The Enigma of Karl Pearson and Bayesian Inference
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School of Social Sciences Economics Division University of Southampton Southampton SO17 1BJ, UK Discussion Papers in Economics and Econometrics Mathematics in the Statistical Society 1883-1933 John Aldrich No. 0919 This paper is available on our website http://www.southampton.ac.uk/socsci/economics/research/papers ISSN 0966-4246 Mathematics in the Statistical Society 1883-1933* John Aldrich Economics Division School of Social Sciences University of Southampton Southampton SO17 1BJ UK e-mail: [email protected] Abstract This paper considers the place of mathematical methods based on probability in the work of the London (later Royal) Statistical Society in the half-century 1883-1933. The end-points are chosen because mathematical work started to appear regularly in 1883 and 1933 saw the formation of the Industrial and Agricultural Research Section– to promote these particular applications was to encourage mathematical methods. In the period three movements are distinguished, associated with major figures in the history of mathematical statistics–F. Y. Edgeworth, Karl Pearson and R. A. Fisher. The first two movements were based on the conviction that the use of mathematical methods could transform the way the Society did its traditional work in economic/social statistics while the third movement was associated with an enlargement in the scope of statistics. The study tries to synthesise research based on the Society’s archives with research on the wider history of statistics. Key names : Arthur Bowley, F. Y. Edgeworth, R. A. Fisher, Egon Pearson, Karl Pearson, Ernest Snow, John Wishart, G. Udny Yule. Keywords : History of Statistics, Royal Statistical Society, mathematical methods. -
MODES for Windows Print
Marshall Library of Economics Marshall Papers Section 9 Autobiography and personal honours Identity code Marshall 9 Description level 3 Content Summary This diverse section contains the few remaining biographical notes by Alfred, longer notes on Alfred by Mary Marshall, lists of recipients of complimentary copies of Marshall's books and subscribers to his portrait fund, his academic honours, a large scrapbook of newspaper cuttings about Alfred's career kept by Mary and her album of watercolour paintings of places visited on European travels Identity code Marshall 9/1 Previous number Marshall LBB 34 (part) [uncertain attribution] Description level 4 Record creation Person Role writer Name Marshall, Alfred Date undated Document form Record type notes Specific type autobiographical Acquisition Summary Possibly a late accession as formerly in Large Brown Box Content Summary Single page annotated 'Reminiscences' down left side by Marshall. Recounts how when at school was told not to take account of accents in pronouncing Greek words and therefore decided to save time by not learning them or using them in written work. The result was he received the only very heavy punishment of his life. 'This suggested to me that classical studies do not induce an appreciation of the value of time; and I turned away from them as far as I could towards mathematics'. Summary In later years he has observed that fine students of science are greedy of time, whereas many classical men value it lightly. Is most grateful to his headmaster [Revd James Augustus Hessey] for making him think out essays in Latin. Person Name Hessey, James Augustus, Revd Subject keywords Physical descript Summary 1 p. -
National Academy Elects IMS Fellows Have You Voted Yet?
