International Journal of Management Sciences and Business Research, 2012, Vol

Total Page:16

File Type:pdf, Size:1020Kb

International Journal of Management Sciences and Business Research, 2012, Vol International Journal of Management Sciences and Business Research, 2012, Vol. 1, Issue 11. (ISSN: 2226-8235) History of the Efficient Market Hypothesis 1) Thian Cheng Lim Abstract Xi’an Jiaotong-Liverpool This paper reviews and summarizes the University work of Sewell (2011). The purpose is to investigate the evolution and development of the Efficient Market 111 Ren’ai Road, Dushu Lake Hypothesis from its inception as theory Higher Education Town, Suzhou of probability to Fama (1965) Industrial Park 215123, China proposition and revision (Fama, 1970; 1991). It discusses the random walk theory and reports the various research papers that have been written on the subject. This paper also clarifies the 2) Xiu Yun Lim debate on the validity of EMH and explains the importance of EMH to National University of Singapore finance theory. Keywords: EMH, history, EMH – Efficient market hypothesis 3) Riuyang Zhai Bentley University I. INTRODUCTION 145 Forest Street, Waltham, Boston There are various ways to describe the MA 02451 USA behavior of the stock market. The efficient market is a concept used to describe the stock market by its level of efficiency in disseminating information. This concept is important for basic assumption in many economic and finance models. EMH as suggested by Fama (1965) is a theoretical proposition, and empirically an efficient market does not exist. Various empirical studies showed that the market is not efficient as described by Fama (1958). Fama reviewed and revised his work and http://www.ijmsbr.com Page 26 International Journal of Management Sciences and Business Research, 2012, Vol. 1, Issue 11. (ISSN: 2226-8235) explain the reason empirical studies did not support his proposition. The purpose of this paper is to investigate the initial concept that leads Fama (1970; 1991) divides market to the proposition of EMH. People had efficiency into three categories of been intrigued by the probability of efficiency: weak-form or how well do beating the market, may it be stocks or past returns predict future returns, semi- other investment market ever since the strong-form or how quickly do security Middle Ages. One of the first works ever prices reflect public information written on the theory of probability is announcements, and strong-form or how Liber de Ludo Aleae (The Book of any investors have private information Games of Chance) written by Girolamo that is not fully reflected in market Cardano a medical doctor from Italy prices. between 1524 to 1550. Furthermore, it is important in the development of the science of probability (Oystein, 1953). There are many practical applications for EMH. For example, stakeholders can measure the performance of the II. EARLY STUDIES ON EMH appointed management by observing the stock price. "In major stock market, a A. Random Walk Hypothesis rational consensus will be reached as to the share prices which best reflect the The random walk hypothesis is a prospects for future cash flows" financial theory stating that stock market (Bowman, 1994)” EMH is of prime prices evolve according to a random importance to the accounting field for walk and thus the prices of the stock performance measurement and financial market cannot be predicted. It is statement reporting (Bowman, 1994, consistent with the efficient-market p2). hypothesis. The idea of random walk was based on Robert Brown observation that grains of pollen suspended in water In an efficient stock market, information had a rapid oscillatory motion when disclosure is a key requirement. If the viewed under a microscope (Brown, managements want the stock market to 1828). The theory that stock prices move correctly value the company's shares, randomly was officially proposed by they must ensure that they provide Maurice Kendall in his 1953 paper, The sufficient information in a timely Analytics of Economic Time Series, Part manner, allowing the market to do so. As 1: Price (Kendall, 1953). Malkiel suggests, "when information arises, the news spreads very quickly and is incorporated into the prices of In 1863 a French stockbroker, Jules securities without delay." (Malkiel, Regnault, observed that the longer you 2003) hold a security, the more you can win or lose on its price variations: the price deviation is directly proportional to the http://www.ijmsbr.com Page 27 International Journal of Management Sciences and Business Research, 2012, Vol. 1, Issue 11. (ISSN: 2226-8235) square root of time (Regnault, 1863). Crash occurred in late October 1929 which, taking into account the full extent and duration of its fallout, was the most Louis Bachelier, another Frenchman devastating stock market crash in the whose Ph.D. dissertation titled "The history of the US. Theory of Speculation" (1900) included some remarkable insights and commentary. Bachelier’s work was way In 1930 Alfred Cowles, 3rd, the ahead of his time and was ignored until American economist and businessman, it