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arXiv:1001

.3272v1[stat.ME]

19Jan2010

Statistical Science

2009, Vol. 24, No. 2, 244254DOI:10.1214/08-STS259c Institute of Mathematical Statistics, 2009

A Conversation with Shayle R. SearleMartin T. Wells

Abstract. Born in New Zealand, Shayle Robert Searle earned a bach-elors degree (1949) and a masters degree (1950) from Victoria Uni-versity, Wellington, New Zealand. After working for an actuary, Searlewent to Cambridge University where he earned a Diploma in mathe-matical statistics in 1953. Searle won a Fulbright travel award to Cor-nell University, where he earned a doctorate in animal breeding, witha strong minor in statistics in 1959, studying under Professor CharlesHenderson. In 1962, Cornell invited Searle to work in the universityscomputing center, and he soon joined the faculty as an assistant pro-fessor of biological statistics. He was promoted to associate professor in1965, and became a professor of biological statistics in 1970. Searle hasalso been a visiting professor at Texas A&M University, Florida StateUniversity, Universitat Augsburg and the University of Auckland. Hehas published several statistics textbooks and has authored more than165 papers. Searle is a Fellow of the American Statistical Association,the Royal Statistical Society, and he is an elected member of the In-ternational Statistical Institute. He also has received the prestigiousAlexander von Humboldt U.S. Senior Scientist Award, is an HonoraryFellow of the Royal Society of New Zealand and was recently awardedthe D.Sc. Honoris Causa by his alma mater, Victoria University ofWellington, New Zealand.

The following interview, with Martin Wells of Cor-nell University, took place over a number of visits tothe home of Professor Searle in Ithaca, NY in theFall of 2007.

1. THE EARLY YEARS

Wells: Shayle, tell me a little about your earlyeducation.Searle:As a small boy I was, so my mother often

told me, in love with numbers and arithmetic. Ap-parently even before starting school I used to scrib-

Martin T. Wells is Professor, Departments of BiologicalStatistics and Computational Biology, Social Statisticsand Statistical Science, Cornell University, Ithaca, NewYork 14853, USA (e-mail: [email protected]).

This is an electronic reprint of the original articlepublished by theInstitute of Mathematical Statistics inStatistical Science,2009, Vol. 24, No. 2, 244254. Thisreprint differs from the original in pagination andtypographic detail.

ble such things as 1 + 2 = 3 in a book of wallpa-per samples used as a scratch pad. And throughoutmost of my school days I was occasionally movedup a class because of being good at mathematics.(Classes were not governed by age, as in the U.S.A.,but by ability.) Mind you, mathematics was not par-ticularly rigorous or conceptual at the kindergarten-type school where I was for a year, nor during mytwo years at a grade school. In 1937 I started at aboarding school (for 814-year-old boys) where the

teaching was very good, including mathematics. Af-ter five years I transferred to a high school where theteaching was generally bad, except for mathematics.Wells: Tell me about your undergraduate days.Searle: It was in March 1945 when I started at

University. I was to be at Victoria University Col-lege in Wellington (N.Z.s capital) 120 miles southof my home town Wanganui. It was a college of theUniversity of New Zealand, at that time, formallyNew Zealands only university with students only atits four colleges and two agricultural colleges dottedaround the countryhalf of them in each island.

1

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2 M. T. WELLS

Fig. 1. Shayle Searle, around 1937, school uniform, aged 9.

They are now, and have been for some years, allautonomous universities, and the University of NewZealand has disappeared.

The difficulty I faced in 1945 was deciding whatcourse of study I would follow. My family (no sib-lings, but a bunch of cousins) knew nothing aboutuniversities; least of all did they know anything aboutcareers based on mathematics. Schoolmaster or ac-countant seemed the only options and because in mythird and last year in high school (having the previ-ous year passed the nationwide university entranceexam) I took and passed two year-long courses forthe B.Com. degree, so I chose accountancy and spenthalf of that first university year as an office boy in alarge accountancy firm in Wellington, and thus wasa part-time student. The firm did a lot of auditingwork and this led to my first apprenticeship, so tospeak, of being an auditor: checking the arithmeticof long columns of journal entries in the books ofa Lever Bros. soap-making plant near Wellington.

I found it to be incredibly dull work. That decidedme; I wanted to do mathematics. So at years endI quit my job, changed courses to do a B.A., andwent home where I could, and did, get some excel-

lent tutoring for three months to bone up on themaths I should have done in my third year at highschool. All the work was algebra from an old andwonderfully good book by Hall and Knight.Wells: How did you resolve these early career is-

sues?Searle:During that first year of mathematics I still

had the crunch question: for what job would a math-ematics training prepare me? Becoming an actuarycame as the answer, surprisingly from a lady whoowned a successful department store. With there be-ing only four actuaries in New Zealand in the 1940s,

none of whom were anywhere near my hometownof 20,000 people, basically a farming town, it wassurprising any resident had even heard of an actu-ary! Sort of a high-level accountant was about thenearest description. Anyway, I found out about it,had another summer of tutoring and in May 1947sat and passed the preliminary exam of the LondonInstitute of Actuaries. The exam consisted of threehour papers in English and mathematics.

