Morris H. DeGroot
Statistical Science \ 1987, Vol. 2, No. 3, 239-258
统计科学 \ 1987, Vol. 2, No. 3, 239-258
George E. P. Box was born in Gravesend, Kent, England, on October 18 , 1919. He received a B.Sc. in 1947, a Ph.D. in 1952, and a D.Sc. in 1961, all in mathematical statistics from London University. He was employed as a statistician at Imperial Chemical Industries from 1948 to 1956 , and from 1957 to 1959 he was Director of the Statistical Techniques Research Group at Princeton University. Since 1960 he has been a professor at the University of Wisconsin, where he was the founding chairman of the Department of Statistics. In 1971 he was appointed Ronald Aylmer Fisher Professor of Statistics, and in 1980 he became Vilas Research Professor of Mathematics and Statistics. He was President of the American Statistical Association in 1978 and President of the Institute of Mathematical Statistics in 1979. He received the Shewhart Medal from the American Society for Quality Control in 1968 and the Wilks Memorial Medal from the American Statistical Association in 1972. He was elected a member of the American Academy of Arts and Sciences in 1974 and a Fellow of the Roval Society in 1985. In 1975 he received an honorary doctorate from the University of Rochester. The following conversation took place during the annual joint statistics meetings in Chicago in August 1986.
乔治·E·P·博克斯（George E. P. Box）于1919年10月18日出生于英国肯特郡（Kent）的格雷夫森德（Gravesend）。他于1947年在伦敦大学获得理学学士，1952年获得哲学博士学位，1961年获得科学博士学位，这些全部都是数理统计学位。1948年至1956年，他在帝国化学工业公司担任统计员，1957年至1959年，他担任普林斯顿大学统计技术研究小组主任。自1960以来，他一直是威斯康星（Wisconsin）大学的教授，在那里他是统计部门的创始主席。1971年，他被任命为罗纳德·艾尔默·费舍尔（Ronald Aylmer Fisher）统计学教授，1980年，他成为维拉斯（Vilas）数学和统计学研究教授。他于1978年任美国统计协会主席，1979年任数理统计研究所所长。于1968年获得美国质量控制学会颁发的休哈特（Shewhart）奖章，1972年获得美国统计协会颁发的威尔克斯（Wilks）纪念奖章。他于1974被选为美国艺术与科学学院院士，并于1985年获得罗尔斯（Roval）学会会员，1975年获得罗切斯特（Rochester）大学荣誉博士学位。以下对话发生在1986年8月的芝加哥年度联合统计会议上。
DeGroot: How did you get interested in statistics and come into the field of statistics?
DeGroot: 你是如何对统计学产生兴趣并进入统计学领域的？
Box: Well, I was in the British Army during the second World War, in the engineers. I had been studying chemistry, so they posted me to the chemical defense experiment station which was where they did work on chemical warfare. I was in the physiology department, where they were working on how you should treat people, particularly the civilian population, if there was extensive bombing with gas. We had a lot of good people there. For example, Gaddum was there, who was probably the best pharmacologist in Great Britain at that time, and a number of people of that sort. I was working for a physiologist who was actually in uniform, a colonel called Cullumbine. I was a lab assistant doing biochemical determinations. We did a lot of experiments on animals to try to find out what would happen if you gassed an animal and then you gave various treatments. But our results were all to hell, and I said to Cullumbine one day; "You know, we really need to have a statistician look at these data because they are very variable." And he said, "Yes, I know, but we can't get a statistician; there isn't one available. What do you know about it?" I said, "Well, I don't know anything much about it, but I once tried to read a book called Statistical Methods for Research Workers by a man called R. A. Fisher. 1 didn't understand it, but I think I understood what he was trying to do." And he said, "Well, if you read the book, you'd better do it."
Box：第二次世界大战期间，我在英国陆军的工程兵部队里。由于此前我一直在学习化学，所以，他们派我去化学防御实验站，那里是军队里研究生化战役的地方。我在生理学部门，他们正在研究如何对人们、尤其是平民，制造大规模的毒气轰炸。这个部门有很多优秀学者。例如，可能是当时英国最出色的药理学家的伽达姆（Gaddum）就在那里，还有很多类似的人。我为一位生理学家工作，实际上、他总穿制服，是一位名叫卡伦宾（Cullumbine）的上校，我是做生化测定的实验室助理。我们在动物身上做了很多实验，试图研究如果用毒气毒死动物、再进行各项治疗，会发生什么。但是，我们的结果都糟透了，有一天我对Cullumbine说：“你知道，我们真的需要一个统计学家来看看这些数据，因为它们的差别总是这么大。” 他说，“是的，我知道，但我们找不到统计学家；没有统计学家。你对此（统计学）了解多少？”我说，“嗯...我对它了解不多，但有一次我试着读一本叫R.A.Fisher的书，名叫《研究工作者的统计方法》。我不能完全理解这本书的全部内容，但我想，我明作者试图在做什么。”他说，“好吧，但你最好试着去读这本书。”
Now this was about 1942 so there were still three years of the war to go. There was an educational corps in the Army that had some arrangements with correspondence schools, and they would send you a correspondence course on anything you wanted. So the first thing I did was to try to get one on statistics. They said, "We don't have one on statistics, but we will try and get you a reading list." So they got me a reading list; I don't know who wrote that list but I suspect that either Fisher or Yates was advising them, because every book was Fisherian. Statistical Methods for Research Workers was the first book, Design of Experiments was the second book, Fisher and Yates' Tables was the third book, and then there were all these derivative books. There was Snedecor. There was a book by Goulden, which is a very good book on designed experiments. It was particularly useful about things like partial confounding. And then there was a book by Linquist on statistical methods in education that was all about the analysis of variance and stuff like that. There was a book by Donald Mainland about statistics in medical studies. And there was a book by Chapman and Shoemaker on forestry and range management with a very nice piece in it about least squares. So I started reading these books. The only book I had with any theory in it was a little book on statistical methods, which had recently been written at that time by Aitken. It had a lot of combinatorial things in it, a lot about factorial moments and things like that.
此时大约是1942年，所以，我们还要继续承受三年的战争。军队里有一个团负责教育，它们与函授学校有一些安排，会送给你一个函授课程，你想学什么就学什么。所以，我做的第一件事就是试图得到一本统计学方面的书。但他们说：“我们没有统计学，不过，我们可以给你一份阅读清单。”于是，他们给了我一份阅读清单；我不知道是谁写下的这份清单，但我怀疑是费舍尔（Fisher）还是耶茨（Yates）给了他们建议，因为每本书都是费舍尔式的。
《研究工作者的统计方法》是第一本书，《实验设计》是第二本书，《Fisher和Yates的表格》是第三本书，然后是关于它们的所有衍生书籍。还有斯内德科（Snedecor）的书，还有古尔登（Goulden）的一本书，是一本关于设计实验的好书。它在某些关于混淆的部分尤为有用。然后是林奎斯特（Linquist）所写的一本有关教育统计方法的书，书中都是关于方差分析之类的东西。还包括唐纳德·坎特兰（Donald Mainland）有一本关于医学研究统计的书。以及查普曼（Chapman）和休梅克（Shoemaker）写了一本关于林业和牧场管理的书，书中有一段很好的关于最小二乘法的内容。于是，我开始读这些书。我唯一一本和理论有关的书是一本统计方法的小书，那是艾特肯（Aitken）在那段时间写的，里面有很多关于组合数学的内容，类似于阶乘矩之类的东西。
图1:George E. P. Box
So I was reading at night to discover what to do the next day. I found out what to do about two groups, and then I found out what to do about three groups, and so on I ran all kinds of designs because we wanted to study a lot of different factors. We had mice, rats, and some larger animals, trying to deduce what would be the best treatment for people gassed with phosgene. It was said that you should lay people down, you should make sure they didn't get any exercise, you should give them hot sweet tea, and stuff like that. Well, we had rats that were exercising, rats that weren't exercising, rats that had hot sweet tea, and rats that didn't have hot sweet tea, and by and large, whatever you did they still died at about the same time But we were trving all sorts of things because London was still being bombed at this time with high explosives and, as far as we knew, it was very possible that one night they might switch to gas. We had a lot of people who came who were called observers. These were guys who had volunteered, and we burned their arms with small amounts of mustard gas. I remember doing Graeco-Latin sauares with these people. I would have six men with three burns on each arm, so there were six men with six positions with six primary treatments and six secondary treatments. That was a simple one, but then you could have more complicated variations.
所以我在晚上阅读、以了解第二天该做什么。我了解到应如何处理两个实验组，然后，我发现了处理三个组的方法，依此类推。我尝试了各种设计，因为我们想研究很多不同因素的影响。我们有小鼠、大鼠和一些更大的动物，以试图推断出，对被光气毒化的人最好的治疗方法。一些治疗方法包括：躺下，不锻炼，喝热的甜茶等等。因此，我们有运动的老鼠，不运动的老鼠，喝热甜茶的老鼠，没有喝热甜茶的老鼠...总的来说，无论我们对它们加以何种处理，它们仍然几乎在同一时间内死亡。但我们仍在尝试各种各样的处理，因为此时伦敦仍在经历高爆炸药的轰炸。据我们所知，很有可能在某天晚上、敌方会改用汽油。此时，有很多人来到我们这里，他们被称为观察员。这些人是自愿的，我们用少量芥子气烧伤了他们的手臂。记得和这些人一起做过Graeco-Latin squares【译者注：Graeco-Latin squares，不清楚含义】。我负责的组里，一组有六个男性观察员，他们每只手臂上有三个烧伤，所以有六个男人，六个位置，六个主要治疗和六个二级治疗。这是一个简单的例子，但是你可以有更复杂的变化。
George Box working in the Army laboratory
图2: 乔治·博克斯在陆军实验室工作
DeGroot: You regarded their arms as blocks?
DeGroot: 你认为他们的手臂是块木头？
Box: Each arm was a block and each man was a block. I had a good time with that. By the time the war was ended, I had about three years of very intensive practical experience doing a lot of designed experiments. And during the course of that time, I got to see Fisher. There was a pathologist there called Cameron who was a Fellow of the Royal Society. This was regarded as important war work, so they brought in some very good people. When I went there I was just a sapper, that's like a private soldier, and then I was a corporal, and then I was a sergeant, and I finally left as a staff sergeant. So I was a sort of nobody, but I was befriended by Cameron. He was interested strangely enough in the history of mathematics, and he lent me several books about the history of mathematics and mathematicians. I had studied chemistry but I also had been interested in mathematics. So we used to talk to each other, and there was one time when I had this problem and I didn't know what to do with it. I must have been looking perplexed because Cameron came along and said, "You don't look very happy today." And I said, "No, I don't know what to do with this data. I was plotting time-mortality data on probability paper and I was hoping my lines would be parallel and straight but they weren't. They were all very unparallel and very unstraight, and some of the data I didn't have because the animals hadn't died." And so he said, "Well, you should go and see Fisher." That was like saying I should go and see God, as far as I was concerned. But anyway, I went to Cambridge and Fisher was very kind and spent the whole day with me. He pointed out that what we should do is make a reciprocal transformation on the times until death, which we did and it came out right. Apart from that I hadn't really at that point had any contact with "official statistics." I was on my own and just managing the best way I could. I've told elsewhere how in order to get me a railway warrant to go to Cambridge, the military pretended I was collecting a horse.