was rediscovered by Savage in 1955. founded and funded both the Five years later Karl Pearson, a Econometric Society and its journal, professor and Fellow of the Royal Econometrica. Two years later, Cowles Society, introduced the term random set up the Cowles Commission for walk in the letters pages of Nature Economic Research. Cowles (1933) (Pearson, 1905). Unaware of Bachelier’s analyzed the performance of investment work in 1900, Albert Einstein developed professionals and concluded that stock the equations for Brownian motion market forecasters cannot forecast. (Einstein, 1905). Holbrook Working concluded that stock In 1923 the English economist John returns behave like numbers from a Maynard Keynes clearly stated that lottery (Working, 1934). In 1936 Keynes investors on financial markets are had General Theory of Employment, rewarded not for knowing better than the Interest, and Money (Keynes, 1936) market what the future has in store, but published. He famously compared the rather for risk bearing, this is a stock market with a beauty contest, and consequence of the EMH (Keynes, also claimed that most investors’ 1923). Frederick MacCauley, an decisions can only be as a result of economist, observed that there was a ‘animal spirits’. striking similarity between the fluctuations of the stock market and those of a chance curve which may be Eugen Slutzky showed that sums of obtained by throwing a dice independent random variables may be (MacCauley, 1925). the source of cyclic processes (Slutzky, 1937). In the only paper published before 1960 which found significant inefficiencies, Cowles and Jones found Unquestionable proof of the leptokurtic significant evidence of serial correlation nature of the distribution of returns was in averaged time series indices of stock given by Maurice Olivier in his Paris prices (Cowles and Jones, 1937). doctoral dissertation (Olivier, 1926). Frederick C. Mills, in The Behavior of In 1944, in a continuation of his 1933 Prices (Mills, 1927), proved the publication, Cowles again reported that leptokurtosis of returns. The Wall Street investment professionals do not beat the http://www.ijmsbr.com Page 28 International Journal of Management Sciences and Business Research, 2012, Vol. 1, Issue 11. (ISSN: 2226-8235) market (Cowles, 1944). Holbrook found evidence of the square root of Working showed that in an ideal futures time rule. Regarding the distribution of market it would be impossible for any returns, he finds ‘a larger “tangential professional forecaster to predict price dispersion” in the data at these limits’ changes successfully (Working, 1949). (Osborne, 1959). In 1953 Milton Friedman pointed out Larson (1960) presented the results of an that, due to arbitrage, the case for the application of a new method of time EMH can be made even in situations series analysis. He notes that the where the trading strategies of investors distribution of price changes is ‘very are correlated (Friedman, 1953). Kendall nearly normally distributed for the (1953) analyzed 22 price-series at central 80 per cent of the data, but there weekly intervals and found to his is an excessive number of extreme surprise that they were essentially values.’ Cowles (1960) revisited the random. Also, he was the first to note the results in Cowles and Jones (1937), time dependence of the empirical correcting an error introduced by variance (nonstationarity). Around 1955, averaging, and still finds mixed temporal Leonard Jimmie Savage, who had dependence results. Working (1960) discovered Bachelier’s 1914 publication showed that the use of averages can in the Chicago or Yale library sent half a introduce autocorrelations not present in dozen ‘blue ditto’ postcards to the original series. colleagues, asking ‘does any one of you know him?’ Paul Samuelson was one of the recipients. He couldn’t find the book Houthakker (1961) used stop-loss sell in the MIT library, but he did discover a orders and finds patterns. He also found copy of Bachelier’s PhD thesis leptokurtosis, nonstationarity and (Bernstein, 1992; Taqqu, 2001). suspected non-linearity. Independently of Working (1960), Alexander (1961) realized that spurious autocorrelation In 1956 Bachelier’s name reappeared in could be introduced by averaging; or if economics, this time, as an the probability of a rise is not 0.5. He acknowledged forerunner, in a thesis on concluded that the random walk model options-like pricing by a student of MIT, best fits the data, but found leptokurtosis economist Paul A. Samuelson in the distribution of returns. Also, this (Mandelbrot and Hudson, 2004). paper was the first to test for non-linear Working (1958) built an anticipatory dependence. In the same year, Muth market model. The following year, Harry introduced the rati in 1961. Roberts demonstrated that a random walk will look very much like an actual stock series (Harry, 1959). Meanwhile, In 1962 Mandelbrot first proposed that M. F. M. Osborne showed that the the tails of the distribution of returns logarithm of common-stock prices follow a power law, in IBM Research follows Brownian motion; and also Note NC-87 (Mandelbrot, 1962).
