## A Realised Path

## The Cambridge Statistical Laboratory upto 1993 (revised 2002)

## Contents

- 1. Clarificatory
- 2. Prehistory
- 3. 1947-55 Creation and confirmation
- 4. 1955-61 Disaster and diaspora
- 5. 1961-66 The Chair of Mathematical Statistics; Resurgence
- 6. 1966-72 The Churchill Chair; Redefinition
- 7. 1972-85 Comings and Goings
- 8. 1985-92 Martingales and the Mabinogion
- 9. 1992- Regeneration
- 10. References

## A Realised Path

The hope that these notes would have some claim to serve as a document of record has limited the character of the anecdotal material that could be included; roughly, it could not be gratuitously hurtful and it had to have some point.

The following abbreviations are used in the less formal parts of the text: Lab for Statistical Laboratory, UL for University Lecturer, UAL for University Assistant Lecturer, OR for Operational Research, DPMMS for the Department of Pure Mathematics and Mathematical Statistics and DAMTP for the Department of Applied Mathematics and Theoretical Physics.

Some of the long-serving members of the computing staff figure in the article. The members of the secretarial staff have been many and various; rough justice is perhaps best achieved by naming the first and the last, both of whom have some special character. Beata Reifenberg was the Lab Secretary in the St Andrew's Hill days. Wally Smith says of her: ``I have seldom encountered an equal in all the days since then. Her great ambition was to be able to afford to buy all the Brandenburg concertos on long-play records''. Sarah Shea-Simonds has been Secretary since 1985; it is Sarah who stirred the Laboratory into the actions, long contemplated but not hitherto undertaken, of celebrating this anniversary and writing this history.

This 2001 revision of the text corrects some minor errors and adds material which came in too late to be incorporated in the 1993 version; notably from Frank Anscombe, Norman Bailey, Colin Campbell, Anthony Edwards, Charles Goldie, David McLaren and Ingram Olkin. These additions still concern only the period up to 1993 (to the point of an apparent obliviousness of staff changes made soon after); events after that are left to some other chronicler.

There had been considerable activity in statistics in Cambridge well before 1947, distinguished initially by some striking individual figures and then by a quickening recognition of the subject as a field in its own right. In coverage of the earliest phases we draw largely (and briefly) on Edwards (1991).

Edwards regards statistics as beginning in Cambridge with Augustus de Morgan (matriculated 1923), followed in that century by R.L. Ellis (1836), J. Venn (1853), J.W.L. Glaisher (1867), all prime names in any history of statistics or probability. F.J.M. Stratton (1901) lectured on the Combination of Observations; Edwards' mention that Fisher attended his lectures in 1911 gives a link with living memory.

In 1912 a University Lectureship in Statistics was established to which G. Udny Yule was appointed, working in the Faculty of Agriculture. Yule was already the author of a very influential textbook ( *An Introduction to the Theory of Statistics*, Griffin, 1911), but is now remembered for his subsequent work in time series analysis. He opened a new era in this subject by his proposal of the autoregressive process. Yule retired in 1931, by then a Reader, but remained an active figure. Maurice Bartlett mentions of his postgraduate year (1932/3) that Yule ``was very much one of my mentors, as he no doubt was of Maurice Kendall, who was a Cambridge student *before* the Wishart era''

While the Statistical Laboratory has been the product of many influences, it is in the School of Agriculture that one rightly sees its genesis. Statistics has been fostered there as a tool and as a discipline from the days of Professor T.B. Wood, Udny Yule was a seminal and international figure and it was the interaction of the School and the Faculty of Mathematics (through the mediation of John Wishart, as we shall see) which produced both the Statistical Laboratory and the Diploma. The School has continued its own vital interest in the subject with the A.R.C. Statistics Group. The history of these developments has been set out very thoroughly by Colin Campbell (1959).

Harold Jeffreys came squarely on to the Cambridge academic scene when he was appointed a College Lecturer (St. John's) in 1922, this being converted to a University Lectureship in 1926. Jeffreys' primary interest, which was geophysics, stimulated him to a strong derived interest in inference. His books *Scientific Inference* (Cambridge University Press, 1931; third edition 1975) and *Theory of Probability* (Clarendon Press, 1939; third edition 1961) established his reputation in that field, then and now. Jeffreys' approach to inference (and by `probability' he often means statistical inference; by `inverse probability' he always does) was explicitly Bayesian, with maximum entropy criteria also clearly formulated, and so still finds considerable resonance.

Yule was succeeded on retirement in 1931 by John Wishart, arriving from Rothamsted. Wishart's Readership was primarily assigned to the Faculty of Agriculture, but the terms of his post directed him to give courses for mathematicians as well as for postgraduate students in agriculture. Bartlett writes: ``as there was space allotted to Wishart in the School of Agriculture, where practical classes in statistics were given, my own inclination is always to think of a `Statistical Laboratory' being in existence from Wishart's arrival in Cambridge''.

Some idea of the activity at this time may be gained from Edwards' observation that a student taking Part III of the Mathematical Tripos in 1935/6 ``could hear Sir Arthur Eddington's `Combination of Observations' in the Michaelmas Term, John Wishart's `Theory of Statistics' in the Lent Term and Harold Jeffreys' `Probability' in the Easter Term''. Indeed, in 1931/2 Maurice Bartlett took just these courses, with the substitution of Fowler's `Statistical Mechanics' for Jeffreys' course.

In these days of student appraisal of lecturers etc. it is interesting to note how common it seemed to be then that even interesting material or brilliant intellects were accompanied by indifferent delivery. Some of us can take heart! Henry Daniels says of Wishart that ``although the lectures themselves were not very well given, the material was very interesting'' and of Eddington ``intriguing, and a little bizarre in some respects''. David Finney writes of Jeffreys that his ``personal charm and enthusiasm did not prevent a steady decline in attendance''. Norman Bailey recalls Jeffreys' lectures as being ``interesting but difficult, not least because from time to time Jeffreys would become inarticulate, simply waving his arms while his brain moved on. When he rearticulated some minutes later in a perfectly lucid way it was apparent that *we* had just missed what he had thought but had been unable to say in those precious minutes''.

One might also note the number of people, later to become prominent statisticians, who passed through Cambridge *before* the foundation of the Statistical Laboratory: e.g. Yates, Bartlett, Finney, Maurice Kendall, Daniels, Cochran, Barnard, Cedric Smith and Armitage.

Wishart was all the time endeavouring to promote the subject of statistics, and in fact to develop a programme in mathematical statistics. In this he was not positively helped by the presence in Cambridge of the two luminaries of the subject: Jeffreys and Fisher (who had been appointed Professor of Genetics in 1943). These two were of course accorded the respect of the Faculty of Mathematics, which Wishart (based in Agriculture) was not, and Wishart had the ambition of creating a working unit in statistics, which they did not. A lofty word from either of them could have a withering effect.

However, the Faculty of Mathematics evidently felt the need for some in-house strength in statistics, and in June 1938 advertised a University Lecturership for which special consideration was to be given ``to candidates with qualifications in the Theory of Statistics''. Maurice Bartlett was appointed. With a break for war-work he held the post until 1947. He lectured first largely in statistical theory, a subject which was still evolving to the shape we would recognise today. Bartlett combined ideas which were in general circulation with his own statistical research (never recognised at its full pioneering worth). Frank Anscombe took notes of this course which Henry Daniels later read, to realise that ``Bartlett's approach to the subject was one that I sympathised with very much''. Violet Cane attended Maurice's statistics course in 1939/40; she recalls finding it difficult at the time, but realised later that she had (and still has!) a beautiful set of notes. Development of ideas was then the consideration, rather than rigour, so, when Dennis Lindley asked Bartlett to prove consistency of the maximum likelihood estimate in class in 1946, this was a little cruel, as he himself admits. It was to be yet a while before a good proof was found by Wald (and, actually, by Lindley also).

Maurice Bartlett is of course specially noted for his early and fundamental contributions to the theory of stochastic processes, but it is first after his return from war work that he seems to have given a course on the subject , whose reach had still not been defined by a text. Bartlett's own text was one of the very first. The course included stationary time series and diffusion processes as special topics. Norman Bailey attended it in 1946/7. He had trouble with time series component, ``but the evolutionary process component was nothing short of inspiring and had considerable importance for a lot of my later applied research". Wishart was also absent on national service during the war years, when his lectures were given by Dr J.O Irwin. Also, for at least one of those years, mathematics undergraduates were required to come up during the summer vacation to study electronics. Norman Bailey recalls enjoying the electronics much more than the statistics. Jeffreys also later gave a short course in statistics, reputedly to Wishart's annoyance.

Maurice Bartlett has kept copies of a three-way correspondence in 1943 between himself, Wishart and F.P. White, then Secretary of the Faculty Board of Mathematics. The former two were both away on national service; Bartlett writes from the Projectile Development Establishment in Aberporth and Wishart from the Civil Establishments Branch, Admiralty, Whitehall. White had written to all teachers of Mathematics in the University, including those on national service, asking for their views on the pattern to be envisaged for the Faculty and its activities after the war. The Faculty still had no collective physical accommodation, and had reported immediately before the war that its most urgent need was ``the foundation of an Institute of Mathematics in close proximity to the Mathematical Laboratory and the Philosophical Library''.

Wishart was of course concerned with the position of Statistics; he plainly wished to escape from Agriculture, whose interest in Statistics he considered too narrow, and very much wished to be associated with the projected Institute. On the other hand, he considered that Statistics should occupy a central position relative to a number of Faculties, and sketched a case for the establishment of a separate Faculty of Statistics. He nevertheless obviously regarded the Faculty of Mathematics as the best single peg on which to cling immediately: ``Returning to the question of the Institute, an `embryo' school of Statistics should certainly be housed therein''. He wished such a school to be open to members of any Faculty, but that its fundamental basis should be mathematical.

Bartlett, already a member of the Faculty of Mathematics, was more concerned with the provision of advanced courses. This meant Part III courses; the Diploma was not yet envisaged. He was particularly concerned to gain coverage for statistical (in fact, probabilistic) thinking in physical contexts, and for a new course on the `theory of stochastic processes', a topic then more familiar to some under the names of `random functions' or `time series'.

