A history of mathematical statistics from 1750 to 1930.

*(English)*Zbl 0979.01012
Wiley Series in Probability and Statistics. New York, NY: John Wiley & Sons. xvii, 795 p. (1998).

Arne Hald (born 1913) was Professor of statistics at the University of Copenhagen from 1948 till 1982. This book is the follow-up to his comprehensive work “A History of Probability and Statistics and Their Applications before 1750” (Wiley, Chichester 1990; Zbl 0731.01001). The main topics are the history of the parametric statistical inference, the development of the corresponding statistical methods, and some typical applications. For a better understanding of the historical development of both the controversies and continuities that developed between the different statistical schools. Here I miss a hint to S. James Press [Bayesian statistics: principles, models, and applications (Wiley, New York 1989; Zbl 0687.62001)].

The British biometric school often ignored the work of the continental European statisticians. Fisher developed his analysis of variance ignorant of Edgeworth’s results before 1900. Here should be added a remark that in this time biometry was seen as servant of eugenics, and for some scholars eugenics was a religion (see Galton’s unpublished Kantsaywhere).

The formulae of the original papers are represented in a uniform modern terminology and notation. The ideas of Laplace, Gauss, and R. A. Fisher dominate the exposition.

For the reader who has some knowledge of the history of statistics the author recommends to read the following topics: 1) approximations to the beta probability integral by Bayes and Price, 2) the early discussion, particularly by Condorcet, of the choice of significance levels and the two types of error in decision problems, 3) the large-sample probability limits for the binomial parameter by Lagrange and Laplace, 4) Laplace’s convolution formula for sum of random variables and its applications to polynomial densities, 5) asymptotic expansions to posterior distributions due to Laplace, Poisson, and de Morgan as forerunners of modern Bayes expansions, 6) criticism of the indifference principle and the rule of succession, 7) the early history of the central limit theorem, 8) Laplace’s diffusions model, 9) Cauchy’s method for determining the number of terms to be included in the linear model and multiplicative model for a two-factor experiment, 10) orthogonalization of the linear model by Laplace, Chebyshev, Gram, and Thiele as basis for the development in the 20s, 11) the asymptotic equivalence of the statistical inference by direct and inverse probability, by Laplace and by Edgeworth, 12) a discussion of Fisher’s contributions before 1930 in a historical perspective.

This very solid monograph is completed by numerous references (36 pages), and an extended index of subjects and persons (19 pages).

The British biometric school often ignored the work of the continental European statisticians. Fisher developed his analysis of variance ignorant of Edgeworth’s results before 1900. Here should be added a remark that in this time biometry was seen as servant of eugenics, and for some scholars eugenics was a religion (see Galton’s unpublished Kantsaywhere).

The formulae of the original papers are represented in a uniform modern terminology and notation. The ideas of Laplace, Gauss, and R. A. Fisher dominate the exposition.

For the reader who has some knowledge of the history of statistics the author recommends to read the following topics: 1) approximations to the beta probability integral by Bayes and Price, 2) the early discussion, particularly by Condorcet, of the choice of significance levels and the two types of error in decision problems, 3) the large-sample probability limits for the binomial parameter by Lagrange and Laplace, 4) Laplace’s convolution formula for sum of random variables and its applications to polynomial densities, 5) asymptotic expansions to posterior distributions due to Laplace, Poisson, and de Morgan as forerunners of modern Bayes expansions, 6) criticism of the indifference principle and the rule of succession, 7) the early history of the central limit theorem, 8) Laplace’s diffusions model, 9) Cauchy’s method for determining the number of terms to be included in the linear model and multiplicative model for a two-factor experiment, 10) orthogonalization of the linear model by Laplace, Chebyshev, Gram, and Thiele as basis for the development in the 20s, 11) the asymptotic equivalence of the statistical inference by direct and inverse probability, by Laplace and by Edgeworth, 12) a discussion of Fisher’s contributions before 1930 in a historical perspective.

This very solid monograph is completed by numerous references (36 pages), and an extended index of subjects and persons (19 pages).

Reviewer: Hilmar Grimm (Jena)

##### MSC:

01A50 | History of mathematics in the 18th century |

01-02 | Research exposition (monographs, survey articles) pertaining to history and biography |

62-03 | History of statistics |

01A05 | General histories, source books |

01A55 | History of mathematics in the 19th century |

01A60 | History of mathematics in the 20th century |

62F03 | Parametric hypothesis testing |