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

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ISBN: 978-0-387-46408-4 (Print) 978-0-387-46409-1 (Online)

Table of contents (21 chapters)

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  1. Front Matter

    Pages I-XVI

  2. The Three Revolutions in Parametric Statistical Inference

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      Pages 1-8

      The Three Revolutions in Parametric Statistical Inference

  3. Binomial Statistical Inference

    1. Front Matter

      Pages 9-9

    2. No Access

      Book Chapter

      Pages 11-15

      James Bernoulli’s Law of Large Numbers for the Binomial, 1713, and Its Generalization

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      Book Chapter

      Pages 17-24

      De Moivre’s Normal Approximation to the Binomial, 1733, and Its Generalization

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      Pages 25-29

      Bayes’s Posterior Distribution of the Binomial Parameter and His Rule for Inductive Inference, 1764

  4. Statistical Inference by Inverse Probability

    1. Front Matter

      Pages 31-31

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      Book Chapter

      Pages 33-46

      Laplace’s Theory of Inverse Probability, 1774–1786

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      Book Chapter

      Pages 47-53

      A Nonprobabilistic Interlude: The Fitting of Equations to Data, 1750–1805

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      Book Chapter

      Pages 55-61

      Gauss’s Derivation of the Normal Distribution and the Method of Least Squares, 1809

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      Book Chapter

      Pages 63-66

      Credibility and Confidence Intervals by Laplace and Gauss

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      Book Chapter

      Pages 67-68

      The Multivariate Posterior Distribution

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      Pages 69-72

      Edgeworth’s Genuine Inverse Method and the Equivalence of Inverse and Direct Probability in Large Samples, 1908 and 1909

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      Book Chapter

      Pages 73-80

      Criticisms of Inverse Probability

  5. The Central Limit Theorem and Linear Minimum Variance Estimation by Laplace and Gauss

    1. Front Matter

      Pages 81-81

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      Book Chapter

      Pages 83-92

      Laplace’s Central Limit Theorem and Linear Minimum Variance Estimation

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      Book Chapter

      Pages 93-101

      Gauss’s Theory of Linear Minimum Variance Estimation

  6. Error Theory. Skew Distributions. Correlation. Sampling Distributions

    1. Front Matter

      Pages 103-103

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      Book Chapter

      Pages 105-109

      The Development of a Frequentist Error Theory

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      Book Chapter

      Pages 111-129

      Skew Distributions and the Method of Moments

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      Book Chapter

      Pages 131-147

      Normal Correlation and Regression

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      Book Chapter

      Pages 149-156

      Sampling Distributions Under Normality, 1876–1908

  7. The Fisherian Revolution, 1912–1935

    1. Front Matter

      Pages 157-157

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      Book Chapter

      Pages 159-173

      Fisher’s Early Papers, 1912–1921

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      Book Chapter

      Pages 175-183

      The Revolutionary Paper, 1922

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      Pages 185-192

      Studentization, the F Distribution, and the Analysis of Variance, 1922–1925

  8. Back Matter

    Pages 199-223

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