Box：每只手臂都是一个块，每个人都是一个块，在这种研究经历中、我留下了愉快的体验。战争结束时，我已经有了约三年的相当密集的实践经验，设计了很多次实验。在那段时间里，我见到了Fisher。当时，那里有一位名叫卡梅伦（Cameron）的病理学家，他是英国皇家学会的会员。由于我们所从事的工作被认为是一项重要的战争工作，因此，那里引进了一些很优秀的人。当我去到那里的时候，我就像一名士兵，接着，我成为了一名下士，然后，我成为了一名中士，最后，我作为一名上士而离开了。所以，我仍然是个无名小卒，但Cameron对我很友好。略显奇怪的是，他对数学史非常感兴趣，他曾借给我几本关于数学史和数学家的书。我学过化学，但我也对数学感兴趣，所以我们常常交谈。有一次，我遇到了一个问题而不知道该怎么办。我想，我那时看起来一定很困惑；因为Cameron走过来和我说，“你今天看起来不太开心。” 我说，“是的，因为我不知道如何处理这些数据。我在概率纸上绘制时间死亡率数据，我希望我的线是平行和笔直的，但事实并非如此。它们都非常不平行，非常不整洁。此外，有些数据是缺失的，因为动物还没有死亡。”于是他说，“好吧，你应该去看看Fisher。“对我而言，这就像说，我应该去见上帝。但不管怎样，我去了剑桥，Fisher非常友善，和我一起度过了一整天。他指出，我们应该做的是在动物死亡之前、对时间进行一次反向变换。我们照做了，且这样得到的结果是正确的。除此以外，当时，我还没有真正接触过“官方统计学”。我只能靠自己，尽自己的最大努力。我在别处曾提到过，为了给自己弄到一张去剑桥的铁路通行证，我不得不拜托军方、让我看起来像在收集一匹马那样。
Another distinguished scientist who befriended me was Gaddum. We had Americans and all sorts there, and there was an American major who was an ophthalmologist and he was working on what you do about people getting a drop of lewisite in their eyes and being blinded. Lewisite was another substance something like mustard gas. Up to the time when they discovered the nerve gases, it was the most toxic stuff around. If you got a drop of this in your eye, you became blind. And so he was trying to produce some sort of ointment which somebody who thought they had this in their eye could put on their eye and prevent blindness. We were working with rabbits and, of course, a rabbit has two eyes. But we were running factorial experiments, and so we had an interesting situation where you had a factorial experiment with a block size of two. By this time I had really got interested in messing around with these designs, and so I said, "Sure, I can fix you up with a design." So I worked out this lovely design and eventually there was this report published by Major Somebody-or-other and Sergeant Box. There was a building aptly called the Main Block, which was where all the officials were, and the report went up to them for approval. Well, my part was a statistical appendix, and they cut it out. I didn't worry about it;
另一位与我成为朋友的杰出科学家是Gaddum。在我曾工作的部门里，有美国人和各种各样的人，其中，有一个美国眼科医生，他正在研究如何防止人们的眼睛被一滴路易斯特（lewisite）污染而失明，Lewisite是另一种类似芥子气的物质。直到神经毒气被发现之前，它是当时毒性最强的东西。如果人的眼睛里被滴了一滴，则会失明。因此，他试图制造一种药膏，可以通过将其涂在眼睛上以防止失明。当时，我们正在兔子上进行实验，当然，兔子有两只眼睛。 但我们正在运行的是析因实验，因此，我们遇到了一个有趣的情况：你拥有的是一个块大小为 2 的析因实验。 此时，我对摆弄这些设计真的很感兴趣，所以，我说，“当然，我可以用一个设计来解决你。” 为此，我制定了这个可爱的设计，最终，这个报告由少校某人或其他人和中士博克斯发表。 有一座被称为主街区的建筑，所有官员都在那里，报告被送到那里并得到了他们的批准。 而我的部分是一个统计附录，虽然他们把它剪掉了，但 我并不为此担心；
George Box (front row center) with the concert party he organized in the Army
图3: George Box（前排中间）参加了他在军队组织的音乐会
I thought, that's the army and that's the way they are. But Gaddum comes along and says, "Oh, Box. Yes, that appendix that you wrote about the rabbits and that very nice design you have. They cut it out. Did you know that?" I said, "Yes, I knew they cut it out." He said, "Why did they do that?" And I said, "Well, I don't know, they just cut it out." He said, "Let's go to the Main Block." And we went. I felt very embarrassed. Here's this very distinguished guy, who reads the riot act to all these civil servants and says, "Put the bloody thing back in." And so in the end it was put back in. It was a curious situation but encouraging.
我想，这就是军队，他们就是这样。但是Gaddum过来说，“Box，你写的关于兔子的附录以及你的设计都很精彩，但他们把它删除了。你知道吗？”我说，“是的，我知道他们把它删除了。”他说，“他们为什么要这样做？”我说，“我不知道，我只知道他们确实把它删除了。”他说，“我们去主楼吧。”然后我们走了。我感到很尴尬。这是一个非常杰出的人，他向所有这些公务员宣读了《暴乱法案》，并说，“把这该死的东西放回去。”最后它又放回去了。这是一个奇怪的情况，但令人鼓舞。
Box: When the war ended I thought I'd better go and study statistics and find out what I'd been doing all that time. I found out that Fisher was really in genetics in Cambridge, and I realized that what I should do was go to see Pearson at University College. I remember this interview with Pearson because I didn't know anything about the controversy between Fisher and Pearson. All I knew was some Fisherian statistics, so I spent the time at the interview telling Pearson what a wonderful guy R. A. Fisher was. [Laughs] And Pearson was very kind; he was a nice man, as you know, a very gentlemanly person. And he said very mildly to me at the end, "Well, by all means you can come. But I think you'll learn there were one or two other people besides Fisher in statistics." So I went to University College and studied there, and I didn't take any more chemistry. I took a Bachelor's degree after a time in statistics and mathematics, and then I went on and worked on a Master's degree. But then they said to me, "You know, you shouldn't submit this stuff for a Master's thesis, you should go on and do a Ph.D."
战争结束后，我想我最好去研究一下统计学，看看我一直在做什么。我发现Fisher真的是剑桥学遗传学专业的，我意识到我应该去大学学院找皮尔逊（Pearson）。我记得这次对Pearson的访问是因为我对Fisher和皮尔逊Pearson之间的争论一无所知。我所知道的只是一些Fisher的统计学，所以我在访问过程中花告诉Pearson，R.A.Fisher是一个多么棒的人。[笑]Pearson非常善良；他是一个很好的人，你知道的，一个很有绅士风度的人。最后，他非常温和地对我说：“好吧，无论如何你都可以来。但我想你会发现，除了Fisher，还有一两个统计学的人。”所以我去了大学，在那里学习，我不再学化学了。经过一段时间的统计学和数学学习后，我获得了学士学位，然后继续攻读硕士学位。但后来他们对我说，“你知道，你不应该为硕士论文提交这些东西，你应该继续攻读博士学位。”
DeGroot: It was too good for a Master's?
DeGroot: 这对硕士来说太好了？
Box: That's what they claimed. By this time Hartley had appeared at University College, and Pearson and Hartley kind of jointly advised me. Anyway around this time some people from ICI appeared-Imperial Chemical Industries-and they had quite a slew of statisticians. In those days there was an arrangement to spend summers with industry, and I thought I'd like to do that. So in the summer of 1947 I went to Blackley, which was near Manchester. It's the dyestuffs division of Imperial Chemicals, but they also make nylon and other things. I went up there and spent the summer. O. L. Davies was there. They had decided that they would have me work in what was called the rubber lab, where they made rubber chemicals that were used for making tires and things like that. This lab was concerned with testing things. There would be rubber bands and pieces of rubber that were being pulled by some machine, and pulled and pulled and pulled. And you'd count how many times they pulled it before it broke. There were other machines that were testing various kinds of plastic materials, which were used for artificial leather and things like that, which were also tested in this lab. They had all these machines working away. It was just a wonderful place for designed experiments. Designed experiments was what I had particularly loved when I was in the Army, and ICI just kind of gave me carte blanche. There was a guy who was in charge of the lab called Buist and essentially he let me run any experiments I wanted to have run.
Box：他们就是这么说的。这时Hartley已经在大学学院，Pearson和Hartley共同给了我一些建议。但不管怎么说，在这个时候，ICI（帝国化学工业公司）的一些人出现了，他们有相当多的统计学家。在那些日子里，有一个安排是和工业界一起度过夏天，我想我也愿意这样做。所以在1947年夏天，我去了布莱克利（Blackley），那里离曼彻斯特（Manchester）很近。那里是帝国化学公司的染料部门，但他们也生产尼龙和其他东西。我去那里过了一个夏天。O.L.戴维斯（O. L. Davies）在那里。他们决定让我在所谓的橡胶实验室工作，在那里他们制造橡胶化学品，用于制造轮胎和类似的东西。这个实验室负责测试此类物品，会有橡皮筋和橡胶片被一些机器拉动，你需要数清他们在它坏之前拉了多少次。还有其他的机器在测试各种各样的塑料材料，这些塑料材料被用于制造人造革等物品，它们也在这个实验室里进行测试。研究员们让所有这些机器一直工作。我想，这个研究室正是一个设计实验的好地方。设计实验是我在军队时特别喜欢的，而 ICI 只是给了我全权委托。有一个叫 Buist 的人负责实验室，基本上他让我运行我想要运行的任何实验。
DeGroot: Had they not been doing any designed experiments?
DeGroot: 他们没有做过任何设计实验吗？
Box: They had been doing some, but I think Davies had told them that there was probably a lot more they could do down there. So anyway we had all these things going on. For example, there was a thing on the Martindale wear-tester, which rubs four samples of artificial leather against emery paper and gradually you get the weight losses on these things. But it was rather too variable, and we wanted to know where the variation was coming from. Now this was one of these ideal situations where you could change the components of the machine around. There were four holders for the samples that could be interchanged, so that you may start out ABCD but you could make it ACBD and so on. There were four pieces of emery paper that you could change around, there were four different positions in the machine, and there was a whole series of things you could change in the components of this machine. So I was trying to find out where this excessive variation was coming from. I was running these hyper-Graeco-Latin squares. Well, we found out that it was mostly position-to-position variation, and you could use Latin squares to get rid of that. But then the question of comparing seven pieces of cloth came up. You know, we'd only four positions; but then we could use Youden squares. And I started to run factorial experiments where we might end up with 32 specimens, and using partial confounding you could test the 32 specimens on a Martindale weartester so as to estimate all the effects clear of block effects. I used to like to do this; there were some very nice problems. It was partly being kind of useful and partly just enjoying myself.
Box：他们已经做了一些，但我想Davies已经告诉他们，在那里他们可能可以做更多的事情。所以不管怎么说，我们一直在做这些事情。例如，Martindale磨损测试仪上有一个东西，它把四个人造革样品在砂纸上摩擦，然后逐渐得到这些东西的重量损失。但是它太多变了，我们想知道变化是从哪里来的。这是一种理想的情况，你可以改变机器的部件。样品有四个支架可以互换，这样您可以从ABCD开始，但您可以把他变成ACBD等等。有四张砂纸可以随意更换，机器中有四个不同的位置，机器的部件中有一系列的东西可以更换。所以我试图找出这种过度的变化是从哪里来的。我在运行这些hyper-Graeco-Latin squares【译者注：hyper-Graeco-Latin squares，不明白这里表示的意思】。嗯，我们发现这主要是位置对位置的变化，你可以用Latin squares【译者注：Latin squares，不明白这里表示的意思】来消除它。但接下来的问题是如何比较七块布。你知道，我们只有四个位置；但是我们可以用Youden squares【译者注：Youden squares，不明白这里表示的意思】。我开始进行析因实验，最终我们可能会得到32个样本，使用部分混淆法，你可以在Martindale磨损测试仪上测试32个样本，这样就可以估计出所有的影响，而不受阻滞效应的影响。。我过去喜欢这样做；有一些非常好的问题。这一部分是有用的，另一部分只是我在自娱自乐。
DeGroot: And this was right after you had received a Bachelor's degree?
