Hald is a well known Danish statistician who previously published a book titled "A History of Probability and Statistics and Their Application before 1750". This book is a sequel to that one. I have not read his earlier work but have read other fine historical accounts by Stigler, Porter and most recently "The Lady Tasting Tea" by Salsburg. This book is up to the high standards set by these other fine authors.
Prior to the late 1800s there was very little theory for statistics. There were many interesting developments in probability prior to 1750 and nearly all of them dealt with gambling situations. One does not need to read Hald's earlier work to be up on these writings as he summarizes many of the key works of James and Nicholas Bernoulli, and de Moivre in Chapter 2 along with the post 1750 work of Laplace and Lagrange.
His Preface describes the aim of the book and relates it to other works. Chapter 1 then maps out the plan of the book. The first three parts of the book cover the period from 1750 to 1853 and the final part covers selected developments in estimation theory from 1830-1935. Part 1 deals with direct or frequentist probability as it developed from 1750 to 1805. Part 2 deals with inverse probability or subjective (Bayesian) probability as it developed from the posthumous publication of Bayes' treatise by Price in 1764 (Bayes died in 1761) and developed as a principle of probability by Laplace in 1774 to its continued development through 1812. Laplace's principle of indifference was rekindled with further developments in Bayesian methods by Jeffreys in the 1930s. Part 3 begins with Gauss in 1809 and covers the early history of the central limit theorem, least squares and the normal distribution. This covers mainly the period from 1810 to 1853 but later related work is also mentioned. Finally Part 4 deals with important select topics in estimation theory from 1830 - 1935.
Hald is thorough and scholarly in the tradition set by Steve Stigler. This is a massive work of 739 pages with an additional 35 pages of bibliography.
Prominent figures in Part 1 include Laplace, de Moivre, Lagrange, Boscovich and Daniel Bernoulli. Part 2 covers the work of Bayes, Price, James Bernoulli and primarily Laplace. Part 3 deals with Laplace, Poisson, Bessel, Cauchy and Gauss. In Part 4 we meet Bienayme, Cauchy, Gram and Schmidt and their orthogonalization process, Quetelet, Condorcet, Cournot, Galton, Thiele, Karl Pearson, R. A. Fisher, Gosset and Edgeworth.
Fittingly the final chapter, Chapter 28 covers the theory of mathematical statistics as it was developed by Fisher from 1912-1935.
This is a great reference source for anyone who wants to collect and cherish the major developments of probability and statistics.
There is still room for a third book covering the period from 1930 to 2000 when the Neyman and Pearson theory of hypothesis testing developed, Bayesian statistics was revitalized, statistical decision theory and sequential analysis developed as did multivariate analysis, time series analysis, robust statistics, quality control methods, spatial statistics and resampling methods. The late 20th and early 21st centuries have seen many advances based on the ability to do intense calculation on amazingly fast computers!
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