Title Page -- Copyright Page -- Contents -- Preface -- Acknowledgments -- Introduction: Landmarks in Pre-laplacean Statistics -- Part One: Laplace -- Chapter 1 the Laplacean Revolution -- 1.1 Pierre-simon De Laplace (1749-1827) -- 1.2 Laplace's Work in Probability and Statistics -- 1.2.1 "mémoire Sur Les Suites Récurro-récurrentes" (1774): Definition of probability -- 1.2.2 "mémoire Sur La Probabilité Des Causes Par Les événements" (1774) -- 1.2.2.1 Bayes' Theorem -- 1.2.2.2 Rule of Succession -- 1.2.2.3 Proof of Inverse Bernoulli Law. Method of Asymptotic Approximation. CentralLimit Theorem for Posterior Distribution. Indirect Evaluation of ¥e-t2dt -- 1.2.2.4 Problem of Points -- 1.2.2.5 First Law of Error -- 1.2.2.6 Principle of Insufficient Reason (Indifference) -- 1.2.2.7 Conclusion -- 1.2.3 "recherches Sur L'intégration Des équations Différentielles Aux Différences Finis" (1776) -- 1.2.3.1 Integration of Difference Equations. Problem of Points -- 1.2.3.2 Moral Expectation. On d'Alembert -- 1.2.4 "mémoire Sur L'inclinaison Moyenne Des Orbites" (1776): Distribution Of finite Sums, Test of Significance -- 1.2.5 "recherches Sur Le Milieu Qu'il Faut Choisir Entre Les Resultants De Plusieurs observations" (1777): Derivation of Double Logarithmic Law of Error -- 1.2.6 "mémoire Sur Les Probabilités" (1781) -- 1.2.6.1 Introduction -- 1.2.6.2 Double Logarithmic Law of Error -- 1.2.6.3 Definition of Conditional Probability. Proof of Bayes' Theorem -- 1.2.6.4 Proof of Inverse Bernoulli Law Refined -- 1.2.6.5 Method of Asymptotic Approximation Refined -- 1.2.6.6 Stirling's Formula -- 1.2.6.7 Direct Evaluation of ¥ e-t20 ò dt -- 1.2.6.8 Theory of Errors -- 1.2.7 "mémoire Sur Les Suites" (1782) -- 1.2.7.1 De Moivre and Generating Functions -- 1.2.7.2 Lagrange's Calculus of Operations as an Impetus for Laplace's GeneratingFunctions.

1.2.8 "mémoire Sur Les Approximations Des Formules Qui Sont Fonctions De Très grands Nombres" (1785) -- 1.2.8.1 Method of Asymptotic Approximation Revisited -- 1.2.8.2 Stirling's Formula Revisited -- 1.2.8.3 Genesis of Characteristic Functions -- 1.2.9 "mémoire Sur Les Approximations Des Formules Qui Sont Fonctions De Très Grands Nombres (suite)" (1786): Philosophy of Probability and Universal Determinism, Recognition of Need for Normal Probability Tables -- 1.2.10 "sur Les Naissances" (1786): Solution of the Problem of Births by Using Inverse Probability -- 1.2.11 "mémoire Sur Les Approximations Des Formules Qui Sont Fonctions De Très grands Nombres Et Sur Leur Application Aux Probabilités" (1810): Second Phase of Laplace's Statistical Career, Laplace's First Proof of the Central Limit theorem -- 1.2.12 "supplément Au Mémoire Sur Les Approximations Des Formules Qui Sont Fonctions De très Grands Nombres Et Sur Leur Application Aux Probabilités" (1810): Justification of Least Squares Based on Inverse Probability, the Gauss-laplace Synthesis -- 1.2.13 "mémoire Sur Les Intégrales Définies Et Leur Applications Aux Probabilités, Et Spécialement à La Recherche Du Milieu Qu'il Faut Choisir Entre Les Résultats Des Observations" (1811): Laplace's Justification of Least Squares Based on Direct Probabili -- 1.2.14 Théorie Analytique Des Probabilités (1812): the De Moivre-laplace theorem -- 1.2.15 Laplace's Probability Books -- 1.2.15.1 Théorie Analytique des Probabilités -- 1.2.15.2 Essai Philosophique sur les Probabilités (1814) -- 1.3. the Principle of Indifference -- 1.3.1 Introduction -- 1.3.2 Bayes' Postulate.

