A History Of Inverse Probability: From Thomas Bayes To Karl Pearson (studies In The History Of Mathematics And Physical Sciences)

Library of Congress Cataloging-in-Publication Data Dale, Andrew I. A history of inverse probability: from Thomas Bayes to Karl Pearson I Andrew I. Dale. p. em. -(Studies in the history of mathematics and the physical sciences; 16) Includes bibliographical references and index. ISBN 0-387-9762().5 1. It is thought as necessary to write a Preface before a Book, as it is judged civil, when you invite a Friend to Dinner, to proffer him a Glass of Hock beforehand for a Whet. John Arbuthnot, from the preface to his translation of Huygens's'De Ratiociniis in Ludo Alooe'. Prompted by an awareness of the importance of Bayesian ideas in modern statistical theory and practice, I decided some years ago to undertake a study of the development and growth of such ideas. At the time it seemed appropriate to begin such an investigation with an examination of Bayes's Essay towards solving a problem in the doctrine of chances and Laplace's Theorie analytique des probabilites, and then to pass swiftly on to a brief consideration of other nineteenth century works before turning to what would be the main topic of the treatise, videlicet the rise of Bayesian statis­ tics from the 1950's to the present day. It soon became apparent, however, that the amount of Bayesian work published was such that a thorough investigation of the topic up to the 1980's would require several volumes - and also run the risk of incurring the wrath of extant authors whose writings would no doubt be misrepre­ sented, or at least be so described. It seemed wise, therefore, to restrict the period and the subject under study in some way, and I decided to con­ centrate my attention on inverse probability from Thomas Bayes to Karl Pearson. It is thought as necessary to write a Preface before a Book, as it is judged civil, when you invite a Friend to Dinner, to proffer him a Glass of Hock beforehand for a Whet. John Arbuthnot, from the preface to his translation of Huygens's "De Ratiociniis in Ludo Alooe". Prompted by an awareness of the importance of Bayesian ideas in modern statistical theory and practice, I decided some years ago to undertake a study of the development and growth of such ideas. At the time it seemed appropriate to begin such an investigation with an examination of Bayes's Essay towards solving a problem in the doctrine of chances and Laplace's Theorie analytique des probabilites, and then to pass swiftly on to a brief consideration of other nineteenth century works before turning to what would be the main topic of the treatise, videlicet the rise of Bayesian statis­ tics from the 1950's to the present day. It soon became apparent, however, that the amount of Bayesian work published was such that a thorough investigation of the topic up to the 1980's would require several volumes - and also run the risk of incurring the wrath of extant authors whose writings would no doubt be misrepre­ sented, or at least be so described. It seemed wise, therefore, to restrict the period and the subject under study in some way, and I decided to con­ centrate my attention on inverse probability from Thomas Bayes to Karl Pearson "This is a history of the use of Bayes's theorem over 150 years, from its discovery by Thomas Bayes to the rise of the statistical competitors in the first third of the twentieth century. In the new edition the author's concern is the foundations of statistics, in particular, the examination of the development of one of the fundamental aspects of Bayesian statistics. The reader will find new sections on contributors to the theory omitted from the first edition, which will shed light on the use of inverse probability by nineteenth century authors. In addition, there is amplified discussion of relevant work from the first edition. This text will be a valuable reference source in the wider field of the history of statistics and probability."--BOOK JACKET. Front Matter....Pages i-xx Thomas Bayes: a biographical sketch....Pages 1-15 Bayes’s Essay....Pages 16-29 Commentary on Bayes’s Essay....Pages 30-51 Miscellaneous Investigations from 1761 to 1822....Pages 52-100 Condorcet....Pages 101-144 Laplace....Pages 145-256 Poisson to Venn....Pages 257-326 Laurent to Pearson....Pages 327-392 Back Matter....Pages 393-495