Statistical Thought: A Perspective and History

S. K. Chatterjee
Oxford University Press
ISBN 0-19-852531-1
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62 Statistics

It is not easy to describe the contents of this book in a few words. Generally speaking, the author describes the course of development of statistical concepts from the perspective of the present state of the subject. Some chapters of the book emphasize the philosophical context and the others are devoted to the history of selected statistical and probabilistic methods. Anyway, the reader is assumed to have a sufficient knowledge of mathematical statistics. The book is divided into two parts. Part I called Perspective is oriented to a philosophical background of statistical thought and an interpretation of probability. Part II called History describes the birth of probability theory, fundamental ideas (including the central limit theorem, maximum likelihood, information criteria, outliers, robustness, and many others), and the role of outstanding scientists like Pascal, Bernoulli, Bayes, Laplace, Gauss, Poisson, Galton, Pearson, Student, and Fisher. However, this volume is neither a book on the history nor on the philosophy of statistics. To illustrate the subject of the book, I would like to mention some details about sufficiency described in it. All statisticians know that this concept was introduced by R.A. Fisher in 1922. It is less known (see p. 255) that Fisher discovered the principle of sufficiency when he solved a problem raised by the astronomer and physicist Eddington in a 1914 book on astronomy (Which of the two given estimators of standard errors has a better performance?). But in fact, sufficiency was used already in 1860 by the American statistician Simon Newcomb (see p. 254), who observed that in a sample X1,…,Xn with replacement from {1,…,N}, the statistic max Xi in some sense summarizes information from the complete sample. The book can be recommended to teachers and students who are interested in philosophical principles of statistics and in the history of probability and statistics.