ベイズの定理をめぐる論争1919-1939年<br>Interpreting Probability : Controversies and Developments in the Early Twentieth Century (Cambridge Studies in Probability, Induction, and Decision Th

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ベイズの定理をめぐる論争1919-1939年
Interpreting Probability : Controversies and Developments in the Early Twentieth Century (Cambridge Studies in Probability, Induction, and Decision Th

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  • 製本 Hardcover:ハードカバー版/ページ数 262 p.
  • 言語 ENG
  • 商品コード 9780521812511
  • DDC分類 519.542

基本説明

Shows how the choice of a certain interpretation of probability depends on the experiences of the individuals involved.

Full Description


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.

Table of Contents

Acknowledgments                                    xi
Introduction 1 (13)
The meaning of probability 1 (1)
The history of probability 2 (2)
Scope of this book 4 (1)
Methods and argument 5 (6)
Synopsis and aims 11 (3)
Probability up to the Twentieth Century 14 (38)
Introduction 14 (1)
Early applications of the probability 15 (2)
calculus
Resistance to the calculation of uncertainty 17 (2)
The doctrine of chances 19 (4)
Inverse probability 23 (4)
Laplacean probability 27 (1)
The eclipse of Laplacean probability 28 (5)
Social statistics 33 (3)
The rise of the frequency interpretation of 36 (2)
probability
Opposition to social statistics and 38 (3)
probabilistic methods
Probability theory in the sciences: 41 (6)
evolution and biometrics
The interpretation of probability around 47 (5)
the end of the nineteenth century
R.A. Fisher and Statistical Probability 52 (29)
R.A. Fisher's early years 52 (1)
Evolution -- the biometricians versus the 53 (3)
Mendelians
Fisher's early work 56 (3)
The clash with Pearson 59 (2)
Fisher's rejection of inverse probability 61 (9)
Fisher's new version of probability 61 (1)
The papers of 1921 and 1922 62 (3)
The Pearson--Fisher feud 65 (5)
The move to Rothamsted: experimental design 70 (2)
The position in 1925 -- Statistical Methods 72 (3)
for Research Workers
The development of fiducial probability 75 (4)
Fisher's position in 1932 79 (2)
Harold Jeffreys and Inverse Probability 81 (47)
Jeffreys's background and early career 81 (2)
The Meteorological Office 83 (2)
Dorothy Wrinch 85 (2)
Broad's 1918 paper 87 (2)
Wrinch and Jeffreys tackle probability 89 (3)
After the first paper 92 (11)
General relativity 92 (2)
The Oppau explosion 94 (2)
New work on probability -- John Maynard 96 (5)
Keynes
Other factors 101(2)
Probability theory extended 103(6)
The Simplicity Postulate 103(4)
The papers of 1921 and 1923 107(2)
The collaboration starts to crumble 109(2)
Jeffreys becomes established 111(2)
Probability and learning from experience -- 113(6)
Scientific Inference
Science and probability 113(1)
Scientific Inference 114(5)
Jeffreys and prior probabilities 119(7)
The status of prior probabilities 119(2)
J.B.S. Haldane's paper 121(5)
Jeffreys's position in 1932 126(2)
The Fisher--Jeffreys Exchange, 1932-1934 128(43)
Errors of observation and seismology 128(5)
Fisher responds 133(4)
Outline of the dispute 137(2)
The mathematics of the dispute 139(4)
Probability and science 143(19)
The status of prior probabilities 144(4)
The Principle of Insufficient Reason 148(2)
The definition of probability 150(2)
Logical versus epistemic probabilities 152(2)
Role of science: inference and estimation 154(8)
Conclusions 162(9)
Probability During the 1930s 171(51)
Introduction 171(1)
Probability in statistics 172(19)
The position of the discipline to 1930 172(1)
Mathematical statistics 173(3)
The Neyman--Fisher dispute 176(4)
The Royal Statistical Society 180(3)
The reading of Fisher's 1935 paper 183(4)
Statisticians and inverse probability 187(4)
Probability in the social sciences 191(8)
Statistics in the social sciences 191(3)
Statistics reformed for the social 194(3)
sciences
The social sciences reformed for 197(2)
statistics
Probability in physics 199(14)
General remarks 199(1)
Probability and determinism: statistical 199(3)
physics
Probability at the turn of the century 202(2)
The rejection of causality 204(2)
The view in the 1930s 206(3)
The interpretation of probability in 209(2)
physics
Quantum mechanics and inverse probability 211(2)
Probability in biology 213(3)
Probability in mathematics 216(4)
Richard von Mises's theory 216(3)
Andrei Kolmogorov's theory 219(1)
Conclusions 220(2)
Epilogue and Conclusions 222(9)
Epilogue 222(4)
Conclusions 226(5)
Appendix 1 Sources for Chapter 2 231(4)
Appendix 2 Bayesian Conditioning as a Model of 235(2)
Scientific Inference
Appendix 3 Abbreviations Used in the Footnotes 237(2)
Bibliography 239(14)
Index 253