DeGroot: 这是在你获得学士学位之后？
Box: That's right, yes. Mostly what I knew about experimental design I knew from the Army, because learning by doing is the only way I ever learn anything. So I wrote a report on that stuff. It's still around actually, and there's lots of good data in there. ICI said to me, "You can join the firm, we'll pay your salary, you can be at University College another year, and then after that you can come and we'll give you a job." So I said fine. So I did another year at University College and then I left. That was in '48. And I worked for ICI from ' 48 on, for a number of years-eight years in all. I didn't actually take my Ph.D. until '52, and that was only because Hartley kept saying to me, "Look, you really should submit your stuff." What happened was something like this. This business about the Martindale wear-tester and other tests they were doing had got me interested in the question of robustness. They were doing some statistical analysis themselves, but some of the things they were doing were raising some questions in my mind. Many of the tests they did were finding out at what point something broke-these were extreme value problems-but were mostly being analyzed using normal theory. Except, as I recall, in one instance where they tested the breaking strength of five elastic bands and for that test they never took the mean, they always took the median. I asked them why and they said the median was more accurate; this made sense because obviously they would have a heavy-tailed distribution. So I became interested in what non-normality did to standard tests. And not only that-on this Martindale weartester, for example, they would run the machine and then look and see how much wear had occurred after say 1000 revs, and then you'd put the same sample back on again and see how much wear there was after 2000 , after 3000 , after 4000 revs, and so on. These successive readings were obviously serially correlated and yet they were all being analyzed as if they were independent. So some of the things I started to do for my thesis were related to that. And I started to worry about how the analysis of variance was affected if things were autocorrelated, or they didn't have the same variance, and that meant you got involved in distributions of quadratic forms. So I started studying quadratic forms, and that was another thing I found very interesting-one of those nice things in normal theory.
Box: 没错，是的。我对实验设计的了解，主要来自于军队那里，因为边做边学是我学习任何东西的唯一途径。所以我写了一份关于那件事的报告。它实际上仍然存在，并且那里有很多好的数据。 ICI 对我说：“你可以加入公司，我们会支付你的薪水，你可以在大学学院再呆一年，然后你可以来，我们会给你一份工作。”所以我说好。所以我在大学学院又做了一年，然后我离开了。那是在'48。我从 48 年起在 ICI 工作了很多年——总共八年。我实际上并没有拿我的博士学位。直到 52 年，那只是因为哈特利一直对我说，“看，你真的应该提交你的东西。”事情是这样的。这项关于 Martindale 磨损测试仪和他们正在进行的其他测试的业务让我对稳健性问题产生了兴趣。他们自己在做一些统计分析，但他们所做的一些事情在我的脑海中引发了一些问题。他们所做的许多测试都是为了找出什么时候出现问题——这些是极值问题——但大多是使用正常理论进行分析的。除了，正如我所记得的，在一个例子中，他们测试了五个松紧带的断裂强度，而在那个测试中，他们从来没有取平均值，他们总是取中位数。我问他们为什么，他们说中位数更准确；这是有道理的，因为显然它们会有重尾分布。所以我开始对非正态性对标准测试的影响感兴趣。不仅如此——例如，在这个 Martindale 磨损测试仪上，他们会运行机器，然后查看在 1000 转后发生了多少磨损，然后您再次将相同的样品放回原处，看看有多少磨损有 2000 之后，3000 之后，4000 转之后，等等。这些连续的读数显然是连续相关的，但它们都被分析为好像它们是独立的。所以我开始为我的论文做的一些事情与此有关。我开始担心如果事物是自相关的，或者它们没有相同的方差，方差分析会如何受到影响，这意味着你参与了二次形式的分布。所以我开始研究二次型，这是我发现的另一件非常有趣的事情——这是正常理论中的一件好事。
My thinking was that the covariance matrix for six successive observations, say, would be a
我的想法是，连续六次观测的协方差矩阵，应该是一个$6 \times 6$的矩阵，理想情况下应该是对角的，方差为常量，但我们得到的是某种更一般的矩阵。嗯，我决定，与其分析1000转、2000转，等等之后的磨损情况，不如先分析前1000转的磨损情况，再分析第二个1000转、第三个1000转的磨损情况，依此类推。但这也让我担心，因为你会在相继的差异之间得到负相关，我开始担心这会产生多大的影响。我开始想到的第一件事是因为我听了Pearson好几年的课，就是如何检验协方差矩阵是否真的是它应该的样子。我发现有一个检验统计量——它是两个行列式的比率——但没人知道它的分布是什么。 我找到了 Plackett 的一篇论文，他提到了 31 种不同似然标准，以及将其用于从正态理论中检验关于协方差矩阵的各种假设。其中有些是非常愚蠢的，但人们仍然只知道其的某些分布或近似分布。所以，我论文的主要内容之一是关于似然比标准分布的业务。我对这个很感兴趣。我在Biometrika杂志上写了一篇论文。[“一类似然准则的一般分布理论”，$\mathbf{36}$（1949）317-346。]好的，根据Sam Wilks的一些结果，这些标准都有特定类型的矩函数，你可以将它们展开得到渐近分布。我在ICI也对最优条件感兴趣，这是另一个故事。但我要说的是，当我在1952年提交我的论文时，我已经发表了几篇论文。其中一两篇是论文的一部分。这在英国是允许的，因为一个证据证明这件事可以在一本好杂志上发表，那就是它已经被发表了。[笑]
Box: ICI was a very interesting place. I was lucky there because I wasn't given much supervision. There was a chap called Dr. Oakshott who was my boss. He decided when he first saw you whether he thought he trusted you or not. If he did you were given a free rein. I was in the "miscellaneous chemicals service" department, which is a polite name for odds'n sods, and there were people in it like x-ray crystallographers and other strange people. So he didn't tell me what I was supposed to do. I used to write a report to him very occasionally, certainly not more than once every six months; it may have been only once a year. But he seemed perfectly happy with that. And I had the whole of the thing to go at, wherever I could do anything. I was at the headquarters of the dyestuffs division, and all the research facilities were there. I think it was the largest concentration of organic chemists in Europe at the time. There was a lot of research going on but I was also interested in trying to run experiments on the processes, and I did that too.
Box: ICI是一个非常有趣的地方。我在那里很幸运，因为我没有得到太多的监督。有一个叫奥克肖特（Oakshott）博士的家伙，他是我的老板。他第一次见到你时就决定是否相信你。如果他这样做了，你就可以自由发挥了。我在“杂项化学品服务”部门，这是对杂项化学品的礼貌称呼，里面有x光晶体学家和其他奇怪的人。所以他没有告诉我该怎么做。我过去常常偶尔给他写一份报告，肯定不超过每六个月一次；可能一年只有一次。但他似乎对此非常满意。我有整个事情要做，无论我能做什么。我在染料部门的总部，所有的研究设施都在那里。我认为这是当时欧洲最大的有机化学家集中地。当时有很多研究正在进行，但我也有兴趣尝试对这些过程进行实验，我也做了。
Half a mile down the road was Blackley Works; it looked like the Slough of Despond down there. I had a hard time getting those guys to run designed experiments. But there was a bright new works at Huddersfield, which was across in Yorkshire, 30 miles away.
沿着这条路走半英里就是Blackley工厂；下面看起来像是绝望的泥沼。我很难让那些家伙去做设计好的实验。但在30英里外的约克郡（Yorkshire）对面的哈德斯菲尔德（Huddersfield）有一个崭新的工厂。
图4
George Box at Dyestuffs Division, Imperial Chemical Industries used to drive over there in my car and I used to say that the number of experiments run per mile traveled was much greater at Huddersfield than it was at Blackley. We had some good designed experiments going at Huddersfield. Now one of the things they told me when I first went there was that it was important to try to improve their efficiency about processes and improve yields. Many chemical processes work with yields which are much less than 100 percent. I mean if you write down a chemical equation, it says that if you put this much of this in and that much of that, it should give you this much of that; but it doesn't. So the yield is like 70 percent, which means it only gives you 70 percent of what it should give you. The other stuff that is made is impurities; of course, it's all got to go somewhere. So high yields are very nice because in the first place they're high yields, and in the second place you don't have to get rid of all those darn impurities. So I started going around looking for people who were interested.
