A History of Mathematical Statistics from 1750 to 1930

Abstract

DIRECT PROBABILITY 17501805. Some Results and Tools in Probability Theory (By Bernoulli, de Moivre, and Laplace). The Distribution of the Arithmetic Mean, 17561781. Chance or Design: Tests of Significance. Theory of Errors and Methods of Estimation. Fitting of Equations to Data, 17501805. INVERSE PROBABILITY BY BAYES AND LAPLACE, WITH COMMENTS ON LATER DEVELOPMENTS. Induction and Probability: The Philosophical Background. Bayes, Price, and the Essay, 17641765. Equiprobability, Equipossibility, and Inverse Probability. Laplace's Applications of the Principle of Inverse Probability in 1774. Laplace's General Theory of Inverse Probability. The Equiprobability Model and the Inverse Probability Model for Games of Chance. Laplace's Methods of Asymptotic Expansion, 1781 and 1785. Laplace's Analysis of Binomially Distributed Observations. Laplace's Theory of Statistical Prediction. Laplace's Sample Survey of the Population of France and the Distribution of the Ratio Estimator. THE NORMAL DISTRIBUTION, THE METHOD OF LEAST SQUARES, AND THE CENTRAL LIMIT THEOREM. GAUSS AND LAPLACE, 18091828. The Early History of the Central Limit Theorem, 18101853. Derivations of the Normal Distribution as a Law of Error. Gauss's Linear Normal Model and the Method of Least Squares, 1809 and 1811. Laplace's Large-Sample Theory of Linear Estimation, 18111827. Gauss's Theory of Linear Unbiased Minimum Variance Estimation, 18231828. SELECTED TOPICS IN ESTIMATION THEORY 18301930. On Error and Estimation Theory, 18301890. Bienaym?'s Proof of the Multivariate Central Limit Theorem and His Defense of Laplace's Theory of Linear Estimation, 1852 and 1853. Cauchy's Method for Determining the Number of Terms to be Included in the Linear Model and for Estimating the Parameters, 18351853. Orthogonalization and Polynomial Regression. Statistical Laws in the Social and Biological Sciences, Poisson, Quetelet, and Galton, 18301890. Sampling Distributions under Normality. Fisher's Theory of Estimation, 19121935, and His Immediate Precursors. References. Index.