Volume 38 • Issue 5 IMS Bulletin June 2009 National Academy elects IMS Fellows CONTENTS The United States National Academy of Sciences has elected 72 new members and 1 National Academy elects 18 foreign associates from 15 countries in recognition of their distinguished and Raftery, Wong continuing achievements in original research. Among those elected are two IMS Adrian Raftery 2 Members’ News: Jianqing Fellows: , Blumstein-Jordan Professor of Statistics and Sociology, Center Fan; SIAM Fellows for Statistics and the Social Sciences, University of Washington, Seattle, and Wing Hung Wong, Professor 3 Laha Award recipients of Statistics and Professor of Health Research and Policy, 4 COPSS Fisher Lecturer: Department of Statistics, Stanford University, California. Noel Cressie The election was held April 28, during the business 5 Members’ Discoveries: session of the 146th annual meeting of the Academy. Nicolai Meinshausen Those elected bring the total number of active members 6 Medallion Lecture: Tony Cai to 2,150. Foreign associates are non-voting members of the Academy, with citizenship outside the United States. Meeting report: SSP Above: Adrian Raftery 7 This year’s election brings the total number of foreign 8 New IMS Fellows Below: Wing H. Wong associates to 404. The National Academy of Sciences is a private 10 Obituaries: Keith Worsley; I.J. Good organization of scientists and engineers dedicated to the furtherance of science and its use for general welfare. 12-3 JSM program highlights; It was established in 1863 by a congressional act of IMS sessions at JSM incorporation signed by Abraham Lincoln that calls on 14-5 JSM tours; More things to the Academy to act as an official adviser to the federal do in DC government, upon request, in any matter of science or 16 Accepting rejections technology. -
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). -
Memorial to Sir Harold Jeffreys 1891-1989 JOHN A
Memorial to Sir Harold Jeffreys 1891-1989 JOHN A. HUDSON and ALAN G. SMITH University of Cambridge, Cambridge, England Harold Jeffreys was one of this century’s greatest applied mathematicians, using mathematics as a means of under standing the physical world. Principally he was a geo physicist, although statisticians may feel that his greatest contribution was to the theory of probability. However, his interest in the latter subject stemmed from his realization of the need for a clear statistical method of analysis of data— at that time, travel-time readings from seismological stations across the world. He also made contributions to astronomy, fluid dynamics, meteorology, botany, psychol ogy, and photography. Perhaps one can identify Jeffreys’s principal interests from three major books that he wrote. His mathematical skills are displayed in Methods of Mathematical Physics, which he wrote with his wife Bertha Swirles Jeffreys and which was first published in 1946 and went through three editions. His Theory o f Probability, published in 1939 and also running to three editions, espoused Bayesian statistics, which were very unfashionable at the time but which have been taken up since by others and shown to be extremely powerful for the analysis of data and, in particular, image enhancement. However, the book for which he is probably best known is The Earth, Its Origin, History and Physical Consti tution, a broad-ranging account based on observations analyzed with care, using mathematics as a tool. Jeffreys’s scientific method (now known as Inverse Theory) was a logical process, clearly stated in another of his books, Scientific Inference. -
Chapter 1: What Is Statistics? Christopher J
Chapter 1: What is Statistics? Christopher J. Wild, Jessica M. Utts, and Nicholas J. Horton Christopher J. Wild University of Auckland, New Zealand President, American Statistical Association Jessica M. Utts University of California, Irvine, United States Chair, Statistical Education Section, ASA Nicholas J. Horton Amherst College, United States e-mail: [email protected], [email protected], [email protected] Abstract What is Statistics? We attempt to answer this question as it relates to grounding research in statistics education. We discuss the nature of statistics (the science of learning from data), its history and traditions, what characterises statistical thinking and how it differs from mathematics, connections with computing and data science, why learning statistics is essential, and what is most important. Finally, we attempt to gaze into the future, drawing upon what is known about the fast-growing demand for statistical skills and the portents of where the discipline is heading, especially those arising from data science and the promises and problems of big data. Key Words Discipline of statistics; Statistical thinking; Value of statistics; Statistical fundamentals; Decision