Then for the next two years I concentrated on theB.A. exams coming in 1948, these being two papersin pure maths and two in applied, the latter involv-ing topics like statics, dynamics and hydrostatics:dull, difficult and for me from an agriculturally ori-ented background, of no use whatsoever. In 1949,after weathering a bout of pneumonia, I took thesix exam papers for the M.A. in mathematics (nothesis required), one of which was on matrices. Theinstructor for that course was senior lecturer J. M.Campbell, using Aitkens 1948 book Determinantsand Matrices. Campbell, a New Zealander as wasAitken also, had done his Ph.D. in statistics at Ed-inburgh where Aitken was having a very eminentcareer.Wells:At that point, what path did you pursue af-

ter an undergraduate and masters training in math-ematics?Searle:After the 1949 M.A. exams I took a job as

assistant to the actuary at Colonial Mutual Life As-surance Company in Wellington. I had no office ofmy own, but merely a desk in a large room with somedozen or so retirees who, day in and day out, werechecking the weekly premiums paid for what werecalled industrial policiessomething like twenty-fivecents a week. The actuarys office was but a few

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steps across the hall. He was a real proper English-man and helped me a great deal in preparing myfirst paper, Probability: Difficulties of Definition.It was published in the Journal of the Institute of

Actuaries Students Society,1951, pp. 204212. Al-though I had read the von Mises book, and Venns, Isoon realized after attending my first lecture or twoat Cambridge that my knowledge of probability wasvery nave and incomplete. (I had not even had acourse in set theory!)

Anyway, in 1950, now in the actuarial environ-ment, I reverted to the actuarial exams, but stillkept an eye on the B.Com. degree to which severalcourses in my B.A. degree (e.g., English and eco-nomics) could also be counted. So I took a statisticscourse for the B.Com. which also helped in prepar-ing for Part I of the actuarial exams destined forMay 1951. These and the following parts were knownto be difficult; the average time for becoming fullyqualified was eleven years! Individual exam ques-tions dealt with annuities and life insurance premi-ums (with absolutely horrible notation) and somestatistics. Many questions had such long descrip-tions that a paper took a full ten minutes to readand after reading it one had to decide which ques-tions to answer to satisfy the instruction Do threefrom the five questions in each section of the exam

paper!! As if all this wasnt going to be difficultenough, there were no lectures available and onlytwo or three books, some of them only in galleyproof form. Notational distinction, in these books,of a population statistic from an estimator of it wassparse: often the same symbol was used for both.From England (where the exams originated) I wasgiven the name and address of an actuary in aninsurance company in Sydney, Australia who wassupposed to be available to me to answer questionsand give advice on my attempted solutions to ex-ercises in the books. But, despite the almost daily

flying-boat services between Wellington and Sydney,it usually took him a month to get his comments tome. Not much use. Anyway, in May 1951 I sat theexam.Wells: How did you initially get interested in the

subject of statistics?Searle:In the 1949 M.A. exam Id done much bet-

ter than expected. By one mark out of 600 I was topof New Zealand; however, no kudos in that sincethere were only four examinees! Nevertheless, as aresult, I became interested in an overseas scholarship

to enable me to study statistics. Interest in statis-tics had been promoted by the course in Wellingtonand by the Part I actuarial exam. Unfortunately Idiscovered that I should have applied for the schol-

arship before, not after, my M.A. exams. I couldapply after, but I knew Id be competing with thenotable New Zealander Peter Whittle (who has re-cently retired from his Cambridge professorship). SoI scrubbed that idea. However, I was told that Icould be supported overseas by a family agriculturetrust (established by my successful maternal grand-father), so I proceeded to get myself accepted atboth Emmanuel College and the statistics labora-tory at Cambridge University.

2. CAMBRIDGE DAYS

Wells: Lets chat about your time at the statisticslaboratory at Cambridge University. Tell me aboutyour introduction to Cambridge University.Searle: Departure from New Zealand in mid Au-

gust, by ship, was not easy; three hours before leav-ing the Wellington wharves I received a phone callfrom the government actuary (the Institutes offi-cial representative) telling me that I had failed thewhole of the Part I exam taken in May. That wasa bitter pill to add to the emotion of a ship pullingout from its berthage for what was to be its usual31-day voyage to Britain. My first days after arrivalin Britain were spent in London during which timeI went to see the Institute of Actuaries. Comparedto the facilities Id struggled with in New Zealandfor trying to pass their exams, the Institute lookedwonderful: a variety of lecture courses, some 80100students, and very nearby was a big Prudential As-surance building where a large number of actuarialstudents were employed. If becoming an actuary hadstill been my intention, Id have been very envious.Coming to the Institute was the obvious thing to do.

But I was going to Cambridge. And a day or two

after getting there, an easy hour by train, I paida visit to the statistics laboratory. After my knockon the directors door, I followed come in and an-nounced myself Shayle Searle, from New Zealand.Who are you? said John Wishart (of Wishartsdistribution). Ive never heard of you! That didnot seem to be a very auspicious start. However,in gentlemanly English manner, Dr. Wishart, saidWell, youve come a long way so we cant send youback.Wells: What happened after this auspicious intro-

duction at Cambridge?

