Chatterjee S.K. Statistical Thought: A Perspective and History

Oxford: Oxford University Press, 2003. — 300 p.The book examines the distinguishing features of the various contending approaches to statistical inference (including decision-making) that are currently available in statistical literature, and traces the historical evolution of the concepts underlying these approaches and their applications. The first part entitled, Perspective, shows that statistical inference is really a prolongation of the philosophical problem of induction, and in it, probability is involved both in the input (in the form of model) and the output (for quantifying uncertainty). Four different approaches (behavioural, instantial, pro-subjective Bayesian, and purely subjective) to such statistical induction arise due to the invocation of different conceptions of probability (objective and subjective) at the two stages of the process. The comparative characteristics, advantages, and disadvantages of the different approaches are considered, and it is concluded that each is appropriate in its natural setting. The second part entitled, History, discusses how the different types of probability originated and evolved, and how their application to statistical induction gave rise to the variety of concepts and principles associated with the different approaches. After some reference to pre-history, the developments made by the principal contributors to probability and statistics during 17th-20th centuries (from Cardano, Pascal, Fermat, Huygens, and James Bernoulli through to Daniel Bernoulli, Bayes, Laplace, Gauss, to Galton, Karl Pearon, Fisher, Jeffreys, de Finetti, Neyman, E. S. Pearson, Wald, and their successors) are delineated.