Interpreting Probability: Controversies and Developments in the Early Twentieth Century (Cambridge Studies in Probability, Induction and Decision Theory)

The term probability can be used in two main senses. In the frequency interpretation it is a limiting ratio in a sequence of repeatable events. In the Bayesian view, probability is a mental construct representing uncertainty. This 2002 book is about these two types of probability and investigates how, despite being adopted by scientists and statisticians in the eighteenth and nineteenth centuries, Bayesianism was discredited as a theory of scientific inference during the 1920s and 1930s. Through the examination of a dispute between two British scientists, the author argues that a choice between the two interpretations is not forced by pure logic or the mathematics of the situation, but depends on the experiences and aims of the individuals involved. The book should be of interest to students and scientists interested in statistics and probability theories and to general readers with an interest in the history, sociology and philosophy of science. Cover......Page 1 Half-title......Page 3 Series-title......Page 5 Title......Page 7 Copyright......Page 8 Contents......Page 9 Acknowledgments......Page 13 1.1. THE MEANING OF PROBABILITY......Page 15 1.2. THE HISTORY OF PROBABILITY......Page 16 1.3. SCOPE OF THIS BOOK......Page 18 1.4. METHODS AND ARGUMENT......Page 19 1.5. SYNOPSIS AND AIMS......Page 25 2.1. INTRODUCTION......Page 28 2.2. EARLY APPLICATIONS OF THE PROBABILITY CALCULUS......Page 29 2.3. RESISTANCE TO THE CALCULATION OF UNCERTAINTY......Page 31 2.4. THE DOCTRINE OF CHANCES......Page 33 2.5. INVERSE PROBABILITY......Page 37 2.6. LAPLACEAN PROBABILITY......Page 41 2.7. THE ECLIPSE OF LAPLACEAN PROBABILITY......Page 42 2.8. SOCIAL STATISTICS......Page 47 2.9. THE RISE OF THE FREQUENCY INTERPRETATION OF PROBABILITY......Page 50 2.10. OPPOSITION TO SOCIAL STATISTICS AND PROBABILISTIC METHODS......Page 52 2.11. PROBABILITY THEORY IN THE SCIENCES: EVOLUTION AND BIOMETRICS......Page 55 2.12. THE INTERPRETATION OF PROBABILITY AROUND THE END OF THE NINETEENTH CENTURY......Page 61 3.1. R.A. FISHER’S EARLY YEARS......Page 66 3.2. EVOLUTION – THE BIOMETRICIANS VERSUS THE MENDELIANS......Page 67 3.3. FISHER'S EARLY WORK......Page 70 3.4. THE CLASH WITH PEARSON......Page 73 3.5.1. Fisher’s new version of probability......Page 75 3.5.2. The papers of 1921 and 1922......Page 76 3.5.3. The Pearson–Fisher feud......Page 79 3.6. THE MOVE TO ROTHAMSTED: EXPERIMENTAL DESIGN......Page 84 3.7. THE POSITION IN 1925 – STATISTICAL METHODS FOR RESEARCH WORKERS......Page 86 3.8. THE DEVELOPMENT OF FIDUCIAL PROBABILITY......Page 89 3.9. FISHER'S POSITION IN 1932......Page 93 4.1. JEFFREYS’S BACKGROUND AND EARLY CAREER......Page 95 4.2. THE METEOROLOGICAL OFFICE......Page 97 4.3. DOROTHY WRINCH......Page 99 4.4. BROAD’S 1918 PAPER......Page 101 4.5. WRINCH AND JEFFREYS TACKLE PROBABILITY......Page 103 4.6.1. General relativity......Page 106 4.6.2. The Oppau explosion......Page 108 4.6.3. New work on probability – John Maynard Keynes......Page 110 4.6.4. Other factors......Page 115 4.7.1. The Simplicity Postulate......Page 117 4.7.2. The papers of 1921 and 1923......Page 121 4.8. THE COLLABORATION STARTS TO CRUMBLE......Page 123 4.9. JEFFREYS BECOMES ESTABLISHED......Page 125 4.10.1. Science and probability......Page 127 4.10.2. Scientific Inference......Page 128 4.11.1. The status of prior probabilities......Page 133 4.11.2. J.B.S. Haldane’s paper......Page 135 4.12. JEFFREYS’S POSITION IN 1932......Page 140 5.1. ERRORS OF OBSERVATION AND SEISMOLOGY......Page 142 5.2. FISHER RESPONDS......Page 147 5.3. OUTLINE OF THE DISPUTE......Page 151 5.4. THE MATHEMATICS OF THE DISPUTE......Page 153 