A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713-1935 / Sources and Studies in the History of Mathematics and Physical Sciences (PDF)

Introduction.- The Three Revolutions in Parametric 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 Generalizations.- Bayes's Posterior Distribution of the Binomial Parameter and His Rule for Inductive Inference, 1764.- 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.- Laplace's Central Limit Theorem and Linear Minimum Variance Estimation.- Gauss's Theory of Linear Minimum Variance Estimation.- The Development of a Frequentist Error Theory.- Skew Distributions and the Method of Moments.- Normal Correlation and Regression.- Sampling Distributions Under Normality, 1876-1908.- 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 .- References.- Subject Index.- Author Index.

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)