A Conversation with George A. Barnard Author(s): Morris H. DeGroot Source: Statistical Science, Vol. 3, No. 2 (May, 1988), pp. 196-212 Published by: Institute of Mathematical Stable URL: http://www.jstor.org/stable/2245568 . Accessed: 24/09/2014 22:01

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This content downloaded from 128.173.127.127 on Wed, 24 Sep 2014 22:01:56 PM All use subject to JSTOR Terms and Conditions StatisticalScience 1988, Vol. 3, No. 2, 196-212 A Conversationwith George A. Barnard MorrisH. DeGroot

GeorgeA. Barnardwas bornon September23, 1915,in Walthamstow, Essex, England.He receiveda B.A. in Mathematicsfrom Cambridge Uni- versityin 1936,did graduatework in mathematicsat PrincetonUniversity from1937 to 1939,and receiveda D.Sc. fromthe Universityof Londonin 1965based on his publications.He was a MathematicalConsultant in the PlesseyCo. from1940 to 1942;a ScientificOfficer in theMinistry of Supply AdvisoryUnit from 1942 to 1945;and a facultymember in theMathematics Department,Imperial College, London, from1945 to 1966, servingas Lecturer(1945-1947), Reader in MathematicalStatistics (1948-1954) and Professorof MathematicalStatistics (1954-1966). He was Professorof Mathematicsat the Universityof Essex from1966 to 1975,and Professor of Statisticsat the Universityof Waterloofrom 1975 untilhis retirement in 1981. He servedas Presidentof the Royal StatisticalSociety in 1971- 1972,Chairman of the Institute of Statisticiansin 1960-1962,President of the OperationalResearch Society in 1962-1964and Presidentof the Insti- tute of Mathematicsand Its Applicationsin 1970-1971.He has been awardedGold Medals fromthe Royal StatisticalSociety and the Institute ofMathematics and Its Applications,and in 1987was namedan Honorary Fellowof the Institute of Statisticians. He has receivedhonorary doctorates fromthe University of Waterloo and the OpenUniversity. The followingconversation took place duringthe ThirdValencia Inter- nationalMeeting on BayesianStatistics in Altea,Spain, in June1987.

"IF YOU'VE DONE THAT,YOU'LL KNOW country.The viewwas thatour generation might well STATISTICS" be preparedto fightfor other causes, but notfor that one. DeGroot: How didyou originally get interested in DeGroot: Was this alreadyresponding to Hitler statistics? cominginto power? Barnard: Well, I was interestedin statisticsat Barnard: Not really.There was troublebrewing school,partly from a philosophicalpoint of viewbut in Germany,it was visible,but Hitlerreally came to also froma politicalpoint of view.In 1932 I won an powerin 1933,the followingyear. However,it was exhibition,that is, a juniorscholarship, in mathemat- associatedwith that. The feelinggrew up that one icsto St. John'sCollege, Cambridge, and whilewaiting mighthave to fightagainst fascism but one wasn't to go up to Cambridgein October1933, I did a survey goingto be fightingjust forking and country.Statis- among the sixth-formersin my school, the senior ticallywhat was interestingto me was whetherthe peoplein school,to discoverwhat their political opin- viewsof people were influencedby the newspapers ions wereand howthey arrived at them. and if so, whetherthey absorbed those views directly DeGroot: You wereinterested in politicseven at fromthe politicalend of the paper or fromjust the thispoint? atmosphere.So I had a questionin the surveyas to Barnard: I was interestedin politicsat school, whattheir opinions were and whatthe opinions of the yes. I thinkit's probablypast historynow, and quite newspaperwere, and whether they first read the sports forgotten,but at thattime there was a famousreso- pages or whetherthey first read the politicalpages. lutionof the OxfordUnion whichsaid, "This house And I was thenstruck because I wantedto establish refusesto fightfor king and country."That was a whetherthe relationship was strongerif they first read greatstir at thetime. The sameresolution was carried thesports pages or weaker. I gotin touchwith Wilfred all overEngland by studentgroups and schoolboys, Stevens,who later was one ofthe coauthors of Fisher and we did it in my school. The idea was that the and Yates' Tables.He was workingwith Fisher at the 1914-1918.War had been foughtand was a bloody timeand he helpedme do thepartial correlations. slaughter,and it was done in the name of kingand DeGroot: Wherewas he and wherewere you?

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This content downloaded from 128.173.127.127 on Wed, 24 Sep 2014 22:01:56 PM All use subject to JSTOR Terms and Conditions CONVERSATION WITH GEORGE A. BARNARD 197

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Barnard: He hadjust joined Fisher, who had gone President.I rememberat that date, I said that I to UniversityCollege London fromRothamsted. By reckonedI hadjust aboutfinished. I had actuallyjust thistime, when I was analyzingthe data, I had already managedto decipherhow he'd gotthe formulae about goneto Cambridge.I had triedto findbooks in the thecomponents of x 2. At theback of the book, there's universitylibrary about statistics with no success.The this stuffabout splittingx2 into componentsand I bookby H. L. Rietzwas theonly one thatI couldfind. had seen a reasonablyneat way of doingthat. Of I used to go to UniversityCollege to see Wilfred course,I didn'tsee any moreof himafter 1933 until Stevensand thatwas howI firstmet Fisher. It must towardthe end of the war. In factI didn'tsee him have been around Christmastime, 1933. I said to then,I onlyhad correspondencewith him. Stevensthat I had triedto read up statisticsin the DeGroot: Whathappened to yoursurvey? Did you universitylibrary and couldn'tfind anything on it. succeedin analyzingit? And he said, "Oh, you'dbetter come and see the old Barnard: Yes, with a lot of help fromWilfred man."And so he tookme in to see Fisher.Fisher took Stevens.Wilfred was a verycareful fellow who, if he downoff the shelf a copyof his StatisticalMethods for tooksomething up, he did it extremelywell. He pro- Research Workersand he said, "Do you see that duced lots of pie chartsand so on to illustratethe book?"And I nodded.I was veryjunior. The curious interpretationof the data. I'm sorryto say that I thingwas, Fisher had redhair at thattime, but I don't forgetwhat the interpretationwas. recallany red hair.All I rememberwas that he was wearingboots because thatwas whereI was looking "AMERICANMATHEMATICS WAS TOTALLY all the time.[Laughs] And he said, "You'rea mathe- DIFFERENTFROM BRITISH MATHEMATICS" matician."And I said, "Well,I hope to becomeone." And he said, "Well,if you read thisbook, you'll find DeGroot: But that led you to continuein statis- thereare a lot of statementsin it that are made tics? withoutproof. You're a mathematician,you should be Barnard: Well, I sortof keptan eye on it, but I able to provethem for yourself. And if you'vedone reallywas moreinterested in philosophyand logicand that,you'll know statistics." I thinkhe wasjust about thefoundations of mathematics as an undergraduate. right. In myfirst term at CambridgeI went to Wittgenstein's DeGroot: [Laughs]Did youdo that? lecturesand theyimpressed me verymuch. In fact, Barnard: Eventually,yes. Fisher became Presi- wheneverI had an option,I alwaystook the founda- dentof the Royal StatisticalSociety in 1952 and the tionsof mathematicsor basic real variablesand such customis that the Presidentannounces four people things.There was a fairbit goingon at that time whowill serve as his Vice Presidents.Quite out of the because Max Newman,who was my tutorat Cam- blue, I heard my name announcedas beinga Vice bridge,was also tutorto Alan Turing.Turing was at

