Preface Excerpts (by Hilda Geiringer)
Richard von Mises' scientific work comprises two major fields: mechanics and probability-statistics; supplemented by numerical analysis, geometry, and philosophy of science they form the leading interests of his scientific life.
In 1931 he published a comprehensive textbook on probability consisting of four parts: the foundations (his frequency theory); limit theorems; statistics and theory of errors; and statistical problems in physics. While in the United States (1939-1953) he became deeply interested in "British-American" statistics (as did his former student A. Wald). Mises' aim was to understand this approach to statistical inference as a part of rigorous probability theory, its application. The results of his thinking were incorporated in Lectures on Probability and Statistics he gave repeatedly at Harvard University to advanced undergraduate and graduate students, and in lectures he gave in Rome (1951-1952) and finally in Zurich(summer 1952).
The Harvard Lectures were mimeographed. Brief but clear notes of the Zurich Lectures were kindly given to me after Mises' death by K. Schoeni, who attended them. Mises had planed to incorporate the various ideas in a comprehensive work on probability and statistics which, more than 20 years after his Wahrscheinlickkeitscrechnung, would have been a very different work, in many respects.
The present book is based on the material mentioned above as well as his papers and notebooks. It presents a unified mathematical theory of probability and statistics. In fact, for Mises there were never two different theories, one "pure" the other "applied," but one theory only, a frequency theory, mathematically rigorous and guided by an operational approach.
Chapter 1. Fundamentals
Appendix One: The Consistency of the Notion of the Collective. Wald's Results
Appendix Two: Measure-Theoretic Approach versus Frequency Approach
Chapter II. General Label Space
Appendix Three: Tornier's Frequency Theory
Chapter III. Basic Properties of Distributions
Chapter IV. Examples of Combined Operations
Chapter V. Summation of Chance Variables Characteristic Function
Chapter VI. Asymptotic Distribution of the Sum of Chance Variables
Appendix Four: Remarks on Additive Time-Dependent Stochastic Processes
Chapter VII. Probability Inference. Bayes' Method
Chapter VIII. More on Distributions
Chapter IX. Analysis of Statistical Data
Chapter X. Problem of Inference
Chapter XI. Multivariate Statistics. Correlation
Chapter XII. Introduction to the Theory of Statistical Functions