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# Acknowledgments

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# References

Memories of Sir David Cox: Friendship and Collaboration

Published onApr 27, 2023

Memories of Sir David Cox: Friendship and Collaboration

This brief account brings together some personal memories from 50 years of friendship and research collaboration with Sir David Cox, a half-century that we celebrated together in September 2021. It is written to complement the obituary by Davison et al. (2022) where a detailed appreciation of Sir David’s hugely distinguished career and world-renowned contributions to science and to every subfield of statistics is given. In the following, I have tried to give just a glimpse of the man behind the legend, whom it was such a pleasure and privilege to know.

I first met David Cox when he interviewed me as a prospective research student at Imperial College, and I started there in September 1971. David is famous for the time he devoted to all who asked for his help, and for his patience, gentle corrections, and always-constructive suggestions. Those of us lucky enough to be supervised by him experienced this first-hand. David would see each of us (then, about a dozen) weekly. This is amazing, given everything else he was then doing: not least, producing research papers and monographs at a prodigious rate, being head of the Mathematics Department at Imperial, and editor of the statistics journal *Biometrika*. David read and commented on our work and encouraged us. He listened, occasionally dozing off, and guided us with references and connections across applied mathematics and statistics using his remarkable memory and encyclopedic knowledge.

I learned a great deal, not least to decipher David’s notoriously tiny marginal notes, and that dimensional analysis is an invaluable tool in spotting mistakes in algebraic results. He led by example: everyone attended all the departmental seminars, as well as the Friday afternoon joint University of London seminars and lectures; and he led us physically too, almost running along Exhibition Road to South Kensington tube station and down the escalators—there was no time to stand still—to position us at just the right train door to enable a quick exit from the station at the other end (an essential life-skill in David’s eyes).

After I finished my PhD, David and I worked together on many problems to do with point processes, either relating to specific applications or contributing to the toolbox of generic models. As our collaboration developed, I gradually gained the confidence to question David’s statements made ‘off the top of his head’ when I didn’t quite understand them. It was reassuring to find that occasionally the issue needed further thought and even possible qualification.

David’s characteristic approach to applied problems to do with physical processes was first to construct a ‘mechanistic’ model by using a clever and insightful stochastic formulation to capture the essence of the process without losing any vital aspects, and then skilfully to apply analytic techniques from across the breadth of applied mathematics to obtain an algebraic solution. He seemed to possess an uncanny instinct to sense what would work. The formal solution then enabled comparison of important properties of the process with those of the model to check for model deficiencies, as well as allowing the estimation of any unknown parameters. The focus was always on gaining understanding of the physical process, and the parameters were often observable quantities whose distribution could be assumed already known. Even then, obtaining estimates from a model could provide a useful way of assessing its validity.

Intuition was always helpful in checking the results, although on one occasion even David’s formidable skills proved inadequate to the task. The problem was to find a correlation between counts in a bivariate point process generated by radioactive decay (Cox & Isham, 1977). The final expression is very simple, but we were never able to find a short, straightforward explanation of its form.

Bringing together our work on point processes in a monograph (Cox & Isham, 1980) was highly rewarding and enjoyable. We divided the material between us, wrote our own parts and then went over each other’s efforts. We included exercises, so I had to make sure that I could do all of David’s. I learned to write concisely, and to blend with David’s elegant and instantly recognizable style, trying never to use a phrase when a word would do. As our homes were only a few hundred yards apart, we met frequently in the evenings to work. Everything was handwritten of course and drafts often went backward and forward between our letter boxes. A long-standing running joke between us involved Christmases when David’s notes would be meticulously dated ‘25 December pm.’ To prepare the index, we each went through ‘our’ parts of the proofs with a big stack of index cards, and then arranged all the cards on the library floor to compile the final version. One item appeared frequently: the doubly stochastic Poisson process (Cox, 1955), universally known as the Cox process, except by David himself. As with the Cox (proportional hazards) model (Cox, 1972), David’s natural modesty prohibited any self-advertisement.

David met the highly distinguished Venezuelan hydrologist, Ignacio Rodríguez-Iturbe, by chance while at a statistics conference in Caracas in 1986, when he asked a random passer-by in a corridor (Ignacio) for directions. Over the following 20 years, the three of us worked together on stochastic spatial-temporal point process–based models, first for precipitation fields (Cox & Isham, 1988; Rodríguez-Iturbe et al., 1987, 1988) and later for soil moisture (Isham et al., 2005; Rodríguez-Iturbe et al., 1999, 2006). We would derive results independently to check each other’s work and, in the early days, we even had to resort to communicating by Telex, spelling out mathematical formulae (Greek) letter by letter. Ignacio was a wonderful collaborator, full of ideas, energy, and enthusiasm, and the three of us became very good friends. We always looked forward to meeting, and had enormous fun working together in Caracas, London, and Oxford. Ignacio, who also died in 2022, was the recipient of many prestigious prizes, including the 2002 Stockholm Water Prize.