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Fig. 2. Cambridge University Statistical Laboratory 1953 personnel. Back row: D. A. East, B. Guss, E. S. Page, G. A.Coutie, K. K. Chaudary, D. J. Newell, F. J. Chatterly, J. R. Bell, R. S. Bawa, J. R. Ashford, P. A. Wallington. Second row:B. Reifenberg, W. L. Smith, D. R. Cox, J. Wishart (Director), F. J. Anscombe, D. V. Lindley, P. A. Johnson. Frontrow: J. N. Darroch, B. D. Gee, W. S. Townson, K. W. C. de Silva, B. Das, G. B. Aneuryn-Evans, S. R. Searle. Absent:H. E. Daniels, Th. Metakides, J. T. Laws. (Faculty)

Searle:I stayed; and from among the star-studdedfaculty of F. Anscombe, D. R. Cox, D. Lindley andH. E. Daniels I was given Dennis Lindley as my tu-tor and into whose class on probability I was di-rected. Boy, was I lost. But fortunately courses didnot have exams; and my learning revolved aroundthe customary 23 hour tutorial session I had eachweek with Lindley. Just he and me. Most of thetime centered on my attempts at answering ques-tions that came from previous years exams for theDiploma. To begin with I was expecting to work fora Ph.D. But after a couple of months or so, Lindleytold me like it was: he recommended that I do theDiploma and not the Ph.D. His reasoning was as fol-lows: statistics has a formal connection to the mathdepartment and mathematicians do not always lookvery favorably at statistics. Yet they usually come tothe final oral exam for statistics Ph.D. candidates.And often they decline to award the Ph.D. but in-stead award an M.A.which in this situation hascome to mean Failed Ph.D. and there was no re-course. Lindley felt that this is what would happen

to me, and as he rightly said, you dont want towork for just a Failed Ph.D. Agreement was clear.Wells: How did you handle this early disappoint-

ment?Searle:During those early years I did have a dis-

appointment or two: mis-timing an application forthe overseas scholarship; getting no help preparingfor the actuarial exams; the Who are you? intro-duction to statistics at Cambridge; and then beingdiscouraged from the Ph.D. degree. You ask howdid I handle all this? Certainly in those days the le-gions of counselors available today for all manner ofsituations did not exist. One largely relied on oneselfand learnt to tough it out.Wells: Tell me about your Cambridge Diploma

project.Searle: The Diploma has stood me well. It con-

sisted of two papers, one theory and one data anal-ysis, and also a written report resulting from beingseconded for the academic year to a data-generatingresearch project within the university: the report todescribe the data analysis and its consequences. I

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was seconded to E. H. Callows lab where he wasmeasuring iodine number in the fat taken from dif-ferent joints of various beef carcassesand my ef-forts finished up as a co-author (see Callow and

Searle,1956). All this was usually considered a one-year effort, but in my case it was set at two years. Atthe end of the first year I sat the two exams for prac-tice! My second year exam results were not as goodas the first year; in fact of seven out of nineteen stu-dents who got Passed with Distinction yours trulywas not among them. Lindley gave me the raspberrylike Ive never had it before or since. Id been enjoy-ing too much the social activities of college end-of-year festivities!

3. THE COMING OF AGE AS A

STATISTICIAN

Wells:After Cambridge, what was your next move?Searle: I then needed to find a job. Cambridge

University had what I believe at the time (1953) wasthe early years of its career center. Although theiradvisors had clearly never previously dealt with a re-search (graduate) student, let alone one with statis-tics qualifications (and from New Zealand!), they didfind me two interviews in London; one was for a jobwith the Colonial Service, in agriculture in Kenya(I resisted the temptation to ask the interviewer ifhis missing leg (or was it arm?) had been eaten bythe Kikuyu), and the other was with Royal DutchShell who wanted to employ me in Venezuela. I de-cided to pursue neither opportunity when I heardof the possibility of a position in New Zealand, asa statistician at Ruakura Research Station, a largeand comprehensive agricultural research farm. So Iappliedbut the position was canceled.Wells: So much for the Cambridge career center;

what did you do after the Ruakura Research Stationjob was canceled?

