Oxford and Liverpool, 1968-1975

Peter Diggle (Lancaster)

Julian Besag, FRS 1945 - 2010

I knew Julian for forty years, first as his student, later as an academic colleague, always as a friend. And I owe him my career - for two different reasons, the one conventional, the other less so.

The conventional reason was that Julian was an inspirational teacher. I took two universities (Edinburgh and Liverpool) and five years to acquire my BSc, and the differences between the organisation of the statistics programmes in the two places probably explains why I found myself taking a succession of statistics courses which seemed to consist of more or less the same material taught with increasing degrees of sophistication. By my final year, in Liverpool, I was ready to finish studying and embark on a career either as a civil servant or an actuary when I took Julian's optional course in stochastic processes. This was a revelation. The material came across as intellectually challenging but always with a clear relevance beyond its technical content. We were taught about the extinction of family surnames (aka branching processes), social mobility (Markov chains), avoiding congestion at oil terminals (renewal theory) and much more. The end result was that I set my heart on an academic career and, in September 1972, went to Oxford to embark on DPhil studies under the supervision of Julian's former supervisor, Maurice Bartlett.

Which brings me to the less conventional reason. A few months later, Bartlett announced that he would be going to Australia the following academic year. Feeling somewhat disenchanted, I wrote to Julian to ask if I could continue my studies under his supervision in Liverpool. Julian visited me in Oxford, took me to dinner, satisfied himself that my request was "not just that you want to come back to Liverpool" and all was agreed. Shortly before I left Oxford, Julian called me to say that he had been asked to apply for a position at Newcastle upon Tyne but that "I told them I'll apply if they also have a job for you." To make a long story short, a job ad duly appeared, I applied for and got a lectureship - and Julian didn't apply at all! I'll never know now whether there really were two jobs on offer, but I suspect not. Happily, Julian did get a senior position at Durham soon after this, and I continued to benefit from his wisdom for many years, until we went our separate ways, Julian to America, I to Australia.

A regular highlight of our academic life was the trip to London for the Royal Statistical Society read paper meetings. These invariably ended up with a few hours of earnest debate in the White Hart on Tottenham Court Road before a dash to Kings Cross to catch the sleeper north and a few hours of alcohol-fuelled sleep. As to the time when I was awoken at Newcastle by two policemen inquiring about the identity of the gentleman who has shared my sleeper compartment until Durham... well, we had better draw a veil over that. Another memory is of the time we agreed to share our sandwiches on the way down to London. After we had demolished Julian's rations, I opened the re-cycled margarine tub in which I had packed my sandwiches to reveal ... a kilogram of margarine. The rest of the journey passed frostily.

Julian was known as a razor-sharp critic. He had an unerring eye for a sloppy argument, and when he saw one he wasn't afraid to point it out to the perpetrator. But if his criticism of others was sharp, his self-criticism was sharper. One of my greatest regrets, shared with other statistical colleagues, was that he refused to allow us to hold a celebratory meeting for him on his 65th birthday because he felt unworthy of it.

Paul Erdos used to say when he was ready for work "my brain is open". Julian's brain and heart were always open to me and to many others. And there was an awful lot inside both of them.

Raj Bhansali (Liverpool)

I am sorry that I am unable to be present at the conference in memory of Julian Besag,

I first met Julian in October 1971 when I had just submitted my PhD thesis at the London School of Economics and came up to take up my appointment as a Lecturer in Statistics at Liverpool University in the Department of Computational and Statistical Science; Julian was also a Lecturer in Statistics in the same department, and had come up only a year earlier from Oxford University. We were both rather young then, in our twenties, and drinking buddies. Apart from the similarities in our respective ages, we also had much in common in terms of our academic backgrounds; for example, our undergraduate degrees were in Statistics and we were both fortunate enough to be taught by some highly distinguished statisticians, Julian by Henry Daniels and his colleagues at Birmingham and I by Alan Stuart, Jim Durbin, David Brillinger and others at LSE.

We thus used to have a lot to talk about while having a pint or two on occasional evenings, or coffee in the staff common room in afternoons; we were often joined by other colleagues like Alan Veevers and David Downham and sometimes by Valerie, Julian's wife. We also used to see each other socially. He was kind enough to invite me to his home several times, and he and Valerie had been to my own home. Julian lived in North Wales and from time to time I would take a lift from him to my own home on the Wirral, which was on his way.