帝国化学工业染料部的乔治·博克斯（George Box）过去常开着我的车去那里，我常说Huddersfield每英里行驶的实验次数比Blackley多得多。我们在Huddersfield进行了一些精心设计的实验。当我第一次去那里时，他们告诉我的一件事是，努力提高他们的流程效率和产量是很重要的。许多化学过程的产率远低于100%。我的意思是，如果你写下一个化学方程式，它说如果你把这个和那个放进去，它会给你这个和那个的大部分；但事实并非如此。所以收益率是70%，这意味着它只给了你应该给你的70%。另一种物质是杂质；当然，这一切都得去某个地方。因此，高产量是非常好的，因为首先，它们的产量很高，其次，你不必去除所有这些该死的杂质。所以我开始四处寻找感兴趣的人。
I met a number of very interesting people, and one of them was a guy called K. B. Wilson. Now K. B. Wilson had an idea about how to improve yields which essentially amounted to the use of the method of steepest ascent. Essentially, you just change the variables
我遇到了很多有趣的人，其中一个叫K.B.威尔逊（K. B. Wilson）的人。现在K.B.Wilson有了一个关于如何提高产量的想法，这基本上相当于使用最陡上升法。本质上，只需将变量$x{i}$按比例更改为一阶导数$\partial y/\partial x{i}$。我们认为，当您开始爬山时，可以这么说，事情可能大致是一阶的，您可以使用高度细分的设计来估计导数，暂时假设线性。如果有我们担心的特定交互，我们会尝试将它们进行比较，这样它们就不会与我们想要估计的东西混淆。我们在实验室实验中取得了很多成功。当时染料部门开发了各种复杂的化学品。通常，他们正在研究的东西会很新，并且可能需要七到八个步骤才能获得他们想要的复杂分子，也许是麻醉剂。在证明了该路线的可行性后，化学家将尝试在实验室条件下确定温度、浓度、流速等，从而在进入中试工厂之前提供合理的产率。他们可能从 20% 或类似的收益率开始，最终会达到 60% 或 70%。但是他们似乎使用我们最陡峭的上升想法更快地到达那里，因此它具有一定的吸引力。但这并不是什么大不了的事。
I had a friend called Phillip Youle-a remarkable person. He was a physical chemist and didn't profess any knowledge of statistics, but he was extremely intelligent and you could tell him about it and he understood it. He was one of the people that really thought statistics was good stuff. And he said to me, "George, you'll never really impress anyone with these lab experiments. The only way they'll ever see how important statistics is will be to do it on the full scale with a big manufacture, where even a one percent increase will make big savings." We had a terrible time getting them to agree to this because people don't like running experiments on the full scale. There wasn't much problem about the experimental error; we knew from looking at past data that we could reproduce the results fairly well. In the end, Phillip managed to persuade these people to run eight experiments, three variables in a
我有一个朋友叫菲利普·尤尔（Phillip Youle）——一个了不起的人。他是一名物理化学家，并自称没有任何统计学知识，但他非常聪明，你可以告诉他，他理解这一点。他是真正认为统计学是好东西的人之一。他对我说：“George，你永远不会用这些实验室实验给任何人留下深刻印象。让他们知道统计数据有多重要的唯一方法是在大型制造厂全面进行，即使增加百分之一，也会带来巨大的节约。”我们花了很长时间才让他们同意这一点，因为人们不喜欢进行全面的实验。实验误差问题不大；通过查看过去的数据，我们知道我们可以很好地重现结果。最后，Phillip成功地说服这些人进行了八个实验，三个变量在一个$2^{3}$的设计中，这是一件大事。总之，他们在全规模的过程中进行了这八个实验。 我们都怀着满腔的心等待着，想着要用最陡峭的山坡上山来提高产量。我们特意选择了这种产品，因为这是一种产量很低的工艺。人们过去常说，人来人往，但这种特殊产品的产量总是40%。[笑]不管怎么说，我们得到了结果，我走了，做了分析。我非常非常难过，因为结果表明，这三个线性效应都非常小，无论是绝对的还是与它们的标准误差相比，这三个双因素的相互作用都非常大。所以我对Phillip说，“我们真的遇到了麻烦，因为最陡的上升，正如我们所做的，真的取决于找到大的一阶效应，现在我不知道该怎么办。”然后我离开去想了想，我想当你处理极大值时，你必须考虑二阶导数的全矩阵。我们得到了一阶导数，并且因为我们知道这两个因子的相互作用，我们得到了混合二阶导数$\partial^{2} y / \partial x_{i} \partial x_{j}$，但是我们没有$\partial^{2} y / \partial x_{i}^{2}$。所以，我对Phillip说，“我们所要做的就是得到这些曲线，然后也许我们可以找到一些东西。做一个二阶拟合。”Phillip说，“对不起，我花了很长时间才让他们跑八次。我们永远也不会让他们跑27次。”“我的意思是，他马上意识到这将涉及到一个三层的设计。所以我离开了，并对它进行了更多的思考，然后我回来说，“也许我们不需要跑27次。”我们将设计设置在一个大鼠笼上，实验点位于立方体的角落。我说，“为什么我们不在这中间加上七个点，一个在中间，两个沿着这个轴。”他说，“我以前从来没有见过。”我说，“我也没有，但无论如何，让我们来运行它。”[笑]于是说服了他们去运行另一套，我们后来称之为“复合”设计。当我们进行分析时，我们发现，就像我们后来发现的很多次一样，我们被困在一个山脊上。
If you think about the chemical kinetics it's obvious that there are bound to be very large interactions between things like time and temperature, time and pressure, time and concentration, concentration and pressure, and so on. So this will lead to these rather sharp diagonal ridges and it will mean that when you do one-factor-at-a-time experiments, you will quite likely get stuck on the ridge. When you look at second order effects it shows you how to find and exploit such oblique ridge surfaces and find and move up ridges. So we did improve that process and that helped a great deal. It also pointed out to me that really nice inverted-bowl-shaped maxima, at least in chemistry, don't exist. Very ridgy systems are the usual ones, and you've got to think about ways of understanding those. And that was why I did this stuff about canonical analysis and so forth on ridge systems. Ridges can happen in any number of dimensions. Thus with, say, four variables there may be a whole hyperplane of nearly alternative processes and there might be a ridge of some sort in three of four dimensions. These things are commercially very important, so I got all involved in that.
如果您考虑化学动力学，很明显，时间和温度、时间和压力、时间和浓度、浓度和压力等因素之间必然存在非常大的相互作用。所以这将导致这些相当尖锐的对角脊，这意味着，当你做一次一个因素的实验时，你很可能会卡在脊上。当查看二阶效应时，它会展示如何找到和利用这种倾斜的脊表面以及如何找到并向上移动脊。所以我们改进了这个流程，这帮助很大。它还向我指出，真正漂亮的倒碗形最大值，至少在化学中，是不存在的。非常粗糙的系统才是常见的系统，必须考虑如何理解这些系统的方式。这就是为什么我在岭系统上做这些关于规范分析等的事情。脊可以出现在任意数量的维度中。因此，例如，对于四个变量，可能存在几乎完全替代过程的整个超平面，并且可能在四个维度中的三个维度中存在某种类型的脊。这些东西在商业上非常重要，所以我全心全意地参与其中。
Box: Stu Hunter was a student with Miss Cox in North Carolina at that time, and she and Stu were good friends. Stu got a copy of this paper that I wrote with Wilson, a Royal Statistical Society paper about this optimal conditions business. ["On the experimental attainment of optimum conditions," J. Roy. Statist. Soc. Ser.
Box: 斯图·亨特（Stu Hunter）当时是考克斯（Cox）小姐在北卡罗来纳州的学生，她和Stu是好朋友。Stu拿到了一份我和Wilson一起写的论文，这是一份皇家统计学会关于最佳商业条件的论文。[“关于最佳条件的实验实现，”J.Roy.Statist.Soc.Ser.$B 13$（1951）1-45.]Stu的背景是工程学，当他读到这篇文章时，他显然对Cox小姐说，“天哪，这是好东西。你必须把这个家伙带到这里来。”他们在陆军研究办公室和弗兰克·格鲁布斯（Frank Grubbs）谈过，接下来我知道的事情是，我收到Cox小姐的一封蓝色航空信，信中说：“邀请您作为客座研究教授来到北卡罗来纳州。”我想这大概是1952年9月吧。我一点也不想成为一名教授或学者。我当时想做的是，继续做一名工业统计学家。 所以不管怎样，我不知道该怎么办，所以我把它拿给了我的老板，他说，“我们也许可以给你一年的假期。”于是我们去董事会，他们给了我一个假期，他们实际上支付了我的车费。我们去了玛丽女王号，非常好。我的老板显然对美国不太了解，因为他对我说，“北卡罗来纳州，现在在西海岸，你知道，所以你得有更多的钱去西海岸。”我说，“不是，在东海岸。”。“不，在西海岸。”我说，“你到达宾夕法尼亚车站”大约四点一刻，你读了一本杂志，然后你就到了巴尔的摩；在餐车里吃晚饭，再没有比在卡罗莱纳州吃火腿和鸡蛋更好的了。一定是在东海岸。”[笑] 我终于说服了他。
DeGroot: Perhaps I should say, for the benefit of our younger readers, that that's a line from the old hit song, "Chattanooga Choo Choo."
DeGroot: 也许我应该说，为了我们年轻读者的利益，这是老歌《Chattanooga Choo Choo》中的一句台词
Box: So I went to North Carolina, and I met Stu Hunter and we worked together. I had kind of come up with response surface "composite" designs just out of the blue. When we met, I said, "Stu, let's see what we can find out about these designs, and let's see if we can find some sort of general principle for what these designs should be like." So we messed about and eventually came out with this idea of rotatability. The idea was that you might characterize a design by its information function, whereby the inverse of the variance of the predicted response was considered as a function of the level of the predictor variables. If the model was linear in the predictors there was much to be said for orthogonality, but you really can't uniquely generalize orthogonality to second-order designs. So you have to generalize some other characteristics. Orthogonal first-order designs gave information functions with spherical contours. We thought it was reasonable to generalize this characteristic for producing information which was constant on spheres around the center. So we came up with this idea of rotatability.
Box:所以，我去了北卡罗来纳州，遇到了Stu Hunter，我们一起工作。我突然想出了响应面“复合”设计。我们见面的时候，我说，“Stu，让我们看看我们能从这些设计中发现什么，让我们看看我们是否能找到一些关于这些设计应该是什么样的一般原则。”所以我们研究了一下，最终提出了可旋转的想法。 其想法是，您可以通过其信息函数来描述设计，其中预测响应方差的倒数被视为预测变量水平的函数。如果预测因子中的模型是线性的，那么正交性就有很多值得一提的地方，但是你真的不能唯一地将正交性推广到二阶设计。所以你必须概括一些其他的特征。正交一阶设计给出了具有球形轮廓的信息函数。我们认为，将这一特性推广到产生围绕中心的球体上恒定的信息是合理的。所以我们提出了旋转性的概念。
About the same time, there was another student that had arrived called Sigurd L. Andersen. I was asked if I would also be prepared to take on Sigurd as a research student, and I said sure. Another problem I was concerned about at that point had come out of this work that I had done in the rubber lab. I had been realizing that some techniques seem to be quite robust, although I don't think I thought of that word then. But anyway, some techniques were robust and some weren't, and this seemed to have something to do with randomization. For example, if you carry through the randomization test, that's one way of making things robust. So what is the randomization test doing in a simple situation? When you are comparing, say, two groups or some number of groups in analysis of variance, we know the significance level is sensitive to the fourth moment, and so randomization must in some way be compensating for this. There was some work by Welch and Pitman on this kind of question about relationships. I got Andersen working on that, and eventually there was a paper by us in the Royal Statistical Society about robustness studied from the point of view of randomization. ["Permutation theory in the derivation of robust criteria and the study of departures from assumptions,"
大约在同一时间，又有一个学生来了，名叫西格德·L·安徒生（Sigurd L. Andersen）。当我被问到我是否也准备以研究生的身份与Sigurd竞争时，我说肯定。当时我所关心的另一个问题来自于我在橡胶实验室所做的这项工作。我一直意识到有些技术似乎相当强大，尽管我当时不认为我想到了这个词。但无论如何，有些技术是稳健的，有些则不然，这似乎与随机性有关。例如，如果你进行随机测试，这是一种让事情更稳定的方法。那么，在一个简单的情况下，随机性测试在做什么呢？当你在方差分析中比较两组或若干组时，我们知道显著性水平对第四个时刻【译者注：the fourth moment的翻译不准确】很敏感，因此随机性一定在某种程度上弥补了这一点。韦尔奇（Welch）和皮特曼（Pitman）在这类关系问题上做了一些研究。我让Andersen做了这方面的工作，最终我们在英国皇家统计学会发表了一篇论文，从随机性的角度研究稳健性。[“稳健标准推导和假设偏差研究中的置换理论”，J.Roy.Statist.Soc.Ser. B17 (1955) 1-34.]最终，Stu和我在年鉴中发表了一篇关于可旋转性的联合论文。[《探索响应面的多因素实验设计》，Ann. Math. Statist. 28 (1957) 195-241.]
I went back to England with every intention of staying there. I had one or two people working with me in a small section in ICI, and ICI started to become interested in computers. I went down to the only one in England at that time, and reported on it. I did a number of things like that, and I got more and more involved with processes. Phillip Youle was a physical chemist, and he was saying, "Well, these ridges you keep finding must mean something in terms of mechanism and the physical chemistry of the thing." We had done a study on an autoclave process where we had a very ridgy kind of situation and I had done a canonical analysis on that yielding a whole plane of near-optimal process conditions. And then Phillip said to me, "You know, I think I could write down a set of differential equations which would represent what might be going on based on the kinetics of the system." We got these systems of mechanistic differential equations, and with certain assumptions we found that we could integrate them and look at the characteristics of the theoretical response surface. Then we found that we could relate the empirical ridge analysis to the characteristics of the physical system. We wrote that up for
我回到英国，一心想留在那里。有一两个人和我一起在ICI的一个小部门工作，这时ICI开始对计算机感兴趣。当时，我去了英国唯一的一家，并报道了此事。我做了很多类似的事情，我越来越多地参与到过程中来。菲利浦·尤尔（Phillip Youle）是一位物理化学家，他说，“你不断发现的这些山脊【译者注：ridges一词翻译不太准确】一定意味着某种机制和物理化学方面的东西。”我们对高压釜工艺进行了研究，在这种情况下，我们会遇到非常棘手的问题，我对其进行了规范分析，得出了一个接近最佳工艺条件的完整平面。然后Phillip对我说，“你知道，我想我可以写下一组微分方程，它代表了基于系统动力学可能发生的事情。”我们得到了这些机械微分方程系统，在一定的假设下，我们发现我们可以把它们结合起来，观察理论响应面的特征。然后我们发现，我们可以将经验岭分析与物理系统的特征联系起来。我们是为Biometrics写了一篇论文。[“响应曲面的探索和利用：拟合曲面和系统基本机制之间联系的一个例子，” Biometrics 11 (1955) 287-323 .]但随后出现了一个问题，好吧，现在你已经得到了这些微分方程，它们是非线性的，所有这些东西，你必须估计系数，这是物理常数，能量，碰撞常数等等。我们的第一种方法相当粗糙。最终我研究了非线性估计，本质上是非线性最小二乘法。当我最终再次来到美国时，我脑子里一直在想着估算这些系统的事情。然后，大约在1955年和1956年，我收到约翰·图基（John Tukey）的来信，他想让我到普林斯顿来领导一个统计技术研究小组，该小组由军队资助。所以最后我决定去。我来到美国。
DeGroot: Did you anticipate that that would be a permanent move to the States at that time?