This content downloaded from 128.173.127.127 on Wed, 24 Sep 2014 22:01:56 PM All use subject to JSTOR Terms and Conditions 198 STATISTICAL SCIENCE that time in factworking on the decisionproblem, insteadof the ordinarynumber field. That sort of demonstratingthe impossibility of the solutionof the thing is totallydifferent from what Baker talked decision problem,and I was followingthat very about.So I reallyhad to learnthat sort of mathematics actively.Newman had reallyintroduced me to that fromscratch, and that took me the best part of the area,and thatwas whatI was keenon. firstyear I was there.Then in the secondyear, I did DeGroot: Were you and Turingcontemporaries go to some lecturesby AlonzoChurch, but he was a there? verydifficult person to approach.I used to go and Barnard: No, he was a yearahead ofme. knockon his doorand hearhim talking to somebody, DeGroot: How didyou revive your interest in sta- so I wouldgo away. I did this forquite a period.It tisticsthen? wasn'tuntil about halfway throughthe yearthat I Barnard: Well, I was still interested,and in my discoveredthat the person he was talkingto was last yearat CambridgeI did go to Wishart'scourse. himself. Wishartgave a coursein statisticsand I had started Turingwas thereat the same time,and we sortof goingto it,but it was so bad thatI gaveit up. [Laughs] saw each othersocially, Church, Turing and I. We He nevergot beyondmoments. I mean,he got in a werethe onlythree people workingin logic at that totalmuddle defining moments about the originand time.Though von Neumannwas slightlyinterested, momentsabout the mean.And I decidedthis was not he didn'tlecture on thataspect. He was interestedin forme, so I gave thatup. My specialsubjects in my the logicof quantum mechanics, and he was working finalyear were in factlogic and topology,and I then withGarrett Birkhoff on that.In fact,I spenta lot of wentto Princetonin 1937to carryon withlogic. timetalking to von Neumannand otherpeople, and In fact,Turing had goneto Princetonto workwith notso muchreally to Church,so I learneda lot.Now AlonzoChurch and Church'slambda calculus. In fact, comingback to statistics,Sam Wilkswas there.I met Churchpreceded Turing. I mean,the actual technical himvery early on becausehe alwaysmade a pointof proofof the impossibilitysolution was firstpublished invitingany Britisher who arrived at Princetonto his by Church,independently, and moreor less simulta- homethe very first week he arrived.I was thenreally neouslydone by Turingin termsof the theoretical supposedto be workingin logic.Wilks hadn't written computingmachine. They were there, and I wentthere his book,and he wasn'tat thattime giving a course, to workwith them. But whenI gotthere I foundthat butI wentto someseminars with him. For example,I Americanmathematics was totallydifferent from rememberHotelling coming and talkingabout multi- Britishmathematics. In Britain the mathematical variateanalysis at one of the seminars.So I was just fieldwas dominatedby G. H. Hardyand Littlewood- sortof not forgettingabout statistics,but not really numbertheory and verydeep analysis, highly special- learningany. ized work.Whereas of coursein Americait was very I went back to England in the summerof 1939 abstract,generalized, axiomatic treatments of every- expectingto come back to Princetonto finishmy thing.So I reallyhad to learnit all again. I was to Ph.D., but the war startedso I stayedthere. At the takea Ph.D. at Princetonand I alwaysremember that beginningof the war the navy obviously realized there I had to go overthe syllabusof mypreliminary exam was a shortageof mathematicians for the fleet-some- withLefschetz. I wentover the algebra,and I had to body decidedthis-and an advertisementappeared learnvast quantitiesof algebrabecause we had vir- sayingthat mathematicsgraduates were required to tuallyno abstractalgebra at Cambridge.It just wasn't serve as instructorlieutenants, the functionsof taught.And functiontheory was all done in termsof the instructorlieutenant being to teachthe midship- specialfunctions and so on,and I had to knowgeneral menbasic mathematicsand also to advisethe captain functiontheory, and Hilbertspace, and all that sort on tacticsin battle. [Laughs] Practicallythe whole of thing.It was totallynew to me. We got as faras of mycontemporaries and I showedup as applicants projectivegeometry and I said, "Wellnow, projective for this job, including,for example,Fred Hoyle. geometry,that's reallysomething that I thinkI do We were introducedfirst of all to InstructorCom- know."Because H. F. Bakerhad written a five-volume manderSomebody-or-other who asked us about our workon projectivegeometry. He was the seniorpro- mathematics-whatdid we specialize in. When I fessor,the LowndeanProfessor, at Cambridgeat the said, "Topology,"he said, "That's some kind of time.They said, "Well, what do youknow?" So I said, n-dimensionalgeometry, isn't it?" And I said, "Yes." "Well,I reckonI've coveredmore or less thefirst four And he said,"Well, if you now go and be interviewed volumesof Baker's book." They just said,"Good God, by InstructorCommander Gascoyne, he'll tell you a youdon't call thatprojective geometry." [Laughs] Of bitmore about what you are expectedto do." Instruc- course,what they meant by projectivegeometry was tor CommanderGascoyne said, "Well now,I gather abstractprojective geometry in termsof Galois fields thatyou've done somemathematics but myjob is to

This content downloaded from 128.173.127.127 on Wed, 24 Sep 2014 22:01:56 PM All use subject to JSTOR Terms and Conditions CONVERSATION WITH GEORGE A. BARNARD 199 makeit clearto youthat your prime function aboard me to staythere as chairmanof shop stewards, not as shipis to answerquestions about bets. You're in the a statistician.But a chap namedJohn R. Womersley Officers'Mess and people will ask you aboutpoker. had got the Ministryof Supplyto set up a unit for How are youat it?" So I said thatI didn'tknow that statisticalquality control, and I was recruitedto that I was verygood at it. Anyway,we all passed through in 1942.That was wherestatistics really got going for thisprocess in whichthe real function was to see how me.Incidentally, you know Fisher's correspondence is youwould get on, and wewent through color blindness goingto be published,and I discoveredjust the other testsand so on. I subsequentlymet most of the rest day that thereis a letterfrom Fisher to Shewhart, ofthe group from my year during the war, and learned dated1940, saying he's readShewhart's book and has that none of us had been appointedas instructor been veryimpressed with it. I was reflectingabout lieutenants.[Laughs] what would have happened if Fisher had gotten involved.You know,Fisher was keptout of anything to do withthe war; he was undersuspicion. "THAT WAS THE MOST FANTASTICLUCK DeGroot: Why? I HAD" Barnard: Nobody knows.My guess is that the Barnard: So I then got a job withthe Plessey Provostof University College was responsible.He was Company,which at that time was a very general a verynarrow-minded man, and Fisherhad a realrow engineeringcompany. In fact,the man that ran it said withhim. The man was a fool. I've neveractually thathe was preparedto makeanything from a hatpin checkedon exactlywhat happened.Fisher was pre- to an elephant,so longas theorder was largeenough. paredto have dealings,I think,with German geneti- It is nowa verybig organization and a majorcompet- cistsin the 1930swhen other people refused to have itorin the radarbusiness, telephone manufacturing anythingto do withthem on the groundsthat they and electronicsgenerally. But at thattime it was not wereterribly racist. I thinkthat was the sumtotal of so large,and theytook me on just as a mathematician. Fisher's sympathy,if you call that sympathy.The The head ofthe designoffice decided that they could otherthing of course was that Fisher did in fact use just a mathematicianaround the place. And that supportthe EugenicsSociety, which again, viewed in was the mostfantastic luck I had,to be appointedto propercontext, I thinkhas got nothingwhatever to a job likethat, because I couldjust wanderaround. I do withfascism either. The mainplank in theirpro- rememberthe firstthing that I was asked to do was gramwas familyallowances to middleclass peopleso to see whetherit was possible,with a givenset of gears as to balance out the birthrate drop in the middle on a millingmachine, to get the machineto cut a classesand largebirth rate in the lowerclasses. Any- metricthread although it was in factmade to non- way,Fisher was in no sense Nazi, and was in fact metricunits, to feetand inches.They said thatevery- intenselypatriotic, really ultrapatriotic in manyways. bodyhad triedto geta set ofgears that would do this But he was neverinvolved in thewar, and it occurred but theyhad neverbeen able to manageit. So I just to me to wonderwhat would have happenedhad he tookthe ratio-we know2.54 centimeters make 1 inch, been,because it mightor mightnot have been a good whichmeans that the ratio has to be 254/loo.If you thing.[Laughs] reducethat to its lowestterms, 127/50, then if you DeGroot: I rememberlearning as a graduatestu- haven'tgot the prime 127 in yourgears, you can't do dentthat in yourwork during the war you had discov- it. I also had thejob oflooking after the manufacture eredand developedsequential analysis, independently of loudspeakers,just as sortof somethingto do when of, and more-or-lesssimultaneously with, Wald's I wasn'tdoing anything else. I learnedabout acoustics developmentin the UnitedStates. Was thatdone in thatway, as wellas manufacturingtechnology and the connectionwith statistical quality control? theoryof designing magnets. Barnard: That was in thisgroup, yes. I was going DeGroot: Did you get involvedin statisticswith to say thatwe had ;Peter Armitage; thatcompany? Robin Plackett;Peter Burman;Patrick Rivett, who Barnard: No, actuallyI finishedup at thePlessey subsequentlywent into operational research and was Companybeing chairmanof theirshop stewards;I the firstprofessor of operationalresearch in the was stillinvolved in politics.By thattime, I had read UnitedKingdom; Dennis Newman,of the Newman- Shewhartand had been persuadedthat the proper Keulstest; and FrankAnscombe. They were all in this thingfor me to do in the war effortwas statistical group.Actually, Dennis Lindleyand PeterArmitage qualitycontrol. But the kindof thing they were doing had been mathematicianswho were given the option at Plessey's,and thatI was doingat Plessey'swas not oftaking an introductorycourse in statisticsby Oscar in that line. So I wantedto leave, but the Plessey Irwinor oftaking a radarcourse. They had to do one people,both the unions and themanagement, wanted or the otherand theytook Irwin'scourse. So they