Recommended publications
  • A Short History of Stochastic Integration and Mathematical Finance
    A Festschrift for Herman Rubin Institute of Mathematical Statistics Lecture Notes – Monograph Series Vol. 45 (2004) 75–91 c Institute of Mathematical Statistics, 2004 A short history of stochastic integration and mathematical finance: The early years, 1880–1970 Robert Jarrow1 and Philip Protter∗1 Cornell University Abstract: We present a history of the development of the theory of Stochastic Integration, starting from its roots with Brownian motion, up to the introduc- tion of semimartingales and the independence of the theory from an underlying Markov process framework. We show how the development has influenced and in turn been influenced by the development of Mathematical Finance Theory. The calendar period is from 1880 to 1970. The history of stochastic integration and the modelling of risky asset prices both begin with Brownian motion, so let us begin there too. The earliest attempts to model Brownian motion mathematically can be traced to three sources, each of which knew nothing about the others: the first was that of T. N. Thiele of Copen- hagen, who effectively created a model of Brownian motion while studying time series in 1880 [81].2; the second was that of L. Bachelier of Paris, who created a model of Brownian motion while deriving the dynamic behavior of the Paris stock market, in 1900 (see, [1, 2, 11]); and the third was that of A. Einstein, who proposed a model of the motion of small particles suspended in a liquid, in an attempt to convince other physicists of the molecular nature of matter, in 1905 [21](See [64] for a discussion of Einstein’s model and his motivations.) Of these three models, those of Thiele and Bachelier had little impact for a long time, while that of Einstein was immediately influential.
    [Show full text]
  • Notes on Stochastic Processes
    Notes on stochastic processes Paul Keeler March 20, 2018 This work is licensed under a “CC BY-SA 3.0” license. Abstract A stochastic process is a type of mathematical object studied in mathemat- ics, particularly in probability theory, which can be used to represent some type of random evolution or change of a system. There are many types of stochastic processes with applications in various fields outside of mathematics, including the physical sciences, social sciences, finance and economics as well as engineer- ing and technology. This survey aims to give an accessible but detailed account of various stochastic processes by covering their history, various mathematical definitions, and key properties as well detailing various terminology and appli- cations of the process. An emphasis is placed on non-mathematical descriptions of key concepts, with recommendations for further reading. 1 Introduction In probability and related fields, a stochastic or random process, which is also called a random function, is a mathematical object usually defined as a collection of random variables. Historically, the random variables were indexed by some set of increasing numbers, usually viewed as time, giving the interpretation of a stochastic process representing numerical values of some random system evolv- ing over time, such as the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule [120, page 7][51, page 46 and 47][66, page 1]. Stochastic processes are widely used as math- ematical models of systems and phenomena that appear to vary in a random manner. They have applications in many disciplines including physical sciences such as biology [67, 34], chemistry [156], ecology [16][104], neuroscience [102], and physics [63] as well as technology and engineering fields such as image and signal processing [53], computer science [15], information theory [43, page 71], and telecommunications [97][11][12].
