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A Note on Knowing David Cox

Published onApr 27, 2023

A Note on Knowing David Cox

I was privileged to have David Cox supervise my PhD studies. My first substantive conversation with him was on foundational inference topics related to the interpretability of the likelihood function without reference to a sampling distribution, when, as I recall, we did not reach complete agreement. This was, perhaps, the only statistical topic on which I ever disagreed with him!

As a supervisor he was very supportive and he would always follow up any request of mine for a conversation very quickly, often coming to my office to say, “Are you free now?” I do not remember saying no! During these conversations in his office, as during seminars, he would sometimes appear to be ‘nodding off’ but his subsequent comments were always incisive.

I arrived at Imperial College, from Canada, interested in medical statistics. With no medical school at Imperial then, David directed me to Peter Armitage to identify potential medical collaborations. The breast cancer research that motivated my PhD work thus arose out of David’s recognition that such collaborations often identified important methodological problems.

I was also influenced greatly by David’s fostering of exposure to the broad spectrum of statistical research and techniques. Generally, this was through his encouragement to all research students to participate in statistical seminars, including the very well-attended Friday afternoon London seminars, organized jointly by various departments and having a wide range of topics and speakers. Royal Statistical Society (RSS) meetings were also given high priority, and a research students’ seminar at Imperial provided an opportunity to consider a variety of topics in an environment of peers but also allowed us to closely examine RSS ‘read’ papers that were presented at a meeting of the RSS, along with invited discussion. In particular, I remember working through the EM (expectation-maximization) algorithm paper (Dempster et al., 1977) and thus becoming convinced that it ‘really does work.’ I think it also says something about David that he was, intentionally, the only staff member attending these student meetings. I remember him as largely quiet, perhaps editing some *Biometrika* papers while listening, but helpfully intervening with timely comments. I believe that broad exposure to statistical research is at risk today as specialization is increasingly the norm, perhaps to some extent inevitably, in the current research climate.

David was also concerned with more detailed exposure to specific statistical topics of general applicability. Two particular examples to which he directed me were asymptotics and stochastic processes. This wider training seemed also to be part of ‘doing a PhD’ with David Cox at that time.

I have been heavily influenced, of course, by David’s papers. I also appreciated the opportunity to develop and teach a short course on survival analysis with him. It was revealing to see his emphases and, also, his openness to new ways of looking at his own work for presentation purposes. However, various informal conversations were also influential, sometimes with substantive results. While my PhD thesis was ‘out for review,’ a corridor conversation led to a short paper on multiple time scales in life testing (Farewell & Cox, 1979). This paper provides an example of David’s approach of trying to simplify the essentials of a problem to a tractable analytic framework. I have found his approach very helpful: focusing on primary aspects of a problem and adopting simplifying assumptions about secondary aspects. Later in my career, another corridor conversation (when I asked him about a paper in the *British Medical Journal*) led to a letter regarding a somewhat unfair characterization of frequentist statistical methods and thus rather imbalanced advocacy of Bayesian methods (Cox & Farewell, 1997). David had personal opinions on foundational aspects of statistical inference, but he also modeled balanced discussion of issues and this motivated our letter. In this regard, I remember him telling me once that his ‘generation’ of British statisticians were influenced in their respect for each other by the pitched, and often unpleasant, battles seen in the previous generation! I should also mention the pleasure of wider ranging interactions with David during conferences organized by Agnes Herzberg on ‘Statistics, Science and Public Policy.’

My son Daniel met David at a very young age, first in the throwing of water balloons and, later, as David demonstrated the attraction of English billiards. However, he also met Daniel on a train to London when he was starting out in medical statistics. Daniel was so impressed that David would take the time to converse with him throughout the journey. This evidenced David’s interest in and support for young statisticians generally. Much more recently, Daniel had an occasion to present to David some foundational inference ideas related to likelihood, somewhat similar to mine many years previously, about which they also did not reach complete agreement. As David said on another occasion, with regard to his reaction to highly spaced presentations from George Barnard, early in the 1940s and then in the mid-1980s (Barnard, 1985), “It’s nice to see invariance.”

Much more could be said but, simply, I am extremely grateful to have known David Cox.

Vernon T. Farewell has no financial or non-financial disclosures to share for this article.

Barnard, G.A. (1985). *A coherent view of statistical inference (with discussion)* (Technical report). Department of Statistics and Actuarial Science, University of Waterloo.

Cox D. R., & Farewell V. T. (1997). Letter: Qualitative and quantitative aspects should not be confused. *British Medical Journal, 314*(7073), 73.

Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM Algorithm (with discussion). *Journal of the Royal Statistical Society, Series B, 39*(1), 1–38.

Farewell V. T., & Cox D. R. (1979). A note on multiple time scales in life testing. *Journal of the Royal Statistical Society, Series C*, *28*(1), 73–75.

©2023 Vernon T. Farewell. 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.

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