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AuthorDale, Andrew I. author
TitleA History of Inverse Probability [electronic resource] : From Thomas Bayes to Karl Pearson / by Andrew I. Dale
ImprintNew York, NY : Springer US, 1991
Connect tohttp://dx.doi.org/10.1007/978-1-4684-0415-9
Descript online resource

SUMMARY

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 statisยญ 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 misrepreยญ 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 conยญ centrate my attention on inverse probability from Thomas Bayes to Karl Pearson


CONTENT

1 Thomas Bayes: a biographical sketch -- 1.1 Appendix 1.1 -- 1.2 Appendix 1.2 -- 1.3 Appendix 1.3 -- 1.4 Appendix 1.4 -- 2 Bayesโ{128}{153}s Essay -- 2.1 Introduction -- 2.2 Priceโ{128}{153}s introduction -- 2.3 The first section -- 2.4 The second section -- 2.5 The Appendix -- 2.6 Summary -- 3 Commentary on Bayesโ{128}{153}s Essay -- 3.1 Introduction -- 3.2 Priceโ{128}{153}s introduction -- 3.3 The first section -- 3.4 The second section -- 3.5 The postulate and the scholium -- 3.6 The Appendix -- 3.7 Appendix 3.1 -- 4 Miscellaneous Investigations from 1761 to 1822 -- 4.1 Moses Mendelssohn (1729โ{128}{147}1786) -- 4.2 Bayes and Price -- 4.3 John Michell (1724โ{128}{147}1793) -- 4.4 Nicolas de Beguelin (1714โ{128}{147}1789) -- 4.5 Joseph Louis de la Grange (1736โ{128}{147}1813) -- 4.6 William Emerson (1701โ{128}{147}1782) -- 4.7 George Louis Leclerc, Comte de Buffon (1707โ{128}{147}1788) -- 4.8 Jean Trembley (1749โ{128}{147}1811) -- 4.9 Pierre Prevost (1751โ{128}{147}1839) & Simon Antoine Jean Lhuilier (1750โ{128}{147}1840) -- 4.10 Carl Friedrich Gauss (1777โ{128}{147}1855) -- 4.11 William Morgan (1750โ{128}{147}1833) -- 4.12 Sylvestre Franร{135}ois Lacroix (1765โ{128}{147}1843) -- 4.13 Conclusions and Summary -- 4.14 Appendix 4.1 -- 5 Condorcet -- 5.1 Introduction -- 5.2 Unpublished manuscripts -- 5.3 The Memoir -- 5.4 Probabilitรฉ, from the Encyclopรฉdie Mรฉthodique -- 5.5 The Essay -- 5.6 Discours sur lโ{128}{153}astronomie et le calcul des probabilitรฉs -- 5.7 Elรฉmรฉns du calcul des probabilitรฉs -- 5.8 Appendix 5.1 -- 6 Laplace -- 6.1 Introduction -- 6.2 Sur les suites rรฉcurro-rรฉcurrentes -- 6.3 Sur la probabilitรฉ des causes -- 6.4 Sur lโ{128}{153}intรฉgration des รฉquations diffรฉrentielles -- 6.5 Sur les probabilitรฉs -- 6.6 Sur les approximations des formules (suite) -- 6.7 Sur les naissances -- 6.8 Sur les probabilitรฉs -- 6.9 Sur les approximations des formules -- 6.10 Supplรฉment: sur les approximations des formules -- 6.11 Sur les intรฉgrales dรฉfinies -- 6.12 Sur les comรจtes -- 6.13 Two memoirs -- 6.14 Thรฉorie analytique des probabilitรฉs -- 6.15 Appendix 6.1 -- 6.16 Appendix 6.2 -- 6.17 Appendix 6.3 -- 7 Poisson to Venn -- 7.1 Simรฉon-Denis Poisson (1781โ{128}{147}1840) -- 7.2 John William Lubbock (1803โ{128}{147}1865) & John Elliot Drinkwater-Bethune (1801โ{128}{147}1851) -- 7.3 Bernard Bolzano (1781โ{128}{147}1848) -- 7.4 Augustus de Morgan (1806โ{128}{147}1871) -- 7.5 Irenรฉe Jules Bienaymรฉ (1796โ{128}{147}1878) -- 7.6 Mikhail Vasilโ{128}{153}evich Ostrogradski? (1801โ{128}{147}1861) -- 7.7 Thomas Galloway (1796โ{128}{147}1851) -- 7.8 Eugรจne Charles Catalan (1814โ{128}{147}1894) -- 7.9 Jacob Friedrich Friess (1773โ{128}{147}1843) -- 7.10 Antoine Augustin Cournot (1801โ{128}{147}1877) -- 7.11 John Stuart Mill (1806โ{128}{147}1873) -- 7.12 Mathurin-Claude-Charles Gouraud (1823 โ{128}{147} ?) -- 7.13 Robert Leslie Ellis (1817โ{128}{147}1859) -- 7.14 William Fishburn Donkin (1814โ{128}{147}1869) -- 7.15 George Boole (1815โ{128}{147}1864) -- 7.16 Charles Hughes Terrot (1790โ{128}{147}1872) -- 7.17 Anton Meyer (1802โ{128}{147}1857) -- 7.18 Albert Wild -- 7.19 John Venn (1834โ{128}{147}1923) -- 8 Laurent to Pearson -- 8.1 Mathieu Paul Hermann Laurent (1841โ{128}{147}1908) -- 8.2 Cecil James Monro (1833โ{128}{147}1882) -- 8.3 William Stanley Jevons (1835โ{128}{147}1882) -- 8.4 Rudolf Hermann Lotze (1817โ{128}{147}1881) -- 8.5 Bingโ{128}{153}s paradox -- 8.6 A question of antisepticism -- 8.7 Francis Ysidro Edgeworth (1845โ{128}{147}1926) -- 8.8 Morgan William Crofton (1826โ{128}{147}1915) -- 8.9 Johannes von Kries (1853โ{128}{147}1928) -- 8.10 George Francis Hardy (1855โ{128}{147}1914) -- 8.11 Joseph Louis Franร{135}ois Bertrand (1822โ{128}{147}1900) -- 8.12 George Chrystal (1851โ{128}{147}1911) -- 8.13 William Matthew Makeham (1826โ{128}{147}1891) -- 8.14 Karl Pearson (1857โ{128}{147}1936) -- 8.15 Miscellaneous -- 8.16 Appendix 8.1 -- 8.17 Appendix 8.2 -- Notes -- Epiphonema


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