DeGroot: 你有没有料到，那会是一次永久性的移民？
Box: Yes. I went through a big soul-search, because I liked a number of things about the States. Many things which as it turned out weren't at all that relevant. I mean, I remembered that in North Carolina I went out in my shirt sleeves on Christmas Day, and I thought that was very nice. Well, I don't do that in Wisconsin. [Laughs]
Box: 是的，这是一次大规模的灵魂探索。因为我喜欢美国的很多东西。事实证明，许多事情根本不相关。我的意思是，我记得在北卡罗来纳州，圣诞节那天我穿着衬衫袖子出去，我觉得那很好。但我在威斯康星州不这么做。[笑]
DeGroot: Did you develop the Statistical Techniques Research Group at Princeton?
DeGroot: 你在普林斯顿领导统计技术研究小组了吗?
Box: Well. there had been a thing called STG, the Statistical Techniques Group, and it had come to an end, as I understand it, at some time before that. They decided that they were going to have a new thing with a new Army research contract. So I went out to be the director of that group. There was a steering committee with John Tukey and Sam Wilks and one or two other people on it. We had many visitors. Henry Scheffé, Colin Mallows. Martin Beale, Stu Hunter, and H. L. Lucas came as visitors. Well, Stu was a permanent member of the group for a time, and Merv Muller was a permanent member of the group for a time. We had a good time at Princeton. I was still interested in things like determining mechanism and nonlinear estimation. We consequently became very involved with auestions about computing at Princeton. At that time they had a thing called the MANIAC, which never worked; but it was put together by von Neumann so it was hard to have a successor for it. We wanted to get an IBM 650 using our own funds, and the administration said, "Well, we looked into that. A 650 is a tremendously fast machine and we've been doing a study at Princeton. We've written to everyone and said. 'If you did all the calculations that you want, how much machine time would you need?' We worked it out, and it would just keep the 650 busy for about a few hours a year; so it would be ridiculous to own a machine that fast." So we said, "Well, but would you let us have it anyway? It's our money." And in the end, somewhat reluctantly, they agreed. So we got a 650 , and, of course, within a very short time it was working three shifts. We had a very liberal policy of letting other people use it at night and so on. It was nice to have a machine that actually worked. I mean the MANIAC only worked sporadically. We needed it because of all the nonlinear-estimation calculations we were doing-numerical integration, iterative nonlinear least squares, and so forth. We needed all that stuff. A number of questions arose when you started to think about confidence intervals and things like that for nonlinear situations. You have to worry about how nonlinear something is, and Martin Beale worked on this and eventually wrote a paper for the Royal Statistical Society about measures of nonlinearity of that kind. That was work that he did when he was at Princeton. Scheffé wrote some of his book on the analysis of variance at Princeton. Scheffé was a wonderful companion. He used to insist at lunchtime that we go swimming, and he would not take no for an answer. [Laughs] So we would all go down to the swimming pool, and it was very nice. I enjoyed that time there. I guess my interest in robustness was also continuing at that time.
Box: 嗯，曾经有一个叫STG的东西，统计技术组，据我所知，在那之前的某个时候它已经结束。他们决定，他们将有一个新的东西，一个新的陆军研究合同。所以我去做了那个小组的主任。有一个由约翰·图基（John Tukey）、山姆·威尔克斯（Sam Wilks）和另外一两个人组成的指导委员会。我们有很多客人。亨利·谢菲（Henry Scheffé），科林·马洛斯（Colin Mallows），马丁·比尔（Martin Beale）、斯图·亨特（Stu Hunter）和H.L.卢卡斯（H. L. Lucas）作为访客来了。Stu曾是该组织的常任理事，梅尔夫·穆勒（Merv Muller）也曾是该组织的常任理事。我们在普林斯顿玩得很开心。我仍然对确定机制和非线性估计等方面感兴趣。因此，我们在普林斯顿大学非常热衷于计算方面的研究。当时他们有一种叫做MANIAC的东西，它从来都没工作过；但它是由冯·诺依曼（von Neumann）组合而成，因此很难找到继任者。我们想用我们自己的资金买一台IBM650，政府说，“我们调查过了。650是一台速度极快的机器，我们在普林斯顿做了一项研究。我们已经写信给每个人，说“如果你做了所有你想要的计算，你需要多少机器时间？”我们计算出来，它只会让650每年忙上几个小时；所以拥有一台那么快的机器是很可笑的。”于是我们说，“好吧，但你会让我们拥有它吗？这是我们的钱。”最后，他们勉强同意了。所以我们有了650，当然，在很短的时间内，它实行了三班制。我们有一个非常自由的政策，让其他人在晚上使用它等等。有一台真正能工作的机器真是太好了。我是说那个MANIAC只是偶尔工作。我们需要它，因为所有的非线性估计计算，我们在做数值积分，迭代非线性最小二乘，等等。我们需要这些东西。当你开始考虑非线性情况下的置信区间之类的问题时，会出现很多问题。你必须担心事物的非线性程度，Martin Beale对此进行了研究，并最终为英国皇家统计学会写了一篇关于这种非线性度量的论文。那是他在普林斯顿大学时做的工作。Scheffé在普林斯顿写了一些关于方差分析的书。Scheffé是一个极好的伴侣。他过去总是在午餐时间坚持让我们去游泳，他不会接受否定的回答。[笑]所以我们都去了游泳池，那里很好。我在那里过得很愉快。我想当时我对鲁棒性的兴趣还在继续。
DeGroot: It sounds as though your interest in robustness started very early. You mentioned robustness when you were talking about the early aspects of your work at ICI.
DeGroot: 听起来你对鲁棒性的兴趣很早就开始了。您在谈到您在ICI工作的早期方面时提到了鲁棒性。
Box: Well, I worried about it. I think the question about what you should worry about and what you shouldn't worry about is tremendously important. Not only in statistics, but sort of in life in general; if we only could figure out what to worry about and what not to worry about. I mean, if you worry about everything you go crazy. I don't believe there are any methods which are free of assumption. These so-called nonparametric methods are a real swindle. I mean the assumption made in a standard nonparametric alternative to the paired
Box: 嗯，我很担心。我认为关于你应该担心什么和不应该担心什么的问题非常重要。不仅是在统计上，在生活中也是如此；如果我们能弄清楚什么该担心什么不该担心就好了。我是说，如果你担心一切，你会发疯的。我不相信有任何方法是没有假设的。这些所谓的非参数方法是一个真正的骗局。我的意思是配对t检验的标准非参数替代假设是n维样本具有对称分布。这是一个非常有力的假设。考虑一个显著性测试，假设你有20对观察结果。在样本空间中，有20个差异样本空间中就有大约100万个n-活性剂【译者注：n-tants,不知道如何翻译】。该空间中临界区域的重要特征主要是包含的n-tant的数量，而不是它们包含的密度的性质。如果你假设每一个n-tant中的概率密度轮廓都是相同的，那么这个假设真的会让你通过。当然，如果误差之间存在某种依赖关系，那么这种对称性就不会成立。所以我从来没有对这些程序印象深刻。
At Princeton, the group was originally housed in a beautiful old house called the Theobald Smith House out at the Forrestal Center. After that, they wanted it for something else, and gave us two old houses on Nassau Street. When I first saw the houses I was appalled because they were so dirty and beat up. They said, "We are going to fix them up for you, and they are going to look very nice. In fact we are going to knock down the walls between the two houses so you'll have just one house, and you'll be able to move from one to the other." I was taking off to go to Europe that summer, so I saw the plans and then I disappeared. When I got back I was supposed to check it over and sign off, and say that it had all been done. But there was one bit that hadn't been done, which was a closet on the ground floor which was supposed to have been removed between the two houses and it hadn't been. So I said to whoever it was that that closet was supposed to be removed according to the instructions, and he said, "Well, we can't remove it because that's the only thing that's holding up the john." And so Colin Mallows and I went off and immediately wrote a poem which went:
在普林斯顿，这群人最初住在福雷斯特中心的一栋漂亮的老房子里，叫做 Theobald Smith House。在那之后，他们想要别的东西，给了我们Nassau街上的两栋老房子。当我第一次看到这些房子时，我感到震惊，因为它们太脏了，而且破烂不堪。他们说：“我们会为你修好它们，它们看起来会很漂亮。事实上，我们会推倒两栋房子之间的墙，这样你就只有一栋房子了，你会能够从一个移动到另一个。”那年夏天我要出发去欧洲，所以我看到了计划，然后我就消失了。当我回来时，我应该检查它并签字，并说一切都已完成。但是还有一点没有完成，那就是底层的一个壁橱，本来应该在两栋房子之间拆除的，但没有拆除。所以我告诉不管是谁，那个壁橱应该按照指示拆除，他说，“好吧，我们不能拆除它，因为那是唯一阻碍约翰的东西。”所以科林·马洛斯和我走开了，立即写了一首诗，上面写着：
If you're walking by the Gauss House
And you look inside the door,
You will see a little closet
And you'll ask, "Now what's that for?"
All the members of the group will come hurrying along,
They'll stand round in a normal curve
And sing this little song,
如果你路过高斯家
你看看门里面，
你会看到一个小壁橱
你会问，“那是干什么用的？”
小组的所有成员都会赶来，
他们将以正态曲线站立
并唱着这首小曲，
Chorus:
副歌:
"It's the closet that holds up our john,
The basis that all rests upon,
Without it the structure would all tumble down,
It's the closet that holds up our john."
“这是支撑厕所的壁橱，
一切赖以生存的基础，
没有它，整个建筑都会倒塌，
是壁橱支撑着我们的厕所。”
We called it the Gauss House because the other place was the Theobald Smith House. Theobald Smith had been a distinguished scientist, but we got a request for a reprint that came to us addressed to the "Old Bald Smith." So after this, we found a painting of a very old bald man, which we put up on the wall, and claimed that it was our founder. But then we didn't have anything when we went to the other place so we named it after Carl Friedrich Gauss and called it the Gauss House.
我们称它为 Gauss House，因为另一个地方是 Theobald Smith House。 西奥博尔德·史密斯 (Theobald Smith) 是一位杰出的科学家，但我们收到了重印本的请求，该请求寄给了“老秃头史密斯”。 所以在这之后，我们发现了一幅非常古老的描绘秃子的画，我们把它贴在墙上，并声称这是我们的创始人。 但是后来我们去另一个地方时什么都没有，所以我们以卡尔·弗里德里希·高斯的名字命名它，并称之为高斯之家。
DeGroot: Was that your first song?