    [Show full text]
  • Newton's Notebook
    Newton’s Notebook The Haverford School’s Math & Applied Math Journal Issue I Spring 2017 The Haverford School Newton’s Notebook Spring 2017 “To explain all nature is too difficult a task for any one man or even for any one age. ‘Tis much better to do a little with certainty & leave the rest for others that come after you.” ~Isaac Newton Table of Contents Pure Mathematics: 7 The Golden Ratio.........................................................................................Robert Chen 8 Fermat’s Last Theorem.........................................................................Michael Fairorth 9 Math in Coding............................................................................................Bram Schork 10 The Pythagoreans.........................................................................................Eusha Hasan 12 Transfinite Numbers.................................................................................Caleb Clothier 15 Sphere Equality................................................................................Matthew Baumholtz 16 Interesting Series.......................................................................................Aditya Sardesi 19 Indirect Proofs..............................................................................................Mr. Patrylak Applied Mathematics: 23 Physics in Finance....................................................................................Caleb Clothier 26 The von Bertalanffy Equation..................................................................Will
    [Show full text]
  • Brownian Motion∗
    GENERAL ARTICLE Brownian Motion∗ B V Rao This article explains the history and mathematics of Brown- ian motion. 1. Introduction Brownian Motion is a random process first observed by the Scot- tish botanist Robert Brown; later independently proposed as a B V Rao, after retiring from the Indian Statistical model for stock price fluctuations by the French stock market an- Institute, is currently at the alyst Louis Bachelier; a little later German-born Swiss/American Chennai Mathematical Albert Einstein and Polish physicist Marian Smoluchowski ar- Institute. rived at the same process from molecular considerations; and still later Norbert Wiener created it mathematically. Once the last step was taken and matters were clarified, Andrei Kolmogorov (Rus- sian) and Shizuo Kakutani (Japanese) related this to differential equations. Paul Levy (French) and a long list of mathematicians decorated this with several jewels with final crowns by Kiyoshi Ito (Japanese) in the form of Stochastic Calculus and by Paul Malliavin (French) with Stochastic Calculus of Variations. Once crowned, it started ruling both Newtonian world and Quantum world. We shall discuss some parts of this symphony. 2. Robert Brown Robert Brown was a Scottish botanist famous for classification Keywords of plants. He noticed, around 1827, that pollen particles in water Brownian motion, heat equation, suspension displayed a very rapid, highly irregular zig-zag mo- Kolmogorov’s formulation of prob- ability, random walk, Wiener inte- tion. He was persistent to find out causes of this motion:
    [Show full text]
  • FINITE ADDITIVITY VERSUS COUNTABLE ADDITIVITY: De FINETTI and SAVAGE
    FINITE ADDITIVITY VERSUS COUNTABLE ADDITIVITY: De FINETTI AND SAVAGE N. H. BINGHAM Electronic J. History of Probability and Statistics 6.1 (2010), 33p R´esum´e L'arri`ere-planhistorique, d'abord de l'additivit´ed´enombrable et puis de l'additivit´efinie, est ´etudi´eici. Nous discutons le travail de de Finetti (en particulier, son livre posthume, de Finetti (2008)), mais aussi les travaux de Savage. Tous deux sont surtout (re)connus pour leurs contributions au domaine des statistiques; nous nous int´eressonsici `aleurs apports du point de vue de la th´eoriedes probabilit´es.Le probl`emede mesure est discut´e{ la possibilit´ed'´etendreune mesure `a tout sous-ensemble d'un espace de proba- bilit´e. La th´eoriedes jeux de hasard est ensuite pr´esent´eepour illustrer les m´eritesrelatifs de l'additivit´efinie et d´enombrable. Puis, nous consid´eronsla coh´erencedes d´ecisions,o`uun troisi`emecandidat apparait { la non-additivit´e. Nous ´etudionsalors l’influence de diff´erents choix d'axiomes de la th´eoriedes ensembles. Nous nous adressons aux six raisons avanc´espar Seidenfeld (2001) `al'appui de l'additivit´efinie, et faisons la critique des plusi`eresapproches `a la fr´equencelimite. Abstract The historical background of first countable additivity, and then finite ad- ditivity, in probability theory is reviewed. We discuss the work of the most prominent advocate of finite additivity, de Finetti (in particular, his posthu- mous book de Finetti (2008)), and also the work of Savage. Both were most noted for their contributions to statistics; our focus here is more from the point of view of probability theory.