The demand for trained statisticians revealed during the war was such that in 1946 a second University Lectureship was advertised, to which Henry Daniels was appointed. Wishart could now see his long-nursed ambition of a Diploma in Statistics approaching realisation. There were discussions about the content of the proposed Diploma. Maurice Bartlett recalls a degree of irritation when, during his convalescence after an appendectomy in 1946, he was ``visited by Wishart in the nursing-home to discuss the final draft Diploma regulations. These included the requirement to take a `field of application', which was facilitated by the link with agriculture and with genetics, following the appointment of Fisher during the war to the genetics chair''. Bartlett himself missed out on the actual foundation; in 1947 he left to become the first Professor of Mathematical Statistics at Manchester. He was replaced in Cambridge late that year by Frank Anscombe, from Rothamsted, who took up the post in January, 1948.

**3. 1947--55 Creation and confirmation**

In 1947 the Faculty of Mathematics submitted a report to the General Board proposing the establishment of a Diploma in Statistics and a Statistical Laboratory, the former to be awarded to mathematicians who had attended a course and been examined in theoretical and applied statistics, and the latter ``to provide primarily for the applied work in Statistics for students of this and possibly of other Faculties, including Diploma and Research Students''.

This was considered by the General Board in a Report dated 14th May 1947 ( *Reporter* , 1946-47, p. 1058), which indeed recommended the institution of a Diploma in Mathematical Statistics. The qualification `Mathematical' had been inserted to quell the concerns of some other Faculty Boards that the statement in the Diploma document that the candidate had displayed a special knowledge of Statistics and of its application in a certain field might be taken to imply that he was an expert in that field. Wishart's lifelong enthusiasm for the teaching of statistics was now being rewarded, and his dreams of a properly-established unit being fulfilled. At a Royal Statistical Society discussion meeting on the Teaching of Statistics which he opened he was able to report with pride that ``it is now possible for a mathematical graduate at the University of Cambridge to take a one-year Diploma in Statistics, during which time he will be attached to a department where practical work is done, and will be examined finally on his work in the chosen field of application'' ( *J. Roy. Statist. Soc.* A (1948) 111 , p. 227). This relates to an interesting theme which emerges repeatedly in the discussion: the need revealed during the war for statisticians with both practical and mathematical competence.

Fisher commented on these developments with his usual blend of soundness and tetchiness; Edwards quotes passages from his daughter's biography of him (Box, 1978). Fisher's own words at the end are from a letter to Wishart in which he agrees to serve on a small advisory Committee for the Diploma.

- ``After the diploma in mathematical statistics at Cambridge was offered, to be awarded in recognition of one year's work in statistics for graduates in mathematics, Fisher expressed the opinion 1949 that the regulations would only work well for those students who had already taken mathematical statistics to Part III [of the Mathematical Tripos] and who gave their year's work principally to understanding an
*applied*field. It seemed to him the attempt by means of a single-year course organised by the faculty of mathematics must necessarily fail to supply the real demand for statistical training: - `
*There is no wide or urgent demand for people who will define methods of proof in set theory in the name of improving mathematical statistics. There is a widespread and urgent demand for mathematicians who understand that branch of mathematics known as mathematical statistics but who are capable also of recognising situations in the real world to which such mathematics is applicable*.' ''

In 1950 the University did indeed amend the regulations for the Diploma so that candidates without adequate mathematical preparation could be required to take two years over the course. Developments in the world of statistics over following years doubtless reinforced Fisher in his apprehensions. However, the Cambridge Diploma has remained true to its initial conception: that the theoretical grounding should be accompanied by close acquaintance with an applied field and a testing investigation of data from that field.

The General Board report quoted above passed over the question of the foundation of the Statistical Laboratory as an institution, but nevertheless discussed the provision of accommodation for the Laboratory. Whether this was deliberate is unclear. The Buildings Syndicate had already indicated its conditional preparedness to ``recommend the assignment of a vacant site in Corn Exchange Street for a temporary hut'' ( *Reporter* , 1946--47, p. 1296). So, the Statistical Laboratory existed to the considerable extent that it was to have its own building, erected to its own specifications submitted through the Faculty Board of Mathematics. More than that, eloquent and conclusive, the structure when completed carried a sign: `Statistical Laboratory'. The building was indeed a `hut': brick, single-storey, 70 feet by 24, with six working rooms, one of these being a larger `students' room' which served also for seminars. It faced on to St Andrew's Hill, a lane off Corn Exchange Street which has since been obliterated by the Lion Yard car park.

Dennis Lindley's recollection of the plan of the building and its eventual occupancy is sketched below. Dennis's impression is that David Cox used whatever room happened to be spare, although this presumably did not continue. He mentions also that Wishart's original plans made no allowances for lavatories. We see them here beside the boiler, of which more anon.

For the session 1947/8 accommodation had perforce to be found in the School of Agriculture, classes being held there and in the Arts School. Frank Anscombe recalls Henry Daniels demonstrating his Bicycle Theory (a counterintuitive steering theory) outside the School of Agriculture building, so remembered with affection. However, in 1948 the staff (namely: Wishart, Daniels and Anscombe, with two computing assistants: Donald East and Ena Laurie) moved to St Andrew's Hill. Wishart seems to have shifted from his quarters of 16 years in the School of Agriculture without hesitation. Bartlett comments: ``Wishart was always keen to `push' statistics, and I don't know whether this contributed to his falling-out in due course with Engledow, then Director of the School of Agriculture, and that in turn to the creation of the Laboratory''. However, that the School of Agriculture had indeed been helpful is indicated by an acknowledgement in the report from the Faculty Board of Mathematics: ``In the past, a number of graduates in Mathematics were encouraged to spend a fourth year in research and in equipping themselves as practising statisticians; the Board have been indebted to the Department of Agriculture for equipping a small laboratory which provided the necessary facilities''. Such an origin certainly made it natural to carry over the title `statistical laboratory' which, while accepted at University College London as given by Galton, sat rather less naturally in a Faculty of Mathematics.

In any case, John Wishart's `pushing' was to good effect. Dennis Lindley was appointed in 1948 to a Demonstratorship and David Cox in 1950 to an Assistant Lectureship. David Cox was well known to Henry Daniels; the two had worked together at the Wool Industries Research Association -- one of those pragmatic institutions whose mark its sometime members happily bear for life (see Daniels and Whittle, 1993).

Ingram Olkin mentions, interestingly, that many of the significant departments of statistics in the USA were founded about this time: Columbia and North Carolina in 1946, Stanford in 1948, Berkeley and Chicago around 1952 and Iowa State somewhat earlier. Wishart set the content and tone of the teaching for the first term of the Diploma; Violet Cane recalls feeling distinctly depressed and ready to quit. However, matters changed greatly for the better after Christmas, when Henry Daniels took over courses, and even more so after Easter (1948), when Frank Anscombe joined. Relief seems to have been general; Norman Bailey writes that ``the General Mathematical Statistics course was given by Henry Daniels most brilliantly, as evinced by the resounding ovation he received at the end''. Norman testifies to the meatiness of the course, as does John Nelder (Diploma 1948/9). Design of Experiments was done thoroughly in those days. Frank Anscombe gave the course in John's year; he dragged the class through Galois fields in lectures and then asked candidates to design a rotation experiment in the practical exam.

Henry Daniels has preserved his class lists from that time. From his Stats II course for 1947/8 we can identify the members of the first Diploma year and recognise many of them: N.T.J. Bailey, V.R. Cane, J. Durbin, G.S. James, S.F. James, F.H.C. Marriott, P. Robinson, D.C. Shaw, N.J. Wang and L. Whitehouse. There are other familiar names on the list; e.g. J.M. Hammersley, J.A. Nelder and E.S. Page from Part II of the Tripos, J.E. Drummond and J.C. Tanner from Part III and R.M. Williams, a research student. C.R. Rao was also in Cambridge that year; as a research student with Fisher, but attending the Lab seminars.

Dennis Lindley recalls some of the early Diploma examinations as being so difficult (in an attempt to impress the mathematicians with the respectability of the subject) that they stumped staff as well as students, laying a supervision minefield for years to come. However, Jim Durbin emphasises that, for the 1947/8 Diploma, the real problem, at least for him, was ``the *seven-hour practical exam* . We had 10 students in a small room grinding away for dear life on Brunsviga manually-driven calculators all day long. The noise was horrific and I found it so hard to concentrate I thought I'd probably made a hash of it and hence, since Wishart was always going on about the practical exam being the most important part of the whole affair, had failed the Diploma. Fortunately, forbearance triumphed and I got a Distinction''.

Both Henry and Violet speak of the particular vividness and exhilaration of the immediate post-war years, as people streamed back from war-work to resume their studies. This cohort represented a store of banked-up talent; individuals who valued the prospects that peace opened and met them with minds at once mature and fresh. One such was Robin Williams, who had been working on electromagnetic separation processes for the Manhattan Project, and who, despite encouragement to stay, chose rather to start research in statistics in Cambridge from 1947. He was disappointed to find that his prospective supervisor, Bartlett, had moved, to be replaced by Wishart. An appeal to Daniels resulted in his being passed on to Frank Anscombe for what turned out to be a rewarding collaboration (on the optimisation of experimental lay-out in the presence of spatial autocorrelation between plots). Robin recalls Anscombe and Daniels with warmth.

Other research students from this time were Dennis Evans, Andrew Ehrenberg (both 1949/52), Wally Smith (1950/3) and Ewan Page (1951/4). Wally very nearly missed the return to graduate work in Cambridge. He had just served three years in the Royal Navy and had now arranged study, grant and marriage. However, with the advent of the Korean War, all releases were cancelled. Wally was appalled at the prospect of the collapse of his plans and urgently required a ``letter that would convince the admirals that I would be serving the nation much better studying Statistics than drowning in the China Sea'' - Wally could not swim. He found it difficult to convince anybody in Cambridge of the urgency of his case, but at last wrung a missive from his supervisor-to-be, Henry Daniels, which, reinforced by support from Dr Stoneley of Pembroke, did the trick.

Wally recalls the Stats Lab as he knew it: housed in the St Andrew's Hill hut. A cosy place, tiny offices, and a library whose excellence he attributes to Lindley. The room containing the gas furnace was off limits, with apparent good reason, as ``every week or two a considerable explosion would erupt''. The furnace was in the care of ``Donald East, who seemed, on first encounter, to be a little distant and saturnine, but, on further acquaintance, proved to be amiable and helpful, and very competent at his work (except, perhaps, for those occasional lapses in the furnace room: once the detonation he produced while making `necessary adjustments' caused a bang of many decibels, and I do believe the doors rattled, while he came out backwards from the furnace room at high velocity)''.