Our conversations were wide-ranging, covering teaching, research, personal life and the statisticians we admired.

Julian used to teach a module on Statistical Distribution Theory to second year undergraduates at Liverpool while I used to teach a module on Statistical Methods to the same group of students. A "bee in Julian's bonnet", as it were, was that the distribution theory was best taught by introducing discrete distributions and the associated ideas of Generating Functions. Julian was also behind some of the innovations in the undergraduate teaching that were introduced about the same time, including a final year undergraduate project in Statistics and a module on Applied Probability.

In terms of research, Julian was at that time working on developing his famous 1974 read paper. He used to talk a lot about the Hammersley-Clifford theorem and the conditional vs simultaneous approach for spatial autoregressions. I had brought to his attention a paper on the frequency domain approach to analysis of spatial data but, I suppose because he was working on developing parametric models for spatial data, he had, wrongly in my view, dismissed it as "classical". I also remember asking him about the spectral density of the model he was proposing and asking whether this was equivalent to specifying that the inverse correlations of the model should vanish outside a finite region.

At one point, out of sheer frustration at having to get on top of some rather technical literature in this area, he offered me joint authorship of his 1974 paper, but I declined on the grounds that my own contribution was not substantial enough.

I was in the audience when Julian had presented his 1974 RSS paper. The meeting was chaired by Jim Durbin as the then Chair of the RSS Research Section. I still remember Peter Whittle getting up and urging that one should avoid being partisan about the conditional vs simultaneous approach, and David Cox remarking that the paper represented a major advance in the analysis of spatial data. In fact, Julian had originally submitted his paper to Biometrika, but David Cox had written back to suggest that it should be submitted for reading to the RSS instead.

Julian had of course "arrived" after the success of his 1974 paper. He was offered a job at Durham University as Reader in Statistics, which he took up. He was also invited to visit Princeton and came back infused, indeed inspired, by John Tukey's ideas on Exploratory Data Analysis. I also remember the sense of elation he had felt at being asked by Pat Moran to be a joint author on their Biometrika paper and the sense of dejection when he was ignored in favour of another person for organizing a session on spatial data at an ISI meeting.

Underneath a tough exterior and an admonishing, if not adversarial, style, Julian was a very kind person. An episode that I distinctly recall concerned a former colleague, who was on a fixed term contract in the OR section of the department. and was about to be denied tenure. Julian had organized a petition in support of this person and helped to secure his tenure. Julian was also very kind towards me personally and helped to instill in me the importance of pursuing research in academic work.

Like many of his friends and colleagues, I am indeed glad to have had an opportunity to come across Julian and to share with him a part of my early career in the academic world.

David Green (Bermuda)

This is a bit late in coming but I wanted to add my tribute. Julian was my lecturer in Liverpool between 1970 and 1974. My first memory of him was of the way he dealt with the wayward behavior of students attending his undergraduate lectures. No doubt the audience attending his research presentations accorded him the respectful silence and total attention his genius deserved, but undergraduates are often less appreciative of reputations, and anyway in the early 70's he had yet to make his mark. If anyone dared to talk whilst he was at the blackboard with his back to us, he would stop, turn to face the offending student and subject them to a silent evil stare until they desisted. One got the impression that real anger was only just below the surface on these occasions, but the fearsome look always achieved the desired effect without ever the need to resort to a verbal assault on the perpetrator. Reference has been made in other contributions as to the importance Julian placed on illustrating the application of his theoretical results to practical problems. I witnessed an early example of this when he posed a statistical question about the likely position of a snail climbing a wall in whom forward and reverse movement was determined by a probability distribution. My solution was liberally illustrated with pictures of a snail at various heights from the ground. When my work was returned, Julian had commented 'excellent' at my pictures of the snail but appeared to be less impressed with my solution!

My mum loved him after meeting him for the first and last time, a meeting that lasted all of 10 minutes; on my graduation day my parents and I were in the local pub celebrating and Julian was sitting alone at a table. I explained to mum who he was. Mum was very shy, but boldly walked over and said "what do you think of my son". Julian would not offer an opinion whilst I was there so I was banished. Apparently he said some nice things and mum was very pleased! I thought, and still do, that it was very human thing for him to do, but then Julian always maintained that common touch despite his genius.