This content downloaded from 128.173.127.127 on Wed, 24 Sep 2014 22:01:56 PM All use subject to JSTOR Terms and Conditions 200 STATISTICAL SCIENCE thenwere recruited to thisgroup. According to Robin designsgot developed.We werevery short of equip- Plackett,what they learned about statistics from Irwin mentand components,and theirdesigns were worked was nottoo sureeither. out in orderto see whattolerances could be allowed DeGroot: Was thisoption because of the war? on the componentsto stillretain the effectivenessof Barnard: Oh yes, it was required.It was either thefuse. And that was howthe sequentialidea arose, thator thearmy. because we were continuallyhaving to do trialson thesethings and theywouldn't work; there were too manyfailures very often. I mean the kind of thing "I HAD NEVER EVEN HEARD OF THE thatused to happenwas thaton theway to the firing NEYMAN-PEARSONLEMMA" rangethe shells were stored in theback ofa lorryand Barnard: And so they were recruitedfor that theywere liable to go off.[Laughs] That wasn'tvery group.I was put in chargeof those people, of Dennis popularwith the surrounding population. Lindley,Robin Plackett, Peter Armitage and others. I had theidea thatwe couldset up a modelin which FrankAnscombe was on hisown because he was older. we wouldhave some old-style fuses made according to But I had themand a fewother people as whatwe the patternthat we now had, and then we would called the researchgroup that studiedproblems for modifythe patternin hope of gettingit to improve. whichthere was no standardsolution. The otherpeo- The questionthen arose of how to designthat exper- ple were basicallyengaged in puttingin Shewhart iment.How manyof the old typeand how manyof charts.Actually although they are called Shewhart the newtype do you make?They all had to be made charts,at thattime one ofthe best references on that anyway,and you want to have 5% significanceof subjecthad been writtenby . It was evidenceof improvement. You hopeby your improve- calledBS600, BritishStandard 600. He had writtenit mentthat you're going to getno failure,so you have in 1935 becausehe had been interestedin industrial a table witha failuresand m - a nonfailuresfor the applicationsthrough the thirties under Gosset's influ- old type, and no failuresand n nonfailuresfor ence. So strictlyspeaking, they were putting in Pear- the new type. What you want to do is minimize son's BritishStandard charts because therewas a m + n to get 5% significance.The answeris that a difference.Shewhart used 3

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"THE REFERENCE SET SHOULD BE THE we did in sequentialtesting up to the time when REFERENCE SET OF CONSTANT Wald's informationarrived from the UnitedStates. LIKELIHOODRATIO" All ofthis stuff was classified,of course, at thattime, but we read the classifiedmaterial and Womersley DeGroot: So by the end ofthe waryou no longer said thatI shouldput on recordwhat we had done.So hadany interest in returningto Princetonto complete I did,and thereis a fairlylong letter in Naturewhich a Ph.D. in mathematics. is usuallynot listed in thebibliographies. ["Economy Barnard: No. I actuallyleft the Ministry of Supply in sampling,"Nature 156 (1945),208]. beforethe warended because the governmenthad an The otherletter was on 2 x 2 tables,["A newtest arrangementwith Imperial College in Londonthat a for2 x 2 tables,"Nature 156 (1945), 177 and 783], skeletalstaff should be leftto continuetraining people on myproposal for what was later called the CSM forradar, one ofwhom was Bill Penney,subsequently test.The thingabout 2 x 2 tableswas thatone had LordPenney, the creator of the British atomic bomb, the feelingthat one had to use muchlarger samples you mightsay. As the Los Alamosproject got going, thanreally ought to have been necessaryto establish he was requiredto go across to help with it. The significance.So I got on to the idea that the actual governmenttold the head of the departmentthat he probabilityof rejectionof the null hypothesiswhen couldnominate anybody he choseto replacePenney, truewas muchsmaller than Fisher's test would suggest and he selectedme. This was in 1944,and as faras it was,and I wroteup theproposal which I claimedto we wereconcerned the war was over.Nothing we were be morepowerful than Fisher'stest. That broughta goingto inventwas evergoing to be used in thatwar replyfrom Fisher attacking my test. In particular,he but theywere still hanging on to us, of course.So I said thatone ofthe reasons I gota lowerp-value than startedteaching at Imperialbefore the war ended, and he gavewas becauseI includedthe case whereall the stayedthere. In fact,until the war ended I was teach- animalsdied. I hadn'tsaid anythingabout animals in ing at Imperialthree days a weekand continuingto myletter, and all theanimals dying came quite out of spendtwo days a weekat the Ministryof Supply. theblue. I learnedmuch later from Harold Ruben why DeGroot: What were you teachingat Imperial this mentionof all the animalsdying arose. He told then? me that Fisher was doing experimentson animal Barnard: Elementary mathematics essentially feedingwith a chapnamed Blaxter in Scotland,trying and statistics.I was by that time startingto teach to workout the most efficient way of providing animal statistics,and I was startingto write thingsup. feedstuffsto cattleto producethe -maximum ratio of Womersleymade me publishtwo papers, two letters meat to inputof foodstuff.The regressionline has in Nature.One of themcontains an accountof what an intercepton they axis ofthe output of meat so, of

This content downloaded from 128.173.127.127 on Wed, 24 Sep 2014 22:01:56 PM All use subject to JSTOR Terms and Conditions 202 STATISTICAL SCIENCE course,theoretically the ratio of the output of meat to agreed,this is an objectivelyexisting prior distribution inputis maximumwhen none of the animalsget any and thefunction of your sampling inspection is to give food.Fisher had, in fact,cut the food down and in fact you a conditionalinference about what the distribu- all his animalsdid die. [Laughs]Apparently Blaxter, tionig and tellyou what to do withthe batches when who was the agriculturalistinvolved in this, was youget them. And that was reasonablyclearly stated veryannoyed because he knewdamn well that would in 1946 in the firstpaper of the revivedindustrial happen. applicationssection of the StatisticalSociety ["Se- DeGroot: That's a funnystory. quentialtests in industrialstatistics," J. Roy.Statist. Barnard: Anyway,I repliedto Fisher'sreply and Soc. Suppl.8 1-26]. we carriedon a friendlycorrespondence in whichhe That was one paper. Then thinkingalong from pointedout to me the exampleI've used manytimes Wald's review,I sort of workedthe ideas out more since: What happens if I plant 10 plants and I'm philosophicallyin thepaper in 1949called "Statistical interestedin theircolor, whether they are whiteor Inference"[J. Roy.Statist. Soc. Ser. B 11 115-149], purple.Then somebodytreads on one of the plants in whichI put forththe notionthat thereare two and it dies. What is the samplesize? Is it 10 or 9? aspectsof uncertainty:forward inferences and back- I actuallyhad a paper in Biometrikadiscussing that wardinferences. The forwardinferences are in terms questionand, in fact,supposing there would be prob- of probabilityand the backwardinferences are in abilityp of somebodydoing that, so thatthe sample termsof likelihood.Well, the thesis isn't all that size wouldhave a binomialdistribution from 0 to 10, clearlystated in thepaper, and I thinkI reallyought and tryingto worksomething out fromthat basis. to rewritethat paper at sometime or other. ["The meaningof a significancelevel," Biometrika 34 DeGroot: There'scertainly still a lotof discussion (1947) 179-182]Then I came to realizethat this is a aboutthat topic. load of nonsense;that's not the properthing to do. Barnard: It needsto be discussed.I sentthat work You oughtto regardthe sample size as a conditioning to Fisher.I had previouslytold him that I was inter- variable.While I was doingthat, I gotWald's book on estedin thefiducial argument but couldn't understand sequentialtesting for review,and in my reviewI it. And in one of his letters,which unfortunately I've discussedthis question that Jimmie Savage picked up. lost,I do recallhe said thathe thoughtthat the way What I said therewas thatit seemedto me thatthe to reallylook at it was in termsof pivotals. But I did referenceset was not a referenceset of fixedsample not pay too muchattention to it at the time;I was size but the referenceset shouldbe the referenceset preoccupiedwith likelihood. So I sentthe 1949paper ofconstant likelihood ratio. That was essentiallywhat to Fisher,and in thatpaper I say thatI cometo the Waldwas doing,and I couldn'tsee whythat shouldn't conclusionthat Fisher was rightabout the 2 x 2 table be appliedjust as wellto allegedlyfixed sample sizes afterall. Whichevidently pleased the old boy, because as to anythingelse. I fortunatelydid hedgeit around HaroldRuben, who was workingwith Fisher at that and exactlywhat I said thereis, I think,still correct. time,told me that he said that Barnardis the only But I gatherit was whattriggered Jimmie Savage to statisticianwho has everadmitted that he was wrong. say that he was amazed that anybodycould be so [Laughs]I had a verynice letterfrom him saying he stupidas to saythat sort of thing. had read this paper and he liked it verymuch. He DeGroot: Well,he said thatthen, but he also said said,"You seemto havedeveloped a generaltheory of thathe latercame to realizethat that was obviously likelihood,and that'sa verygood thing to do." So we thecorrect way to thinkabout it. werevery friendly from then on, until 1958. DeGroot: Whathappened then? Barnard: In 1958he published Statistical Methods "FISHER SAID THAT BARNARDIS THE ONLY and ScientificInference. In there,there is a pieceabout STATISTICIANWHO HAS EVER ADMITTED Bayes-Bayes' billiardtable-and an argumentin THAT HE WAS WRONG" whichhe saysthat the fiducial argument is essentially Barnard: I shouldtuck back a little.At theend of thesame as theargument used by Bayes in thebilliard the warthe StatisticalSociety started meeting again tablecase. As a matterof fact, there's a paperof mine and I was asked to give a paper on the workof the bearingon thisthat will be comingout in the Inter- SR17,the Ministryof Suppliesunit. I discussedwhat nationalStatistical Review in August["R. A. Fisher- we had doneabout sampling inspection. I laid it down a true Bayesian?"Internat. Statist. Rev. 55 (1987) quite clearlythere that the properway to approach 183-189]. What happenedwas that when Fisher's samplinginspection problems is to use Bayes'theorem bookwas published,Dennis Lindleyreviewed it very andto takewhat we call theprocess curve as theprior. critically[Heredity 11 (1957) 280-283].Fisher was The probabilitythat a givenbatch would have a given rightup thewall. I thinkactually what annoyed Fisher qualitywould appear in the analysis.As Fisherlater was whenhe could see that people werebright and