At about the same time as we started working with Ignacio, David triggered my interest in epidemics. Epidemics and hydrology and, in both cases, the development and use of mechanistic stochastic models to inform the control of physical processes, have been a focus of my research ever since. In the mid-1980s the HIV pandemic was getting underway in the United Kingdom, and David suggested that I write a review paper (Isham, 1988) on epidemic models for HIV for a Royal Statistical Society discussion meeting. He also invited me to be part of a (British) Department of Health Working Group that he was chairing, charged with producing predictions of HIV and AIDS cases for England and Wales (Great Britain, Department of Health, 1988), and we worked together again to update these predictions 2 years later ( Public Health Laboratory Service Working Group, 1990).

We often discussed the interplay between science and policy that this work involved, and the problems and misunderstandings that can arise in communicating with nonspecialists. No doubt it was all good practice for some of the later consultancy roles on controversial topics with which David was involved (perhaps the ‘dreaded’ badgers, as David used to describe them). Most recently, we would mull over the many points of similarity between HIV then and SARS-CoV-2 some 30 years later.

David had many interests and was widely read. We especially shared a love of music and I treasure memories of several visits to the opera with him. He had a dry, deadpan humor and enjoyed gently teasing his friends—those twinkling eyes are much missed.

I am most grateful to Nancy Reid for her valuable comments on this essay.

Valerie Isham has no financial or non-financial disclosures to share for this article.

Cox, D. R. (1955). Some statistical methods connected with series of events (with discussion). *Journal of the Royal Statistical Society (Series B*), *17*(2), 129–164.

Cox, D. R. (1972). Regression models and life-tables (with discussion). *Journal of the Royal Statistical Society (Series B), 34*(2), 187–220.

Cox, D. R., & Isham, V. (1977). A bivariate point process connected with electronic counters. *Proceedings of the** **Royal Society of London*, *A 356*, 149–160.

Cox, D. R., & Isham, V. (1980). *Point processes*. Chapman and Hall.

Cox, D. R., & Isham, V. (1988). A simple spatial-temporal model of rainfall. *Proceedings of the** **Royal Society of London*, *A 415*, 317–328.

Davison, A. C., Isham, V. S., & Reid, N. M. (2022). Sir David Cox: 1924–2022. *Journal of the* *Royal Statistical Society (Series A), 185*(4)*,* 2295–2306. https://doi.org/10.1111/rssa.12964

Great Britain, Department of Health. (1988). *Short-term prediction of HIV infection and AIDS in England and Wales: Report of a Working Group (the Cox Report)*. H.M.S.O.

Isham, V. (1988). Mathematical modelling of the transmission dynamics of HIV and AIDS: A review (with discussion). *Journal of the Royal Statistical Society (Series A),* *151*(1), 5–30, 120–123.

Isham, V., Cox, D. R., Rodríguez-Iturbe, I., Porporato, A., & Manfreda, S. (2005). Representation of the space-time variability of soil moisture. *Proceedings of the** **Royal Society of London,* *A 461*, 4035–4055.

Public Health Laboratory Service Working Group. (1990). *Acquired Immune Deficiency Syndrome in England and Wales to end 1993*. Communicable disease report. Public Health Laboratory Service (CDSC).

Rodríguez-Iturbe, I., Cox, D. R., & Isham, V. (1987). Some models for rainfall based on stochastic point processes. *Proceedings of the** **Royal Society of London,* *A 410*, 269–288.

Rodríguez-Iturbe, I., Cox, D. R., & Isham, V. (1988). A point process model for rainfall: Further developments. *Proceedings of the** **Royal Society of London, A 417*, 283–298.

Rodríguez-Iturbe, I., Isham, V., Cox, D. R., Manfreda, S., & Porporato, A. (2006). Space-time modeling of soil moisture: Stochastic rainfall forcing with heterogeneous vegetation. *Water Resources Research*, *42*(6), Article W06D05, https://doi.org/10.1029/2005WR004497

Rodríguez-Iturbe, I., Porporato, A., Ridolfi, L., Isham, V., & Cox, D. R. (1999). Probabilistic modeling of water balance at a point: The role of climate, soil and vegetation. *Proceedings of the** **Royal Society of London,* *A 455*, 3789–3805.

©2023 Valerie Isham. This article is licensed under a Creative Commons Attribution (CC BY 4.0) International license, except where otherwise indicated with respect to particular material included in the article.