Something has been said of lecturing styles; Wally's pen-pictures are too good not to reproduce in full.

- ``Wishart was actually very friendly to me, and in truth I liked him. I was in awe of someone who had a distribution named after him, and especially one whose derivation was so dreadfully awkward. He lectured very rapidly in a high-pitched squeaky voice with a Scottish accent, and wrote very neat notes in very small writing...made me think of an economical user of postcards, getting as much information home as he could for the least postage.
- ``Henry Daniels' course was on Stochastic Processes, and was the one in which I had far and away the most interest, and I very much enjoyed it. Though I confess that, even to this day, I often feel when I am listening to Henry lecture that he is constantly hinting in a mysterious and barely verbal way, as an undercurrent to what he is actually saying, that there is a very subtle implication or explanation or ramification...which I am far to dumb or unsubtle to understand.
- ``Frank Anscombe...had such a debonair gentlemanly way of addressing the class; we were all damn good types meeting in the club-room for a jolly good chat about factorial experiments or whatever, don't you know; and he had worked the material out with such painstaking detail.''

Wally refers to Dennis Lindley and David Cox repeatedly with unreserved gratitude and respect. David made ``everything he discussed seem so very very easy and straightforward. One kicked oneself at being so stupid as to need any instruction at all on such a seemingly trivial matter.'' Dennis's purple hectographed notes on the Kolmogorov treatment of probability summarised ``the most important for me of all the lectures I ever attended as a graduate student''.

Wally entered research with some travail. ``Henry sent me over the road to the Zoology lab to work with a research man called J.W.S. Pringle who was obtaining an abundance of photographic records of the nerve response of giant South American cockroaches. He would pin (literally) the poor but unphotogenic creature to a large block of wax, plunge an electrode somewhere into its brain, and then tickle its leg with a camel-hair brush...I had little knowledge of the chemistry of nerve transmission and so on. Thus the months in which I should have been mastering measure theory and semi-groups and Fourier analysis and all those other good worthwhile things, I was floundering around trying to teach myself the rudiments of subjects I found very unattractive.''

Before Wally managed to obtain relief from the cockroach Ewan Page introduced him to EDSAC, of which both were then early users. Relief came via Dennis Lindley, who was then in the middle of his classic work on queues. Wally was fascinated by the Wiener-Hopf arguments. When Henry took a sabbatical in Chicago in 1952 Wally was reassigned to David Cox, ``the two years of work on cockroaches went out the window'' and Fourier ideas, Wiener-Hopf theory and renewal processes came in. Ewan Page was supervised by Frank Anscombe, of whom he speaks with the same warmth as does Robin Williams. `Inspirational' he says, with the capacity to `let his mind wander' as they discussed problems. When Frank took sabbatical leave in Princeton 1953/4 Ewan was taken over by David Cox, who warned him: ``I don't have many ideas; I hope you don't want me to give you an idea!''.

Wally and Ewan together wrote a pools forecasting guide one weekend, which they tried to publish, without success. However, Ewan scored one of the historic triumphs of the Lab the following year (1953) when, using random numbers from the Fisher and Yates statistical tables, he won a First Division treble chance. According to a financially-straitened Wally, ``enough in those days to buy a modest house and a modest new car (if one chose)''.

Ewan tells how he was in Dennis Lindley's room one day, discussing a change-point problem on the board, when Wishart brought in A.C. Aitken. Aitken was of course famed for his feats of memory, and, some considerable time later at a seminar in Edinburgh, Ewan challenged him to recall what had been on the board that day. Aitken obliged.

Courses were of course given for the Mathematical Tripos as well as for the Diploma. Anscombe started and Lindley then developed the first Part II course in probability. It had to be entitled `Random variables', however -- Jeffreys objected to use of the term `Probability', which he reserved to describe his own brand of Bayesian inference.

In 1953 the reality of the Laboratory became formally recognised. Regulations for the Statistical Laboratory, which covered also the post of Director, were proposed by the Faculty Board of Mathematics in October 1952 ( *Reporter*, 1952-53, p. 810) and approved by the University on 21st March, 1953. In April 1953 J. Wishart, still a Reader in Statistics with primary appointment in the Faculty of Agriculture, was appointed Director.

Colleagues from that period give Wishart credit for the single-mindedness which at last brought the Diploma and the Laboratory to being. They give him less credit for sensitivity and tact. He would introduce a member of the Lab staff to a visitor as ``My assistant'' - save in the case of David Cox. Youth still rested so clearly on David that he was more appropriately introduced as ``My student''.

All unknowing, the Statistical Laboratory was now at a zenith it would not hold for long and would not reach again for many years - some would say `never', in that the character of those times will not recur. It was fully set up, with a staff consisting of a Reader (Wishart), three University Lecturers (Anscombe and Daniels with a recently-promoted Lindley) and one Assistant Lecturer (Cox) plus computing staff. It set the pattern and the standard for departments of statistics throughout the country. In particular, one can say that the Diploma was the model for all the postgraduate courses in statistics which have been set up since. The Diploma itself was thriving, and its products occupied many of the key statistical posts in the country, university posts among them. The staff were leading in research in their respective fields: Daniels in stochastic processes, position-finding, steepest descents and components of variance, Anscombe in the design of experiments and sequential analysis, Lindley in inference and decision theory, and Cox in the design of experiments, sequential estimation, renewal theory and point processes. Wally Smith was just completing his Ph.D. in a late rush: he had developed insights into the analytic theory of renewal processes and the like. He and David Cox went on to collaborate fruitfully.

All the staff were heavily engaged in consultation for other University departments, regarded as one of the prime functions of the Lab. Lindley recalls: ``In common with other members of the Lab I did some applied work, almost essential in order to provide facilities for the Diploma candidates. The one I enjoyed most was for Rothschild on the movement of sperm, giving a process that was not Markov of any order''. The Lab also had close relations with the statisticians placed in other departments, e.g. Norman Bailey in Medicine, Violet Cane in Psychology, and Colin Campbell in Agriculture. Norman Bailey held a post as Statistician to the Cambridge Medical School 1948/52; he was succeeded first by Wally Smith and then by Bob Carpenter. He speaks feelingly of the extent to which these lone statisticians relied on the Statistical Laboratory for back-up and advice when in need. He also wonders whether this increasing dispersion of applied statistics over other departments may not, in the course of time, have had some consequences for the central focus.

The Faculty recognised the function of the Statistical Laboratory, in that so many mathematics graduates found employment in statistics, and doubtless recognised the Lab's worth, in that it considered its statisticians better than other peoples' statisticians. Recognition of the quality of the subject as such was slow to come, however, and it was a source of chagrin, particularly to senior members of the Laboratory, that their status and function were not acknowledged by the offer of a college fellowship. Indeed, no statistician was a college fellow at that time; not even Wishart, who had been a Reader for 22 years.

On the other hand, the `problem of the non-fellows' was by no means particular to the statisticians. The Bridges Report (*Reporter* 13/3/1962, p.1075) found that in 1961 only some 500-odd out of 950 University Teaching Officers and equivalent held fellowships.

William Jackson Hall spent the year 1953/4 in the Lab as a Fulbright Scholar, working on his dissertation for the University of North Carolina. He remembers particularly Dennis Lindley's good research advice, the clouds of pipe-smoke which Henry Daniels generated in seminars and, of course, Ewan Page's pools win.

Robert Curnow took the Diploma in 1954/5, the same year as Maurice Priestley and Mervyn Stone. The Brunsviga lives in his memory, too, as does the occasion when David Cox became vexed by the time the class took to invert a 7 ? 7 matrix on it. He also recalls Wishart's course on distributions, which stopped at the exciting part: evaluation of the fourth moment of the fifth cumulant. Ewan Page likewise shudders at the memory of the `acres' of pattern coefficient calculations required for these evaluations.

An innovation accompanying the change in status in 1953 was the annual photograph of current Laboratory members: staff, computing and secretarial staff, research and Diploma students. The rows of these photographs on the Laboratory walls fascinate all who call. They provide quite the quickest way of determining who was in the Lab when, but also constitute an invaluable and evocative historical record. They manifest something which has been evident from those days: a sense of Laboratory identity and character, an esprit de corps which has persisted through weal and woe.

**4. 1955--61 Disaster and diaspora**

In 1955 the Laboratory suffered a serious setback when David Cox's appointment was not renewed. A University Assistant Lectureship was a purely probationary appointment; for three years in the first instance, extendable at most to five. It was in fact merely a stage in an open competition for one of the restricted number of lectureships; a competition in which the statisticians felt that they carried a handicap, especially relative to the pure mathematicians. In this case the post indeed went to a pure mathematician.

Nevertheless, David Cox was then regarded by the statistical world as being of exceptional quality; a view which he has since confirmed by becoming the leading figure in British statistics in his generation, powerfully bridging probability models, theoretical and applied statistics, and repeatedly honoured overseas. That the Faculty should not recognise this seemed unjust and inexplicable; an affront to both him and the subject. David himself has put the matter behind him; it is others who still feel outrage. Norman Bailey writes: ``Feelings were very strong, both amongst members of the Statistical Laboratory itself and peripheral statisticians in other University departments, that the growing and indeed talented mathematical statistical nucleus was not being properly recognised, and that this was compounded by no offer of college fellowships. I believe that this led to an inevitable diaspora in the years up to around 1957.''

The loss of the youngest staff member was then followed, in a most curious way, by the loss of the oldest. In 1956 John Wishart was in Mexico, on leave. In July news came through that he had drowned while bathing in the sea off Acapulco.

Such events are not only tragic in themselves; they are sudden and shattering. Henry Daniels, deputising for Wishart during the latter's leave, had now to wind up Wishart's affairs and take charge of the Lab as Acting Director. Frank Anscombe left shortly after for a post at Princeton, moving later to Yale. In the following year, 1957, Henry Daniels himself left to take up the Chair of Mathematical Statistics at Birmingham.