This content downloaded from 128.173.127.127 on Wed, 24 Sep 2014 22:01:56 PM All use subject to JSTOR Terms and Conditions CONVERSATION WITH GEORGE A. BARNARD 203 thatthey disagreed with him. That reallyshook him. It's onlythe firstobservation, being continuous, that If somebodywas just a fool,he couldbrush that off. can generatea fiducialdistribution. All thatthe other But he was veryupset by Dennis' review. Dennis went ones can produceis a likelihoodfunction. He does in on to show that if you took Fisher'sargument, the factmake that perfectlyclear, that the argumentis argumenthe was using about Bayes, then two different restrictedto thatsituation where you have one source fiducialdistributions would arise. You would get a ofa fiducialdistribution and theother one is a likeli- contradictionif you took two samples.Fisher and I hood.And Dennis' examplefails because each of his musthave talked about this, as wellas writingletters. samplescan generatea fiducialdistribution. In fact, I've lost the lettershe wroteto me up until about that'show the contradiction arises because it depends 1950,but from then on Fisherkept copies of his letters on whichone youtake first.So Dennis'example does so thosestill exist and HenryBennett's got the copies. notin factcontradict what Fisher said. So I've actuallyjust been readingthe lettershe was writingto me in 1958.And he had toldme aboutthis "THEY ALL SAID, 'IT WASN'TME; IT WAS argument.But thenwe metin Brussels;there was an GEORGE BARNARD"' ISI specialmeeting in Brusselsto celebrate,I think, thecentenary of the founding of the ISI or something DeGroot: What is your position about fiducial of that kind.At a cocktailparty there, Fisher and distributions? GeorgeBox and JoanBox and I, the fourof us, were Barnard: I tryto explainthat in theInternational havingdrinks together and thisquestion of the Bayes StatisticalReview article. Essentially what I thinkis argumentcame up again. I said, "Well that didn't that Fisher is entitledto say that a statementof seemto meto be theargument that Bayes was using." fiducialprobability is a probabilitystatement about a Whereuponhe stormedat me,"You talklike that and parameterbut, as I say in the paper,the parameter you'llruin the whole development of the subject. You does not therebybecome a randomvariable in the should keep yourselfquiet. You don't know what senseof Kolmogorov.The reasonwhy it failsto be a you'retalking about," and so on. I just stoodthere and randomvariable is thatin Kolmogorov'sdefinition a said, "Well,you know,I'm afraidI'll just have to go randomvariable is a functionon a probabilityspace, and see whatit was thatBayes said, and I'll do that fromwhich it immediatelyfollows that a functionof tomorrowmorning." I remember itwell because I went a randomvariable is again a randomvariable, and to the BibliothequeNational in Brussels.And Brus- that is not trueof fiducialdistributions. It is not in sels,Belgium, didn't begin until 1832 so theirrun of generaltrue that if you have a fiducialdistribution for theRoyal Society Proceedings starts in 1832.I had to 0 youcan derivefrom it a fiducialdistribution for any waituntil I gotback to London.Another letter in this measurablefunction of 0. Specifically,you typically correspondenceis fromme whenI gotback saying"I cannotmarginalize. If you'vegot a two-dimensional have nowreread Bayes' paperand I nowsee thatyou parameter,you can't project onto the subspace. are right." Actually,Dave Sprottand I had laid downconditions DeGroot: Fisherwas right? whichyou have to satisfyin orderthat you can operate Barnard: I thinkso. Whetherhe's rightin saying like that on a functionof a parameterthat has a "This is whatBayes meant"can't be certainbecause fiducialdistribution ["The generalizedproblem of the you can't be absolutelycertain of whatit was Bayes Nile:robust confidence sets for parametric functions," did mean. But I thinkhis interpretationis entirely Ann.Statist. 11 (1983) 104-113]. consistentwith what Bayes actuallyis on recordas Of course,the notionof randomvariable in that sayingin hiswriting. That's the argument of the paper Kolmogorovsense didn'texist in the 18th century, inthe International Statistical Review. But in anycase, and I thinkit is perfectlypossible to interpretBayes he had made that clear,and made it moreclear in as followingon Fisher'sline of argument.And it is a subsequenteditions, and he had reallyalready made plausibleinterpretation in the sense that thereis a it clearto me in thiscorrespondence. That's whyhe sectionin Bayes' paper wherehe seems to take an lost his temper,because he had actuallytold me. I awfullot of troubleto do somethingwhen he could nowsee thatreading through the correspondence. He have done it veryquickly. And he wasn'tthat bad a had said that and I just hadn't listenedor read it mathematician;in fact,he was a good one, contrary carefully.He was entitledto be annoyed.One of the to what Steve Stiglerargues [Stephen M. Stigler points,you see, withDennis' example,was thatit's a (1986). The Historyof Statistics, Harvard University case of two continuousvariates, two continuousdis- Press,Cambridge, Massachusetts]. You know,Steve tributions,and the sectionin Fisher'sbook is headed says Bayes was just a minorfigure and it was really "Observationsof two distinct kinds." It's a case where Laplace who did it all. In fact,I thinkBayes had a the initialthrow of the ball has a continuousdistri- subtlesense of logic. But thatwas myrow with Fisher butionand the subsequentobservations are discrete. in Brussels.The reason I put this thinginto the

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StephenStigler and GeorgeBarnard, 1979.

InternationalStatistical Review was so that Henry City,is his name still remembered?We set up a Bennettcould referto it whenhe publishesFisher's Liberal Club amongstthe undergraduates-"liberal" correspondence.As it is, there'sa gap in thesequence in the Americansense of theterm-and decidedthat of letterswhich doesn't make sense unlessyou know this chap Hague was not the sort of characterwho whatwas happening. shouldbe doingwhat he was doing. DeGroot: Let's talk a littleabout yourpolitical DeGroot: He was sortof a prototypeof the big city activitiesand politicalinterests. You have mentioned boss. thateven in yourschool days you wereinterested in Barnard: Oh yes,he reallyran the city. It was his politicalissues. habitthat anybody who objected to whathe was doing Barnard: Actually,my main interest above every- gotran out of Jersey City. And then he was facedwith thingwas politicsfrom about 1933 until1956. Well, a bunchof Princetonundergraduates whose fathers that'snot true-until the end ofthe war,it wouldbe werequite prominent. I recallWendell Willkie's son fairto say. At the end of the war,when Hitler was was one of them and the son of the presidentof defeated,I had the feelingthat therewas no longer StandardOil. Hague didn't knowquite what to do anyneed to go in forpolitics. I had been veryactive, withthem because they wouldn't have acceptedbeing and I discontinued.In fact,when I was recruitedto run out of town.He was in factfinished. That trip theMinistry of Supply it was verystrange because the fromPrinceton was the beginningof the end for Ministryhad beengiven a reportby MI5, themilitary Hague. intelligence,that I was labeleda subversivecharacter DeGroot: You joined the CommunistParty in and shouldnot be employedby them. England? DeGroot: Whydid theyfeel that way about you? Barnard: Yes, I was a memberof the Communist Barnard: Oh, because I'd been activeas a com- Partyall thattime and was activein it,and madeno munistsince 1933. I was activeat CambridgeUniver- secretof the fact.But thenI thinkwhat happened in sity and also in the United States. You wouldn't the States was that quite a numberof people that I rememberJoe Lash, Joseph P. Lash? I was in contact had knownin Americawere put on the stand by withhim and, in fact,used to go aroundmaking lots McCarthyand they,I thinkperfectly rightly, said it ofspeeches at thattime. wasn'tthem, it was me. You knowthe various things, DeGroot: Whileyou were at Princeton? who did this and who did that;and theyall said, "It Barnard: Yes. We organizedthe firstpiece of wasn'tme, it was GeorgeBarnard." [Laughs] I have politicalactivity on the partof the Princetonunder- beentold, I've neverchecked on it,that there are five graduateswhen I was there.Mayor Hague of Jersey volumesof subversiveactivity which are on recordin

