS IN BELGIUM By Dr. Armand Julin Director-General of the Belgian Labor Bureau, Member of the International Statistical Institute Chapter I. Historical Survey A vigorous interest in statistical researches has been both created and facilitated in Belgium by her restricted terri- tory, very dense population, prosperous agriculture, and the variety and vitality of her manufacturing interests. Nor need it surprise us that the successive governments of Bel- gium have given statistics a prominent place in their affairs. Baron de Reiffenberg, who published a bibliography of the ancient statistics of Belgium,* has given a long list of docu- ments relating to the population, agriculture, industry, commerce, transportation facilities, finance, army, etc. It was, however, chiefly the Austrian government which in- creased the number of such investigations and reports. The royal archives are filled to overflowing with documents from that period of our history and their very over-abun- dance forms even for the historian a most diflScult task.f With the French domination (1794-1814), the interest for statistics did not diminish. Lucien Bonaparte, Minister of the Interior from 1799-1800, organized in France the first Bureau of Statistics, while his successor, Chaptal, undertook to compile the statistics of the departments. As far as Belgium is concerned, there were published in Paris seven statistical memoirs prepared under the direction of the prefects. An eighth issue was not finished and a ninth one * Nouveaux mimoires de I'Acadimie royale des sciences et belles lettres de Bruxelles, t. VII. t The Archives of the kingdom and the catalogue of the van Hulthem library, preserved in the Biblioth^que Royale at Brussells, offer valuable information on this head. -
This History of Modern Mathematical Statistics Retraces Their Development
BOOK REVIEWS GORROOCHURN Prakash, 2016, Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times, Hoboken, NJ, John Wiley & Sons, Inc., 754 p. This history of modern mathematical statistics retraces their development from the “Laplacean revolution,” as the author so rightly calls it (though the beginnings are to be found in Bayes’ 1763 essay(1)), through the mid-twentieth century and Fisher’s major contribution. Up to the nineteenth century the book covers the same ground as Stigler’s history of statistics(2), though with notable differences (see infra). It then discusses developments through the first half of the twentieth century: Fisher’s synthesis but also the renewal of Bayesian methods, which implied a return to Laplace. Part I offers an in-depth, chronological account of Laplace’s approach to probability, with all the mathematical detail and deductions he drew from it. It begins with his first innovative articles and concludes with his philosophical synthesis showing that all fields of human knowledge are connected to the theory of probabilities. Here Gorrouchurn raises a problem that Stigler does not, that of induction (pp. 102-113), a notion that gives us a better understanding of probability according to Laplace. The term induction has two meanings, the first put forward by Bacon(3) in 1620, the second by Hume(4) in 1748. Gorroochurn discusses only the second. For Bacon, induction meant discovering the principles of a system by studying its properties through observation and experimentation. For Hume, induction was mere enumeration and could not lead to certainty. Laplace followed Bacon: “The surest method which can guide us in the search for truth, consists in rising by induction from phenomena to laws and from laws to forces”(5). -
Strength in Numbers: the Rising of Academic Statistics Departments In
Agresti · Meng Agresti Eds. Alan Agresti · Xiao-Li Meng Editors Strength in Numbers: The Rising of Academic Statistics DepartmentsStatistics in the U.S. Rising of Academic The in Numbers: Strength Statistics Departments in the U.S. Strength in Numbers: The Rising of Academic Statistics Departments in the U.S. Alan Agresti • Xiao-Li Meng Editors Strength in Numbers: The Rising of Academic Statistics Departments in the U.S. 123 Editors Alan Agresti Xiao-Li Meng Department of Statistics Department of Statistics University of Florida Harvard University Gainesville, FL Cambridge, MA USA USA ISBN 978-1-4614-3648-5 ISBN 978-1-4614-3649-2 (eBook) DOI 10.1007/978-1-4614-3649-2 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012942702 Ó Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. -