Of the five 1955 members of the academic staff of the Lab only one then remained in October, 1957: Dennis Lindley. On him fell the task of reviving the fortunes of the Lab; he was appointed Director. The staff situation had been somewhat shored up, in that Wally Smith had been appointed to a ULship in 1956, replacing Frank Anscombe. However, he could return to the UK first at the beginning of 1957. Wally had been rather unsettled (a `yo-yo', says Ewan Page) since completing his Ph.D. He had held the post in the Medical School at Fenner's 1953/4. Earlier meetings with American visitors to Cambridge (Sam Wilks, Harold Hotelling, Leo Goodman, Jimmy Savage) had opened his eyes. Far from showing the brashness believed to be the American characteristic, they exemplified ``the acme of gentlemanly courtesy'' and a ``quiet respectfulness'' not to be found in the RSS Research Section meetings, for example. So, when offered an attractive post at Chapel Hill in 1954, he had taken it, although only after three months' indecision and then with many a backward glance to the UK. Ewan Page recalls his plaint: ``Don't forget me so quickly!''. In 1956 he took the chance to return to a full Lectureship in Cambridge.

After Henry's departure in the summer of 1957 only Dennis and Wally were left to carry the full burden of the Lab's teaching and activity. Every moment of day and evening was committed; a desperate time, although Wally also recalls it as exhilarating. However, Wally was dispirited by what Neyman had characterised as the `second-class citizen' status of the statisticians in Cambridge, and found the social life cold or absent compared with the friendliness and informality of Chapel Hill. What must have been a difficult decision and a time of deep disillusion is only hinted at in Dennis Lindley's brief recollection: ``Wally and Mary paid a visit to our house on the day the Russians launched the first Sputnik. Neyman and Elizabeth Scott were also there. They had to cycle out to our house in the rain. They decided a car in sunny Chapel Hill was better and left soon after.'' They left in summer, 1958, in fact, although often to return in body, and perhaps more often in spirit. Wally never found it easy; his lament for the days that had passed should be quoted in full.

- ``I do not think that, outside the blitz, I have lived, or will ever again live, through such heroic times as those days seemed to be, in retrospect, when Dennis and I alone held the fort. And we did it.
- ``The Statistical Laboratory building is long gone. Smashed down. The site is now buried in a large parking garage. [The Lion Yard car park.] A few years ago I walked into that garage and tried to estimate where my office had been; where I had stood giving that first scary seminar talk; where the library had stood, in which I had done so much studying and learnt so much, where David Cox first told me what a Martingale was (I wonder if he had it right?). Various annoyed motorists hooted at me, and I had to dodge cars constantly. I should have picked a quieter time. But it was all footling. I could not recapture any of it.''

Dennis had a desperate task to keep the Lab going, although he took it evenly enough. There were two immediate recruitments; Morris Walker took up a University Lectureship in early 1958 (replacing Henry Daniels) and Peter Whittle in late 1959 (replacing Wally Smith). Whittle had no previous Cambridge connection at all, and Lindley had to press the Faculty hard to secure the appointment, even resorting to the then unheard-of extravagance of telephoning New Zealand. In his turn, it took Whittle time to become aware of the cross-currents created by events, realised and incipient. Some closer personal impressions of these and later years at the Laboratory are given in Whittle (1994).

The Laboratory left St Andrew's Hill in 1958. Thanks to some uncharacteristic maladroitness of the chemists it was given quarters in the basement of the new Chemistry Building in Lensfield Road. Parquet floors and lofty ceilings provided a degree of state unimaginable, at any time, to the Faculty of Mathematics.

As mentioned, L.J. Savage had already visited Cambridge, in 1952. Dennis Lindley developed a closer contact with him while on sabbatical in Chicago in 1954, and became impressed by his ideas in a fashion which was to prove lasting. Savage again visited Cambridge for the summer of 1958 and briefly in 1959.

Despite the reduction in its fortunes, the Lab still had a wonderful feeling of camaraderie - perhaps because staff and graduate students were so close in age. The names of the research students from that time are now familiar: Ann Mitchell, John Bather, John Kingman, Bob Loynes, Roger Miles, and Hilton Miller. Mervyn Stone had just completed. Staff and students seemed always to be adjourning to the Spread Eagle together to celebrate the augmentation of someone's family.

Donald East was the principal member of the computing staff, surviving from the days in Agriculture, when he had acted virtually as Wishart's secretary. He used an electromechanical Marchant, Dennis Lindley a Facit. The Diploma students at that time were still using the manual Brunsvigas of which Jim Durbin spoke; now museum pieces which have unfortunately been disposed of. (However, Violet Cane possesses one, and Jeffreys' machines are displayed in DAMTP.)

Dennis Lindley left to take up a new chair at Aberystwyth in 1960. Donald East went too, changing his hobby from gardening to golf. This was the first chair in statistics which had been created in the UK for several years and there was little reason to expect that it would be followed at all soon by others. Dennis also found the Aberystwyth prospect attractive. In fact, the expansion of the sixties was about to balloon, and there was a quickening even in Cambridge. The possible establishment of a chair of statistics, mooted already in 1953, was now being discussed more definitely in the Faculty, and colleges were beginning to make cautious overtures to Laboratory staff.

The disintegration of the `Wishart' Laboratory should perhaps not be seen as a disaster, but as the natural fruiting of success. The Laboratory had reached a stage of maturity; that its members should be dispersed over other universities was very likely for the general good. The event itself that triggered that dispersal was, of course, tragic.

Lindley, the last of the old guard, had a considerable influence - broadening, innovatory and lasting - on the activity of the Laboratory. The contribution he then made to queueing theory is a classic of applied probability, which to this day generates new work. His Bayesian enthusiasms are associated with his championing of the ideas of L.J. Savage and B. de Finetti, but they also led him to decision theory and some of the classic decision problems. This latter interest may be seen as the germ of some of the courses in `applicable mathematics' which were later to develop. A point of interest: Dennis's undergraduate supervisor had been Besicovitch, himself a student of Markov, so Dennis could claim Markov as his academic grandsire.

Violet Cane was appointed UL in 1960 to replace Dennis. However, Peter Whittle left the next year to succeed Maurice Bartlett in the Chair of Mathematical Statistics at Manchester. The Lab photograph for 1961/2 is graphic: the total group is now reduced to a handful. Morris Walker, taking his turn as Acting Director, peers anxiously into the future.

Indeed, the future of the Statistical Laboratory had been under consideration for some time; deliberations whose murmur seemed, however, not to reach the Lab itself.

**5. 1961--66 The Chair of Mathematical Statistics; Resurgence**

The buffets which the Laboratory had suffered since 1956 had brought the Faculty to the realisation that its teaching of statistics could be stabilised only by the creation of a senior post in the Faculty: a Chair of Statistics. Outside Cambridge, the absence of such a chair was regarded as frankly anomalous.

The future form envisaged for the Laboratory was bound up with the structure of the Faculty itself, which was at that time preparing to divide into the two existing departments. A 1958 Report of the Faculty Board to the General Board ( *Reporter*, 1958--9, p. 1375) proposed the establishment of a Department of Theoretical Statistics and Applied Mathematics, and added ``As regards the Statistical Laboratory, its ultimate status is bound up with the possible establishment of a Chair of Mathematical Statistics. It may well be appropriate to convert the Statistical Laboratory into a Department once such a Chair exists, but it would be premature to do so now''.

The formal record is unrevealing on the question of whether the true initiative for the establishment of a chair came from the University itself, but one contributor to this account is in no doubt. ``In spite of pressure from Wishart, Lindley, the RSS and probably others, Cambridge University declined to create a Chair of Statistics. The RSS Council, probably at Lindley's instigation, decided in disgust to try and raise enough money to endow a chair. They gave the job to the next President, Maurice Kendall. At first he was a bit put out at being asked to raise a huge amount of money for *another* university at a time when he was hard at work drumming up support for statistics at LSE, but then he threw himself into the task with characteristic generosity and energy and was brilliantly successful.''

The formal records are blander. The Faculty Board's passing mention of a Chair quoted above became a firm proposal from the Faculty of Mathematics; this is referred to in a report from the Council of the Senate to the University in June 1960 ( *Reporter*, 1959-60, p. 1684) The establishment of a chair was considered desirable ``both because of the long association of the University with advances in Mathematical Statistics and the high calibre of Cambridge mathematical students, and because...a number of other Faculties who call upon the services of the Statistical Laboratory would warmly welcome it''. ``The [General] Board have said that they now have reason to believe that, by appealing to certain persons and bodies interested in the theory and application of the study of statistics, it may be possible to secure all or a large part of the funds necessary to maintain the Chair.''

The `reason' mentioned by the General Board was the preparedness of the Council of Royal Statistical Society to launch an appeal to raise money for the chair. According to the RSS itself, it had been approached by the Faculty of Mathematics with a request that it ``sponsor an appeal...'' (see *J. Roy. Statist. Soc. A* (1961) 124, p. 562). The Society saw this as a good cause and put its full weight behind the venture. Its President, Dr Maurice Kendall, was indeed outstandingly active in pressing the appeal, which by 1961 had been brought to a successful conclusion. The contributing companies and banks are listed in *J. Roy. Statist. Soc. A* (1962) 125 , p. 616.

The University had agreed to the Council of the Senate's proposal. In October 1961 the Council announced the successful completion of the appeal ( *Reporter* , 1961--2, p. 326); it recommended the establishment of the Professorship and that the Professor should be *ex officio* Director of the Statistical Laboratory, whose ``establishment on a firm basis'' the Faculty Board of Mathematics regarded ``as a matter of great importance''. The University accepted these recommendations without comment.

The title of the Professorship corresponded to that of the Diploma. The duties of the Professor were not prescribed by any ordinance, but the origins of the Laboratory, the involvement of the Royal Statistical Society and the appeal to `persons and bodies interested in the theory and application of the study of statistics' made clear the intention.

The Electors to the new Chair met in May 1962 and elected David Kendall to the post; he took up duties in October of that year.