This content downloaded from 128.173.127.127 on Wed, 24 Sep 2014 22:01:56 PM All use subject to JSTOR Terms and Conditions CONVERSATION WITH GEORGE A. BARNARD 205 he coulddo was to giveus a certificatesaying, "These peoplehave already been fined $10. If anyother judge has to, willyou bear thatin mind."By thattime, we werenearer to Washingtonthan we were to Princeton, so we decidedthat the bestthing to do was to go on -h ...... l[.h~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.....::Of! . to Washington.I always remember that. We askedthe congressmanwhat he thoughtabout the Spanish War, and he said, "Well that was over a long time ago, wasn'tit?" We made it clear thatwe didn'tapprove ofthe government's policy of not allowing the Spanish governmentto havearms. - . -~~~~~i, ~~~. .4

. -.N B "THEY ALWAYS HAVE TO GO BACK AND LOOK UP MY FILE" DeGroot: Whydo you say that you thinkit was - Xl XsS,: -z perfectlyproper for these otherpeople to mention yourname in congressionalhearings as havingbeen theone whodid all thesethings? Barnard: Well,I was in England.There was noth- ingthey could do to me. Except,of course,the result F >1w%t(4 K was thatwhen I was invitedto go to the Statesand I had to havea visa,the answer was no. DeGroot: When was that? What year was your firsttry? Barnard: I thinkmy first refusal would have been

*' -,- in the mid50s. McCarthywas stillalive and had not It been totallygotten rid of, though he wasn'tdoing at GeorgeBarnard with his eleventh grandchild, Clare, all wellat thetime. I had an invitationto visitsome- December1987. whereand I appliedfor a visa,and was askedto state mypast political associations. I had beenadvised that the McCarthyfiles which all belongto me. In fact,I the thingto do is to say nothingat all, because if I thinkthe extentof the subversiveactivity that I had said ainythingI would then have been put on the actuallyengaged in was this kind of thingagainst standunder oath and I mighthave been requiredto Major Hague. And a trip-I alwaysremember going recallother people I knewwho wereat risk.I mean, downto Washingtonto lobbythe local congressman the worstthey could do to me was to send me back on the subjectof arms forSpain. The Spanish War home.So I was advisedthe thingto do was to say was stillcontinuing, and a bunchof us gotin a car to nothingat all. So myvisa applicationsaid thatI did drivedown there. We werestopped just afterwe got notbelieve in theviolent overthrow of the government intoMaryland by a policemanwho wanted to tell us of the United States. In fact,my generalviews on thatthe speed limit in Marylandwas 50 milesan hour. politicalmatters at thattime were that principles of He just wantedto tell us so we wouldn'tgo overit, operationalresearch could be appliedwith value to becausewe hadbeen. But he wantedto see ourlicense. problemsof government.General liberal principles, Therewere five of us in thecar and the nearestthing but so far as my past politicalactivities were con- to a licensethat anybodypossessed was a licenseto cerned,I did notconsider that they were any concern drivein thecity of Chattanooga, Tennessee, for 1932. ofthe UnitedStates or any othergovernment. I was We weretherefore in a difficulty,and so was the cop preparedto giveany assurance they wanted as to what because he couldn'treasonably allow us to continue I shoulddo in the UnitedStates, but notprepared to to driveanywhere. So he got in the car. There were tell them my past history.And so theyturned me twoof them, they were a motorcyclecombination, and down.I had severalinterviews with a counselin which the otherchap drovehis motorcycleto the nearest we discussedthe pros and cons of variousways of judge.The judge asked us how muchmoney we had, handlingthe situation.The communistswere getting andbetween us we had somethinglike $15. So he fined in and outof the United States as easyas anythingat us $10. Therewe wereabout half way between Prince- the time,no problem.But theyturned me down.It tonand Washingtonwith no wayof driving. The best wasn'tuntil 1961 whenJerry Cornfield organized for

This content downloaded from 128.173.127.127 on Wed, 24 Sep 2014 22:01:56 PM All use subject to JSTOR Terms and Conditions 206 STATISTICAL SCIENCE me to go to the NationalInstitutes of Health that I Barnard: Oh, Fisher of course primarily.But was admitted. actually,again talkingabout politics and goingback Theydecided in effectto modifythe procedures in biographically,I first met Neyman in 1948in a taxi. sucha waythat I was givena specialwaiver. Actually DeGroot: Not by accident? eversince then I've alwayshad trouble.They always Barnard: No, I was withsomebody who was with haveto go and lookup myfile, and thenthey see this Neyman,and we all jointlytook the taxi. There was a longfile with yeses and noes and maybes.[Laughs] I congresson the historyand philosophyof scienceat was visitingWaterloo at one timeand MarvinZelen, whichhe and I and de Finettiwere all speaking.I who was thenat Buffalo,said "Whydon't you come recallthat I gottalking to Neymanabout likelihood to Buffalo?"I said, "Fine, I'd be glad to come to in thetaxi. And he broughtup whatwas in effectthe Buffalo,but I alwayshave thisdamn nuisance." And Neyman-Scottproblem of inconsistency of maximum he said,"Oh, I'll fixit." I said thatI was at Waterloo likelihoodfor n samples each of size two. I then fromSeptember until December and it wouldbe con- decidedI couldtalk to Neymanabout politics but not venientif I couldget, say, six entriesin thatperiod. about statistics.Just as I couldtalk to Fisherabout Andsure enough they gave me an entryin Octoberto statisticsbut not aboutpolitics. I followedthat rule leave in December,but onlyone entry.So I had one fairlyfirmly for the rest of the time I knewthem. I've visitto Buffaloand that was it. And everytime it's alwayshad the absolutely highest regard for Neyman's likethat. It's nothingserious, nothing other than sheer principlesas a liberalacademic. He was reallythe tops bureaucraticmuddle. One time SeymourGeisser and a verycourageous man. Do youknow the incident arrangedfor me to go to Minneapolis.By thattime I that David Kendall put into Neyman'sobituary for had a specialthing stamped in mypassport indicating theRoyal Society? Just after the war the Greekelec- thatI couldgo thereanytime. Well, anticipating trou- tions wereheld and the countryactually wanted to ble,I startedthe process nearly a yearahead oftime. getrid of the monarchy. But theAmerican and British I thought,"Look, I'll getthis fixed. Just so everything governmentswanted to restorethe monarchy.They goessmoothly, I'll applyfor the visa." Theylooked at set up an electionsystem which was supposedto be mypassport and said, "You don'tneed a visa,you've freeand liberal,and Neymanwas one of the people got one." I thought,"That's fine,that's remarkable." whowas appointedto go as a commissionof statisti- My wife,Mary, was coming,and she wouldneed a cians to see to it thatthe electionwas fair.He went visa. So she appliedabout three weeks before we were to Greece,and do youknow what he did?He resigned going.For herto geta visa she wouldhave to explain fromthat commission. Went back to Paris and gave howshe would not become a chargeon thepublic, and an interviewto theFrench communist paper Human- thatI was goingto be paid forlecturing and so on. So itein whichhe said thatthe electionwas a complete theyhad to see myvisa. By thattime the policy had fraud.I mean,his citizenship could have been revoked, changed.They cancelled my visa, and didn't give Mary and it was a verycourageous thing to do. At thattime hers. So I said, "'Allright, then I'm not givingthe thingswere very tense. When David Kendall asked lectures,and I'll let SeymourGeisser know. I'm fed me whatI thoughtabout Neyman, I said thatI had a up withthis." And theysaid, "Oh, no don'tdo that. veryhigh opinion of him, particularly for what he did Don't do that."It was literallythe Fridaybefore the at thattime. I thoughthe was a verygreat man indeed Mondaywe flewthat I gota visa. and deservedthe highestcredit. Though, of course, DeGroot: Whatyear was this? what he did to statisticsis anotherquestion. In a Barnard: That would have been about 1968. I certainsense Neyman made mathematicians take sta- subsequentlyhad severalother visits to theStates. In tisticsseriously. That was a verybig service,but in anycase, whatwith my legs giving out, I'm nottrav- doingthat I fearhe did a lot ofdamage as well. elingfar anyway. I've sortof taken the viewthat it's DeGroot: Were there other major influences reallytoo much.It's veryannoying to neverquite besidesFisher? knowand alwayshave the feeling that you might even Barnard: Egon Pearson, of course. We worked getthere and thenthey'd turn you back. I reallywould veryclosely together and got on extremelywell, but be fedup at that.It's theimmigration service and the we neveractually wrote any joint papers.He helped bureaucratsthere. But theyhave their jobs to do,and me a greatdeal withthat first paper on 2 X 2 tables thelaws on thatsubject are totallycrazy. in whichI put forwardthe CSM test.He publishedin parallelwith it anotherpaper from himself saying that he had similarideas, which was true.We wentaround "HE WAS SOMEBODY WHO REALLY WANTED togetherconsulting with the BritishStandards Insti- TO BE CLOSE FRIENDS WITH PEOPLE" tutionon qualitycontrol. British Standards had a DeGroot: Who do you feel have been the major qualitycontrol scheme called the Kite Mark scheme. influenceson yourcareer in statistics? Egonand I usedto go aroundthe factories supervising