    [Show full text]
  • Bachelier and His Times: a Conversation with Bernard Bru ∗†‡
    First appeared in FINANCE AND STOCHASTICS (2001) Appears in the book MATHEMATICAL FINANCE -- BACHELIER CONGRESS 2000 H. Geman et al. editors, 2002, Springer Verlag Bachelier and his Times: A Conversation with Bernard Bru ¤yz Murad S. Taqqu Boston University April 25, 2001 Abstract Louis Bachelier defended his thesis \Theory of Speculation" in 1900. He used Brownian motion as a model for stock exchange performance. This conversation with Bernard Bru illustrates the scienti¯c climate of his times and the conditions under which Bachelier made his discover- ies. It indicates that Bachelier was indeed the right person at the right time. He was involved with the Paris stock exchange, was self-taught but also took courses in probability and on the theory of heat. Not being a part of the \scienti¯c establishment," he had the opportunity to develop an area that was not of interest to the mathematicians of the period. He was the ¯rst to apply the trajectories of Brownian mo- tion, and his theories pre¯gure modern mathematical ¯nance. What follows is an edited and expanded version of the original conversation with Bernard Bru. Bernard Bru is the author, most recently, of Borel, L¶evy, Neyman, Pearson et les autres [38]. He is a professor at the University of Paris V where he teaches mathematics and statistics. With Marc Barbut and Ernest Coumet, he founded the seminars on the history of Probability at the EHESS (Ecole¶ des Hautes Etudes¶ en Sciences Sociales), which bring together researchers in mathematics, philosophy and the human- ities. ¤This article ¯rst appeared in Finance and Stochastics [119].
    [Show full text]
  • Once in a Lifetime March 29, 2020
    Once In A Lifetime March 29, 2020 The Moving Finger writes; and, having writ, Moves on: nor all thy Piety nor Wit Shall lure it back to cancel half a Line, Nor all thy Tears wash out a Word of it. - Rubaiyat of Omar Khayyam (c. 1080) That's a poem attributed to Omar Khayyam, an 11th century Persian philosopher and all-around genius who lived near the modern-day city of Qom, the epicenter of the COVID-19 plague wracking Iran today. Here's another philosopher and all-around genius, David Byrne, saying the same thing one thousand years later. And you may ask yourself Am I right? Am I wrong? And you may say to yourself "My God! What have I done?" - Once In A Lifetime (1981) ©2020 Ben Hunt 1 All rights reserved. David Byrne lives in the modern-day city of New York, the epicenter of the COVID-19 plague wracking the United States today. It's all the same, you know. The dad in Qom coughing up a lung who loves his kids and is loved by them is exactly the same as the dad in New York coughing up a lung who loves his kids and is loved by them. I know we don't think of it that way. Hell, I know plenty of people in my home state of Alabama who don't even think a dad in Montgomery is the same as a dad in New York, much less a dad in freakin' Qom, Iran. But they are. The same, that is.