Cramer, and Rao
2000 PARZEN PRIZE FOR STATISTICAL INNOVATION awarded by TEXAS A&M UNIVERSITY DEPARTMENT OF STATISTICS to C. R. RAO April 24, 2000 292 Breezeway MSC 4 pm Pictures from Parzen Prize Presentation and Reception, 4/24/2000 The 2000 EMANUEL AND CAROL PARZEN PRIZE FOR STATISTICAL INNOVATION is awarded to C. Radhakrishna Rao (Eberly Professor of Statistics, and Director of the Center for Multivariate Analysis, at the Pennsylvania State University, University Park, PA 16802) for outstanding distinction and eminence in research on the theory of statistics, in applications of statistical methods in diverse fields, in providing international leadership for 55 years in directing statistical research centers, in continuing impact through his vision and effectiveness as a scholar and teacher, and in extensive service to American and international society. The year 2000 motivates us to plan for the future of the discipline of statistics which emerged in the 20th century as a firmly grounded mathematical science due to the pioneering research of Pearson, Gossett, Fisher, Neyman, Hotelling, Wald, Cramer, and Rao. Numerous honors and awards to Rao demonstrate the esteem in which he is held throughout the world for his unusually distinguished and productive life. C. R. Rao was born September 10, 1920, received his Ph.D. from Cambridge University (England) in 1948, and has been awarded 22 honorary doctorates. He has worked at the Indian Statistical Institute (1944-1992), University of Pittsburgh (1979- 1988), and Pennsylvania State University (1988- ). Professor Rao is the author (or co-author) of 14 books and over 300 publications. His pioneering contributions (in linear models, multivariate analysis, design of experiments and combinatorics, probability distribution characterizations, generalized inverses, and robust inference) are taught in statistics textbooks. -
The Theory of the Design of Experiments
The Theory of the Design of Experiments D.R. COX Honorary Fellow Nuffield College Oxford, UK AND N. REID Professor of Statistics University of Toronto, Canada CHAPMAN & HALL/CRC Boca Raton London New York Washington, D.C. C195X/disclaimer Page 1 Friday, April 28, 2000 10:59 AM Library of Congress Cataloging-in-Publication Data Cox, D. R. (David Roxbee) The theory of the design of experiments / D. R. Cox, N. Reid. p. cm. — (Monographs on statistics and applied probability ; 86) Includes bibliographical references and index. ISBN 1-58488-195-X (alk. paper) 1. Experimental design. I. Reid, N. II.Title. III. Series. QA279 .C73 2000 001.4 '34 —dc21 00-029529 CIP This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. -
Statistical Inference: Paradigms and Controversies in Historic Perspective
Jostein Lillestøl, NHH 2014 Statistical inference: Paradigms and controversies in historic perspective 1. Five paradigms We will cover the following five lines of thought: 1. Early Bayesian inference and its revival Inverse probability – Non-informative priors – “Objective” Bayes (1763), Laplace (1774), Jeffreys (1931), Bernardo (1975) 2. Fisherian inference Evidence oriented – Likelihood – Fisher information - Necessity Fisher (1921 and later) 3. Neyman- Pearson inference Action oriented – Frequentist/Sample space – Objective Neyman (1933, 1937), Pearson (1933), Wald (1939), Lehmann (1950 and later) 4. Neo - Bayesian inference Coherent decisions - Subjective/personal De Finetti (1937), Savage (1951), Lindley (1953) 5. Likelihood inference Evidence based – likelihood profiles – likelihood ratios Barnard (1949), Birnbaum (1962), Edwards (1972) Classical inference as it has been practiced since the 1950’s is really none of these in its pure form. It is more like a pragmatic mix of 2 and 3, in particular with respect to testing of significance, pretending to be both action and evidence oriented, which is hard to fulfill in a consistent manner. To keep our minds on track we do not single out this as a separate paradigm, but will discuss this at the end. A main concern through the history of statistical inference has been to establish a sound scientific framework for the analysis of sampled data. Concepts were initially often vague and disputed, but even after their clarification, various schools of thought have at times been in strong opposition to each other. When we try to describe the approaches here, we will use the notions of today. All five paradigms of statistical inference are based on modeling the observed data x given some parameter or “state of the world” , which essentially corresponds to stating the conditional distribution f(x|(or making some assumptions about it). -
