Introduction to Fisher (1922) On the Mathematical Foundations of Theoretical Statistics

Abstract

This rather long and extraordinary paper is the first full account of Fisher’s ideas on the foundations of theoretical statistics, with the focus being on estimation. The paper begins with a sideswipe at Karl Pearson for a purported general proof of Bayes’ postulate. Fisher then clearly makes a distinction between parameters, the objects of estimation, and the statistics that one arrives at to estimate the parameters. There was much confusion between the two since the same names were given to both parameters and statistics, e.g., mean, standard deviation, correlation coefficient, etc., without an indication of whether it was the population or sample value that was the subject of discussion. This formulation of the parameter value was certainly a critical step for theoretical statistics [see, e.g., Geisser (1975), footnote on p. 320 and Stigler (1976)]. In fact, Fisher attributed the neglect of theoretical statistics not only to this failure in distinguishing between parameter and statistic but also to a philosophical reason, namely, that the study of results subject to greater or lesser error implies that the precision of concepts is either impossible or not a practical necessity. He sets out to remedy the situation, and remedy it he did. Indeed, he did this so convincingly that for the next 50 years or so almost all theoretical statisticians were completely parameter bound, paying little or no heed to inference about observables.