DeGroot: 那是你的第一首歌吗？
Box: No, I don't think so. [Laughs] I've always been interested in songs. For that particular one, I think Colin wrote the verses and I wrote the chorus.
Box: 不，我不这么认为。[笑]我一直对歌曲感兴趣。对于那首歌，我认为是Colin写的诗，我写的是合唱。
One of the people who came to the group was Curly Lucas from North Carolina. He had been working for some years in nonlinear things as well, and so we got together and wrote a paper for Biometrika about nonlinear design. ["Design of experiments in non-linear situations," Biometrika 46 (1959) 77-90.]
来自北卡罗来纳州的柯莉·卢卡斯（Curly Lucas）是参加这个团体的人之一。他也在非线性方面工作了几年，所以我们聚在一起，为Biometrika写了一篇关于非线性设计的论文。[“非线性情况下的实验设计”，Biometrika 46（1959）77-90。]
DeGroot: What did you say his first name was?
DeGroot: 你说他的名字是什么？
Box: Well, we called him Curly because he didn't have any hair. His name was Henry. He died some years ago. Curly was a person with a lot of insight. Our paper hasn't been followed up very much. The problem of designing experiments when you have a nonlinear function is a difficult one because the design depends upon the values of the parameters. But the reason you're running the thing is to find out what the parameters are. So you're in this sort of circle and you have to think about iterative solutions and things like that, and iterative experimentation as well. Anyway, we had a first go at it. Well, it wasn't actually a first go because I think the first person who considered nonlinear design was Fisher. He was the first person to consider almost everything. There's a problem he has about dilution, asking what concentrations of solutions would you choose to estimate best the number of bacteria. You plate out a number of high dilutions of a bacterial suspension. There's either no bacteria, in which case vou get no growth, or else there's one or more bacteria, in which case you get growth. Supposing that you want to estimate how many bacteria there were in the original undiluted solution, how do you choose the dilutions so that you get the best estimate in the smallest number of experiments? Cochran was also interested in the topic and gave a special address on it. I think this is a problem which everyone sort of steers clear of because it's rather messy, and because although there's only one way something can be linear, there's an infinite number of ways it can be nonlinear. [Laughs]
Box: 我们叫他Curly是因为他没有头发。他的名字叫亨利（Henry）。他几年前去世了。Curly是一个很有洞察力的人。我们的论文没有得到太多的跟进。当你有一个非线性函数时，设计实验是一个困难的问题，因为设计取决于参数的值。但是你运行它的原因是为了找出参数是什么。所以你在这个圈子里，你必须考虑迭代的解决方案以及类似方法，还有迭代的实验。无论如何，我们是第一次尝试。其实这不是第一次，因为我认为第一个考虑非线性设计的人是Fisher。他是第一个考虑几乎所有事情的人。他有一个关于稀释的问题：选择什么浓度的溶液以最好地估计细菌的数量。如果将细菌悬浮液的大部分用高度稀释液处理并铺平，则要么没有细菌（因为在这种情况下细菌不会生长），要么有一种或多种细菌，在这种情况下会生长。假设你想估计原始的未稀释溶液中有多少细菌，你要如何选择稀释度，以便在最少的实验次数中获得最佳估计？科克伦（Cochran）也对这个话题感兴趣，并就此发表了特别演讲。我认为这是一个每个人都回避的问题，因为它相当混乱，因为尽管线性的方法只有一种，但非线性的方法有无数种。[笑]
We had some communication with the engineering departments at Princeton, particularly the chemical engineering department. An interesting problem occurs when several mechanisms are proposed for a particular reaction, and different mechanisms lead to different sets of differential equations. I became aware of the problem while attending a Ph.D. final for one of the chemical engineers. He'd run some experiments which, he said, did not contradict the model-which was true, they didn't contradict the model-but they also didn't contradict almost any other model you'd like to name. If you think of a bunch of experiments that produce data which don't cover much of a range, then you can put all kinds of lines through them. So what I decided to think about was how do you test a model, and how do you run experiments that put a model in jeopardy.
我们与普林斯顿大学的工程系进行了一些沟通，特别是化学工程系。一个有趣的问题是，对于一个特定的反应提出了几种机制，不同的机制导致不同的微分方程组。我是在参加一位化学工程师的博士期末考试时意识到这个问题的。他曾做过一些实验，他说，这些实验与真实的模型没有矛盾，它们与模型没有矛盾，但它们也与你想命名的其他模型几乎没有矛盾。如果你想到一堆实验产生的数据覆盖范围不太广，那么你可以在它们中间放上各种线。所以我决定考虑的是如何测试一个模型，以及如何进行使模型处于危险境地的实验。
At Princeton I got my first sight of Bill Hunter, who was an undergraduate student there. I taught a course to the chemical engineering students on the design of experiments, which he attended, and he came to my notice as being someone who was really interested in statistics. This was maybe 1959 , and at that time I was getting ready to leave and go to Madison. He knew that, and he came to me and said, "I'm going to go to Illinois and take a Master's degree in chemical engineering." He had done a Bachelor's in chemical engineering at Princeton and had done very well. "And then I'd like to come to Madison and be your student in statistics." I said that would be great, and so he did. Bill Hunter and I worked upon that problem of straining the model. We tried to find some diagnostics as to how you can tell not only that the model doesn't fit but also, if it doesn't fit, what's wrong with it. The basic idea was that if a model is true then estimates of constants stay constant apart from estimation errors. So if you run experiments at different levels of the factors, and then from each of these experiments you estimate the constants-like rate constants, for example-then these rate constants should, apart from experimental error, all be the same. If they start changing up and down as one of the factors, say temperature, moves up and down, that means that you haven't allowed for temperature in the right way. ["A useful method for model building” (with W. G. Hunter), Technometrics 4 (1962) 301-318.] So we were interested in diagnostics like that.
在普林斯顿，我第一次见到了比尔·亨特（Bill Hunter），他是那里的一名本科生。我给化学工程系的学生们讲授了一门关于实验设计的课程，他参加了，我注意到他是一个对统计学非常感兴趣的人。那可能是1959年，当时我正准备离开去麦迪逊（Madison）。他知道后，就来找我说：“我要去伊利诺伊州（Illinois）攻读化学工程硕士学位。”他在普林斯顿大学获得了化学工程学士学位，成绩非常好。“然后我想去麦迪逊，成为你们统计学的学生。”我说那太好了，他也这么做了。Bill Hunter和我研究了使模型变形的问题。我们试图找到一些诊断方法，不仅可以判断模型不合适，还可以判断模型不合适时有什么问题。其基本思想是，如果一个模型是正确的，那么除去估计误差，对常数的估计保持不变。所以如果你在不同的因子水平上进行实验，然后从每个实验中估算常数，比如速率常数，那么除了实验误差，这些速率常数都应该是相同的。如果它们随着其中一个因素，比如温度，开始上下变化，那就意味着你没有正确考虑温度。[“建模的有用方法”（与W.G.Hunter合著），Technometrics 4（1962）301-318.]因此我们对这样的诊断很感兴趣。
One of the reasons for my going to Madison was because I like to have graduate students; there were some difficulties at Princeton because there wasn't a statistics department at the time, there was only a math department. But I also wasn't happy about the way that statistics departments were. I thought that statistics departments in some places tended to be too theoretical and in other places tended to be too cookbook. I thought that it might be possible to have a department which would have a proper attitude toward theory but also a proper attitude toward practice, and kind of blend these appropriately.
我去麦迪逊的原因之一是我喜欢研究生;在普林斯顿有一些困难，因为那时还没有统计学系，只有数学学系。但我也不满意统计部门的做法。我认为有些地方的统计部门往往过于理论化，而另一些地方的统计部门往往过于老套。我想可能会有这样一个系既对理论有正确的态度，也对实践有正确的态度，并将它们适当地融合在一起。
DeGroot: Did you go to Madison when the statistics department was just starting up there?
DeGroot: 统计部门刚开始工作时，你去麦迪逊了吗？
Box: They wanted to start a statistics department. A mathematician called Langer, who was the director of the Mathematics Research Center, was going around looking for people for his research center. I think he knew Henry Scheffé quite well, and Henry told him to come talk to me. By that time I did go around and talk to different people at different universities since I had decided to leave Princeton, and I got a number of offers. But the one that I liked was Madison. Essentially what happened at Madison was that they invited me there and told me that they wanted to start a statistics department. They had a thing called the statistics division, which was a very unwieldy collection of anyone who was interested in statistics. So about 150 people turned up for the statistics division meeting from all over - economics, agriculture, engineering, mathematics, and so forth. They asked me to give two talks; one talk was about some technical thing-I forget what it was now-but the other one was what a statistics department should be like. I remember that one thing I said was that I thought the statistics department should have a number of members who had joint appointments, and that these joint appointments should be genuine in the sense that these people really did have an interest in this other subject and were also people who were competent statisticians. I thought it would be difficult but not impossible to find these people. I drew a diagram which looked like a wheel with the statistics department in the middle and then a series of lines going out to the medical school and the engineering school and the business school and so on.
Box:他们想成立一个统计部门。一位名叫兰格（Langer）的数学家，他是数学研究中心的主任，正在四处寻找他的研究中心的人员。我想他很了解Henry Scheffé，Henry 让他来和我谈谈。自从我决定离开普林斯顿以来，我确实四处走动，与不同大学的不同人交谈，并且收到了许多录取通知书。但我喜欢的是麦迪逊。在麦迪逊发生的事情可以基本概括为：他们邀请我到麦迪逊去，同时，他们想开办一个统计部门。他们有一个叫做统计部门的东西，这是一个相当笨拙的代称，囊括了任何对统计感兴趣的人。因此，大约有 150 人参加了统计部门的会议——来自经济、农业、工程、数学等各个领域。他们让我做两次演讲；一次演讲是关于一些技术性的事情——我忘记了现在是什么——但另一次演讲是关于，统计部门应该是什么样的。我记得我提到的一个方面是，我认为统计部门应有一些联合任命的成员，而且这些联合任命应是真实的，因为这些人确实对另一个主题感兴趣并且还有那些称职的统计学家。我认为找到这些人会很困难，但并非不可能。我画了一个像轮子的图，中间是统计系，然后是一系列通往医学院、工程学院和商学院等等的线。
DeGroot: This was a talk you gave before you actually accepted the position?
DeGroot: 这是你在接受这个职位之前做的一次演讲？
Box: Yes. So I gave the talk and the net result was that they said. "We like that. Why don't you come and do it." Well, at Madison I think they have tried very hard to help. It's been a series of things where I've kind of gone up to the door and expected to press very hard and they've said, "Well, it's open. Why don't you come through." Except when I did have ideas which weren't very good, and then I was argued out of them.
Box: 对。所以我做了演讲，最终结果是他们说：“我们喜欢这样。你为什么不来做呢。”嗯，在麦迪逊，我想他们已经尽力帮助了。这是一系列的事情，我走到门口，期待着使出浑身解数，他们说，“好吧，这是开放的。你为什么不过来呢？”除了我确实有一些不太好的想法，然后我被说服了。
DeGroot: Such as what?
