History of Parametric Statistical Inference from Bernoulli to Fisher, 1713-1935 (eBook)

Contents 6
Preface 11
The Three Revolutions in Parametric Statistical Inference 14
Part I BINOMIAL STATISTICAL INFERENCE. The Three Pioneers: Bernoulli (1713), de Moivre (1733), and Bayes (1764) 22
James Bernoulli’s Law of Large Numbers for the Binomial, 1713, and Its Generalization 23
De Moivre’s Normal Approximation to the Binomial, 1733, and Its Generalization 28
Bayes’s Posterior Distribution of the Binomial Parameter and His Rule for Inductive Inference, 1764 36
Part II STATISTICAL INFERENCE BY INVERSE PROBABILITY. Inverse Probability from Laplace (1774), and Gauss (1809) to Edgeworth (1909) 41
Laplace’s Theory of Inverse Probability,1774—1786 42
A Nonprobabilistic Interlude: The Fitting of Equations to Data, 1750—1805 56
Gauss’s Derivation of the Normal Distribution and the Method of Least Squares, 1809 63
Credibility and Confidence Intervals by Laplace and Gauss 70
The Multivariate Posterior Distribution 74
Edgeworth’s Genuine Inverse Method and the Equivalence of Inverse and Direct Probability in Large Samples, 1908 and 1909 76
Criticisms of Inverse Probability 80
Part III THE CENTRAL LIMIT THEOREM AND LINEAR MINIMUM VARIANCE ESTIMATION BY LAPLACE AND GAUSS 88
Laplace’s Central Limit Theorem and Linear Minimum Variance Estimation 89
Gauss’s Theory of Linear Minimum Variance Estimation 99
Part IV ERROR THEORY. SKEW DISTRIBUTIONS.CORRELATION. SAMPLING DISTRIBUTIONS 108
The Development of a Frequentist Error Theory 109
Skew Distributions and the Method of Moments 114
Normal Correlation and Regression 133
Sampling Distributions Under Normality,1876—1908 150
Part V THE FISHERIAN REVOLUTION, 1912—1935 158
Fisher’s Early Papers, 1912—1921 159
The Revolutionary Paper, 1922 174
Studentization, the F Distribution, and the Analysis of Variance, 1922—1925 183
The Likelihood Function, Ancillarity, and Conditional Inference 191
References 196
Subject Index 213
Author Index 217