A history of parametric statistical inference from Bernoulli to Fisher, 1713-1935

Abstract

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.