That David Kendall should have been elected was not an entirely unexpected outcome, his personal claims on grounds of quality being overwhelming. It was a maverick outcome, however, in that David was much more obviously a probabilist -- and at that time of fairly pure leanings -- than a statistician. The matter has been debated then and since, not least because it may be argued that the appointment set a precedent for the two subsequent elections to the same post. One point that must be made is that the Board of Electors was a balanced one (with the RSS represented by its President, Maurice Kendall), well aware of the nature of the case that had been made both for the post and for the appeal which supported it, and the Board certainly considered all factors in reaching its decision. An interesting light is thrown by Dennis Lindley. He writes that, at the time when he was considering whether or not to apply for the Aberystwyth post, ``Maurice Kendall was well-advanced in his appeal for money for a chair at Cambridge, and had politely made clear to me that David Kendall would get it''. The coincidence of surnames is fortuitous -- Maurice and David are unrelated -- so Maurice's intention, typically robust, was disinterest itself. The quotation makes clear that Maurice was not ambushed by other Electors, although another account represents this rather as a reluctant acceptance of the fact that David Kendall was intrinsically the strongest candidate.

More to the point, one can maintain that David Kendall subsequently met the criticisms, in that he became a statistician in his own individual way, and an ingenious and enthusiastic one. In addition to his continuing work in pure probability (Markov processes, stochastic analysis and geometry and random sets) and applied probability models (bird navigation, structure of the retina, epidemic waves and rumours) he became deeply interested in the inference and reconstruction problems of archaeology, such as grave sequencing, the reconstruction of local maps from information on contiguity etc., and the recognition of regularities such as quanta of measurement and the placement patterns of standing stones. These applications all had a particular sense of intangibility, and were in fact pioneering and advanced examples of the analysis of latent variable models.

David Kendall also `strove for statistics' (in David McLaren's phrase) at the operational level. he made efforts to establish contacts with statisticians in applied posts, such as Colin Campbell and Bob Carpenter; he secured David McLaren (who had joined the group from Manchester as a research student), appointment as a senior Assistant in research (later an Assistant Director of Research), with partial responsibility for statistical consulting, he set up a course on inference in Part IB and pioneered the use of TITAN in the Lab.

David's appointment brought one immediate political benefit to the Laboratory; the mathematicians recognised David as one of their own, with the consequence that the standing in the Faculty which the Laboratory had earned but not received was now granted overnight. John Kingman, now a Fellow of Pembroke and a member of the Lab, was also greatly influenced in bringing about change in attitude. Harold Davenport's reported reaction to the appointment was: ``Eeh, I did worry about who we might get, but eeh, we got a Professor of Statistics who knows about lattice points!''. The colleges opened their doors and, indeed, from that time there has generally been competition to secure the services of Laboratory staff as teaching fellows.

This rapport brought other consequences, however. Given the will, the Laboratory could indeed have become a separate department. However, it would then have been expected to unify of statistics in the University, so reversing the dispersion Norman Bailey mentions. In particular, it would have been expected to absorb the statisticians rather loosely attached to other Faculties such as Agriculture and Medicine and probably to provide service teaching -- teaching for Faculties other than Mathematics. Such a course would have meant an increase in role but a change in character; there are obvious arguments both for and against it. In the event, the Laboratory joined the pure mathematicians to constitute the existing Department of Pure Mathematics and Mathematical Statistics (DPMMS).

The Lab was still housed in the basement of the Chemistry Building when David arrived in 1962. It was honoured in the first term by a courtesy call from Fisher. He was carrying a stout stick; John Kingman later affected to believe that this was for the administration of a cudgelling in case of displeasure. In fact, the occasion seems to have been totally amicable, ending in lunch.

John may be playing down his own doughtiness; david McLaren recalls the seminar which Fisher had given in Cambridge the previous summer. in David's words ``A very recent graduate of the Diploma, I arrived rather too promptly, when Fisher was already on his feet. However, he insisted on shaking my hand most warmly; presumably his short sight prevented him from being sure that I was not the Vice-Chancellor".

Fisher's topic was `Sampling the reference set'. John Kingman bravely took issue with some of this, advancing to the blackboard to demonstrate some counter-argument. Fisher started swinging his stick in a most menacing way, not amicable at all. Eventually he dismissed John by demanding "What does it matter if the mouse is a Unitarian?"."

In 1964 the whole Faculty was concentrated at the former Printing House in Mill Lane, rendered vacant by the University Press's move to new premises. The Statistical Laboratory moved with the rest of DPMMS into the warehouse building. One may now begin to use the present tense. The Mill Lane building is not an elegant one, but it is conveniently sited and has served the Department well. Strongly and squatly built around a steel frame with a full-plan basement, it rather incongruously suggests a war-time bunker. The ground is weak near the surface of the river bank; the bridging of the Cam at this point has historically presented a civil engineering challenge. As a consequence, the Pure wing (the `old warehouse') of the L-shaped building tends to slip away from the Statistical wing (the `new warehouse'), giving rise to the `Daniels fault' at the junction -- a vertical crack which indeed staggers the window of Henry Daniels' present room.

John Kingman accompanied David from Oxford in 1962, as a UAL. He was upgraded to UL from April, 1964, at the end of which year he left for a term's sabbatical and a post in Brighton. It was immediately before his departure and before the move to Mill Lane that John rendered his last great service to the Lab. John was a very junior member of the committee concerned with allocation of space in the Mill Lane building; he saw reconnoitre as his first necessity. ``The credit for getting into the warehouse lies with Violet, who had a friend (whose name I had better suppress) in the Press. Thus Violet and I got into the warehouse, by then cleared of paper but having no internal walls except that between the old and the new warehouses. With its iron stanchions holding up the heavy floors it was like being on a C19th sailing ship.'' However, it turned out that the appointed Master of the vessel (Sir William Hodge) had already provisionally consigned the Statistical Laboratory to the bilges (the basement -- commodious but dismal). Thither it would indeed have been cast had not the brave cabin boy (John Kingman) spoken up, sturdily enough that he secured for the Lab all of the upper two decks (the upper two floors of the new warehouse) aft of the sole bulkhead (the aforesaid wall). John now had a free hand in the partitioning of this space. Perhaps in reaction to the depths into which he had peered, he was particularly insistent that there should be a large common-room with many soft chairs and *no* blackboards.

When David Kendall arrived in 1962 the staff consisted just of Violet Cane and Morris Walker, with now the addition of John Kingman. On this slight but genetically-rich base the Laboratory began to develop life again, in somewhat mutated form. Alfred R?nyi (soon to die tragically early) was a visitor in 1963/4 and Jessie McWilliams, Joe Kruskal and Ronald Pyke in 1964/5. Through his connections with the Atlas Laboratory at Harwell David managed to arrange an Atlas Fellowship at Churchill. John Hartigan held this in 1963/4 and helped out with lecturing (while Morris Walker was on sabbatical leave in Australia). Roy Hodson held it for a time after that -- David was by this time well into his archaeological phase. David was elected FRS in 1964. In that year John Kingman left for Brighton and was replaced by Bob Loynes, from Manchester. Bob Bechofer, who visited in 1966/7, was prevailed upon to lecture. When leaving he confided to David, in amiable honesty: ``Your statistics is terrible!''.

It is not practicable to follow the passage of individual research students in the same detail as that of staff. What is natural is to recall the members of the research-student group at the times - quite definite - when this was especially flourishing. Some notable singletons are then likely to be missed; they should be sure that they are remembered.

The research students played a particular role during these recovery years in giving the group substance; David McLaren, Nick Bingham, Daryl Daley, Charles Goldie, John Haigh, Peter Lee, David Mannion, and Jane Speakman speak to us from the photographs.

David Williams performed his first transit of the Lab in 1966/7, when he held a Research Fellowship at Clare. He recurs. Nick Bingham recalls him from that time as ``a force of nature - unforgettable for linguistic as well as mathematical reasons''.

**6. 1966--72: The Churchill Chair; Redefinition**

There was a continuing concern to bring up the Lab's strength and, in particular, to restore its historic strength in statistics. Esso Petroleum Ltd seemed disposed to be helpful, and David Kendall had conversations with Leo Govier of that firm. Initial suggestions were modest: that support might be provided for a Diploma student. A year or more of discussion, back-reference and variation led to something startingly more ambitious: Esso generously endowed the Churchill Chair in the Mathematics of Operations Research. This was to be located in the Faculty of Mathematics; more specifically, in the Statistical Laboratory.

The new chair was advertised in 1966. Peter Whittle was elected to the post in August of that year and took up duties in July 1967. The number of people in the UK who might be said to be knowledgeable in the mathematics of OR was small, but Whittle's increasing interest in optimisation was deemed sufficiently qualifying, and made the move an appropriate one as far as he was concerned.

There may have been an expectation in some quarters that the new professor would be, effectively, a professor of statistics, so restoring the desired balance. However, Whittle saw the matter in a more literal light. For one thing, Esso's intention was clearly that the post should be in operational research. But, more than that, Whittle considered that what needed development was, not just narrow-sense operational research, but the whole area for which there is still no good name, but which is variously called `applicable mathematics' or `non-physical applied mathematics'. This includes, for example, probability, statistics, optimisation, systems theory, game theory and those aspects of disciplines such as control theory, communication theory and mathematical economics which might be pursued by someone technically based in probability and optimisation. Developments in the USA since the war have demonstrated, not only the practical importance of these topics, but also the depth and coherence of the theory they generate.

Surprisingly, Cambridge was ready for these developments. Both students and other Faculties had been pressing the Faculty of Mathematics to modernise its coverage in precisely these areas, and the Faculty had conceded the case. So, the proposal of new Part II courses (in convex optimisation, dynamic optimisation and statistical communication theory, as it turned out) was welcomed, rather than met with the incredulity and resistance which precedent would have led one to expect. The new courses had a chequered beginning, but ultimately took shape and became accepted components of the Tripos. One may say that the optimisation courses have not prospered as they should, but the changes in courses and staff anticipated for 1994 promise regeneration.

Statisticians outside Cambridge may have watched the partial displacement of statistics in Cambridge by probability and optimisation, etc. with some dismay, seeing this as an abandonment of honourable traditions or a snobbish mathematical elitism. They could not be more wrong. There is surely substance in the view that the complacency lay *outside* Cambridge rather than within. The many departments of statistics in the country interpreted their brief far too narrowly - more narrowly than Galton or Fisher would have found natural! It was Cambridge which saw the lack and tried to remedy it; a task requiring much hard work and inducing some humility. Further, contrary to general belief, Cambridge has continued throughout to recognise the special role of statistics and tried to restore its own strength in this area. The attempt to cover much of applicable mathematics with a smaller staff than is devoted to statistics alone in many universities has made this difficult. However, strenuous efforts have been made to bring statistics to its proper representation, and 1994 may see also these efforts crowned with success.