making; Trends in statistical practice; Data science; Computational thinking 1.1 Introduction In this, the opening chapter of the International Handbook of Research in Statistics Education, we ask the question, “What is statistics?” This question is not considered in isolation, however, but in the context of grounding research in statistics education. Educational endeavour in statistics can be divided very broadly into “What?” and “How?” The “What?” deals with the nature and extent of the discipline to be conveyed, whereas any consideration of “How?” (including “When?”) brings into play a host of additional factors, such as cognition and learning theories, audience and readiness, attitudes, social interactions with teachers and other students, and learning and assessment strategies and systems. -
A Complete Bibliography of Publications in Biometrika for the Decade 1960–1969
A Complete Bibliography of Publications in Biometrika for the decade 1960{1969 Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Tel: +1 801 581 5254 FAX: +1 801 581 4148 E-mail: [email protected], [email protected], [email protected] (Internet) WWW URL: http://www.math.utah.edu/~beebe/ 19 May 2021 Version 1.02 Title word cross-reference #4315 [Har79]. 0 · 1 [dVW66]. 2 × 2 [BH60a, BH61a, OI61a, OI61b, Pla64]. 50 [Bar66d]. k [Bur60b]. A [Hol66, Mar63]. A + B [Mar63]. b2 [Pea65b]. β [Mos62]. β2 [JNAP63, JNAP65]. χ [JP69, JP70]. χ2 2 [Hit62, MA65, Put64, Tik65b, Wis63a, Wis63b, You62]. χr [Sen67]. d [dVW66]. Ek=M=1 [Bur60c]. [RK69a]. exp(−a)+ka = 1 [BDM60]. exp(b) − b=(1 − p) = 1 [BDM63]. F [Ati62, BDO60, CB63, CB66, GS62b, PB61, Pri64a, SZ60, Tik65b, Tik66]. GI=G=1 [Kin62]. GI=M=1 [Fin60a]. k [DG68a, Kor69, Maa66]. M [Har69a, Pea69, Cro61, Lin60]. M=M=1 [GS65]. X2 [Wis63a, Wis63b]. N [Gil65, Hai65b, ST66, Arc62, Arc64, Hof63]. p [Rao68b, Rao69]. Q [Gow66a]. 3 2 2 R [Mil65a]. ρ [Sno63]. S [Bur60a, Bar66d].p s = 1 [Bar66d].p smax=s0 2 2 [Cha67a]. SU [Joh65b]. σB/σ [Sis68]. b1 [Pea65b]. β1 [JNAP63]. 1 2 P m p 0 f(Yt) [Con65]. β1 [JNAP65]. t [Amo64, FKM67, GJ68, Haj61, HPW61, Joh61, MSA66, Owe65, SA62a, Sis64]. 2 2 2 2 T0 [IS64]. U [Maa66]. UM;N [Ste65b]. UN [PS62b, Ste63a, Ste64, Tik65a]. (s) 2 2 V1 [Bar66d]. VN [Ste65a]. -
1 the MAKING of INDEX NUMBERS in the EARLY 1920S
THE MAKING OF INDEX NUMBERS IN THE EARLY 1920s: A CLOSER LOOK AT THE FISHER–MITCHELL DEBATE Felipe Almeida Victor Cruz e Silva Universidade Federal do Paraná Universidade Estadual de Ponta Grossa Área 1 - História do Pensamento Econômico e Metodologia RESUMO O surgimento sistemático da abordagem axiomática dos números de índice ocorreu no início dos anos 1920, um período marcado pelo pluralismo na academia econômic estadunidense. Promovida por Irving Fisher, a abordagem axiomática dos números de índice teve como objetivo selecionar uma fórmula ideal universalmente válida para números de índice, empregando uma série de testes estatísticos. No entanto, desde a primeira apresentação da abordagem de Fisher, no Encontro Anual da Associação Estadunidense de Estatística em 1920, até a publicação de seu livro “The Making of Index Numbers” em 1922, Fisher enfrentou uma série de críticas, não endereçadas à sua fórmula ideal propriamente dita, mas à própria idéia de uma fórmula universal para números de índice. Os principais indivíduos envolvidos nesse debate foram Wesley Mitchell, Warren Persons, Correa Walsh (que foi o único que apoiou a proposta de Fisher) e Allyn Young. Entre eles, o principal representante dos antagonistas de Fisher era Mitchell. Este estudo argumenta que as divergências entre Fisher e Mitchell resultam de seus distintos entendimentos da economia como uma "ciência". Portanto, o objetivo deste estudo é ilustrar como Fisher, como economista matemático, privilegiou a universalidade das teorias econômicas, enquanto Mitchell, como institucionalista, entendeu a economia como uma disciplina contextual e histórica e como essas preconcepções estão presentes no debate sobre números de índice. Para ilustrar suas posições, este estudo explora evidências baseadas em arquivo. -
AN INVESTIGATION INTO the FORMATION of CONSENSUS AROUND NEOCLASSICAL ECONOMICS in the 1950S
