Now available in paperback. This is a text comprising the major theorems of probability theory and the measure theoretical foundations of the subject. The main topics treated are independence, interchangeability, and martingales; particular emphasis is placed upon stopping times, both as tools in proving theorems and as objects of interest themselves. No prior knowledge of measure theory is assumed and a unique feature of the book is the combined presentation of measure and probability. It is easily adapted for graduate students familar with measure theory as indicated by the guidelines in...

Whyanothertextbook? The statistical community generally agrees that at the upper undergraduate level, or the beginning master s level, students of statistics should begin to study the mathematical methods of the ?eld. We assume that by thentheywillhavestudiedtheusualtwo yearcollegesequence, includingcalculus through multiple integrals and the basics of matrix algebra. Therefore, they are ready to learn the foundations of their subject, in much more depth than is usual in an applied, cookbook, introduction to statistical methodology. There are a number of well written, widely used textbooks...

Problems of calculating the reliability of instruments and systems and the development of measures to increase efficiency and reduce operational costs confronted physicists and mathe- maticians at the end of the '40's and the beginning of the '50's in connection with the unrelia- bility of electro-vacuum instruments used in aviation. Since then steadily increasing demands for the accuracy, reliability and complexity required in electronic equipment have served as a stimulus in the development of the theory of reliability. From 1950 to 1955 Epstein and Sobel 67,68] and Davis 62], in an...

The theory of optimal design of experiments as we know it today is built on asolid foundation developed by Jack Kiefer, who formulated and resolved some of the major problems of data collection via experimentation. A principal ingredient in his formulation was statistical efficiency of a design. Kiefer's theoretical contributions to optimal designs can be broadly classified into several categories: He rigorously defined, developed, and interrelated statistical notions of optimality. He developed powerful tools for verifying and searching for optimal designs; this includes the "averaging...