Front Matter
Cambridge University Press 978-1-107-61967-8 - Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction Bradley Efron Frontmatter More information Large-Scale Inference We live in a new age for statistical inference, where modern scientific technology such as microarrays and fMRI machines routinely produce thousands and sometimes millions of parallel data sets, each with its own estimation or testing problem. Doing thousands of problems at once involves more than repeated application of classical methods. Taking an empirical Bayes approach, Bradley Efron, inventor of the bootstrap, shows how information accrues across problems in a way that combines Bayesian and frequentist ideas. Estimation, testing, and prediction blend in this framework, producing opportunities for new methodologies of increased power. New difficulties also arise, easily leading to flawed inferences. This book takes a careful look at both the promise and pitfalls of large-scale statistical inference, with particular attention to false discovery rates, the most successful of the new statistical techniques. Emphasis is on the inferential ideas underlying technical developments, illustrated using a large number of real examples. bradley efron is Max H. Stein Professor of Statistics and Biostatistics at the Stanford University School of Humanities and Sciences, and the Department of Health Research and Policy at the School of Medicine. © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-61967-8 - Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction Bradley Efron Frontmatter More information INSTITUTE OF MATHEMATICAL STATISTICS MONOGRAPHS Editorial Board D. R. Cox (University of Oxford) B. Hambly (University of Oxford) S. -
The Enigma of Karl Pearson and Bayesian Inference
The Enigma of Karl Pearson and Bayesian Inference John Aldrich 1 Introduction “An enigmatic position in the history of the theory of probability is occupied by Karl Pearson” wrote Harold Jeffreys (1939, p. 313). The enigma was that Pearson based his philosophy of science on Bayesian principles but violated them when he used the method of moments and probability-values in statistics. It is not uncommon to see a divorce of practice from principles but Pearson also used Bayesian methods in some of his statistical work. The more one looks at his writings the more puzzling they seem. In 1939 Jeffreys was probably alone in regretting that Pearson had not been a bottom to top Bayesian. Bayesian methods had been in retreat in English statistics since Fisher began attacking them in the 1920s and only Jeffreys ever looked for a synthesis of logic, statistical methods and everything in between. In the 1890s, when Pearson started, everything was looser: statisticians used inverse arguments based on Bayesian principles and direct arguments based on sampling theory and a philosopher-physicist-statistician did not have to tie everything together. Pearson did less than his early guide Edgeworth or his students Yule and Gosset (Student) to tie up inverse and direct arguments and I will be look- ing to their work for clues to his position and for points of comparison. Of Pearson’s first course on the theory of statistics Yule (1938, p. 199) wrote, “A straightforward, organized, logically developed course could hardly then [in 1894] exist when the very elements of the subject were being developed.” But Pearson never produced such a course or published an exposition as integrated as Yule’s Introduction, not to mention the nonpareil Probability of Jeffreys. -
The Future of Statistics
THE FUTURE OF STATISTICS Bradley Efron The 1990 sesquicentennial celebration of the ASA included a set of eight articles on the future of statistics, published in the May issue of the American Statistician. Not all of the savants took their prediction duties seriously, but looking back from 2007 I would assign a respectable major league batting average of .333 to those who did. Of course it's only been 17 years and their average could still improve. The statistical world seems to be evolving even more rapidly today than in 1990, so I'd be wise not to sneeze at .333 as I begin my own prediction efforts. There are at least two futures to consider: statistics as a profession, both academic and industrial, and statistics as an intellectual