MODERN ERA: THE SUPERSTRUCTURE BUILDS UP
MODERN ERA: THE SUPERSTRUCTURE BUILDS UP
In the modern era, the methods of statistics were further abstracted from particular practical problems and the subject gained a distinct identity. In the first phase, Edgeworth and Karl Pearson worked vigorously on model-selecting induction, leading to the formulation of the famous Pearsonian chi-squared test. In the second phase, ‘Student’ started the small-sample theory for model-specific induction with his pioneering work, and Fisher, following up, developed a variety of sampling theory procedures and laid the foundations of the general theory of estimation, multivariate analysis, and the theory of design of experiments. All these areas were subsequently enriched by the contributions of a galaxy of workers. The logic of the behavioural approach to induction was consolidated by Neyman and E. S. Pearson, and was later extended and generalized by Wald. After the emergence of a rigorous theory of subjective probability, there was a revival of interest in the pro-subjective Bayesian and the purely subjective approach in the second half of the 20th century. Work on model-free induction covering large sample procedures, nonparametric methods, and the theory and practice of finite population sampling also progressed steadily during this period.
Keywords: model-selecting induction, Pearsonian chi-squared, model-specific induction, Student, Fisher, Neyman-Pearson, Wald, Bayesian, model-free induction, finite population sampling
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