DeGroot: 比如什么？
Box: Well, I can't remember any of them. [Laughs] I was very impressed with the quality of the administration at Madison. For example, while I was chairman, Kleene was one of our deans. Kleene was a world famous logician, but he was also a splendid dean. I liked him; we were good friends. But he used to apply his logic when you went to see him, and he might say, "I don't think that's a very good idea for the following reasons. . ." I've gone away from Kleene and sat down and thought about it, and I thought, "Well, by golly, he's right; that doesn't make very much sense." But if you could convince him, then he'd say, “OK, let's try to do that. I don't know if I've got any money but I'll try." So I've been impressed with the administration at Madison, which seems to consist of scholars with abilities in administration.
Box: 嗯，我一个都不记得了。[笑]我对麦迪逊的管理质量印象深刻。例如，当我担任主席时，克莱恩（Kleene）是我们的院长之一。Kleene是世界著名的逻辑学家，但他也是一位杰出的院长。我喜欢他；我们是好朋友。但是当你去看他时，他总是运用他的逻辑，他可能会说，“我认为这不是一个好主意，原因如下……”我离开Kleene，坐下来想了想，我想，“天哪，他是对的，那没有多大意义。”但如果你能说服他，他会说，“好吧，让我们试试。我不知道我有没有钱，但我会试试。”因此，我对麦迪逊的管理印象深刻，那里似乎由具有管理能力的学者组成。
DeGroot: How long were you the chairman?
DeGroot: 你当主席多久了？
Box: In 1960 I started the department, and I was chairman for the first seven years or so. According to Wisconsin tradition, you act like a Head of Department until you've got enough people so you can start rotating the chairmanship, and then you slowly sort of disappear into the distance. And that suited me very well. Afterwards I said, "OK, I've done my bit and I won't do it anymore." And I haven't been chairman since the middle or late 1960s. The department has managed to go on, and by and large, I think it's done quite well. We have tried to have a broadly based department. My philosophy on that is that one should try to get excellent people; concentrate on the people and not so much on the subject. There isn't that large a number of really excellent people, and that's what you want. If you haven't got people who can think for themselves, then you haven't got a very good department. So that was the way it evolved. We've got all kinds. I certainly never thought that I should try to get people who thought the way I thought. In fact, rather the contrary, because it seems to me that out of argument you get closer to the truth. The only thing I was worried about, initially anyway, was whether we would run into factionalism. You know in some places it's become a problem. Although people do have strongly-held views, they have been prepared over the years to recognize that, "Well, that's what I think but it's possible that I might be wrong." It seems to me that one of the most important things anyone ever said was said by Oliver Cromwell: "I beseech you, in the bowels of Christ, think it possible you may be mistaken." Anyway, they seem to have managed not to get much into that factionalism business, which is a deadly thing to happen to anybody.
Box: 1960 年，我创办了这个部门，在最初七年左右的时间里，我一直担任该部门主席。根据威斯康星州的传统，在有足够的人手可以轮换主席职位之前，你会像部门主管一样行事，然后逐渐消失在远处。这非常适合我。后来我说：“好吧，我已经尽力了，我不会再做了。”我从 1960 年代中后期开始就没有担任过董事长。该部门设法继续前进，总的来说，我认为它做得很好。我们试图建立一个基础广泛的部门。我的理念是，应该努力吸引优秀的人；专注于人，而不是专注于过多主题上。因为，真正优秀的人并不很多，他们才是你真正需要的。如果你没有一些能独立思考的人，那么你就没有一个好的部门。所以，这就是它进化的方式。我们有各种各样的优秀人才。当然，我从没想过尝试去找到那些与我想法一样的人。事实上，恰恰相反，因为在我看来，通过争论才会更接近真相。无论如何，最初我唯一担心的是我们是否会遭遇派系之争。你要知道，在某些地方，这已经成为了一个问题。尽管人们确实持有足够强烈的观点，但多年来，他们已经逐渐认识到，“好吧，这就是我的想法，但我可能是错的。”在我看来，奥利弗·克伦威尔（Oliver Cromwell）所说的最重要的话之一是：“我恳求你，在基督的内心里，你可能是错的。”不管怎样，他们似乎没有在派系事务中投入太多，这对任何人来说都是致命的事情。
Some people say you shouldn't hire your own Ph.D.s. I don't think any rule is inviolate. I mean the two Ph.D.s that we did hire at Madison were George Tiao and Bill Hunter, and neither of those did badly. [Laughs] We started this initiative of having joint appointments, and I have a joint appointment in engineering, and Bill had a joint appointment in engineering. We got some courses going in engineering and we've had various research projects with engineering over the years. Then, of course, Norman Draper came to the department quite early, and I worked with Norman on quite a number of things. We wrote the book together on evolutionary operation [Evolutionary Operation-A Statistical Method for Process Improvement. Wiley, New York, 1969.] Evolutionary operation was something that I originally developed when I was at ICI. Norman at one time was also at ICI, in the paints or plastics division. But he came to Madison and has been there a long time. We knew each other in England. He came as a student summer worker in my department at one point when I was at ICI in the early days. After he came to the department in the early 1960s we continued to work on various problems in response surfaces and other things. We've always been good friends, and he's been a strength to the department. Stu Hunter came early on and was a person that helped get the department started.
有些人认为，你不应该雇佣自己的博士。但我认为，没有什么规则是不可违反的。我的意思是，我们在麦迪逊聘请的两位博士是乔治·蒂奥（George Tiao）和比尔·亨特（Bill Hunter），他们都做得很好。[笑]于是我们开始了这项联合任命的计划，我和Bill在工程方面有一个联合任命，Bill在工程方面有一个联合任命。此外，我们还有一些工程方面的课程，这些年来有各种各样的工程研究项目。当然，诺曼·德雷珀（Norman Draper）很早就来到了这个部门，我和Norman一起做了很多事情。我们一起写了一本关于进化操作的书【进化操作——过程改进的统计方法。威利，纽约，1969年。】进化操作是我在ICI时最初开发的东西。Norman曾经也在ICI的油漆或塑料部门工作。但他来到麦迪逊，在那里呆了很长时间。我们在英国认识。我在ICI的早期，他曾在我的系里做过学生暑期工。在他于六十年代初来到该部门后，我们继续研究响应面和其他方面的各种问题。我们一直是好朋友，他是这个部门的一个强项。Stu Hunter来得很早，是帮助该部门起步的人。
The first thing that happened to me when I got to Madison was that I had to teach, and I hadn't really done much teaching. When I was at ICI, I taught design of experiments there and sometimes in a technical college in the evening. And when I was at Princeton I taught a bit, but not very much. So I had to think about what I was going to do. The math department at that point couldn't have been happier to get rid of their statistics courses. They had two or three statistics courses that they taught and apparently they would get some poor guy who was very junior or something and say, "OK, you've got to teach the statistics course." In particular, there was one course called the advanced theory of statistics, and I thought maybe I had better try and teach that. And so I did. In my class I had seven people. One of them was Bill Hunter and another one was George Tiao. I always regarded George Tiao as a sort of weather vane because if George was looking worried, I knew I had done something wrong. So I used to look at the board and think, "What the heck have I done?" It was while I was teaching that advanced theory of statistics course that I really became more interested in Bayes. I've always believed basically in the simplicity of nature, I guess. I mean there's a sign at Princeton over the fireplace which says something like "God is sometimes obscure but he is seldom mean." And I really couldn't imagine that all this tremendous complication that you get into with sampling theory could possibly be necessary. I mean there must be some better way of thinking about it without getting into all that rigamarole. So I started to teach some Bayes, and then I found I was teaching more of it, and so on. I got very interested in it. I was still interested in this nonnormality question, but I thought now that we've got Bayes we could get a whole new look at this robustness thing. Because now you were really looking for robustness the proper way, as it were. I mean previously it had been what 1 called criterion robustness and now it was becoming inference robustness. What I mean by that is that criterion robustness was saying, for example, what would be the significance level if you applied the t test and instead of being a normal distribution it was some other distribution. But then, if it was some other distribution you shouldn't really be applying the t test, and that's automatically taken care of with Bayes. So it just seemed to me that it was very nice and in the first instance interested me because it gave a different, and I thought better, perspective on robustness.
我到麦迪逊时，发生在我身上的第一件事是我必须教书，而我实际上并没有做多少教书的工作。当我在ICI时，我在那里教实验设计，有时晚上在一所技术学院教学。当我在普林斯顿的时候，我教过一点，但不是很多。所以我不得不考虑我要做什么。当时的数学系很高兴能摆脱他们的统计课程。他们教了两三门统计学课程，显然他们会找一个年纪很小的可怜家伙，或者说，“好吧，你得教统计学课程。”特别是，有一门课程叫做高级统计学理论，我想也许我最好试着教这门课。我也这样做了。我班上有七个人。其中一个是Bill Hunter，另一个是George Tiao。我一直把George当作风向标，因为如果他看起来很担心，我就知道我做错了什么。所以我过去常常看着黑板想，“我到底做了什么？”当我教授高级统计理论课程的时候，我真的对贝叶斯更感兴趣了。我想，我一直相信大自然的简单性。我的意思是，普林斯顿大学的壁炉上方有一块牌子，上面写着“上帝有时是模糊的，但他很少卑鄙。”但我真的无法想象，在取样理论中，我们遇到的所有这些庞大的复杂情况、可能都是必要的。我的意思是，一定有更好的方式来思考这个问题，而不必陷入那些繁琐的事情。因此，我开始教一些贝叶斯方法，然后我发现我教的更多，等等。我对它很感兴趣。对这个非正态性问题感兴趣，但我认为，现在我们有了贝叶斯，我们可以对鲁棒性问题有新的认识。因为，现在你真的在用正确的方法寻找鲁棒性。换言之，以前，它被我称为标准鲁棒性，现在它变成了推理鲁棒性。标准鲁棒性指的是，例如，如果应用t检验，显著性水平是多少，不是正态分布，而是其他分布。但是，如果它是其他分布，你就不应该真正应用t测试，这是贝叶斯自动处理的。因此，在我看来，它非常好，首先让我感兴趣，因为它为鲁棒性提供了一个不同的、我认为更好的视角。
Box: Of course, about this time, just as I was leaving Princeton, I had met Gwilym Jenkins and I became extremely interested in time series. So that started a collaboration which went on for many years. Gwilym visited Madison for a year, and I would go to England and stay with him for the summer and do writing. We had decided at some point to write a book. Some of the time he was really quite ill; he had Hodgkin's disease which was first diagnosed when he was with us in Madison in the early 1960s. When we started off, I don't think we had any intention of writing a book; we just got interested in time series. My interest in it was very oblique and pertained to optimum conditions. I had met some problems in my consulting where the maximum was actually moving. I mean the catalyst was decaying, so the temperature that gave you the best yield was changing. And so the question was, how do you pursue a moving maximum. I had this idea of putting a sine wave into the temperature, say, and you look for the sine wave in the yield measurement. You can detect the output sine wave in noise by multiplying by another in phase sine wave and integrating. The integrated signal can then drive the temperature forward or backward depending on whether the first derivative is positive or negative. Well, I tried to get them to build a reactor at Princeton which actually did that so that we could study it, but I never got it built. But at Madison there was a famous chemical engineer called Olaf Hougen. Olaf died only last year at the age of 93. We had a National Science Foundation grant and together with a couple of graduate students under his direction we actually built the automatic optimizer. Gwilym Jenkins became very interested in it and pointed out to me that we now had to contend with a dynamic system. He said, "When you change the temperature by putting a sine wave into it there will be a delay in the system because of the mixing and the reaction, and so you'll get a delayed and attenuated sine wave coming out. You'll get a shift in the phase, and all this kind of stuff. And not only that, but if you don't take proper account of the serial correlation in the noise, you'll get more wrong answers." So that's what we started to work on. We had no intention of working on time series. We were working on optimization to begin with, and then gradually we realized that it was a control problem. Finally we realized that control involved forecasting because you can regard simple control algorithms as forecasting how big the deviation will be at the end of the next interval and then taking an action which cancels out the forecast deviation. We started looking at methods that had been used in forecasting; the ones that seemed to work well were things like exponential smoothing, which implied the importance of particular kinds of nonstationary time series models, which we then worked on.