Searle: I returned to New Zealand and in Octo-

ber 1953 got a newly established post as ResearchStatistician with the Herd Improvement Departmentof the New Zealand Dairy Board, in Wellington. Itturned out to be a decisive moment for my lifesactivities.Wells:Tell me about your time at the New Zealand

Dairy Board.Searle:The work consisted of deriving ways of us-

ing dairy cow milk production records for decidingwhich cows and bulls would be used for breedingoffspring (by artificial insemination) that would in-crease milk production not only for the individual

farmer but for the nation also, since New Zealandhas, for more than a century, lived by its exports ofagricultural products; butter, cheese and milk pow-ders being important parts thereof. The outstand-

ing researcher in this discipline of animal breedingwas Professor C. R. Henderson of Cornell University.And it was my good fortune that he came to NewZealand for his first sabbatical, and actually had adesk in my office for eight months from September1955. His own Ph.D. from Iowa State University wasin animal breeding, under the eye of Professor Lush,the father figure of the discipline. But Hendersonhad strong interests and training in statistics, andmore than a nodding acquaintance with matrices.So we got on well together, especially after I showedhim the formula for the inverse of a partitioned ma-

trix needed in estimating environmental and genetictrends (see Henderson et al., 1959).Wells:What was the consequence of your relation-

ship with Professor Henderson?Searle: The result of all this was that in August

1956 I went to Cornell and did a Ph.D. with Dr.Henderson. Before leaving New Zealand (with a Ful-bright travel grant) I knew what my thesis topicwould be, and by August 1958 had finished my Ph.D.That coincided with the New Zealand Dairy Boardsending me data they wanted analyzed to investigatethe possibility of having yearly production recordsestimated from just 3 or 4 months measured (sam-pled) production instead of the then-usual 9 months.Dr. Henderson was interested in this, too, and kindlykept me on as a Research Associate.Wells: What did Cornell uniquely offer you as a

graduate student?Searle:I cannot describe Cornells offerings as be-

ing unique because I have no comparison with otherplaces since I applied nowhere else. But Cornells tol-erance of my special circumstances was wonderful:I arrived late, some two weeks into the semester, as aresult of the travel arrangements made by Fulbright.Forming my degree committee was greatly aided byHenderson. Animal breeding was to be my major(with Henderson with his strongly statistical inter-ests); one minor was to be statistics with Federer,head of Biometrics. The second minor was trouble-some because I refused to do mathematics (I felt Ihad enough), and I couldnt do anything related toembryology because I had absolutely no backgroundin chemistry or biology or physiology. Hendersoncame to the rescue by reassuring the departmenthead to take me on with a minor of Animal Science

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doing a few undergraduate courses, in at least twoof which (dairying and sheep husbandry) I gave thelectures on breeding. So I scrambled through!

Above all, the greatest benefit of Cornell was the

complete freedom and encouragement to get on withwhat I wanted to do. I knew what my thesis topicwas to be, I was getting the data for it from the N.Z.Dairy Board, the department had just got its owncomputer (an IBM 650), I wrote my own programsand worked many nights on the computer from 10pm till 6 am. The freedom was superband produc-tive.Wells: After writing your Ph.D. with Professor

Henderson what did you do?Searle:I finished the Ph.D. at the end of 1958 and

was hired as a Research Associate under Hender-

son, attending to an extension or two of my thesis,writing several papers for publication, and learn-ing as much as I could about computing facilitiesneeded for this kind of work. Henderson and I gavea semester-long seminar on unbalanced data and Iwrote it up as an extensive set of notes, the proof-reading of which was left to me.Wells: What was your next move?Searle:In late 1959 I returned to N.Z. and my po-

sition with the New Zealand Dairy Board where asire-proving scheme was being inaugurated for se-lecting bulls to be sires in the artificial breedingprogram. For me it was a period of successful pub-lication, for example, nine publications in 1961, notonly in The Journal of Dairy Sciences, but in Bio-metrics, Journal of Agricultural Science, Annals ofMathematical Statistics. During this time I becamea one-third-time scientist of the N.Z. Department ofScientific and Industrial Research in their Mathe-matics laboratory where I took part in their intro-ducing computing and programming to the coun-trys scientists.

1961 was also the year I was asked to reduce myresearch and spend time visiting dairy farmer meet-ings and giving talks. The happy coincidence wasthat, without my knowing it, I was being consideredfor a job at Cornell as statistician to their Comput-ing Center. The official offer to me was delayed sev-eral months because two members of the committeedeciding to employ me each thought the other hadwritten to me. When the offer did come I of courseaccepted it to start on June 1, 1962 after finishingsome responsibilities in New Zealand.Wells: How did working at the N.Z. Dairy Board

influence you?

Searle:Dealing with dairy cow production recordsmade me realize that unbalancedness of data canmaterially affect the meaning ofmanyof the calcula-tions (e.g., sums of squares) that were being used in

(at least agricultural) research literature. And thiswas before the flood of computer software that wehave today. The Dairy Board work simply startedme down the path of unbalanced data, matrices andvariance components. Genetic studies use a ratio ofvariance components and that prompted estimatingthose components and that was highlighted by the1953 Henderson paper in Biometrics.Wells:Tell me about Hendersons influence on your

work.Searle:His greatest influence on me was his enthu-

siastic encouragement. For example, it was a cus-tom in the Animal Science Department that eachsemester every graduate student had to be part ofa team to give a seminar. In my first doing this Idbeen allocated to talking about the uptake of iodinein the thyroidsomething I knew absolutely noth-ingabout. So for my remaining five semesters I sug-gested a topic on breeding to Henderson, he roped inanother graduate student and the job got done. Hewas also very tolerant of my asking questions, andwas exceedingly patient of my saying I still dontfollow you, and he would try again to placate me.He was also greatly helpful in suggesting improve-ments to whatever I was writingalthough whenit came to proofreading a supposedly final draft ofa paper, a modicum of procrastination and delaywould sometimes set in!Wells: What was the state of random effects mod-

eling in the 1950s?Searle: It was quite limited: mostly for balanced

data. And almost the only method of estimatingvariance components was what we today call theanalysis of variance method. In its general terms

it consists of equating sums of squares (or otherquadratic forms) of data to their expected values,in which the random effects give rise to their vari-ances. The trouble was that no real criteria wereused for deciding on which sums of squares to use.With balanced data, analysis of variance seemed anobvious choice, and usually yielded as many sumsof squares as variances being sought. But for unbal-anced data there could be an excess number of sumsof squares which made a problem for the desired es-timation.