Even back then I found him an inspirational guy and I had the honour of 'helping' him in his research by undertaking a final year honours project with him and subsequently being appointed as his research assistant for an all too short six weeks immediately after I had just finished my degree - he had offered me the post as I sat at the examination desk having just started my finals exam paper in statistics. I said yes just to get rid of him so I could concentrate on the job in hand! It was a magical six weeks and during that time I experienced his impatience, his quick temper, his phenomenal intellect but also his humanity. He would often interrupt my efforts at lunchtime and 'drag' me off to the pub for a few beers, which seem to stretch into the late afternoon most times! He would then go back to his office and continue his research, whilst I was too wasted to do anything. My work involved writing computer simulation programs to support the theoretical results of his seminal 1974 paper. On completion he invited me to attend the Royal Statistical Society meeting in London when his paper was read. It remains one of my biggest regrets that I was too stupid to realize what an honour it was to be invited to such a momentous occasion. In truth I was so impecunious I could not afford the train fare, not that I admitted it to Julian. If he was disappointed I don't recall that he showed it, but he had his 'revenge' when an original draft of his written reply to the commentary, in which my name was mentioned three times, was reduced to a solitary mention for the final draft! I jest of course; I was witness on several occasions the lengths Julian went to to ensure his written contributions were devoid of unnecessary verbiage. There are 3 other episodes I would like to mention since they illustrate various facets of Julian's complex character.

It had been rumoured (and Julian confirmed to me it was true) amongst the postgraduate students in the Department of Computational and Statistical Science at Liverpool, that Julian had cornered the head of department and threatened to thump him because he had complained about Julian's excessive use of his office phone! Julian also admitted to me that whilst employed as Bartlett's research assistant in Oxford he was unable to afford to rent accommodation so he slept on the floor of his office. On another occasion he called me into his office and said it was the worst day of his entire academic career. He had discovered a flaw in his work that potentially invalidated all that had gone before. I can't remember the details now, but I do recall he talked me through the steps that had led to this conclusion and at a critical point in the argument asked me what the next step should be. In a rare (for me) flash of insight I gave him the correct answer, but in reality it was because of his own clarity of thought and in his ability in making complex ideas accessible that made my response possible.

Julian went off to Princeton and suggested I come with him and start a PhD. He had inspired me sufficiently to want to do a PhD, but I had personal reasons for wanting to remain in UK. On his return to Durham he asked me to present my own research at one of his departments regular research meetings. It was a bit daunting to have such august statisticians minutely scrutinizing my work, but Julian put me at ease and seemed genuinely interested and enthusiastic about what I had to say. He was however, incensed that his own PhD student had failed to attend the meeting. I remember thinking I wouldn't want to be in that person's shoes when Julian next saw him!

When Julian went to Seattle we exchanged infrequent personal letters for a few years but met up only once when he returned to Liverpool for a hockey reunion. He stayed over at my house and we spent a very pleasant evening drinking and catching up. Our written correspondence eventually became an email exchange. I was new to email and rather abused the situation. I 'foolishly' included in my emails trivia such as my squash score, not realising how irritating it can be to receive such 'junk' mail. He tried hinting that he wasn't interested, but when I paid no heed, he told me to stop wasting his time and not to email again (typical Julian)! I must admit I was more than a bit miffed at the time and I didn't make contact until many years later when I sent him a copy of a paper I had published that stemmed from my PhD thirty years earlier. I guess I still felt guilty about what had transpired and wanted to impress him. Thankfully we renewed our friendship, but shortly afterwards he became ill. I realized during my PhD that I didn't have the ability to be successful as a research statistician, so after its completion I retrained as a medical doctor. I therefore had sufficient insight to justifiably feel appalled to learn from Julian that failings by the medical profession may have contributed to the onset of the renal disease that eventually led to his untimely demise. Julian, from what I have heard, had enough self-inflicted demons to deal with, without having to live with the knowledge that his illness could have been avoided.

My final regret is that I never took him up on his offer to visit him on his houseboat. I always thought there would be plenty of time to do that. Requiescat In Pace.

