Complex Stochastic Systems

by D.R. Cox (Editor)

Complex stochastic systems comprises a vast area of research, from modelling specific applications to model fitting, estimation procedures, and computing issues. The exponential growth in computing power over the last two decades has revolutionized statistical analysis and led to rapid developments and great progress in this emerging field. In Complex Stochastic Systems, leading researchers address various statistical aspects of the field, illustrated by some very concrete applications. A Primer on Markov Chain Monte Carlo by Peter J. Green provides a wide-ranging mixture of the mathematical and statistical ideas, enriched with concrete examples and more than 100 references. Causal Inference from Graphical Models by Steffen L. Lauritzen explores causal concepts in connection with modelling complex stochastic systems, with focus on the effect of interventions in a given system. State Space and Hidden Markov Models by Hans R. Künschshows the variety of applications of this concept to time series in engineering, biology, finance, and geophysics. Monte Carlo Methods on Genetic Structures by Elizabeth A. Thompson investigates special complex systems and gives a concise introduction to the relevant biological methodology. Renormalization of Interacting Diffusions by Frank den Hollander presents recent results on the large space-time behavior of infinite systems of interacting diffusions. Stein's Method for Epidemic Processes by Gesine Reinert investigates the mean field behavior of a general stochastic epidemic with explicit bounds. Individually, these articles provide authoritative, tutorial-style exposition and recent results from various subjects related to complex stochastic systems. Collectively, they link these separate areas of study to form the first comprehensive overview of this rapidly developing field.

127 pages, Paperback

First published March 27, 1992

About the author

Sir David Roxbee Cox FRS, FBA is a prominent British statistician who is often credited as D.R. Cox in the literature.

Cox studied mathematics at St John's College, Cambridge and obtained his PhD from the University of Leeds in 1949, advised by Henry Daniels and Bernard Welch.

He was employed from 1944 to 1946 at the Royal Aircraft Establishment, from 1946 to 1950 at the Wool Industries Research Association in Leeds, and from 1950 to 1956 worked at the Statistical Laboratory at the University of Cambridge. From 1956 to 1966 he was Reader and then Professor of Statistics at Birkbeck College, London. In 1966, he took up the Chair position in Statistics at Imperial College London where he later became head of the mathematics department. In 1988 he became Warden of Nuffield College and a member of the Department of Statistics at Oxford University. He formally retired from these positions in 1994.

Cox has received numerous honorary doctorates. He has been awarded the Guy Medals in Silver (1961) and Gold (1973) of the Royal Statistical Society. He was elected Fellow of the Royal Society of London in 1973, was knighted by Queen Elizabeth II in 1985 and became an Honorary Fellow of the British Academy in 2000. He is a Foreign Associate of the US National Academy of Sciences and a foreign member of the Royal Danish Academy of Sciences and Letters. In 1990 he won the Kettering Prize and Gold Medal for Cancer Research for "the development of the Proportional Hazard Regression Model." In 2010 he was awarded the Copley Medal of the Royal Society "for his seminal contributions to the theory and applications of statistics." It is given for "outstanding achievements in research in any branch of science, and alternates between the physical sciences and the biological sciences". Awarded every year, the medal is the oldest Royal Society medal still being awarded, having first been given in 1731.

He has supervised, collaborated with, and encouraged many younger researchers now prominent in statistics. He has served as President of the Bernoulli Society, of the Royal Statistical Society, and of the International Statistical Institute. He is an Honorary Fellow of Nuffield College and St John's College, Cambridge, and is a member of the Department of Statistics at the University of Oxford.

He has made pioneering and important contributions to numerous areas of statistics and applied probability, of which the best known is perhaps the proportional hazards model, which is widely used in the analysis of survival data. An example is survival times in medical research that can be related to information about the patients such as age, diet or exposure to certain chemical substances. The Cox process was named after him.

In 1947 he married Joyce Drummond and they have four children and two grandchildren.