The visitors for the year 1967/8 included Ingram Olkin, Al Marshall, Mike Perlman and, again, Alfred R?nyi . Olkin and Marshall started a seminar series on inequalities, attended by R?nyi among others. This was novel both in content and format: it provided the first local experience of a `bag seminar', to which one brought one's lunch. Ingram and Al presented their developing ideas on majorisation at this seminar, ideas which constituted the basis of their later text on the subject. Al also took the chance to enlarge his collection of old flutes.

Anthony Edwards was attached to the Lab 1968/70, and began a course in Mathematical Genetics which remains a standing option in the Diploma, although Anthony sees this course as a development of on begun by Fisher and George Owen in 1952/3. While his primary interest is mathematical genetics, Anthony is a scholar of both statistical inference and the history of statistics in Cambridge; most of the formal record in sections 2, 3 and 5 of this account is derived from his 1991 notes. His book *Likelihood* (1972, Cambridge University Press) was written during his period of attachment. One may also see him as the high priest of those who tend the memory of Fisher in the sacred groves of Caius (of which college Fisher was a Fellow, as is Anthony). He read a paper to the Royal Statistical Society in 1969 on the estimation of evolutionary trees ( *J. Roy. Statist. Soc. B* (1970) 32 , 155--208). Solution of this difficult and fascinating problem was later taken considerably further by his research student, Elizabeth Thompson. Robin Sibson tackled the same problem in a different way in his study with Nick Jardine of dendrogram techniques (Jardine, N. and Sibson, R. (1970) *Mathematical Taxonomy*, Wiley). Both Elizabeth and Robin were appointed at that time to University Lectureships in the Lab; Robin from 1970 and Elizabeth from 1971. This activity again demonstrates the falsity of the impression that statistics lapsed in the Lab after the fifties: the estimation of evolutionary trees is an important, subtle and difficult statistical problem; exactly the kind of problem that many mainstream statisticians will regard as lying outside their brief.

Books published by the staff must serve as an informative if insufficient statistic of activity. Peter Whittle published *Optimisation under Constraints* (1971, Wiley) as a text for one of the optimisation courses and *Probability* (1970, Penguin). Since this latter took the unconventional approach of axiomatising the expectation functional, it was unlikely to be adopted for any course, but it was interestingly parallel to the work by de Finetti, appearing in English just at that time, which Dennis Lindley so espoused.

John Gittins was also loosely attached to the Lab in 1969/70. It was at this time that he was developing his solution of the multi-armed bandit problem, motivated by the need for a rational approach to the allocation of exploratory research effort he had encountered while working with Unilever. The multi-armed bandit problem was *the* problem of decision theory over the years 1945-1980; it embodies the essential problem of balancing experimentation against immediate dividend, but seemed so difficult that people of some mathematical sophistication regarded it as intrinsically insoluble in any conventional sense. Few would have believed it if they had been told in 1969 that John had slain the dragon. It would be 1979/80 before his classic advance was recognised, since when it has transformed a large part of the subject of stochastic scheduling.

Violet Cane was instrumental in bringing in the rule that the Head of the new department, DPMMS, should be appointed for only five years at a time, rather than until retirement. Thus it was that Sir William Hodge yielded the Headship to Ian Cassels in 1969.

The unlikely symbiosis of Pure Mathematics and Mathematical Statistics might not have succeeded but for Cassels' sympathetic and enlightened attitude. A distinguished number theorist himself, Cassels could see, not only that a high proportion of the Faculty's graduates found a career in statistics and related disciplines, but also that these subjects were intrinsically interesting. Indeed, he was the first mathematician to give the Part II course in Mathematical Economics (previously given by a member of the Faculty of Economics), developing and publishing his own course text. It was Ian who repeatedly encouraged the Lab to think big. This venturesome attitude was in contrast to his lesser concern for domestic matters. When money had to be found it was always taken off the cleaning budget, which, despite its consequent exponential decline, always seemed to have some capacity for sacrifice left in it.

In 1969 David McLaren left for a post in Glasgow; cross-border balance was preserved by recruitment of Ted Harding from Edinburgh. His was regarded as a post in statistics.

Robin Sibson was appointed in 1970 to a new University Lectureship notionally assigned to Operational Research. He developed a later interest in optimal experimental design, a subject experiencing a renaissance at that time, and in which Cambridge, Imperial College and Glasgow for a while formed a triumvirate. All three groups enjoyed visits from Valery Federov, who had just written his book on the subject. The pleasantness of his company was not diminished by the possibility that he was perhaps more than a simple academic.

Another statistical appointment was made in 1970. Pat Altham was appointed as Assistant Director of Research (ADR) and also given specific responsibility for the running of the Diploma by being nominated Director of Studies. She had continued in these duties ever since (although later as UL) and has become less dispensable than anybody should be allowed to be. As a relic of her ADRship Pat fields the statistical queries that come in both from other departments and from outside the University, and herself deals with most of them. As Director of Studies she does much of the teaching for the Diploma itself plus all of the administration: e.g. the organisation of admissions, courses, examinations and applied projects. The project retains its central role in the Diploma course, but to find applied areas of the right level and interest equipped with a willing applied supervisor is by no means easy. In fact, the scheme is workable only because of the contacts and goodwill Pat has built up through her consultation work.

David Kendall's `fields of application' continued to be archaeology and astronomy, but there were outliers. A pig-breeder called to see him, and David listened, silently but sympathetically, to a long discourse on swine fever. At the end of this his client rose and thanked him cordially for a most valuable discussion. Years later the same man wrote, recalling the conversation and thanking David profusely for opening his mind to totally new insights on the question of swine fever.

The Laboratory suffered a sad loss in the summer of 1970 by the death of Rollo Davidson in a climbing accident in the Alps. Rollo had been a research student in the Lab, had held a Junior Research Fellowship at Trinity and just been elected to a Teaching Fellowship at Churchill. He was regarded as being of quite exceptional promise. Rollo had published on Delphic semi-groups, p-functions and stochastic geometry, and was beginning to pose questions in statistics and optimisation. The talent that had been lost was commemorated by the compilation of two memorial volumes (eds. Kendall and Harding, 1973 and 1974). The income from these was used to found the Rollo Davidson Trust, from which prizes for distinguished research by younger workers have been awarded annually since 1976.

A course introduced about this time was based on a suggestion of Rollo's, which he would have developed himself had he lived. This was the `Markov methods' course in Part IB. A need was felt for a probability course of an applied character; to build it around the Markov theme gave a natural lead into stochastic processes. As nobility is said to need the constant (if covert) infusion of common blood to maintain its vigour, so probability courses need a constant reminder of applications if they are not to waft themselves to Gallic heights and disappear. This seems to be a law of nature, and is the reason why probability is too important to be left to the probabilists.

In 1971 Violet Cane left for the Manchester chair. She was replaced by Elizabeth Thompson, a formidable young lady who handled all the statistics courses with laconic ease. Elizabeth naturally took over the Mathematical Genetics course as well, and tackled the Communication Theory course (which a few loved and most would not touch) with relish -- perhaps because it gave her a chance to talk about DNA sequences. Her work on inference problems for evolutionary trees continued; in 1975 she was to publish *Human Evolutionary Trees* (Cambridge University Press).

**7. 1972-85 Comings and goings**

The terms of the Chair of Mathematical Statistics made the Professor *ex officio* Director of the Laboratory. However, these had been formulated in the days when the Laboratory had but one chair. Perhaps David Kendall was aware of the belief that eleven or twelve years is the maximal natural term of office; in any case, in 1973 he managed to have the tie loosed and Peter Whittle appointed as Director.

The new stage was set in the pleasantest fashion by the appointment of Geoff Eagleson to a ULship and the appearance of Bruce Brown as a visitor in 1972. Geoff Eagleson played a profoundly positive role in the Laboratory; in teaching, research, student contact and the good thrift of the Laboratory generally. When one thinks back to the founding fathers of the Laboratory, one regards them as examples of ancient virtue which cannot be equalled. However, in dedication and character Geoff equalled anybody. He is one of a whole sequence of Australians who have contributed to the Laboratory's life and success. Bruce Brown was conspicuously another, but one thinks particularly of the magnificent succession of research students: Daryl Daley, John Pollard, Richard Tweedie, Tim Brown, Iain MacPhee, Phil Pollett, Adrian Baddeley, Alan Branford, Steve Evans, Ben Hambly, Terence Chan, Steve Hanly, Nigel Bean, Jo Kennedy and Owen Jones. These were all good, some of them the very best, and they have kept the Lab's graduate research going at times when UK recruitment was thin. After all these years one may reveal a fact known to Charles Goldie: that John Pollard secretly doubled up his studies for his Ph.D. and his actuarial examinations.

In fact, recruitment was by no means thin in the early/mid seventies, which was one of those periods when the research-student group developed a particularly vivid and productive life of its own. One recalls David Aldous, Frank Kelly, John Kent, Bill McGinley, David Probert, Brian Ripley, Jeremy Rudge and Bernie Silverman.

Geoff Eagleson worked closely with Andrew Barbour, who had been associated with the Lab from 1969; successively as Diploma student, research student, Fellow of Caius and Director of Studies for that college. Andrew made a succession of strong advances in probability on the pure/applied borderline. His talents were recognised adequately first when he was appointed to a chair in Z?rich in 1984.

Ian Cassels' continued exhortation and support bore fruit in 1974 in the form of another Lectureship, to be notionally assigned to Operational Research. Doug Kennedy was appointed; immediately from Sheffield but, before that, from Trinity College Dublin and Stanford. With his Stanford background Doug was the only staff member with any formal OR training.

Life was enriched when Wally Smith, Joel Cohen and John Hajnal spent a sabbatical year at the Lab in 1974/5 and Henry Daniels in 1975/6. It was a particular pleasure to have Henry and Wally back - a link with the St Andrew's Hill days. Henry divided his time between the Lab and the King's College Research Centre, where he was charged with the organisation of a seminar in mathematical biology.