Frank Kelly (Cambridge)

For me, personally, an influential paper of Julian's was:

"On spatial-temporal models and Markov fields" published in the Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, and of the 1974 European Meeting of Statisticians (1974, Czechoslovak Academy of Sciences). It linked reversibility, local dependence structure of the spatial-temporal model, and Markov field stationary distributions.

In those early days I was privileged to have been on the receiving end of Julian's intense questioning, and very much encouraged by his fierce interest and special charm.

Bernard Silverman (London)

Others will have written appreciations of many aspects of Julian's work and life, but I wanted to say a few words about the way he encouraged a whole group of us who were graduate students or new PhDs in the mid 1970s. In those days RSS read paper meetings one Wednesday a month were a kind of "gathering of the clan" of a group who came from various parts of the country, whatever paper was being read. We used to hear the paper discussed at the London School of Hygiene, then go to the original Bertorelli's in Charlotte Street for dinner, and then on to a pub near Warren Street Station whose name I regret I can't remember. Bertorelli's was probably the same as it had been in the 1920s ... white tablecloths and white-coated waiters, traditional Italian food at what would nowadays be very moderate prices, and so on.

There was a regular group of us there, of whom Julian was probably the senior and I the most junior. Some of the others are also here today, but I am probably the only one who still had to pay his bus fare to get here from the station (and that won't be for much longer!). It was at these meetings that I first got to know Julian, and there were all sorts of ways in which he was enormously encouraging to me at that time.

Julian often contributed to the discussions of the papers himself and encouraged others to do so. It's not surprising that one of his discussion contributions has attracted over 200 citations. He set an example of genuine intellectual curiosity and the desire to get to the truth of the matter through straightforward discussion. His public approach during the meetings themselves of course spilled over into all the informal conversation afterwards. And of course the networks started off at RSS meetings grew into the lifelong friendships that have brought so many of us here today.

To me, Julian was always engaging and encouraging. There were a number of people at that time who gave me the impetus to pursue research in statistics as a career but Julian was one of the foremost. I am very grateful to him.

It's perhaps inevitable, given the specialisation within the subject and the pressures on people's time, that RSS Ordinary Meetings aren't the more universal networking opportunity they used to be. I remember a distinguished American colleague once saying at that time that if you wanted to know everything about what was going on in the subject, all you had to do was to read the published discussions in the RSS journals. What made it work was a combination of factors: the willingness of editors and committees to take risks and publish often controversial and unfinished papers; leaders in the field like Dennis Lindley and David Cox who brought insightful comments to almost every topic; but perhaps above all what I now realise were younger researchers like Julian who often spent a lot of time thinking about the particular paper under discussion, and who also made the meetings far more than just the discussion of a paper!

Kanti Mardia (Leeds)

Julian Besag and Leeds

Julian Besag was a good friend to me and to our Statistics Department, and supported activities at Leeds including our Leeds Annual Statistical Research (LASR) Workshops.

I met Julian in 1973 while, I think, giving a seminar in Liverpool University. I recall he had shown me what he was working on for his RSS discussion paper; he mentioned about Markov Random Fielda (MRFs) with great enthusiasm but I did not have a clue what he was talking about until he mentioned its connection with some of Bartlett's work which was a hot topic then. I thought he would be a great presenter at the International Statistical Conference in Delhi in 1977, and I was really delighted that he accepted the invitation. We enjoyed his presentation on spatial point processes (Besag, 1977, ISI) and learnt that still there were a few things needed. I could see even then that he was already doing his own computation (in APL); his computational skill became an important point in developing modern statistics. I always found him very focussed and could see him using the same data in different ways so as to extract the hidden truth.

Julian enjoyed his trip to India in 1977, and in LASR 2000 he showed the group photograph (especially pointing out my absence from the photograph) saying humorously that perhaps I had disappeared to a Jain temple. I later edited two volumes on statistics and images. In Volume 1 (1993) he revised his paper, previously published in 1989 in the Journal of Applied Statistics, which I also edited. Also in the same volume, I reproduced his discussion paper from JRSS B in 1986, for which, if I am not mistaken, he made some corrections. He declined the invitation to contribute to the second volume (1994), but suggested whom I might contact.

