Probability, Statistics and Optimization,
A Tribute to Peter Whittle


In September 1994 Peter Whittle retires from his position as Churchill Professor of Mathematics for Operational Research in the University of Cambridge. We, a small selection of his friends, colleagues and former students, take this opportunity to pay tribute to a man whose broad interests and penetrating insights have greatly enriched our subjects.

Peter Whittle's eight major volumes have covered time series, prediction, constrained optimization, dynamic programming, optimal control, stochastic systems and the foundations of probability theory. Throughout these works the reader is struck by the simplicity and generality of approach, and by the author's open search for an underlying unity. Several of these works were ahead of their time: indeed of his early books some now appear to have been written for the audience of today, such is the extent to which they have anticipated and shaped subsequent developments.

In this volume we have attempted to represent the spread of Peter Whittle's professional interests, and there are papers on quantum probability, polymers, communication theory, epidemics, queues, large deviations, nonlinear systems, neural networks, spatial statistics, sequential analysis, optimization, Gittins indices, and Markov decision processes. Peter Whittle has often emphasized the coherence of the broad area of applicable mathematics, and the context it provides for the disciplines of statistics and operational research. His books make this point most eloquently, but we hope he will enjoy reading some of the linkages made in this volume, for example between the simplex method and order statistics, nonlinear systems and data analysis, statistics and neural nets, or dynamic programming and network flow. The papers have been arranged into seven Parts, but the reader will quickly realize that several other groupings are possible!

My thanks are due to all the authors for their help with this project, and for their cooperation in editorial changes. It is a pleasure to acknowledge the secretarial help of Sarah Shea-Simonds. Finally I am most grateful to Helen Ramsey of Wiley for her unfailing assistance in the production of this volume.

Frank Kelly
October 1993