discipline. (And maybe a third -- demographic – with the center of mass of our field moving toward Asia, and perhaps toward female, too.) We tend to think of statistics as a small profession, but a century of steady growth, accelerating in the past twenty years, now makes "middling" a better descriptor. Together, statistics and biostatistics departments graduated some 600 Ph.D.s last year, with no shortage of good jobs awaiting them in industry or academia. The current money-making powerhouses of industry, the hedge funds, have become probability/statistics preserves. Perhaps we can hope for a phalanx of new statistics billionaires, gratefully recalling their early years in the humble ranks of the ASA. Statistics departments have gotten bigger and more numerous around the U.S., with many universities now having two. -
David Donoho. 50 Years of Data Science. Journal of Computational
Journal of Computational and Graphical Statistics ISSN: 1061-8600 (Print) 1537-2715 (Online) Journal homepage: https://www.tandfonline.com/loi/ucgs20 50 Years of Data Science David Donoho To cite this article: David Donoho (2017) 50 Years of Data Science, Journal of Computational and Graphical Statistics, 26:4, 745-766, DOI: 10.1080/10618600.2017.1384734 To link to this article: https://doi.org/10.1080/10618600.2017.1384734 © 2017 The Author(s). Published with license by Taylor & Francis Group, LLC© David Donoho Published online: 19 Dec 2017. Submit your article to this journal Article views: 46147 View related articles View Crossmark data Citing articles: 104 View citing articles Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=ucgs20 JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS , VOL. , NO. , – https://doi.org/./.. Years of Data Science David Donoho Department of Statistics, Stanford University, Standford, CA ABSTRACT ARTICLE HISTORY More than 50 years ago, John Tukey called for a reformation of academic statistics. In “The Future of Data science Received August Analysis,” he pointed to the existence of an as-yet unrecognized , whose subject of interest was Revised August learning from data, or “data analysis.” Ten to 20 years ago, John Chambers, Jeff Wu, Bill Cleveland, and Leo Breiman independently once again urged academic statistics to expand its boundaries beyond the KEYWORDS classical domain of theoretical statistics; Chambers called for more emphasis on data preparation and Cross-study analysis; Data presentation rather than statistical modeling; and Breiman called for emphasis on prediction rather than analysis; Data science; Meta inference. -
A Conversation with Richard A. Olshen 3
Statistical Science 2015, Vol. 30, No. 1, 118–132 DOI: 10.1214/14-STS492 c Institute of Mathematical Statistics, 2015 A Conversation with Richard A. Olshen John A. Rice Abstract. Richard Olshen was born in Portland, Oregon, on May 17, 1942. Richard spent his early years in Chevy Chase, Maryland, but has lived most of his life in California. He received an A.B. in Statistics at the University of California, Berkeley, in 1963, and a Ph.D. in Statistics from Yale University in 1966, writing his dissertation under the direction of Jimmie Savage and Frank Anscombe. He served as Research Staff Statistician and Lecturer at Yale in 1966–1967. Richard accepted a faculty appointment at Stanford University in 1967, and has held tenured faculty positions at the University of Michigan (1972–1975), the University of California, San Diego (1975–1989), and Stanford University (since 1989). At Stanford, he is Professor of Health Research and Policy (Biostatistics), Chief of the Division of Biostatistics (since 1998) and Professor (by courtesy) of Electrical Engineering and of Statistics. At various times, he has had visiting faculty positions at Columbia, Harvard, MIT, Stanford and the Hebrew University. Richard’s research interests are in statistics and mathematics and their applications to medicine and biology. Much of his work has concerned binary tree-structured algorithms for classification, regression, survival analysis and clustering. Those for classification and survival analysis have been used with success in computer-aided diagnosis and prognosis, especially in cardiology, oncology and toxicology. He coauthored the 1984 book Classi- fication and Regression Trees (with Leo Brieman, Jerome Friedman and Charles Stone) which gives motivation, algorithms, various examples and mathematical theory for what have come to be known as CART algorithms.