A History of Inverse Probability

This a history of the use of Bayes' 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.

1 On inverse probability.- 1.1 Introduction.- 1.2 Inverse problems.- 1.3 Inverse probability.- 2 Thomas Bayes: a biographical sketch.- 2.1 Appendix 2.1.- 2.2 Appendix 2.2.- 2.3 Appendix 2.3.- 2.4 Appendix 2.4.- 3 Bayes’s Essay.- 3.1 Introduction.- 3.2 Price’s introduction.- 3.3 The first section.- 3.4 The second section.- 3.5 The Appendix.- 3.6 Summary.- 4 Commentary on Bayes’s Essay.- 4.1 Introduction.- 4.2 Price’s introduction.- 4.3 The first section.- 4.4 The second section.- 4.5 The postulate and the scholium.- 4.6 The Appendix.- 4.7 Appendix 4.1.- 5 Miscellaneous Investigations from 1761 to 1822.- 5.1 Moses Mendelssohn (1729–1786).- 5.2 Johann Heinrich Lambert (1728–1777).- 5.3 Bayes and Price.- 5.3.1 Bayes’s paper on divergent series.- 5.3.2 The supplement to the Essay.- 5.3.3 Bayes’s Notebook.- 5.3.4 Price’s Four Dissertations.- 5.4 John Michell (1724–1793).- 5.5 Nicolas de Beguelin (1714–1789).- 5.6 Joseph Louis de la Grange (1736–1813).- 5.7 William Emerson (1701–1782).- 5.8 George Louis Leclerc, Comte de Buffon (1707–1788).- 5.9 Jean Trembley (1749–1811).- 5.10 Pierre Prevost (1751–1839) & Simon Antoine Jean Lhuilier (1750–1840).- 5.11 Carl Friedrich Gauss (1777–1855).- 5.12 William Morgan (1750–1833).- 5.13 Sylvestre François Lacroix (1765–1843).- 5.14 Conclusions and Summary.- 5.15 Appendix 5.1.- 6 Condorcet.- 6.1 Introduction.- 6.2 Unpublished manuscripts.- 6.3 The Memoir.- 6.4 Probabilité, from the Encyclopédie Méitthodique.- 6.5 The Essay.- 6.6 Discours sur l’astronomie et le calcul des probabilités.- 6.7 Eléméns du calcul des probabilités.- 6.8 Appendix 6.1.- 6.9 Appendix 6.2.- 7 Laplace.- 7.1 Introduction.- 7.2 Sur les suites récurro-récurrentes.- 7.3 Sur la probabilité des causes.- 7.4 Sur l’intégration des équations différentielles.- 7.5 Recherches sur le milieu.- 7.6 Sur les probabilités.- 7.7 Sur les approximations des formules (suite).- 7.8 Sur les naissances.- 7.9 Sur les probabilités.- 7.10 Sur les approximations des formules.- 7.11 Supplément: sur les approximations des formules.- 7.12 Sur les intégrales définies.- 7.13 Sur les comètes.- 7.14 Two memoirs.- 7.15 Théorie analytique des probabilités.- 7.15.1 Introduction.- 7.15.2 Livre 1: Calcul des fonctions génératrices.- 7.15.3 Livre 2: Théorie générale des probabilités.- 7.16 Appendix 7.1.- 7.17 Appendix 7.2.- 7.18 Appendix 7.3.- 8 Poisson to Whitworth.- 8.1 Siméon-Denis Poisson (1781–1840).- 8.2 John William Lubbock (1803–1865) & John Elliot Drinkwater-Bethune (1801–1851).- 8.3 Bernard Bolzano (1781–1848).- 8.4 Augustus de Morgan (1806–1871).- 8.5 Irenée Jules Bienaymé (1796–1878).- 8.6 Mikhail Vasil’evich Ostrogradski? (1801–1861).- 8.7 Thomas Galloway (1796–1851).- 8.8 Eugène Charles Catalan (1814–1894).- 8.9 Jacob Friedrich Friess (1773–1843).- 8.10 Antoine Augustin Cournot (1801–1877).- 8.11 John Stuart Mill (1806–1873).- 8.12 Lambert Adolphe Jacques Quetelet(1796–1874).- 8.13 Mathurin-Claude-Charles Gouraud (1823-?).- 8.14 Robert Leslie Ellis (1817–1859).- 8.15 Viktor Yakovlevitch Buniakovski? (1804–1889).- 8.16 William Fishburn Donkin (1814–1869).- 8.17 George Boole (1815–1864).- 8.18 Charles Hughes Terrot (1790–1872).- 8.19 Anton Meyer (1802–1857).- 8.20 Albert Wild.- 8.21 John Venn (1834–1923).- 8.22 William Allen Whitworth (1840–1905).- 9 Laurent to Pearson.- 9.1 Mathieu Paul Hermann Laurent (1841–1908).- 9.2 Cecil James Monro (1833–1882).- 9.3 William Stanley Jevons (1835–1882).- 9.4 Rudolf Hermann Lotze (1817–1881).- 9.5 Charles Saunders Peirce (1839–1914).- 9.6 Bing’s paradox.- 9.7 A question of antisepticism.- 9.8 Francis Ysidro Edgeworth (1845–1926).- 9.9 Charles Lutwidge Dodgson (1832–1898).- 9.10 Morgan William Crofton (1826–1915).- 9.11 Johannes von Kries (1853–1928).- 9.12 George Francis Hardy (1855–1914).- 9.13 Joseph Louis François Bertrand (1822–1900).- 9.14 George Chrystal (1851–1911).- 9.15 William Matthew Makeham (1826–1891).- 9.16 Henri Poincaré (1854–1912).- 9.17 Hugh MacColl (1837–1909).- 9.18 Karl Pearson (1857–1936).- 9.19 Miscellaneous.- 9.20 Appendix 9.1.- 9.21 Appendix 9.2.- Notes.- Epiphonema.