Prakash Gorroochurn 
Classic Topics on the History of Modern Mathematical Statistics 
From Laplace to More Recent Times

‘There is nothing like it on the market…no others are as encyclopedic…the writing is exemplary: simple, direct, and competent.’
–George W. Cobb, Professor Emeritus of Mathematics and Statistics, Mount Holyoke College

Written in a direct and clear manner, Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times presents a comprehensive guide to the history of mathematical statistics and details the major results and crucial developments over a 200-year period. Presented in chronological order, the book features an account of the classical and modern works that are essential to understanding the applications of mathematical statistics.

Divided into three parts, the book begins with extensive coverage of the probabilistic works of Laplace, who laid much of the foundations of later developments in statistical theory. Subsequently, the second part introduces 20th century statistical developments including work from Karl Pearson, Student, Fisher, and Neyman. Lastly, the author addresses post-Fisherian developments. Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times also features:

* A detailed account of Galton’s discovery of regression and correlation as well as the subsequent development of Karl Pearson’s X² and Student’s t

* A comprehensive treatment of the permeating influence of Fisher in all aspects of modern statistics beginning with his work in 1912

* Significant coverage of Neyman-Pearson theory, which includes a discussion of the differences to Fisher’s works

* Discussions on key historical developments as well as the various disagreements, contrasting information, and alternative theories in the history of modern mathematical statistics in an effort to provide a thorough historical treatment

Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times is an excellent reference for academicians with a mathematical background who are teaching or studying the history or philosophical controversies of mathematics and statistics. The book is also a useful guide for readers with a general interest in statistical inference.

Table of Content

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

About the author

Prakash Gorroochurn, Ph D, 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.