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4. BACK TO CORNELL

Wells: When did you return to Cornell?Searle: At Christmas time 1961 I received a let-

ter from a friend at Cornell saying he was glad tohear that I was to be returning to Cornell. That wasnews to me; Id heard nothing. Around March 1962 Iwrote to Henderson to find out what the story was.It turned out that two members of the universitycomputing committee each thought the other hadwritten to me, but in fact neither had. So then I didget a letter; could I start in six weeks? I pointed outI was nine thousand miles from Cornell and my wifewas expecting our second child, and I was alreadycommitted to some Dairy Board responsibilities, butyes, I could arrange to start on June 1st of that year,

1962.Wells: What was your new position at Cornell?Searle: In 1962 when I started in Cornells Com-

puting Center there was no commercial softwareavailable. Will Dixon and colleagues at UCLA werewell on the way with BMDP package; but SAS hadbarely started (its first annual user conference was1976) so part of my responsibility was to decide whatstatistical packages we should have and to get themprogrammed. The Computing Center had a statisti-cal programmer who could do a credible job, and weproceeded to provide for regression and for analysis

of variance of data from well-designed and executedexperiments (i.e., balanced data).Wells:What was the state of modern computing

in 1962?Searle:Computing in 1962 was rudimentary com-

pared to todays activities. Cornell had begun in1956 with an IBM 650 (2000 words of 10-digits plussign) and in 1962 had a 1604 CDC. There was nocommercial software, no data editing and few pro-gramming languages: Fortran and Algol. The con-sulting work was often quite elementary, such as cor-recting the following misadventures: regression anal-ysis that used as data the

1s that had been entered

in place of missing observations; the reproductionof data so that there were 800 of them because the400 actual data were too few in number to makea correlation estimate be significant; the scrutiniz-ing of some six pages of data for which a publishedanalysis of variance seemed spurious; it was, becauseamongst 300 3-digit data we found two values hadbeen entered as 5 digits (only 100 times too big!).Wells:How did you get affiliated with the Biomet-

rics Unit?

Searle:My consulting job also came with a cour-tesy appointment as assistant professor in the Bio-metrics Unit of Cornells College of Agriculture asit was then named, but with . . .and Life Sciences

added to it later. This was where I had formallydone the statistics part of my Ph.D. under the veryhelpful eye of Professor W. T. Federer, head of theBiometrics Unit. And that helpfulness and encour-agement re-asserted itself on my joining the Biomet-rics Unit as faculty in 1962. I was enthusiasticallyurged to write up whatever I was working on. AndI certainly did; five papers both that year and thenext.

In 1965, just as computing was becoming a bigitem on campus, I accepted a line item assistant pro-fessorship in Biometrics and gave up my responsi-

bilities as consultant at the Computing Center. TheCollege of Agriculture started to have its own com-puting facilities and I became lightly involved withsome aspects of that operation. But I had decided Iwanted to be a statistician and not a computer-nic.That started my thirty years in the Biometrics Unitwhich revolved around three interrelated topics: ma-trix algebra, linear models and variance componentsestimation. For each of these three I started a courseand wrote a book or two. Writing, to me, was an en-joyable form of hard work so I kept at it.

5. VARIANCE COMPONENTS, LINEAR

MODELS AND MATRICES

Wells: What researchers showed an early interestin variance components?Searle:In the 1950s only a small coterie of statisti-

cians (many of them with animal breeding interests)felt comfortable with random effects. Occasional pa-pers by such people as Crump, Daniels, Eisenhart,Winsor and Clark, Tippett, and Cochran made in-teresting but not earth-shattering contributions andmostly dealt with analysis of variance methods forbalanced data. I remember, as a graduate student,being at a 6-week research gathering in 1957 calleda seminar on analysis of variance held in Boulder,Colorado under the direction of Oscar Kempthornewith such notables as David (now Sir David) Cox,Bill Kruskal and Jerry Cornfield and others in atten-dance. Following my lecture there on variance com-ponents I had several people come up to me and askme to really explain random effects, one such be-ing Jerry Cornfield. Well, after all, I suppose 1957is half a century ago!