Various references have been made to the less than palatial housing of the Department. In this connection, Kevin Donnelly (research student 1976/9, now answering to Caoimhin O Donnaile) tells how he found Thomas Bruss (research student from Germany, now in Brussels) taking a photograph of the main entry to the Department, a warehouse back-door flanked by milk-bottles and randomly-packed bicycles. He intended to send this to his parents, who could not otherwise be convinced that such a prestigious department was to be approached through such portals. Kevin also tells a story which charity bids us dismiss as apocryphal. One student was heard asking another the purpose of the gigantic rubbish bins outside the actual back-door of the Department. His friend explained that these were for discarded notes and that ``they are sometimes picked through by Oxford research students desperate for material for their theses''.

Alistair Mees was appointed to a ULship in 1975, again notionally allocated to Operational Research. It was always difficult to find staff in OR; since there were virtually no mathematically advanced courses in OR in the country very few had such a training. With luck one could find someone with USA training (as in Doug Kennedy's case) or else someone of approximating interests and sufficient enthusiasm to bridge the gap (as in Robin Sibson's case). The latter was the case also for Alistair. He had worked in control theory, largely in the analysis of nonlinear systems, and later won an Adams Prize for his essay *Dynamics of Feedback Systems* em> (Wiley, 1981). While maintaining his interest in nonlinear dynamics he also moved seriously and permanently into optimisation and associated algorithmics.

Jim Pitman was appointed to a ULship in 1976, bringing both the highest standards in probability and an honoured name. Jim's natural sphere is the USA and in 1978 he returned to Berkeley. He was replaced by the appointment of Frank Kelly to a ULship. This meant reiving a valued young member of staff from the Control and Management Studies Group of the Department of Engineering, but its Head, Alastair MacFarlane, bore no grudge. Relations of the Lab with the Department of Engineering have always been good, particularly with Control Engineering and with Management Studies (which for a time had a joint existence but are now again separate). There are natural communities of interest, of course, although this is in general no guarantee of amicability, and there has been movement of members between the groups in both directions (e.g. John Gittins, Stephen Watson, Frank Kelly and Richard Weber).

Frank's return was to have profound long-term consequences for the Lab. It was a return, because Frank had been a Ph.D. student in the Lab 1973/6. He had been supervised by Peter Whittle in the area of Jackson networks, with its associated reversibility and balance concepts. This class of ideas turned out to be butter to Frank's remarkable intuition. Frank achieved extensions of the Jackson theory not only for the queueing context but also for other and apparently unrelated application areas. His book *Reversibility and Stochastic Networks* (Wiley, 1979) demonstrated the striking unification thus achieved, and made Frank's name instantaneously.

The tempo seemed to increase in those years. Peter Whittle was elected FRS in 1978. His discovery in 1979 of an alternative proof of the optimality of the Gittins index policy for the multi-armed bandit problem had the effect of bringing about the long-overdue recognition of John Gittins' solution of the problem.

Retiring professors were also beginning to home back to the Lab: Henry Daniels from Birmingham in 1978 and Violet Cane from Manchester in 1981. That Violet should return was expected, since she had kept her cottage in Little St Mary's Lane. However, that Henry should wish to do so was both surprising and gratifying. Henry had a respect for red-brick virtues and found these notably lacking in Cambridge; the college slights of earlier years still rankled. However, perhaps he found some of the Lab's work in applied probability to his taste. The reverse compliment certainly holds; he is held in high regard and affection, and is doughty enough in controversy to be allowed no quarter, despite his age. He was elected FRS in 1980, bringing the Lab count to three. Belated but generous justice was achieved by David Williams in 1992, when Henry was made an Honorary Fellow of Clare.

Manfred Gordon, a polymer chemist who had published classic work on the statistics of polymers with Jack Good, had been a visitor in the Lab 1972/3. In 1978 he retired from Essex and also took up residence in the Lab. Manfred had hoped that the interest in the probabilistic aspects of polymerisation which he shared with Peter Whittle would form the basis for some real programme. Alas, the Laboratory was in its familiar quandary of having to split its limited human capital too many ways, and simply could not afford this venture. Interestingly, B?la Bollob?s and his stable of random graph theorists were working along parallel lines, although in a style different enough that collaboration was never natural. However, Manfred, even if disappointed, continues to illuminate the Lab with his gentle erudition and wide culture.

Martin Barlow was appointed to a ULship in 1982. He reinforced the extraordinarily high quality of the group, many of them research students, working on stochastic integrals, stochastic differential equations and flows and spatial processes on strange manifolds.

In 1983 there was a contentious move, in a literal sense. The DPMMS library, which had been housed on the first floor of the DPMMS building, was moved into the library vacated by the Faculty of Classics at the top of the Mill Lane Lecture Block, just over the road. The old quarters had been cramped; the new quarters are not merely roomy, but also beautiful. The former Classics Library is light, lofty and elegant; a sequence of two-tiered galleried bays in light oak is suffused by a clear natural light from above. Undoubtedly some convenience has been lost in the translation, probably more from the vertical component than the horizontal one. However, this is perhaps one case when academics' known inability to refuse an offer has led to the right outcome.

Publications again: in 1981 Elizabeth Thompson published *Genealogical and Genetic Structure* with Chris Cannings (Cambridge University Press) and in 1982/3 Peter Whittle published the two-volume *Optimisation over Time* (Wiley).

There were a number of losses in 1984. The Lab lost a friend in office when Ian Cassels retired. Martin Barlow resigned to concentrate on research, and Alistair Mees resigned to take up a chair in Western Australia.

With the loss of Alistair the difficulty of finding an OR replacement had again to be faced. It was solved by the appointment of Colin Sparrow, highly regarded for his work in nonlinear dynamics, notably chaos theory. Colin's actions are based on pragmatism and principle; convention is not so much disregarded as irrelevant. To fill a longish gap between graduation and the securing of a post in King's he had driven a bus in Cambridge and had sold ice-cream on King's Parade (wearing a top-hat, to the tourists' delight). The appointment stretched the range of interests represented in the Laboratory by more than was wise or comfortable, but the Lab has benefited greatly from Colin's idiosyncratic virtues.

**8. 1985--92 Martingales and the Mabinogion **

David Kendall was due to retire in 1985. The usual measures were taken to advertise the post, in the sober and sincere intention that a genuine statistician should be appointed if possible. However, that the Lab is part of the Faculty of Mathematics places its own constraints. One has to meet the standards of the Faculty (the students would be merciless towards anyone who did not) and the Lab now had its own developed standards as a group in applicable mathematics.

It is perhaps not divulging too much to say that there were two very strong statistical figures in the running; one of these ultimately withdrew and the other presented special problems. The Electors were then faced with a rerun of the 1962 scenario; David Williams was so clearly the strongest residual candidate that he was elected. He then joined the Laboratory in 1985. Two others effectively came with him from Swansea; Chris Rogers was appointed as a UL and, in 1986, James Norris to a New Blood post as UAL. With these two appointments the strength of the Lab in pure probability was clearly maintained, and its average age decreased.

David Williams brought the highest degree of professional strength, together with a particular warmth and generosity of personality. Sensitive to the possible charge of mathematical preciousness (which he of all people could have disregarded) he lectured and supervised a whole range of courses in probability and statistics. He gave two graduate lecture series (Connections and Percolation) which bridged probability, modern physics and pure mathematics with rare power and evoked sustained interest from the staff of the whole Faculty. His breadth manifested itself in the truest fashion; students left David's courses knowing something of the Mabinogion as well as of martingales.

In retirement David Kendall developed his study of standing-stone configurations into a `theory of shape', working with a very bright visitor from mainland China: Huiling Le. In the following years he was awarded the Royal Statistical Society's Guy Medal in Gold and the De Morgan Medal of the London Mathematical Society, complementing the Sylvester Medal already awarded by the Royal Society. However, David maintains that it is his founding of the Bernoulli Society, jointly with Jerzy Neyman, which gives him the greatest satisfaction.

David Kendall continued to occupy a room in the Lab and use computing facilities. University departments vary widely in their practice towards retired members. University policy must of course be that they have no rights, and departments under the severest resource pressures must also see it this way. However, groups which consider that they can both stretch resources and avoid the problems an insensitive senior retir? might pose do in fact offer a continuing home. Henry Daniels had been given a room on this basis, as David was now. Violet Cane and Manfred Gordon had received partial facilities on the same basis. One must not see this practice as resting on pure charity or sentiment; the `Advanced Fellows' offer depth to the group in several ways, and their presence is often particularly appreciated by the youngest members of the group: the graduate students. One might also say that any other attitude would scarcely be consistent with a healthy feeling of group identity.

It was in 1986 that Elizabeth Thompson published her *Pedigree Analysis in Human Genetics* (Johns Hopkins Press) and then resigned to take a chair of statistics at the University of Washington. It was a pity to lose her from the Lab, but a greater pity to lose her from the country. She had applied for chairs of statistics in the UK, but committees with a narrow concept of statistics appointed candidates clearly her inferior.

As argued earlier, books published by the staff do not reflect everything, but they must reflect something. In 1986 Wiley published Peter Whittle's *Systems in Stochastic Equilibrium* and in 1987 the revision by Chris Rogers and David Williams of Vol. 2 of David's *Diffusions, Markov Processes and Martingales*. To anticipate somewhat, in 1990 Wiley published Peter Whittle's *Risk-sensitive Optimal Control* and in 1991 Cambridge University Press brought out two sets of lecture notes based on existing Part II courses. These were *Communication Theory* (Charles Goldie and Richard Pinch) and *Probability with Martingales* (David Williams).

A very significant and encouraging development was the emergence in 1985 of the Stochastic Networks Group. Frank Kelly's interest in queueing networks had developed, through a contact with British Telecom which was later formalised, into an interest in communication networks. Communication and computer specialists worldwide were beginning to recognise that such systems generate interesting and difficult stochastic problems, with optimisation (or at least good performance) very much a consideration. Frank had attracted some very good students to this field early in the decade (e.g. Iain MacPhee and Ilze Ziedins). However, by the mid-eighties a very bright and substantial group had been formed by the arrival of Richard Gibbens, Graham Louth, Phil Hunt and Neil Laws; this was reinforced by the development of a close working relationship with British Telecom. The group now constituted itself the Stochastic Networks Group. It also provided the first case in which the Lab had clearly achieved critical mass on any research topic. Over the years a modest staff had been trying to cover a wide field, with the result that real concentration was reached on no single topic. The critical local density was now achieved for the first time. Moreover, the group was answering an advanced technological need at just the right time. The introduction of electronic telephone exchanges means that, for example, new call-routing methods are both possible and necessary. Frank Kelly and Richard Gibbens evolved the Dynamic Alternative Routing scheme, which provides near-optimal performance by simple means and has since been put into practice by British Telecom. This is only an example of the type of challenge large systems are offering. The Stochastic Networks Group (and with it the Lab), although small enough in all conscience, now has a high international reputation in the study of communications networks. It is likely that an Institute of Telecommunications will be founded in the University of Cambridge in the near future, supported by industry, with the Stochastic Networks Group as one of its prime components.