This content downloaded from 128.173.127.127 on Wed, 24 Sep 2014 22:01:56 PM All use subject to JSTOR Terms and Conditions CONVERSATION WITH GEORGE A. BARNARD 207 the workingsof that. We workedon committees makeit clear what I was gettingat. I put too much together,and because he was at UniversityCollege intoit; it's too longa paper. Londonand I was at ImperialCollege London, I was DeGroot: Your name has alwaysbeen associated alwayson his examiningboard. He couldnever be on withbeing a leading"likelihoodist," basing inference ours because the laws of our college didn'tpermit on the likelihoodfunction. Is thatstill your view? outsidepeople to be on ours.But he couldhave people Barnard: Well, to some extent. Though more fromoutside on his boardand he wouldalways have recently,as you know,I've comeback to the idea of me. I verymuch liked Egon. Of the threecharacters, pivotalsand havebeen playing with that. I realizeyet I admiredNeyman, as I said; I admiredFisher for his againthat it's a pityI didn'tread carefully what Fisher statistics;but as faras the personwas concerned,I wroteto me back in the late '40s becauseI thinkthe mostliked Egon. He was a shy and quiet man,but pivotalidea in a senseallows you to be a Bayesianin veryinsightful. You know,he neverreally wanted to so faras you need to be. My opinionnow is thatthe be a statistician;he was morekeen on painting.His properprocess of statisticalinference is conditioning fathersort of decided he shouldbe a statistician.That on knownvalues of variableswhose distributionis was theamazing thing, that he had thissense of filial known.And thenthe questionis, of whichvariables dutywhich led himto acceptthings which certainly do youknow the distributions? In effectthe Bayesian nowadayschildren wouldn't accept. Egon got on view is that you can assume all of yourunknown extremelywell with Gosset. I neverknew Gosset, but quantitieshave knowndistributions. I don't think he musthave been a veryattractive character. that'sactually true. In anycase, againcoming back, I DeGroot: He seemsto have gottenon withevery- acceptde Finetti'sargument about personal probabil- body. ity.That's a valid argument.In fact,I'm sayingthat Barnard: He got along witheverybody, yes. He in the paper at this conference.I thinkit shouldbe fellout with Fisher at theend, and I thinkhis opinion taughtto undergraduates.But in the sense ofproba- of Fisher'stemper was quite stronglydisapproving. bilityas usedin science,what I liketo call experimen- But so was Fisher's own opinionof his temper.I tal probability,I do not thinkthat an experimental alwaysremember walking with him from a Statistical quantitylike the velocity of lightcan be said to have Societycouncil meeting when he was President.I used a knownprobability distribution. In any case, for to walkwith him to theLiverpool Street Station where reasonableagreement among scientistsyou would he'd catchthe trainback to Cambridge.I forgethow have to have reasonableagreement about any prior it came up but he said that he wishedhe hadn'tthe distributionswhich you would use, and in the way labiletemper that he actuallyhad, and thatit could statisticsis used in science,it will not in generalbe costone a lot.He was somebodywho really wanted to possible to assign agreed distributionsto all the be close friendswith people, but he had thistemper unknownparameters. If you could, I'm perfectlyhappy and everynow and thenhe wouldfly off. And it was to use them.But I thinkyou would not always be able a matterof luckwhether people could take it or not. to do that,so youwould either have to say thatsome He certainlypaid forit-he was a poor lonelyold problemsare not solvable or adopt some other method. man.Although he did quitewell in Australia;he got Andsometimes you can; I thinkyou can getaway with on withthem. There was nobodythere he wouldupset. usinga pivotalargument without using assumptions By thetime he leftEngland he had sortof upset most ofprior distributions. That's a longstory actually. ofthe people he wantedto be friendswith. But I think I've beendoing a lot ofwork on theBehrens-Fisher thatthe correspondence that will be comingout gives problem,the two-sampleproblem, just lately.In the a differentpicture of Fisher'spersonality from the t problem,the single-sample location-parameter prob- one that is broadlycurrent. He was willingto be lem,you can removethe nuisance parameter by simple Verypatient and write helpfulletters to people. marginalizationof the pivotal involvingthe scale He certainlydid that with me. He was the biggest parameter,leaving you witha pivotalinvolving the influence. locationparameter. And that's all you need because that essentiallycontains the answer.The Behrens- Fisherproblem has gotthis other parameter and it is "ONE SHOULDN'T PUT IN AN ASSUMPTION typicallydone in terms of two independentscale THAT ONE DOESN'T NEED TO PUT IN" parameters,which I think is wrongbecause you DeGroot: Do youhave particular favorites among wouldnot be comparingtwo samplesin relationto yourown publications,or ones that you thinkwere theirlocation unless you had some idea that their the mostinfluential? scale parameterswere at least of the same orderof Barnard: Well, not the mostinfluential, but the magnitude,that they were reasonablycomparable. onethat contained the best theory was theone of1949 And so what you shoulddo thereis to introducea about likelihood.But the troublewas that I didn't singlescale parameterapplying to bothsamples, and

This content downloaded from 128.173.127.127 on Wed, 24 Sep 2014 22:01:56 PM All use subject to JSTOR Terms and Conditions 208 STATISTICAL SCIENCE thena secondparameter which expresses how much theyshould worry, as to whetherit's goingto cause ofthe total variance arises from one sample,how it is trouble.But the thingI like aboutthe pivotalidea is sharedbetween the two.It's that sharingparameter thatyou don'treally have to say in advancewhether thatcauses the problems;you getrid of all the other you'rea Bayesianor not.Because you can put in your parameters.That one has theproperty that the usual assumptionsstep by step and say,"If you makethat ignoranceprior daldU2/(ol U2)corresponds to a singu- assumptionthen this follows. If you additionally make lar priorfor this sharingparameter with the prior thisassumption then this follows. If you additionally elementd/l[/(1 - #)]with a singularityat bothends. make *--" Just like that, go on as long as you want If youmake it go between0 and 1, thenthat in effect to, in orderto get the kindof answerthat you find is sayingthat as soon as youget a finitevalue for the useful.For example,with a t,Student's answer to the observedvariance ratio, your data are contradicting confidencedistribution for iu is a perfectlysatisfactory yourprior. So I thinkthat there, to solvethe problem, answer.You can say it's a posteriordistribution with youdo in facthave to assumea prior.You haveto say a uniformprior, but so what?That's whatit is and that we are comparingthese two samples,we are that'swhat you believe rationally, whether it's a ran- thereforeimplying that we do believe them com- domvariable or nota randomvariable in thetechnical parable,we thereforebelieve that this P does nottake Kolmogorovsense. thevalue 0 or 1 withvirtually infinite probability and DeGroot: But you do thinkthat the important thatit is boundedbetween 0 and 1. One priorwould thingis to getan answerthat you believe in as repre- be a uniformprior or somekind of proper beta prior. sentingyour uncertainty about the quantityin ques- The way it shouldbe lookedon and in factis quite tion. easy to do, is to have a programwhich will generate Barnard: Yes. I mean,it's clear that it will not yourp-value, your posterior probability for the differ- reallyrepresent your uncertainty about ,u in the rig- enceif that's what you're interested in, as a functionof orous sense of Kolmogorov,which theoreticallyit theinput beta prior. You can varythat as youwish and shouldif you reallyare a strongBayesian. Because see whatdifference it makes.And that's the way to do that would mean that if you had 100 such ,u's you it. But the singularityat bothends is somethingthat would have a 100-dimensionalt distribution,which is not tolerable.I've been writingpapers recently- has all those Stein problemsattached to it, and you theyare mostly not out yet-in whichI spellignorance obviouslydon't believethat. But it doesn'tmatter, witha double g, "iggnorance."The Behrens-Fisher and that'sthe importantthing. I thinkone shouldn't solution and Jeffreys'solution to the Behrens- put in an assumptionthat one doesn'tneed to put in. Fisher problemreally assumed "iggnorance"which But I am preparedto acceptthat assumption, unlike does notin fact-represent your true state of mind. Fisher.Actually this correspondence will showthat's DeGroot: Whatdo youmean by "iggnorance"? not altogethertrue with Fisher. I thinkFisher went Barnard: Justbloody ignorant; you know,total ratheroverboard against Bayes in thedesign of exper- ignorance.You're saying that you don't know the scale imentsbecause he was attackinga viewthat had been parameterof this distribution,you don't know the held.I thinkif he had nothad thatview to attackhe scale parameterof that one, and furthermoreif you wouldhave been less extreme.What I am sureof is knewthe scale parameterof this one, you stillwould thathe and Jeffreyswere far closer to each otherthan knowabsolutely nothing about the scale parameterof commonlyis thought.Jeffreys, in that videotapehe thatone. Andthat's not sensible. The furtherpoint is made with Dennis Lindley,said that when he and thatthe t testis robustto departuresfrom ignorance, Fisheragreed, they both knewthat theywere right. in the sense thatif you nowsay, "Well, let's suppose Andwhen they disagreed, they knew they didn't really that we knew a littlebit about a, what difference know,as it were.There's no questionabout it: in their is thatgoing to make?"It's a mathematicalproperty general approach,Jeffreys and Fisher were much ofthe way the thing comes in thatputting in a proper closer to each other than to Neyman.They both prior,so longas it doesn'tconcentrate unduly, is not appliedit in theirrespective scientific fields, and they goingto makemuch difference to yourt answer.But bothapplied it in essentiallythe same way.The cor- puttingin a properprior to this/ variabledoes make respondenceshows that they were good friends, there's a considerabledifference in some cases. With large no questionabout that. I thinkFisher attacks Jeffreys samplesit doesn'tmake muchdifference, but with sortof by wayof a joke. Fisherused to writereviews smallsamples it can makea .verybig difference.And of Jeffreys'books in whichhe alwayshad a dig at one shouldbe aware of that.What worriesme with Jeffreysand theprior distributions, but I thinkit was anygeneral Bayesian approach is thatpeople can get a sortof joking dig. I don'tthink he reallymeant it as intoa frameof mindwhereby they happily go ahead veryserious. I'm not sayinghe agreedwith Jeffreys; and put in a noninformativeprior and not worry,as but you could read the thingas meaningthat he