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Wells: What computational issues were there invariance component modeling those days?Searle: Not only were random effects not widely

understood, but the computations were horrendous

for unbalanced data. There was a series of papersgiving scalar formulae for sampling variances of vari-ance components estimates obtained from the anal-ysis of variance method of estimation and on un-balanced data, but these formulae were incrediblycomplicated. And there was no software; indeed,in 1955 before going to Cornell, I struggled witha very small data set to do these calculations witha Powers-Samas punched card tabulator using themethod of successive digiting (see Searle, 1993) forobtaining sums of squares and products. It was hor-rible.

Wells: How did you get interested in unbalanceddata?Searle:My strong interest in unbalanced data (hav-

ing unequal numbers of observations in the sub-classes of the data) arose from dealing with dairyproduction records when working for the DairyBoard. Herds do not all have the same number ofcows, not all cows give milk every year, and withina herd varying numbers are of the same age. I clearlyremember being puzzled for a long time in statisticalmethods giving two different least squares estimatesof fixed effects in a one-way classification depend-ing upon whether one assumed that one effect waszero, or that all the effects summed to zero. Even aslate as my second year as a graduate student (1957)when Henderson and I gave a weekly 23-hour sem-inar on unbalanced data we were still confused bythis situation.Wells: How did the notion of the g-inverse change

your thoughts on linear models?Searle:One of our troubles was we had not kept

up with the concept of estimability propounded byR. C. Bose in North Carolina [linear combinations ofthe parameters, sayA, are defined as estimable ifthe rows of the matrix A belong to the vector spacespanned by the rows of the design matrix; Bose,1949]. Nor were we aware of Penroses (1955) gener-alized inverse matrix which, as Rao (1962) demon-strated, clarified the whole business of solving leastsquares equations which are so often not of full rank,and thus have an infinite number of solutions, butwhich, with the aid of a generalized inverse, easilylead, for every solution, to unbiased estimators of es-timable functions. Some details of this situation arein my 1966 book Matrix Algebra for the Biological

Fig. 3. Shayle, 1952, on St. Johns Bridge, Cambridge.

Sciences; they are considered more fully in LinearModels (1971).Wells: You were an early advocate of using matri-

ces in statistics; looking back this perspective seemsobvious. Do you have a conjecture why early progresson the application of matrices to statistics was soslow?Searle: The first of my Annals papers of 1956,

1958 and 1961 was Matrix Methods in Varianceand Covariance Components Analysis. Its title begsthe question: Why has it taken so long for matricesto get widely adopted where they are so extremelyuseful? After all, matrices are two hundred and someyears old and their use in statistics is only slowly be-coming commonplace. But this was not so, even asrecently as the 1950s. Even at Cambridge, in lec-tures on regression in 1952 there was no use of ma-trices. In Aitkens two 1939 books, one on matri-ces and one on statistics, neither mentions the maintopic of the other! The very first paper in the firstissue of Annals of Mathematical Statistics (Wick-sell,1930) is entitled Remarks on Regression yetit has no matrices. And even the Williams (1959)book on regression has only a tiny mention of ma-

trices. Maybe this tardiness of adoption of matricesarose from their being treated so much a topic ofpure mathematics that they remained hidden fromtheir practicalities.Wells: Tell me more about your early efforts in

teaching linear models using matrices.Searle: Around 1960 a visitor to the Biometrics

Unit taught a course out of Graybills excellent 1961book An Introduction to Linear Statistical Models.He made very slow and pedantic progress and nevergot anywhere near the difficulties of unbalanced data.A year later D. S. Robson took on the course but

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after a few weeks had to be absent at research meet-ings and I was left with the teaching. In progressingtoward the all-important result about a quadratic

form in normal variables having a chi-squared dis-

tribution, Graybill (1961) had nineteen preparatorytheorems! That struck me as just too much. To high-light the differences between each theorem and the

next I summarized the nineteen in one line each.That immediately showed most of those differencesto be very small; for example, normal variables withzero mean in one theorem had nonzero mean in the

next. Among my biometry colleagues was a Ph.D.graduate of Graybills who explained that was whatGraybill wanted his students to learn and so be ablein exams to regurgitate theorems and their proofs.

Not for me, I decided. I wanted students to knowwhere they could read the importantly useful theo-rems (which they might need to use in practice), andto thoroughly understand them. So I concentratedon the overriding theorem in this topic, namely the

conditions under which a quadratic form of nonzero-mean normal variables has a noncentral chi-squareddistribution. Armed with that, many of Graybillsnineteen theorems became just special cases. This

appealed to me as a mathematically tidy way of han-dling things. Thus there was only one theorem, but

a vital one, that students needed to know and in do-ing so needing to know that they understood it andknew how to use it. This set me to thinking about

doing a book.So then, armed with matrix algebra and the gen-

eralized inverse, and motivated by unbalanced data,I went on to describe in detail the various sums of

squares and their corresponding hypotheses that canbe derived from unbalanced data in the analysis of

variance context. Not much of this was dealt withby Graybill or any other book. None of it was pretty,

but it was only the use of matrices that made it atall feasible. As well as fixed effects models, Linear

Modelsalso (in its last three chapters) deals with ap-plying to unbalanced data the analysis of variancemethod of estimating variance components, namelyequating observed sums of squares to their expectedvalues. Nearly all of that has now been relegated

to history by the widespread application of max-imum likelihood (starting with Hartley and Rao,1967) and other methods, and the amazing growthof computability.