The impression created by the many references to the Brunsviga should now be corrected; computing facilities in the Lab have of course kept pace with the times. They are used as a teaching adjunct only for the Diploma practical class and occasional other courses, such as the multivariate analysis class. However, everybody computes, of course, and reactionaries who do not have this basic skill are now so rare as to be acquiring antiquity value.

The manual Brunsvigas continued in class use until at least 1947/8, although being progressively replaced by electromechanical machines from about 1944. By 1964 the mainframe Titan was then also available, using autocode and paper tape. Hewlett-Packard pocket calculators were adopted in 1973, followed by programmable calculators in the late seventies. Fortran was by now used for calculations on the IBM mainframe. In 1983 the change was made to BBC micros, using a Torch disc drive, BASIC, and with Glim available on disc. Statistical packages also became available on the mainframe: SAD, BMDP, Genstat and SPSS. Computing power in the Lab was greatly enhanced in 1987 by Hewlett-Packard's donation of several Unix work-stations. It was the manifest success of the Stochastic Networks Group which prompted Hewlett-Packard to make this generous and much-appreciated gift. These work-stations were linked; about this time the ethernet local area network was installed throughout the Lab. Now, in 1993, the network is being greatly enhanced, with the provision of X-windows and packages such as Splus, Glim and Mathematica.

A refreshing interlude was provided in 1986/7 by David Banks, who gave highly appreciated and capable relief teaching in statistics for the year. David came from Berkeley and returned to Carnegie-Mellon, and it was he who made us realise what a positive benefit such a `casual' can be. In both classroom and commonroom David at once fitted in and brought a breath of fresh air; we feel that he left us rather than that he visited us.

There were various developments in 1987. One was David Williams' resigned assumption of the Directorship. Another was the Royal Statistical Society's celebration of its Charter Centenary by a three-day meeting in Cambridge (more particularly, in the Cambridge Union). The Lab provided local organisation, a task it carried out willingly and enjoyed. Finally, there was a welcome accession of strength on the statistical side with the appointment of Alastair Young to a UALship. He and Henry Daniels cooperated on a mathematical evaluation of the bootstrap method.

Peter Whittle was awarded an SERC Senior Fellowship for the years 1988/91 to enable him to work on another variety of networks: neural networks. The consequent necessity of finding a temporary teaching replacement again provided a bonus. Charles Goldie was appointed for a two-year period which was, reasonably enough, as much absence as the University of Sussex would allow him. Charles proved eager and capable in high degree. He took on the courses in convex optimisation and communication theory, which were quite new to him, with enthusiasm and thoroughness. An byproduct in the second case was the CUP course text, already mentioned, written with Richard Pinch.

There was little expectation that one would find a third-year replacement to match Charles, who had been the happiest solution in every respect. However, Yurii Suhov, from Moscow, showed interest. He had already visited the Lab and, with his background in statistical communication theory among other things, seemed a very good bet, although obviously in some respects an outside one. Visa trouble delayed him in Dublin until late January 1991, which made him thrice welcome when he came. He was appointed to a regular ULship later that year. Yurii brings skill in the applications of probability to statistical physics; also the well-known strengths of the mathematical culture in which he was brought up.

In 1989 Frank Kelly was elected an FRS; a happy development in itself, and one which brought the Lab's tally to five (Henry Daniels and David Kendall being assuredly counted always as Lab members). This was followed by his appointment to a personal chair.

Chris Rogers left in 1991 for a chair at Queen Mary and Westfield College, London, joining Charles Goldie there. Chris had been a great enthusiast for all stochastic analysis related to Brownian motion. In recent years he had also developed an interest in applications: to some part in statistical consultancy but to some part also in financial modelling. The quite sophisticated mathematical analysis of option-pricing and the like has engaged the attention of many probabilists over recent years: in Cambridge, of Chris Rogers, Doug Kennedy and David Williams. In 1993/4 it will find its way into a Part II course.

Chris Rogers was replaced (although the correspondence between resignations and appointments is inexact) by the appointment of Gareth Roberts as a UAL in 1992. Gareth's background was originally in probability, but he had moved much more into statistics while at Nottingham with Adrian Smith.

In 1991 David Williams resigned from his chair, characteristically giving for notice as much time as would be needed to find his replacement. He had made earlier resignation attempts, alleging his own inadequacy for the post, a charge so ludicrous that words could scarcely be found to counter it. David Kendall and Peter Whittle had baulked these by writing independently to the Vice-Chancellor and asserting (sincerely and without collusion) that David Williams was the best Director the Laboratory had ever had. However, he was now resolved. His real reasons were perhaps the obvious ones: a weariness with administration, a desire to get more of his own work done, and hiraeth -- longing for Wales. However, strangely, and as no one in Cambridge had realised, when David left Swansea in 1985 he had announced to the Senate there that he intended to occupy the Cambridge post for just seven years.

The fixity of David's decision was recognised, and Frank Kelly took over the Directorship in 1991. The intention that David should thus be spared worry in his last year at Cambridge was not in fact fulfilled; the difficulties of house-moving had reached their now-familiar intensity, and David suffered serious health problems. It was with great regret that the Lab saw him depart in 1992; an era of particular warmth and vitality had closed.

David Williams had given the Electors good time in which to replace him, and the same care was taken to prepare a good field as in 1985, with the same genuine anxiety to do right by statistics. However, to the outside observer the election also provided a re-run of history. Several outstandingly strong probabilists had applied; the statistical field was sound, but less outstanding, even if one measured each of the two fields by the world standards of its own discipline. The statisticians were certainly given a margin of preference; against this one must perhaps reckon an anxiety that the existing strengths of the Laboratory should not be gratuitously jeopardised.

The outcome was that Geoffrey Grimmett was elected; he left Bristol and took up his post in October of 1992. Geoffrey had made a very strong name in the study of percolation processes and of random graphs, interests which abut those of several in the Lab and the University.

The long-felt unease within the Laboratory itself that the subject of statistics was inadequately represented was now supplemented by a growing realisation that the regime in which the Lab's first chair continued to be filled by a probabilist might be self-perpetuating, and indeed that such a pattern might not even be unreasonable if the Lab's existing strength in the central topic of probability was to be preserved. Moves were then set afoot to establish a third chair, to be called the Chair of Statistics or whichever variant would emphasise its protected nature: that it should under no circumstances be filled by any other than a genuine statistician.

The course of this last election reinforced the unease; indeed, the conscience of some of the Electors was appeased only by the undertaking from John Coates, now the Head of DPMMS, that the proposed Chair of Statistics would be the top Faculty priority. This is no light undertaking, but John, whose understanding and support for the Lab have matched those of Ian Cassels, gave it unequivocally. It was further decided that the search for suitable candidates for the new chair would be undertaken much more deliberately and systematically than is the Cambridge habit: that a Search Committee would be formed to actively beat the world of statistics, and that the members of this committee would ultimately form the nucleus of the Board of Electors. At the time of writing the case for the establishment of the Chair has just been accepted by the General Board of the University, and it is hoped that the post will be filled by October 1994.

Despite the great widening of its interests, the Laboratory remains the Statistical Laboratory and the Diploma remains the Diploma in Mathematical Statistics. However inadequate these may now seem as descriptions, the feeling has been that to change them would be like trying to doctor one's foundation stone. It is believed on the other hand that they constitute no false claim.

In particular, the term `Operational Research' has not crept into either title. For reasons which would take too long to recount, OR activity in the Lab has been even more divorced from the activity of the `OR community' than has been the corresponding case in statistics. Nevertheless, it is notable that the Lab has supplied the only winners in the UK (and among the few in Europe) of the Lanchester Prize of the Operational Research Society of America: Peter Whittle in 1987 and Frank Kelly in 1992. Perhaps the term `operational research' is no longer a fair description of what one is trying to do; something like `the mathematics of systems' may be nearer.

The success of the Laboratory depends on all its staff and the depth they supply; to measure the state of the Laboratory by the state of its professorial staff would be invidious and misleading. Nevertheless, the fact that the Statistical Laboratory has now progressed to a professorial staff of four does underline the great change in its circumstances since the fifties, and the composition of this staff signals rejuvenescence and promise. Frank Kelly and Geoffrey Grimmett are both young and of high international reputation. If, as one may reasonably expect, they are matched by those soon to be elected to the Churchill Chair and to the new Chair of Statistics, then, whatever the Lab does in the coming years, it will lead.

- Bartlett, M.S. (1982) Chance and Change In
*The Making of Statisticians*(Ed. J. Gani), Springer. - Box, F.J. (1978)
*R.A. Fisher, The Life of a Scientist*. Wiley. - Campbell, R.C. (1959) Statistics -- a retrospect. University of Cambridge, School of Agriculture, Memoir No. 31,5-10.
- Edwards, A.W.F. (1991)
*Statistics in Cambridge*. Unpublished notes. - Kendall, D.G. and Harding, E.J. (1973)
*Stochastic Analysis*and (1974)*Stochastic Geometry*, Wiley. - Smith, W.L. (1993)
*The Cambridge Stats Lab*. Unpublished notes. - Whittle, P. (1993) A Conversation with Henry Daniels.
*Statistical Science,*, 342-353. - Whittle, P. (1994) Almost Home.
*In Probability, Statistics and Optimization*(Ed. F.P. Kelly), Wiley, 1-28.

#### Published by the Statistical Laboratory, Wilberforce Road, Cambridge, CB3 0WB, University of Cambridge.

First Published 1993, Revised 2001

Copy @ Peter Whittle, 1993 All rights reserved

The moral right of the author has been asserted