    [Show full text]
  • Leonard Savage, the Ellsberg Paradox and the Debate on Subjective Probabilities: Evidence from the Archives
    LEONARD SAVAGE, THE ELLSBERG PARADOX AND THE DEBATE ON SUBJECTIVE PROBABILITIES: EVIDENCE FROM THE ARCHIVES. BY CARLO ZAPPIA* Abstract This paper explores archival material concerning the reception of Leonard J. Savage’s foundational work of rational choice theory in its subjective-Bayesian form. The focus is on the criticism raised in the early 1960s by Daniel Ellsberg, William Fellner and Cedric Smith, who were supporters of the newly developed subjective approach, but could not understand Savage’s insistence on the strict version he shared with Bruno de Finetti. The episode is well-known, thanks to the so-called Ellsberg Paradox and the extensive reference made to it in current decision theory. But Savage’s reaction to his critics has never been examined. Although Savage never really engaged with the issue in his published writings, the private exchange with Ellsberg and Fellner, and with de Finetti about how to deal with Smith, shows that Savage’s attention to the generalization advocated by his correspond- ents was substantive. In particular, Savage’s defence of the normative value of rational choice the- ory against counterexamples such as Ellsberg’s did not prevent him from admitting that he would give careful consideration to a more realistic axiomatic system, should the critics be able to provide one. * Dipartimento di Economia, Universita degli Studi di Siena. Contact: [email protected] This “preprint” is the peer-reviewed and accepted typescript of an article that is forthcoming in revised form, after minor editorial changes, in the Journal of the History of Economic Thought (ISSN: 1053-8372), issue TBA.
    [Show full text]
  • Bayesian Statistics: Thomas Bayes to David Blackwell
    Bayesian Statistics: Thomas Bayes to David Blackwell Kathryn Chaloner Department of Biostatistics Department of Statistics & Actuarial Science University of Iowa [email protected], or [email protected] Field of Dreams, Arizona State University, Phoenix AZ November 2013 Probability 1 What is the probability of \heads" on a toss of a fair coin? 2 What is the probability of \six" upermost on a roll of a fair die? 3 What is the probability that the 100th digit after the decimal point, of the decimal expression of π equals 3? 4 What is the probability that Rome, Italy, is North of Washington DC USA? 5 What is the probability that the sun rises tomorrow? (Laplace) 1 1 1 My answers: (1) 2 (2) 6 (3) 10 (4) 0.99 Laplace's answer to (5) 0:9999995 Interpretations of Probability There are several interpretations of probability. The interpretation leads to methods for inferences under uncertainty. Here are the 2 most common interpretations: 1 as a long run frequency (often the only interpretation in an introductory statistics course) 2 as a subjective degree of belief You cannot put a long run frequency on an event that cannot be repeated. 1 The 100th digit of π is or is not 3. The 100th digit is constant no matter how often you calculate it. 2 Similarly, Rome is North or South of Washington DC. The Mathematical Concept of Probability First the Sample Space Probability theory is derived from a set of rules and definitions. Define a sample space S, and A a set of subsets of S (events) with specific properties.
    [Show full text]
  • Ronald A. Thisted April, 1997
    Ronald A. Thisted April, 1997 (revised) Department of Statistics Robert Wood Johnson Clinical Scholars Program The University of Chicago Department of Health Studies 5734 University Avenue 5841 South Maryland Avenue (MC 2007) Chicago, IL 60637 Chicago, Illinois 60637 (773) 702-8332 (773) 702-2313 email: [email protected] http://www.stat.uchicago.edu/~thisted Education: Ph.D. (Statistics) Stanford University, 1976. M.S. (Statistics) Stanford University, 1973. B.A. (Mathematics, Philosophy) Pomona College, 1972. Magna cum laude Professional: All at the University of Chicago: 1996- Professor, Department of Health Studies 1993- Co-Director, Robert Wood Johnson Clinical Scholars Program 1993- Professor, Committee on Clinical Pharmacology 1992- Professor, Departments of Statistics, Anesthesia & Critical Care, and the College 1989-1992 Associate Professor, Department of Anesthesia and Critical Care 1982-1992 Associate Professor, Department of Statistics and the College 1979-1982 Leonard Jimmie Savage Assistant Professor, Department of Statistics and the College 1976-1982 Assistant Professor, Department of Statistics and the College Honors: Phi Beta Kappa, Pomona College, 1972. National Science Foundation Graduate Fellow, 1973-1976. Sigma Xi, The University of Chicago, 1977. The Llewellyn John and Harriet Manchester Quantrell Award for Excellence in Undergraduate Teaching, 1981. Faculty, National Center for Advanced Medical Education, 1990-1992. Professional Societies: American Association for the Advancement of Science (Elected Fellow,