THE ECLIPSE OF INSTITUTIONALISM? AN INVESTIGATION INTO THE FORMATION OF CONSENSUS AROUND NEOCLASSICAL ECONOMICS IN THE 1950s A Dissertation Submitted to the Temple University Graduate Board In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy By Julie Ragatz May, 2019 Committee Members: Dr. Miriam Solomon, Department of Philosophy Dr. David Wolfsdorf, Department of Philosophy Dr. Dimitrios Diamantaras, Department of Economics Dr. Matthew Lund, Department of Philosophy, Rowan University, External Reader © Copyright 2019 by Julie Ragatz Norton All Rights Reserved ii ABSTRACT The Eclipse of Institutionalism? An Investigation into the Formation of Consensus Around Neoclassical Economics in the 1950s Julie Ragatz Norton Temple University, 2019 Doctoral Advisory Committee Chair: Dr. Miriam Solomon As the discipline of economics professionalized during the interwar period, two schools of thought emerged: institutionalism and neoclassical economics. By 1954, after the publication of Arrow and Debreu’s landmark article on general equilibrium theory, consensus formed around neoclassical economics. This outcome was significantly influenced by trends in the philosophy of science, notably the transformation from the logical empiricism of the Vienna Circle to an ‘Americanized’ version of logical empiricism that was dominant through the 1950s. This version of logical empiricism provided a powerful ally to neoclassical economics by affirming its philosophical and methodological commitments as examples of “good science”. This dissertation explores this process of consensus formation by considering whether consensus would be judged normatively appropriate from the perspective of three distinct approaches to the philosophy of science; Carl Hempel’s logical empiricism, Thomas Kuhn’s account of theory change and Helen Longino’s critical contextual empiricism. -
A Parsimonious Tour of Bayesian Model Uncertainty
A Parsimonious Tour of Bayesian Model Uncertainty Pierre-Alexandre Mattei Université Côte d’Azur Inria, Maasai project-team Laboratoire J.A. Dieudonné, UMR CNRS 7351 e-mail: [email protected] Abstract: Modern statistical software and machine learning libraries are enabling semi-automated statistical inference. Within this context, it appears eas- ier and easier to try and fit many models to the data at hand, thereby reversing the Fisherian way of conducting science by collecting data after the scientific hypothesis (and hence the model) has been determined. The renewed goal of the statistician becomes to help the practitioner choose within such large and heterogeneous families of models, a task known as model selection. The Bayesian paradigm offers a systematized way of as- sessing this problem. This approach, launched by Harold Jeffreys in his 1935 book Theory of Probability, has witnessed a remarkable evolution in the last decades, that has brought about several new theoretical and methodological advances. Some of these recent developments are the focus of this survey, which tries to present a unifying perspective on work carried out by different communities. In particular, we focus on non-asymptotic out-of-sample performance of Bayesian model selection and averaging tech- niques, and draw connections with penalized maximum likelihood. We also describe recent extensions to wider classes of probabilistic frameworks in- cluding high-dimensional, unidentifiable, or likelihood-free models. Contents 1 Introduction: collecting data, fitting many models . .2 2 A brief history of Bayesian model uncertainty . .2 3 The foundations of Bayesian model uncertainty . .3 3.1 Handling model uncertainty with Bayes’s theorem . -
Francis Ysidro Edgeworth
Francis Ysidro Edgeworth Previous (Francis Xavier) (/entry/Francis_Xavier) Next (Francis of Assisi) (/entry/Francis_of_Assisi) Francis Ysidro Edgeworth (February 8, 1845 – February 13, 1926) was an Irish (/entry/Ireland) polymath, a highly influential figure in the development of neo classical economics, and contributor to the development of statistical theory. He was the first to apply certain formal mathematical techniques to individual decision making in economics. Edgeworth developed utility theory, introducing the indifference curve and the famous "Edgeworth box," which have become standards in economic theory. He is also known for the "Edgeworth conjecture" which states that the core of an economy shrinks to the set of competitive equilibria as the number of agents in the economy gets large. The high degree of originality demonstrated in his most important book on economics, Mathematical Psychics, was matched only by the difficulty in reading it. A deep thinker, his contributions were far ahead of his time and continue to inform the fields of (/entry/File:Edgeworth.jpeg) microeconomics (/entry/Microeconomics) and areas such as welfare economics. Francis Y. Edgeworth Thus, Edgeworth's work has advanced our understanding of economic relationships among traders, and thus contributes to the establishment of a better society for all. Life Contents Ysidro Francis Edgeworth (the order of his given names was later reversed) 1 Life was born on February 8, 1845 in Edgeworthstown, Ireland (/entry/Ireland), into 2 Work a large and wealthy landowning family. His aunt was the famous novelist Maria 2.1 Edgeworth conjecture Edgeworth, who wrote the Castle Rackrent. He was educated by private tutors 2.2 Edgeworth Box until 1862, when he went on to study classics and languages at Trinity College, 2.3 Edgeworth limit theorem Dublin.