Classic topics on the history of modern mathematical statistics. From Laplace to more recent times (Q2801707)

The book under review presents a comprehensive coverage of the history of mathematical statistics from the eighteenth century to the mid-twentieth century by chronicling the accomplishments of many scholars, particularly stressing the contributions of Laplace, Galton, Pearson, and Fisher. The author gives a short biography of each followed by a detailed, chronological description of their work. Original quotes and detailed derivations of mathematical results are also included. The author provides the context in which the statistical theories were developed, however the role of the applications in their development is not stressed. Overall, the book is well written and engaging. It is a valuable addition to other publications on the history of statistics, especially for statisticians and educators.NEWLINENEWLINEChapter 1 contains a detailed description of the work of Laplace. Topics include his contributions to the formulation of probability and development of its theory, characteristic functions, generating functions, proofs of the central limit theorem, the development of the theory of errors, least squares, and the method of asymptotic approximation. The author also describes Laplace's philosophical approach to probability, the introduction of moral expectation, and discussion on the Principle of Indifference and Hume's Problem of Induction. Related works of several other mathematicians are also covered, e.g., Fourier, Lagrange, Adrain, Poisson, Gauss, Lyapunov.NEWLINENEWLINEChapter 2 describes Galton's contribution to the development of regression and correlation. In addition to Galton's work, topics include a history of the derivation of the multivariate normal distribution, the Karl Pearson product-moment formula for the sample correlation coefficient, and Yule's application of the method of least squares to compute the regression coefficients.NEWLINENEWLINEChapter 3 provides a detailed description of Karl Pearson's work. It also describes his philosophy about science and the many technical and philosophical debates he had with other scholars. Many of his contributions are noted, but special emphasis is given to his work related to the chi square distribution and multivariate normal distribution as well as to the method of moments. An extensive history of the chi square distribution is also included.NEWLINENEWLINEChapter 4 describes the discovery of the \(t\)-distribution and its use in statistical tests. It stresses its importance in the development of small sample size statistics.NEWLINENEWLINEChapter 5 deals with the work of Fisher and related works of several other scholars. Among the numerous topics covered are Fisher's contributions to experimental design, the introduction of ANOVA, his thoughts on the theory of probability and statistics, hypothesis testing, and his development of estimation theory, i.e., the introduction of the concepts of consistency, efficiency, sufficiency, the maximum likelihood principle, conditional inference. While many other scholars are mentioned, a central role is given to Neyman and Egon Pearson for their contributions to the development of a new paradigm for hypothesis testing and statistical inference.NEWLINENEWLINEChapter 6 deals with the development of statistics after Fisher. The main topics are extensions of the theory of estimation through the work of Darmois, Pitman, Cramer, Rao, Blackwell, Lehmann, and Scheffé, the development of the theory of statistical decision due to Wald, and the new perspective on the Bayesian method due to Ramsey, De Finetti, Savage, and Robbins.