This content downloaded from 128.173.127.127 on Wed, 24 Sep 2014 22:01:56 PM All use subject to JSTOR Terms and Conditions CONVERSATION WITH GEORGE A. BARNARD 209 regardsJeffreys' views as perniciousnonsense, and thepeople involved in it was a likelihoodman, and he that'snot actually what's meant. saidthat he wanted to use thelikelihood. Cedric Smith and I werethere and we agreedthat it's not strictly likelihoodhe's using,he's reallyusing the posterior LIKELIHOODS "TO MOVE THEM TOWARD probability.But you don't see Bayesian arguments THING" WOULD BE A GOOD used veryoften in naturalscience and that'sa situa- DeGroot: You've seen the field of statistics tionwhich I thinkis nottoo happy. undergoa lot ofdevelopment and changeduring your DeGroot: Therewas verylittle use of statisticsat career.Are you optimisticabout the futureof statis- all in physicsand chemistryfor so long.Now they're tics? just beginning. Barnard: I worrya bit. As faras broadapplica- Barnard: They startedusing statisticsseriously tionsin economicsand suchfields are concernedthere in,for example, high-energy physics at least 25 years is clearlya verybig future.I worrya littleabout the ago because I went to CERN about then at their positionin naturalscience. And although statistics in invitationto tell themwhat to do. Theywere taking medicineis verypopular currently, I'm notaltogether statisticsquite seriously then. Basically, and I thinkI happyabout the way things are therebecause I don't said this in myPresident's Address to the RSS, the thinkthe foundations are altogether firm. The medical physicistsused to say whatBlackett said to me: "If I peoplecontinue to use p-valuesand so on. They use needstatistics to analyzemy data, it meansI haven't them with some commonsense, which of course got enoughdata." And that used to be true.But of enables themto avoid seriousblunders. But really coursehigh-energy physics is so damnedexpensive veryoften what they are doingshould not be looked that you can't affordto get enoughdata and you've at in that way at all. Don Berryhas writtenabout bloodywell got to use statistics.[Laughs] But they someof this. also recognize,I think, that it's not the usual statistics DeGroot: Theyshouldn't be testinghypotheses. thatthey have seen. They do tendto use thingslike Barnard: They shouldn'tbe testinghypotheses, likelihoodarguments, that could be easilytranslated no; but that'swhat they think they are doing.And it into posteriorprobability. What's the difference worriesme that thereis a discrepancybetween the betweena likelihoodand a posteriorrelative to the model of what it is they'redoing and what they uniformprior? But those thingsdon't square as it actuallyare doing. werewith what they've learned about statistics from DeGroot: Whyare youworried about applications the statisticians,and that's an unsatisfactorysitua- in thenatural sciences? tion. Barnard: On the same grounds.Their view of Even nowthe bulkof elementary statistics courses statisticsis stillbeing presented largely as a matterof startoff with the traditional p-values and so on. They p-valuesand so on. The proposalI was suggestingto mighthave a Bayesianchapter somewhere about three movethem off that toward likelihoods would be a good quartersof the waythrough the book,but theystart thing.Indeed, people like the high-energyphysicists offin that way and I don'tthink that is the wayto alreadydo that.They do use likelihood,and geneticists start.Bayesian theory, things like de Finetti'sargu- do too. ments,should be put rightat thebeginning. There is DeGroot: Theyreport likelihood functions? no earthlyreason why they shouldn't be. Barnard: Yes, they reportlikelihood functions. DeGroot: In introductorycourses? Actually,some geneticists I knoware fullyBayesian. Barnard: Quite. I did it with psychologistsat Incidentally,you knowthat they'verecently located Waterloo. Mind you, it shook them somewhat. whichchromosome the cystic fibrosis gene is on. They Actuallyit was sortof a secondintroductory course. didthat last year. I was at a meetingof geneticists the Theyhad alreadyhad somestatistics, but in principle yearbefore last in whichthey had narrowedit down this was the firstcourse they were getting. So they to threechromosomes and therewas the questionof thoughtthey knew about statistics, but thiswas very whichof these threeto concentrateon to tryand differentfrom what they had heard.So I thinkthere's locateit further.And the decisionas to howthat was a bigroom for improvement. The otherthing that has donedid involvea Bayesiananalysis of the data that shakenme is the lengthof timeit took to establish was currentlyavailable. The Bayesianargument was relationshipswith computing. I knewabout Turing's that you assume that the numberof genes on the workon the computer,having known Turing and chromosomeis roughlyproportional to thesize ofthe knownwhat he was doing.I remembersaying, when chromosome.You had to makesome such assumption theyproduced the firstcomputer, "That means we to findthe probability of the genebeing on one chro- can now actuallyplot likelihoodfunctions." And I mosomeor another.It was interestingbecause one of rememberthat you werethe firstperson actually to

This content downloaded from 128.173.127.127 on Wed, 24 Sep 2014 22:01:56 PM All use subject to JSTOR Terms and Conditions 210 STATISTICAL SCIENCE have a likelihoodfunction printed in the Annals, or less knownthat the thingmust either lie on one weren'tyou? axis or the other.The maximumlikelihood estimate DeGroot: Was I?,That's a surpriseto me. was verynear one of the axes and the ordinarycal- Barnard: Yes, youwere. At least as faras I know culationwould suggest that it was almostcertainly youwere because I watchedfor it. You had a paperin withinthat neighborhood and nowherenear the other whichyou actually had diagrams. one. The factwas thatthe banana wentright across DeGroot: That's right.But I didn'tknow that I to theother one, and theother one was theright one. heldthe record. [Laughs] Barnard: That was some years ago, but not all "THERE WAS A REPORT thatlong ago and longafter it shouldhave happened. KNOWNAS THE BARNARD The firstlikelihood functions that I actuallypublicly REPORT" producedas graphswere on nylonstockings. There's DeGroot: Tell me whatyou like to do whenyou're a journalcalled Whichpublished by The Consumer notdoing statistics. Associationin theU. K. in whichthey test things on Barnard: I used to play the viola. I also used to themarket and giveyou information about what's the play second violin-the secondis important-butI bestbuy and so on. Thereis a similarmagazine called gaveup playingthe violin. ConsumerReports, I think,in the UnitedStates. DeGroot: You playedin a quartet? DeGroot: Published by ConsumerUnion. Yes, Barnard: Yes, we had a fairlyregular quartet at theydo thesame thing. Imperialwhen I was there.We used to play concerts Barnard: Well,they did a studyon nylonstock- at the college.But thenI managedto geta viola and ings,about how they wore. Their failure time is very learnedto play it, and movedover there because it's muchan exponentialfailure time. It dependson how easierto get into a quartet.There are not as many quicklyyou catchyour stocking on somethingand it violistsas there are violinists.You known,Henry startsa ladder.So the data werehighly nonnormal, Danielsplays the piano verywell, but his real instru- veryskew, and the best way of conveyingthe infor- mentis a concertina.The registerof a concertinais mation about the relativemerits of the different thesame as theregister of a clarinet,so he can playa brandsof stocking was to givethe likelihood functions clarinetpart or a violinor violapart with his concer- that theywould last fora givenlength of time.We tina.The lasttime we played actually was withBertha drewpictures which had a maximumat themaximum Jeffreys[' wife]. We playedthe Mozart likelihoodestimate of the life,and thenthey tapered triofor clarinet, viola and piano. Henryplayed the off,down to 0 hereand offto infinitythat way. We clarinetpart with his concertina,I playedviola, and showedthem alongside each other,and youcould see Berthaplayed the piano. That's whatI likedoing the thatthe mean lifeof some stockingswas longerbut best.I also haveto go and lookafter the garden; we've thechance of failure at an earlystage was higher.This gota sizeablegarden where we live. was all conveyedin thepicture. DeGroot: You retiredin 1981. Did that change DeGroot: Whenwas that? yourlifestyle very much? Barnard: That musthave been in 1963. Barnard: Yes, in the sense that we had got this DeGroot: Were you a consultantto that organi- placeat Brightlingsea-MillHouse-in 1966when we zation? decidedthat it was a verynice place to live.But until Barnard: Well, actually my colleague Chris thatpoint, I had neverlived there. [Laughs] But since Winstenis theirofficial consultant. He gotme intoit I've retired,that is wherewe have lived and that's and I suggestedthey should do that. But the first wherewe like living.It's overlookingthe sea and it's ones that wereactually used, as faras I know,in a quiet. I'm afraidI'm ratherglad to be out of the scientificissue were done some years before that by a universitiesin theUnited Kingdom at thistime. Well, chapwho was workingfor the atomic energy authority actuallyI don't know whetherI should say that at the time-a chap namedMercer who is now Pro- becausewhen I gave up partypolitics I got involved fessorof OperationalResearch at Lancaster.They in a lot of governmentadministration. I was on werelooking at assaysof blood constituents and there money-allocatingbodies like the Social Science was a theoryabout the way a chemicalreaction went. ResearchCouncil and theUniversity Grants Commit- Theyhad donesome experiments collecting data and tee and the ComputerBoard. theyhad a two-parameterlikelihood surface to plot. DeGroot: Arethese countrywide bodies? What do It was one of these cases wherethe actual contours theydo? were banana shape. That meantthat if you did a Barnard: Yes, these are national institutions. straightforwardmaximum likelihood calculation you How muchmoney each universitygets is decidedby gotthe wrong answer completely, because it was more the UniversityGrants Committee. How muchmoney

