Classic Topics on the History of Modern Mathematical Statistics (eBook)

Prakash Gorroochurn, PhD, is Associate Professor in the Mailman School of Public Health's Department of Biostatistics at Columbia University, where he is also a statistical consultant in the School of Social Work. Dr. Gorroochurn has published in the fields of history of probability and statistics, mathematical population genetics, and genetic epidemiology. He is the author of Classic Problems of Probability, which is the winner of the 2012 PROSE Award for Mathematics from The American Publishers Awards for Professional and Scholarly Excellence.

Preface 5

Acknowledgements 9

Introduction: Landmarks in Pre-Laplacean Statistics 18

Chapter 1: The Laplacean Revolution 21

1.1 Pierre-Simon De Laplace (1749-1827) 21

1.2 Laplace's Work in Probability and Statistics 26

1.3. The Principle of Indifference: Bayes' Theorem, Laplace's Rule of Succession, Hume's Problem Of Induction, Bertrand's Paradox, Invariance. 156

1.4. Fourier Transforms, Characteristic Functions, and Central Limit Theorems 179

1.5. Least Squares and the Normal Distribution 226

Chapter 2: Galton, Regression, and Correlation 275

2.1 Francis Galton (1822-1911) 275

2.2 Genesis of Regression and Correlation 280

2.3 Further Developments after Galton 313

2.4 Work On Correlation and the Bivariate (And Multivariate) Normal Distribution Before Galton 394

Chapter 3: Karl Pearson's Chi-Squared Goodness-of-Fit Test 426

3.1 Karl Pearson (1857-1936) 426

3.2 Origin of Pearson's Chi-Squared 430

3.3 Pearson's Error 445

3.4 The Chi-Squared Distribution before Pearson 463

Chapter 4: Student's T 501

4.1 William Sealy Gosset (1876-1937) 501

4.2 Origin of Student's Test: The 1908 Paper 502

4.3 Further Developments 514

4.4 Student Anticipated 522

Chapter 5: The Fisherian Legacy 533

5.1 Ronald Aylmer Fisher (1890-1962) 533

5.2 Fisher and the Foundation of Estimation Theory 537

5.3 Fisher and Significance Testing 608

5.4 Anova and the Design of Experiments 620

5.5 Fisher and Probability 664

5.6 Fisher vs. Neyman-Pearson: Clash of The Titans 729

5.7 Maximum Likelihood before Fisher 780

5.8 Significance Testing before Fisher 806

Chapter 6: Beyond Fisher and Neyman-Pearson 853

6.1 Extensions to the Theory of Estimation 853

6.2 Estimation and Hypothesis Testing Under a Single Framework: Wald's Statistical Decision Theory (1950) 913

6.3 The Bayesian Revival 929

Photo Credits 984

"The nearly 800-page volume
is well written and extensively footnoted. It would be impossible in even a long review to
do justice to the range of topics it discusses...Suffice it to say that the book will be of great value to working
mathematical statisticians interested in important episodes from the discipline's past." (Mathematical Reviews/MathSciNet 11/05/2017)