1.3.3 Laplace's Rule of Succession. Hume's Problem of Induction -- 1.3.4 Bertrand's and Other Paradoxes -- 1.3.5 Invariance -- 1.4. Fourier Transforms, Characteristic Functions, And central Limit Theorems -- 1.4.1 the Fourier Transform: from Taylor to Fourier -- 1.4.2 Laplace's Fourier Transforms of 1809 -- 1.4.3 Laplace's Use of the Fourier Transform to Solve a Differential Equation (1810) -- 1.4.4 Lagrange's 1776 Paper: a Precursor to the Characteristic Function -- 1.4.5 the Concept of Characteristic Function Introduced: Laplace in 1785 -- 1.4.6 Laplace's Use of the Characteristic Function in His First Proof of the Central Limit Theorem (1810) -- 1.4.7 Characteristic Function of the Cauchy Distribution: Laplace in 1811 -- 1.4.8 Characteristic Function of the Cauchy Distribution: Poisson in 1811 -- 1.4.9 Poisson's Use of the Characteristic Function in His First Proof of the Central Limit Theorem (1824) -- 1.4.10 Poisson's Identification of the Cauchy Distribution (1824) -- 1.4.11 First Modern Rigorous Proof of the Central Limit Theorem: Lyapunov in 1901 -- 1.4.12 Further Extensions: Lindeberg (1922), Lévy (1925), and Feller (1935) -- 1.5. Least Squares and the Normal Distribution -- 1.5.1 First Publication of the Method of Least Squares: Legendre in 1805 -- 1.5.2 Adrain's Research Concerning the Probabilities of Errors (1808): Two Proofs of the Normal Law -- 1.5.3 Gauss' First Justification of the Principle of Least Squares (1809) -- 1.5.3.1 Gauss' Life -- 1.5.3.2 Derivation of the Normal Law. Postulate of the Arithmetic Mean -- 1.5.3.3 Priority Dispute with Legendre.

1.5.4 Laplace in 1810: Justification of Least Squares Based on Inverse Probability, the Gauss-laplace Synthesis -- 1.5.5 Laplace's Justification of Least Squares Based on Direct Probability (1811) -- 1.5.6 Gauss' Second Justification of the Principle of Least Squares in 1823: The gauss-markov Theorem -- 1.5.7 Hagen's Hypothesis of Elementary Errors (1837) -- Part Two: from Galton to Fisher -- Chapter 2 Galton, Regression, and Correlation -- 2.1 Francis Galton (1822-1911) -- 2.2 Genesis of Regression and Correlation -- 2.2.1 Galton's 1877 Paper, "typical Laws of Heredity": Reversion -- 2.2.2 Galton's Quincunx (1873) -- 2.2.3 Galton's 1885 Presidential Lecture and Subsequent Related Papers: Regression, Discovery of the Bivariate Normal Surface -- 2.2.4 First Appearance of Correlation (1888) -- * 2.2.5 Some Results on Regression Based on the Bivariate Normal Distribution: regression to the Mean Mathematically Explained -- 2.2.5.1 Basic Results Based on the Bivariate Normal Distribution -- 2.2.5.2 Regression to the Mean Mathematically Explained -- 2.3 Further Developments After Galton -- 2.3.1 Weldon (1890 -- 1892 -- 1893) -- 2.3.2 Edgeworth in 1892: First Systematic Study of the Multivariate Normal Distribution -- 2.3.3 Origin of Pearson's R (pearson Et Al., 1896) -- 2.3.4 Standard Error of R (pearson Et Al., 1896 -- Pearson and Filon, 1898 -- Student, 1908 -- Soper, 1913).

2.3.5 Development of Multiple Regression, Galton's Law of Ancestral Heredity, first Explicit Derivation of the Multivariate Normal Distribution (pearson Et Al., 1896) -- 2.3.5.1 Development of Multiple Regression. Galton's Law of Ancestral Heredity -- 2.3.5.2 First Explicit Derivation of the Multivariate Normal Distribution -- 2.3.6 Marriage of Regression with Least Squares (yule, 1897) -- 2.3.7 Correlation Coefficient for a 2.×.2 Table (yule, 1900). Feud between pearson and Yule -- 2.3.8 Intraclass Correlation (pearson, 1901 -- Harris, 1913 -- Fisher, 1921 -- 1925) -- 2.3.9 First Derivation of the Exact Distribution of R (fisher, 1915) -- 2.3.10 Controversy Between Pearson and Fisher on the Latter's Alleged Use of Inverse Probability (soper Et Al., 1917 -- Fisher, 1921) -- 2.3.11 the Logarithmic (or Z-) Transformation (fisher, 1915 -- 1921) -- * 2.3.12 Derivation of the Logarithmic Transformation -- 2.4 Work on Correlation and the Bivariate (and Multivariate) Normal Distribution Before Galton -- 2.4.1 Lagrange's Derivation of the Multivariate Normal Distribution from the Multinomial Distribution (1776) -- 2.4.2 Adrain's Use of the Multivariate Normal Distribution (1808) -- 2.4.3 Gauss' Use of the Multivariate Normal Distribution in the Theoria Motus (1809) -- 2.4.4 Laplace's Derivation of the Joint Distribution of Linear Combinations of two Errors (1811) -- 2.4.5 Plana on the Joint Distribution of Two Linear Combinations of random variables (1813) -- 2.4.6 Bravais' Determination of Errors in Coordinates (1846).

2.4.7 Bullet Shots on a Target: Bertrand's Derivation of the Bivariate Normal Distribution (1888).