This content downloaded from 128.173.127.127 on Wed, 24 Sep 2014 22:01:56 PM All use subject to JSTOR Terms and Conditions CONVERSATION WITH GEORGE A. BARNARD 211 theuniversities can spendon computersis decidedby produceat all. It wouldhave been farbetter if people the ComputerBoard. Actuallythere was a report had listenedto him.He was at least 15 yearsahead of knownas the BarnardReport. It's not muchreferred histime. He publishedit as a paperin the RSS journal. to nowadaysbut it was the reportwhich said that I always thinkof that as a warningabout simply universitiesshould be providedwith moneyto buy adoptingthe currentfashion. Everybody, including computersfor uses otherthan scientificcomputing; me, thoughtit mustbe wrong.So his paper wasn't thatthere should be fundsfor using computers in all actedon, but it shouldhave been. fieldsof study,including the humanitiesand so on. This was one of the fewreports that was everacted "I WOULD MOST LIKE TO GET CLEAR ON THE uponby the government. FOUNDATIONS" DeGroot: So you have to be carefulwhat you say aboutthe government now. When was that,George? DeGroot: Whatdoes thefuture hold for you? Barnard: That wouldhave been in about1970. Up Barnard: Well, I wouldmost like to getclear on to thatpoint, physicists had been able to get money the foundations.I believe in Jack Good's Bayes- to buycomputers as partof their experimental equip- nonBayescompromise. He now calls it the Bayes- ment,strictly for use on theirexperiments. People Fishercompromise, doesn't he? And I thinkthat's likestatisticians or anybodyelse couldn'ttypically get rightbecause Fisher believed in conditioning.The key access.That was aboutthe time of transition from the thingis, do youbelieve in conditioning.That's thekey major valve machinesto the solid state machines. as the inferentialprocedure. Just exactly what you Soon afterthat it became veryobvious that people meanby probability and howyou interpret the mean- should use these machinesall over the place, and ing of thatword is relativelyminor. I thinkthat it's essentiallywe just said so. And as I say, what was importantto get clear on the foundationspartly to unusualabout it was thatthey actually did it; they did teach people,to teach students,and partlyto lay a providethat money.I was on the grantscommittee proper foundationfor the use of statistics in forfive years. In the U. K. there'sa Social Science scienceand, for that matter, ultimately in socialdeci- ResearchCouncil, and a Science ResearchCouncil sion making. whichis naturalscience. I was on the mathematics DeGroot: How come we've neverseen a book by subcommitteeof the Science ResearchCouncil, and youexpressing your view of statistics? thingslike that. There was an inquiryinto the supply Barnard: Laziness.I couldalways find it nicerto of studentsin scienceand I was a memberof that talk thanto write.But maybeyou will.I've had this committee.I've beendoing that more or less sincethe embarrassment,you know.I inheritedmore or less late fifties. fromEgon Pearsona largemanuscript which he had I was on a committeecalled the Building Operations writtenabout Gosset, and the correspondence between and EconomicsCommittee of the BuildingResearch Gossetand Egon. I've been tryingto arrangeto have Stationnot longafter the war,at the timewhen all thispublished, and mostpublishers think they don't the postwarplanning was the rage. Everybodywas reallywant what it was thatEgon wroteabout. And I sayingthat we've got to buildhighrise blocks of flats can understandit. Gosset was responsiblefor Egon to preservethe green countryside; otherwise the place goingto Winchesteras a school,and Egon did very willbe coveredwith little houses and nobodywill be well at Winchester.It's a remarkableschool. Gosset able to moveanywhere. It was the architecturalfash- was the manwho said thatKarl shouldsend Egon to ion to buildhigh. There was a chap namedStone in Winchester.So there'sa lot about Gossetas a man theBuilding Research Station who seemed a dullsort and aboutWinchester as a schoolwhich is notstrictly of statisticianthat nobodypaid muchattention to, statisticalat all. So it mustbe edited.And then there's and he wrotea paper pointingout that if you built the quite importantletters which really establish, I two-storyhouses with gardens in the standarddull, think,that the idea ofconfidence intervals originated unimaginativeBritish suburban way, that you would in the Gosset-Pearsoncorrespondence back in 1926, get more agriculturalproductivity, and you'd have and variousother things. I've got Robin Plackettto moreopen space foreverybody and moreaccess to the agree to join me in workingon this, and we got land. I verywell remember the committeemeeting at togetherjust a coupleof weeksago and decidedthat whichhe producedthis report, and it wentaround the the way to tackle it is to have a seriesof chapters table and everybodythere said, "We can't see what's involvingthe Fisher-Gossetcorrespondence which is wrongwith the argument,but it must be wrong." unpublishedas well.I had suggestedto JoanBox after [Laughs]The factis he was bloodywell right.This she had writtenthe lifeof her father[R. A. Fisher] fashionof highrisebuildings is absolutelydisastrous, thatshe shouldwrite something about Gosset, which and it didn'tproduce the resultsit was supposedto she did. But she agrees that it's not completely

This content downloaded from 128.173.127.127 on Wed, 24 Sep 2014 22:01:56 PM All use subject to JSTOR Terms and Conditions 212 STATISTICAL SCIENCE satisfactoryas it stands either.The Gossets were admitthough, that is the othertrouble about writing Huguenots;the name is a Frenchname. They came a book.You decideyou're going to writeone bookand over afterthe revocationof the Edict of Nantes in getyourself committed, and thenyou get much more 1685.Gosset's great great great grandfather was silver- interestedin somethingelse. smithto GeorgeIII. There'sall kindsof information DeGroot: We've waiteda longtime for this book ofthat type, which again is not relevantto statistics. ofyours on the foundations.I hope you do it. But we shouldsomehow or othertry to mergeall this Barnard: Well,Mary won't go intomy study now. materialinto a coherentaccount. It's leftthat I've got She refusesto haveanything to do withit essentially. a listof chapters, the first of which is howthe situation Piledwith paper, large amounts of which are draftsof stoodin 1920,what the position in statisticswas then. essays on experimentalprobability versus personal WhichI shall write.It is intendedthat the book will probability,and thatkind of thing. go throughthe variousstages of developmentof sta- DeGroot: Well,you've certainly had a tremendous tisticsfrom roughly 1920 up to 1950,sort of telling influenceon the fieldand on individualsin the field. the storyin the chaptersand thenhaving as appen- Everyoneappreciates that. dices the actual correspondencepeople werewriting Barnard: It's kindof you to say so. at thetime. DeGroot: I wantedto saythank you for your many DeGroot: That wouldbe reallyfascinating. contributions,and thankyou for this conversation. Barnard: That's whatI wantto do beforeI write Barnard: Thankyou. anythingabout the foundationsof statistics.I must

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