    [Show full text]
  • Léon Walras, Irving Fisher and the Cowles Approach to General Equilibrium Analysis
    LÉON WALRAS, IRVING FISHER AND THE COWLES APPROACH TO GENERAL EQUILIBRIUM ANALYSIS By Robert W. Dimand December 2019 COWLES FOUNDATION DISCUSSION PAPER NO. 2205 COWLES FOUNDATION FOR RESEARCH IN ECONOMICS YALE UNIVERSITY Box 208281 New Haven, Connecticut 06520-8281 http://cowles.yale.edu/ Léon Walras, Irving Fisher and the Cowles Approach to General Equilibrium Analysis Robert W. Dimand Department of Economics, Brock University, St. Catharines, ON L2S 3A1, Canada E-mail: [email protected] Abstract: This paper explores the relationship of Walras’s work to a particularly influential tradition of general equilibrium, that associated with the Cowles Commission for Research in Economics in Colorado in the 1930s and at the University of Chicago from 1939 to 1955, and its successor, the Cowles Foundation, at Yale University from 1955. Irving Fisher introduced general equilibrium analysis into North America with his 1891 Yale dissertation Mathematical Investigations in the Theory of Value and Prices (published 1892) and was responsible in 1892 for the first English translation of a monograph by Walras. Fisher was only able to obtain copies of books by Walras and Edgeworth when his thesis was almost ready for submission, discovering that he had independently reinvented a general equilibrium approach already developed by others, but went beyond Walras in constructing a hydraulic mechanism to simulate computation of general equilibrium and, before Pareto, in using indifference curves. Fisher was closely involved with Alfred Cowles in the Cowles Commission, the Econometric Society and Econometrica in the 1930s, promoting formal mathematical and statistical methods in economics, including drawing attention to the contributions of Walras, Edgeworth and Pareto.
    [Show full text]
  • When Did Bayesian Inference Become “Bayesian”?
    Bayesian Analysis (2003) 1, Number 1, pp. 1–41 When Did Bayesian Inference Become “Bayesian”? Stephen E. Fienberg Department of Statistics, Cylab, and Center for Automated Learning and Discovery Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A. Abstract. While Bayes’ theorem has a 250-year history and the method of in- verse probability that flowed from it dominated statistical thinking into the twen- tieth century, the adjective “Bayesian” was not part of the statistical lexicon until relatively recently. This paper provides an overview of key Bayesian develop- ments, beginning with Bayes’ posthumously published 1763 paper and continuing up through approximately 1970, including the period of time when “Bayesian” emerged as the label of choice for those who advocated Bayesian methods. Keywords: Bayes’ Theorem; Classical statistical methods; Frequentist methods; Inverse probability; Neo-Bayesian revival; Stigler’s Law of Eponymy; Subjective probability. 1 Introduction What’s in a name? It all depends, especially on the nature of the entity being named, but when it comes to statistical methods, names matter a lot. Whether the name is eponymous (as in Pearson’s chi-square statistic1, Student’s t-test, Hotelling’s T 2 statistic, the Box-Cox transformation, the Rasch model, and the Kaplan-Meier statistic) or “generic” (as in correlation coefficient or p-value) or even whimsical (as in the jackknife2 or the bootstrap3), names in the statistical literature often signal the adoption of new statistical ideas or shifts in the acceptability of sta- tistical methods and approaches.4 Today statisticians speak and write about Bayesian statistics and frequentist or classical statistical methods, and there is even a journal of Bayesian Analysis, but few appear to know where the descriptors “Bayesian” and “frequentist” came from or how they arose in the history of their field.
    [Show full text]