5.5. PROBABILITY AND SCIENCE......Page 157 5.5.1. The status of prior probabilities......Page 158 5.5.2. The Principle of Insufficient Reason......Page 162 5.5.3. The definition of probability......Page 164 5.5.4. Logical versus epistemic probabilities......Page 166 5.5.5. Role of science: inference and estimation......Page 168 5.6. CONCLUSIONS......Page 176 6.1. INTRODUCTION......Page 185 6.2.1. The position of the discipline to 1930......Page 186 6.2.2. Mathematical statistics......Page 187 6.2.3. The Neyman–Fisher dispute......Page 190 6.2.4. The Royal Statistical Society......Page 194 6.2.5. The reading of Fisher’s 1935 paper......Page 197 6.2.6. Statisticians and inverse probability......Page 201 6.3.1. Statistics in the social sciences......Page 205 6.3.2. Statistics reformed for the social sciences......Page 208 6.3.3. The social sciences reformed for statistics......Page 211 6.4.2. Probability and determinism: statistical physics......Page 213 6.4.3. Probability at the turn of the century......Page 216 6.4.4. The rejection of causality......Page 218 6.4.5. The view in the 1930s......Page 220 6.4.6. The interpretation of probability in physics......Page 223 6.4.7. Quantum mechanics and inverse probability......Page 225 6.5. PROBABILITY IN BIOLOGY......Page 227 6.6.1. Richard von Mises’s theory......Page 230 6.6.2. Andrei Kolmogorov’s theory......Page 233 6.7. CONCLUSIONS......Page 234 7.1. EPILOGUE......Page 236 7.2. CONCLUSIONS......Page 240 Appendix 1 Sources for Chapter 2......Page 245 Appendix 2 Bayesian Conditioning as a Model of Scientific Inference......Page 249 Appendix 3 Abbreviations Used in the Footnotes......Page 251 Bibliography......Page 253 Index......Page 267 This book is a study of the concept of probability as it has been used and applied across a number of scientific disciplines from genetics to geophysics. Probability has a dual aspect: sometimes it is a numerical ratio; sometimes, in the Bayesian interpretation, a degree of belief. David Howie examines probabilistic theories of scientific knowledge, and asks how, despite being adopted by many scientists and statisticians in the eighteenth and nineteenth centuries, Bayesianism was discredited as a theory of scientific inference during the 1920s and 1930s. Through a close examination of a dispute between two British scientists, the author argues that a choice between the two interpretations of probability is not forced by pure logic, or the mathematics of the situation, but depends on the experiences and aims of the individuals involved, and their views of the correct form of scientific inquiry.

this Investigates How Bayesianism As One Theory Of Probability Was Discredited In The 1920s And 1930s.

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howie Focuses On Two Types Of Probability, The Frequency Interpretation And The Bayesian Interpretation,and Investigates How, After Widespread Adoption By Scientists And Statisticians, Bayesianism Was Discredited As A Theory Of Scientific Inference In The 1920s And 1930s. The Work Of Two British Scientists, Sir Harold Jeffreys (1891-1989) And Sir Ronald Aylmer Fisher (1890-1962), And Their Dispute During The 1930s, Is Central To Howie's Analysis. This Volume Grew From The Author's Recent Doctoral Dissertation In The Department Of History And Sociology Of Science At The U. Of Pennsylvania. For Academics And Students In History, Philosophy, And Sociology Of Science, Particularly In Probability And Statistics. Annotation C. Book News, Inc., Portland, Or

This 2002 book investigates how Bayesianism as one theory of probability was discredited during the 1920s and 1930s by two British scientists and shows how the choice of a certain interpretation of probability depends on the experiences of the individuals involved.