I learnt more about MRFs in 1979 and thought there was great scope for future development, so invited Julian to our LASR workshop in 1981, 30 years ago! At that time the Workshop meant that the speaker had to give an instructional course for three days; he gave a very thorough review. Julian stayed with us in our house in Ilkley, very near the Cow and Calf Rocks, and I am sure he went up the Rocks.

I was already teaching an MSc course in Geostatistics (Kriging) in 1979, but he was never happy with Kriging; in my notes of 1981 I recorded his comment that a continuous system cannot be self-consistent, in that `what is observed and what is to be predicted cannot be on the same footing'. In fact he told me many times that one should use MRFs even for irregular data. However, I thought MRFs were alright for lattice data but had challenges for irregular data.

Now and then he would pose deep problems, that were not easy by any means. In 1991 we went to an interface meeting in Seattle and he kindly agreed to be a discussant to a paper by Michael Miller and Ulf Grenander. I recall when we were coming back I had a lot of luggage (antiquarian books that I had acquired, in particular). He was kind enough to carry a very heavy suitcase at Heathrow, on the underground train, and subsequently until I was on the train at King's Cross. I think in 1981 he said to me that he would come to LASR if I invited him - a promise he kept! This led to invitations to LASR 2000 and LASR 2006, which he attended although he was not well. In LASR 2000 and LASR 2006, as usual he had new topics, generating a great discussion in both workshops.

The proceedings of LASR 2000 were special in that all the participants signed the copy presented to me; on his joint abstract in his own style he simply wrote "With every good wish, Julian".

Two problems in particular arose from the 1981 LASR Workshop: 1. How should one formulate multivariate MRFs? 2. When is pseudo-likelihood exact?

The first problem led to my paper in the Journal of Multivariate Analysis (1988), and the second to my joint paper (Biometrika, 2009). The second topic has also become important, eg. in certain directional problems the full probability density has an awkward normalizing constant, but the conditional and/or marginal distributions are much more tractable. The main emphasis in the paper is on n independent, identically distributed multivariate observations. In 2006 at the LASR workshop I gave him the manuscript for his comments, reminding him that we had discussed the problem in 1981. I warned him that as yet there was no spatial context, and he said he would definitely look at it, but I am sure his health problems prevented him sending comments to me, though he might have been a referee!

He was always generous in quoting my work, for example the intrinsic random field (IRF-0) which John Kent and I used for fuzzy classification (1988, IEEE PAMI). I believe we at Leeds learnt a lot from him about spatial statistics. Julian impressed me as a kind and generous person, always full of ideas, very focussed and innovative; he was ahead of his time. He was a man of quality who went for perfection, and will be missed as a great friend.

Noel Cressie (Ohio)

I first ran into Julian at Princeton University, during the 1974-5 academic year. He was visiting the Department of Statistics there (with his wife, Valerie, and their young son David), on his way to Durham University and the next stage of his career. I was a PhD student in the Department. Julian had written a remarkable paper the year before, on Markov random fields, and it had just been read before the Royal Statistical Society. I took his course on stochastic processes and had the amazing good fortune to learn this material directly from the master. He prepared meticulous notes in a way that only those who knew Julian would understand. When I came to know him better, I sometimes saw him tear up two hours of preparation and start again. The course was fabulous, but I confess that I didn't fully understand the material until a few years later. Julian was also an examiner of my PhD dissertation, written under the guidance of Geof Watson, although the research was on goodness-of-fit testing, not spatial statistics.

We bonded on several fronts, through statistics, our Commonwealth roots, and our love of hockey. I played for a team called the North Jersey Field Hockey Club, and Julian quickly became a regular on our team. We suffered long hours of travel, rough pitches, awful referees, and crazy weather, all for that "hockey rush". In the years that immediately followed, we found ourselves together on various continents, and we were both fanatical enough to have packed our hockey sticks. We would boast sometimes that we had played hockey on every continent except Antarctica - that was probably a stretch, but anything is possible when you're telling stories in a pub.

Julian's research on Markov random fields and spatial point processes was path-breaking. He was my teacher; at times we disagreed about things that seemed small to me. They weren't small to him, and our relationship suffered. I had always hoped for it to improve.

We are the poorer for his passing. Vale Julian.

Peter Green, School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK.
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