6. BOOK WRITING

Wells:You just mentioned that when teaching lin-ear models that set you off to start thinking about

doing a book. Tell me about writing your first book.Searle: Federer was on sabbatic leave 19621963,and in his absence Professor D. S. Robson chairedthe Biometrics Unit. In January 1963 he told me thesecretaries were short of work, and he asked, Dontyou have some notes on matrices they could type?I protested that although Id written the notes forteaching a 1957 summer course when I was a grad-uate student, they needed plenty of work to makethem worthy of a typists time. Robsons reactionwas, Why dont you write a book? So I did. I sentit in 1964 to four publishers: two turned it down, one

never replied and Wiley & Sons accepted it. Monthslater they had a change of editors and turned itdown. But luckily one of their senior editors, Ms.Beatrice Shube, saw the manuscript and promotedits publication. Thus was born my first book, Searle(1966) which sold more than 10,000 copies before go-ing out of print. It spawned a mildly plagiarized ver-sion in the form of Searle and Hausman (1970) whichthrough getting little or no promotion from businessacademia sold barely 5,000 copies. Nevertheless in1974 it did have reprint editions in Taiwan (in En-glish) and in Russia (in Russian), both of which were

initially denied by their respective publisher. Thesuccessor to both the 1966 and 1970 books is Ma-trix Algebra Useful for Statistics. It (Searle, 1982)has sold more than 10,000 copiesthanks to GeorgeStyan for the Useful. Prior to that helpful word,reviewers of the manuscript had strongly dislikedthe title.

I started, in 1965, and for thirty years taught aMatrix Algebra course at Cornell; it never had lessthan twenty students and up to seventy one year.They were from as many as 812 departments inagriculture most years, despite the 8:00 am startingtime three days a week. Because of that early hourI never admonished anyone for b eing late; to be latewas better than not coming. Thirty and more yearsago teaching matrix algebra because of its practicaluse in statistics was never doubted as being useful(in contrast to some of the concepts of linear alge-bra). But nowadays, because, I suppose, of the com-puting software for doing the algebra, the teachingof the algebra seems to have become somewhat ofjust an add-on, if that. What a pity; matrix alge-bra is fun. My initial intrigue at being able to have

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10 M. T. WELLS

Fig. 4. Shayle at the blackboard, Hoehenheim University,July, 1977.

AB= 0 without having A= 0 or B= 0 has neverleft me.Wells: How did your classic Linear Models book

come about?Searle:In 1968 I was invited by H. O. Hartley to

take my sabbatic at Texas A&M University and itwas there that I started my Ph.D. level Linear Mod-elsbook, published by Wiley & Sons in 1971. It hashad sales of more than 15,000 and another 1,800 inthe paperback Wiley Classic Edition which startedin1997. It is, I believe, a book which did make an

impression on the understanding of linear models,especially of the complications emanating from un-balanced data. This was, and still is, especially im-portant for using the high-powered computing soft-ware designed for doing linear model and analy-sis of variance calculations of such datasoftwaresuch asSAS, SPSS, STATAand many others. Theirearly output descriptions and labels were often nota model of clarity, so that knowing the mathematicsof the calculations was important.

The book led to many interesting and enjoyableinvitations to give short courses for George Washing-

ton University in Washington, D.C. and in Berlin,Germany; and to lecture in such various locales asBudapest, Sydney, Auckland, and Freiburg am Breis-gau and a raft of conferences and seminars in the

U.S.A. and elsewhere. This included in each of 1985and 1986 a 4-month stay in the mathematics de-partment of the University of Augsburg in Bavaria,funded as a U.S. Senior Scientist by the Alexandervon Humboldt Foundation of Bonn, Germany. Aswell as having a thoroughly enjoyable time in thehistorical city of Augsburg, I finalized a number ofpapers, gave some seminars and made a good startonLinear Models for Unbalanced Datapublished byWiley in 1987.

To whatever extent all this represented success forLinear Models it motivated me to more books, five

more actually, the most recent being Generalized,Linear, and Mixed Models co-authored with C. E.McCulloch, published by Wiley & Sons in 2001. Animportant feature of this book is its distinct em-phasis on mixed models, a topic which is very muchin evidence in todays statistical research. A con-tributing reason for this is that todays computingfacilities can handle the arithmetic that is neededfor coping with random effects when modeling un-balanced data.

7. SOME PERSPECTIVEWells: Looking back over your career, do you see

a recurring theme?Searle: I find it hard to believe that through my

activities with animal breeding data it was morethan fifty years ago when I was first trying to dealwith random effects and variance components in un-balanced data. After all, half the genetic contribu-tion to a cows milk production comes from its sirebut it is only a random halfand thus we have arandom effect when including the effect of sire ina linear model for its daughters milk productionrecord. And this in turn gives rise to a variance com-ponent for the random effect. This has been a statis-tical interest of mine ever since the C. R. Henderson(1953) paper Estimation of variance components. . .in Biometrics. My contributions motivated by thatpaper are in the Annals of Mathematical Statisticsin 1956, 1958 and 1961. My most recent effort onthis topic is the1992Wiley book Variance Compo-nentswith G. Casella and C. E. McCulloch.Wells: Where do you see basic statistical research

heading?

