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A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713-1935


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Table of Contents

The Three Revolutions in Parametric Statistical Inference.- The Three Revolutions in Parametric Statistical Inference.- Binomial Statistical Inference.- James Bernoulli's Law of Large Numbers for the Binomial, 1713, and Its Generalization.- De Moivre's Normal Approximation to the Binomial, 1733, and Its Generalization.- Bayes's Posterior Distribution of the Binomial Parameter and His Rule for Inductive Inference, 1764.- Statistical Inference by Inverse Probability.- Laplace's Theory of Inverse Probability, 1774-1786.- A Nonprobabilistic Interlude: The Fitting of Equations to Data, 1750-1805.- Gauss's Derivation of the Normal Distribution and the Method of Least Squares, 1809.- Credibility and Confidence Intervals by Laplace and Gauss.- The Multivariate Posterior Distribution.- Edgeworth's Genuine Inverse Method and the Equivalence of Inverse and Direct Probability in Large Samples, 1908 and 1909.- Criticisms of Inverse Probability.- The Central Limit Theorem and Linear Minimum Variance Estimation by Laplace and Gauss.- Laplace's Central Limit Theorem and Linear Minimum Variance Estimation.- Gauss's Theory of Linear Minimum Variance Estimation.- Error Theory. Skew Distributions. Correlation. Sampling Distributions.- The Development of a Frequentist Error Theory.- Skew Distributions and the Method of Moments.- Normal Correlation and Regression.- Sampling Distributions Under Normality, 1876-1908.- The Fisherian Revolution, 1912-1935.- Fisher's Early Papers, 1912-1921.- The Revolutionary Paper, 1922.- Studentization, the F Distribution, and the Analysis of Variance, 1922-1925.- The Likelihood Function, Ancillarity, and Conditional Inference.


From the reviews:

"In this very enjoyable and interesting book, Hald ... presents his subject in a very lively style; many ideas and developments in statistics are treated with great clarity. It is very suitable as a course resource in history of statistical inference ... . Throughout, the author provides brief biographical sketches of researchers whose contributions to statistics are included here. ... A very useful and valuable work on the history of statistical inference. ... Summing Up: Highly recommended. Lower- and upper-division undergraduates through faculty." (D. V. Chopra, CHOICE, Vol. 44 (11), July, 2007)

"This is a useful account of the historical development of the theory that underlies the empirically observed stability of data averages for large samples and how their precision may be measured. ... The resultant book is a suitable text for a one-semester course on what is arguably the core piece of statistical history." (C. C. Heyde, SIAM Review, Vol. 50 (1), 2008)

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