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SHAYLE R. SEARLE 11

Fig. 5. Shayle and his wife Helen enjoying the benefits of a conference with Harold Henderson in Bavaria, 1986.

Searle:Certainly statistics research seems to havebecome increasingly computing oriented with greatreliance (maybe indeed faith) being put on software.With this has also come diminishing interest in thealgebraic development of new methods. Does thisnot arouse the questions How will new methods be

developed? and By whom? And might not greatreliance on software contain the possibility of veryoccasionally getting spurious output? These ques-tions worry me. Especially so in the case of a stu-dents own Ph.D. computer program that yieldedseveral intelligible results from extensive data butalso one completely outlandish result for which noadequate reason could be found. I insisted that ithad to be a mistake in the students own program-mingbut my insistence was eventually sidelined.That seemed to me to be not very good science.

8. RETIREMENT

Wells: I can speak for my Cornell statistics col-leagues and let you know that we are sorry not tosee you at the office more often these days.Searle:Along with my own hip and knee replace-

ment surgeries, my wifes illness and death, and thecompletion of two books, I slipped away from re-search, or perhaps more accurately research slippedaway from me.Wells: Tell me about some of your recent acco-

lades.

Searle:Since retiring in 1995 I have had two veryrewarding events bestowed upon me. In 1999 I waselected an Honorary Fellow of the Royal Society ofNew Zealand. The Honorary here indicates profes-sional connection to New Zealand even when livingand working beyond New Zealand. And the secondevent was the awarding in 2005 of the D.Sc. Hon-oris Causaby my alma mater, Victoria University ofWellington, New Zealand. Both events are acknowl-edged with gratitude.Wells: As always Shayle, it has been delightful

chatting with you. Thank you for granting me theopportunity to do this interview for Statistical Sci-ence.

REFERENCES

Aitken, A. C. (1939). Determinants and Matrices. Oliverand Boyd, Edinburgh.

Bose, R. C. (1949). Least Squares Aspects of Analysis ofVariance. Institute of Statistics Mimeo Series 9. Univ.North Carolina, Chapel Hill.

Callow, E. H. andSearle, S. R. (1956). Comparative stud-ies of meat: V Factors affecting the iodine number of thefat from the fatty and muscular tissues of cattle. J. Agri-cultural Science 48 6373.

Graybill, F. A.(1961).An Introduction to Linear StatisticalModels. McGraw-Hill, New York. MR0126316

Hartley, H. O. and Rao, J. N. K. (1967). Maximum likeli-hood estimation for the mixed analysis of variance model.Biometrika 5493108.MR0216684

Henderson, C. R. (1953). Estimation of variance and co-variance components.Biometrics 9 226252.MR0055650

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Henderson, C. R., Kempthorne, O., Searle, S. R. andVon Krozigk (1959). Estimation of environmental andgenetic trends from records subject to culling. Biometrics15192218.

McCulloch, C. E. and Searle, S. R. (2001). Generalized,

Linear, and Mixed Models. Wiley, New York.MR1884506Penrose, R. A. (1955). A generalized inverse for matri-

ces. Proc. Cambridge Philosophical Society 51 406413.MR0069793

Rao, C. R. (1962). A note on a generalized inverse of a matrixwith applications to problems in mathematical statistics.J. Roy. Statist. Soc. Ser. B. 24 152158.MR0138149

Searle, S. R. (1951). Probability: Difficulties of definition.J. Inst. Actuaries Students Soc. 10204212.MR0047269

Searle, S. R. (1956). Matrix methods in variance and covari-ance component analysis. Ann. Math. Statist. 27 737748.MR0081051

Searle, S. R. (1958). Sampling variances of estimates ofcomponents of variance. Ann. Math. Statist. 29 167178.

MR0093879Searle, S. R.and Henderson, C. R.(1961). Variance com-

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Math. Statist. 3211611166.MR0133930Searle, S. R. (1966). Matrix Algebra for the Biological Sci-

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Wiley, New York.MR0670947Searle, S. R. (1971). Linear Models. Wiley, Chichester.

(1997, Wiley Classics Library.)MR1461543Searle, S. R. (1993). Analysis of variance computing then

and now, with reference to unbalanced data. In Proceedings18th SAS Users Group Conference10771087.

Searle, S. R. (1997). Linear Models for Unbalanced Data.Wiley, New York.MR0907471

Searle, S. R., Casella, G. andMcCulloch, C. E.(1992).Variance Components. Wiley, New York.MR1190470

Searle, S. R. and Hausman, W. H. (1970). Matrix Algebrafor Business and Economics. Wiley, New York.

Wicksell, S. D.(1930). Remarks on regression.Ann. Math.Statist. 11.

Williams, E. J. (1959). Regression Analysis. Wiley, NewYork.MR0112212