Box: 当然，大约在这个时候，就在我离开普林斯顿的时候，我遇到了格威琳·詹金斯（Gwilym Jenkins），我对时间序列产生了极大的兴趣。于是开始了一场持续多年的合作。Gwilym在麦迪逊待了一年，我会去英国，和他一起过暑假，写作。我们曾在某个时候决定写一本书。有时他真的病得很重；他患有霍奇金病（一种肿瘤病），这是 1960 年代初，他在麦迪逊和我们在一起时，首次被诊断出来的。当我们开始的时候，我不认为我们有任何写书的打算；我们只是对时间序列感兴趣。我对它的兴趣是间接的，与最佳条件有关。起初，我在咨询中被问到了一些问题，如，最大值实际上在移动。一个常见的实例是，催化剂正在衰变，因此，提供最佳收率的温度也需要相应发生变化。由此产生的问题是，我们要怎样求出这个正在移动的最大值？当时，我有一个想法：把一个正弦波放到温度中，比如说，你在产量测量中寻找正弦波。通过乘以另一个同相正弦波并积分，可以检测噪声中的输出正弦波。然后，根据一阶导数是正还是负，积分信号可以向前或向后驱动温度。我试着让他们在普林斯顿建造一个反应堆，实际上是这样做的，这样我们就可以对它进行研究，但我从来没有建造过。但在麦迪逊有一位著名的化学工程师叫奥拉夫·霍根（Olaf Hougen）。Olaf去年才去世，享年93岁。我们有一个国家科学基金补助金，还有几个研究生在他的指导下，我们实际上建立了自动优化器。Gwilym Jenkins对此非常感兴趣，并向我指出，我们现在必须应对一个动态系统。他说，“当你通过向系统中加入正弦波来改变温度时，由于混合和反应，系统中会出现延迟，因此会出现延迟和衰减的正弦波。会在这一阶段发生变化，诸如此类的事情。不仅如此，如果不考虑噪声中的序列相关性，你会得到更多错误的答案。“这就是我们开始时的研究内容。我们无意研究时间序列，并开始致力于优化，然后，我们逐渐意识到这是一个控制问题。最后，我们认为这种控制还涉及到预测，因为，我们可以将控制算法视为预测下一个间隔结束时的偏差有多大，再采取相应行动消除预测偏差。于是，我们开始研究用于预测的方法；一些看上去很有效的方法包括指数平滑法，这意味着，特定类型的非平稳时间序列模型是相当重要的。我们随后就研究了这些模型。
The book that finally came out [Time Series Analysis, forecasting and control. Holden-Day, San Francisco, 1970 ; 2nd edition, 1976] is sort of backward compared to the way we got in. The control part is at the end and I don't think the actual problem we started with, pursuing the maximum, even gets mentioned in the book. But that's the place we actually started. We worked back and then we realized we had to do something about nonstationary time series in order to do that. So that was the way that book evolved.
最终出版的书[时间序列分析，预测和控制。Holden Day，旧金山，1970；第二版，1976 ]与我们进入的方式相比有些落后。控制部分在最后，我认为我们开始的实际问题，追求最大化，甚至没有在书中提到。但那才是我们真正开始的地方。我们回到过去，然后意识到我们必须对非平稳时间序列做些什么才能做到这一点。这就是这本书的发展方向。
I used to go to England in the summer time and stay with Jenkins, who had a lovely house which was just outside Lancaster. It stood all on its own among the hills; there was a salmon river down in the valley and there were just beautiful walks all around. I remember getting up early in the morning and working with Gwilym. He had his office at one end, and I had the maid's room at the other end-there wasn't any maid, but I had a little apartment of my own. We would go and talk to each other and then we'd go off and work. Then we'd go and talk again, and then I'd go for a walk. Sometimes, if he was well enough, he'd come with me. I still know every walk around there for miles. I can remember one day a thunderstorm came along and I was drenched; and Meg Jenkins, Gwilym's wife, was wandering all around the lanes in a car looking for me with a macintosh to put on. It was fun writing that book.
我曾经在夏天去英国和詹金斯（Jenkins）住在一起，詹金斯在兰开斯特郊外有一栋漂亮的房子。 它独自屹立在群山之中； 山谷中有一条鲑鱼河，周围只有美丽的步道。 我记得我一大早起床和 Gwilym 一起工作。 一端是他的办公室，另一端是我的女仆房间——没有女仆，但我有一间自己的小公寓。 我们会去互相交谈，然后我们会去工作。 然后我们再去谈谈，然后我去散步。 有时，如果他足够好，他会和我一起来。 我仍然知道在那里走几英里。 我记得有一天，一场雷雨来了，我浑身湿透； Gwilym 的妻子 Meg Jenkins 开着一辆汽车在巷子里四处游荡，找我带着 Macintosh。 写那本书很有趣。
我曾经在夏天去英国和詹金斯（Jenkins）住在一起，Jenkins在兰开斯特（Lancaster）郊外有一所漂亮的房子。 它独自屹立在群山之中； 山谷中有一条鲑鱼河，周围只有美丽的步道。 我记得我一大早起床和 Gwilym 一起工作。他在一端有他的办公室，在另一端是我的女佣的房间——但那里没有女佣，但我有一间自己的小公寓。我们会互相交谈，然后就去工作。然后再聊天，然后我去散步。有时，如果他身体好的话，他会和我一起去散步。我仍然知道几英里内的每一次步行。我记得有一天雷雨袭来，我浑身湿透；Gwilym的妻子梅格·詹金斯（Meg Jenkins）开着一辆车在小巷里游荡，找我带着 Macintosh。总之， 写那本书的过程很有趣。【
DeGroot: It had a great impact.
DeGroot: 它产生了巨大的影响。
Box: Yes, and that was somewhat of a surprise to us. We brought together a lot of things which other people had done. I mean, there was some original things in it but we didn't regard it as all that much of a sensation. But anyway, it seemed to start a movement, or at least to accelerate a movement, in time series and that was probably a good thing.
Box: 是的，这让我们有些惊讶。我们把其他人做过的很多事情汇集在一起。我的意思是，里面有一些原创的东西，但我们并不认为这是一种轰动。但无论如何，它似乎在时间序列中启动了一个运动，或者至少加速了一个运动，这可能是一件好事。
DeGroot: What about the book with George Tiao?
DeGroot: 和George Tiao在一起的那本书怎么样？
Box: George was one of the very early graduates at Wisconsin. He actually graduated in the economics department, but he came to the statistics department and we worked together a great deal. George was another person who was a great friend and just a good guy. So we were then, and have remained ever since, good buddies. George was very interested in this Bayesian business and so was I. We were talking to each other and beginning to think about a book, and in the end we put it all together. [Bayesian Inference in Statistical Analysis. Addison-Wesley, Reading, Mass., 1973.] In this case it was a fairly painless thing. Books with me usually take a long time but this one with George didn't take all that much time. Toward the end of the 1960 s we both got leaves of absence and we went to the Harvard Business School for a year, the two of us. We didn't really have any duties there. We went and hid up there and just essentially wrote the book.
Box: George是威斯康星州最早的毕业生之一。他实际上毕业于经济系，但他来到了统计系，我们一起工作了很多。George是另一个很好的朋友，一个好人。 因此，我们当时是好朋友，从那时起一直是好朋友。George和我都对贝叶斯学派很感兴趣。我们互相交谈，开始思考一本书，最后我们把它放在一起。[统计分析中的贝叶斯推断。Addison Wesley，马萨诸塞州雷丁市，1973年]在这种情况下，这是一件相当轻松的事情。和我一起的写书通常需要很长时间，但这本和George在一起的书没有花那么多时间。20世纪60年代末，我们两人都请假去哈佛商学院学习了一年。我们在那里真的没有任何职责。我们去了，藏在那里基本上写了这本书。
The house I lived in there was a great rambling old thing like the old dark house in a Boris Karloff-type film. We used to work there quite a bit together. So we got that book about Bayes done fairly fast.
我住在那里的房子是一个非常杂乱的老房子，就像鲍里斯·卡洛夫（Boris Karloff）类型电影中的老黑房子一样。我们过去常常一起在那里工作。所以我们很快就完成了关于贝叶斯的书。
DeGroot: Who do you feel have been the major professional influences on your career? Are there others besides some of the people you have already mentioned?
DeGroot:你认为谁对你的职业生涯产生了主要的影响？除了你提到的一些人之外，还有其他人吗？
Box: Well, I had only a very brief contact with Fisher, but certainly in the early days what I was reading was mostly Fisherian. So I got a big dose of Fisher early on, and got a very strong feeling of almost reverence for his writings. Another very important influence was George Barnard. When I was still a student in London, I would go to the Royal Statistical Society meetings. Early on I met George Barnard, who was then a Professor at Imperial College. George immediately befriended me and was a very great help to me. George is a wonderful person in the sense that I would say I didn't understand about such and such a thing, and he'd say, "Well, there are only two things you have to really understand about that." Then he would explain what they were, and something which previously had been a great mystery to me suddenly became very clear. We quickly became very close friends as well, and have been ever since. I think George has had a tremendous influence not only on me but on many many people; he's clear-minded and he has a very good perception of what statistics is all about. Another person that certainly had an influence on my career early on was Bartlett. I don't know if I was lucky or what, but as l've already said, ICI took a very liberal attitude toward what I did. In particular, I was very close to Manchester, where Bartlett was, and if I wanted to take off and go and listen to some lectures or attend seminars or something, I didn't even need to tell anyone I was going; I just went. So quickly I got to know Bartlett. I would go to the seminars at Manchester and there was always a tea and he'd be encouraging and welcoming, and asking me what I was doing and things like that. I could talk to him. Bartlett was a statistician who I particularly found very easy to follow. I attended his classes on multivariate analysis. He had a very strong geometrical inclination and I found that just what I wanted. I could see these things and understand them better that way, and then the algebra seemed to follow automatically. I felt I had a deeper understanding because of geometry. I've always felt that if I could see something geometrically, I really understood it in a deeper way than I could understand it any other way.
Box: 嗯，我只和Fisher有过一次非常短暂的接触，但在早期我读到的大部分著作都是Fisher式的。所以我很早就接触到了Fisher，对他的作品产生了一种非常强烈的敬意。另一个非常重要的影响是乔治·巴纳德（George Barnard）。当我还是伦敦的学生时，我会去参加皇家统计学会的会议。早些时候，我遇到了George Barnard，他当时是帝国理工学院的教授。George立即成为我的朋友，对我帮助很大。George是一个了不起的人，如果我说，“我不理解这样那样的事情.."，他会说，“好吧，关于这件事，只有两件事你必须真正理解。”然后他会解释它们是什么。此时，某些以前对我来说是一个巨大的谜的事情，就会突然变得异常清楚。很快，我们也成为了非常亲密的朋友，并且从那以后一直都是。我认为，George不仅对我，还对许多人都产生了巨大影响；他头脑清晰，对统计数据的理解极为出测。另一个对我早期职业生涯有影响的人是巴特利特（Bartlett）。我不知道我是否幸运，但正如我已经说过的，ICI对我所做的事情持非常开放的态度。特别是，我离Bartlett所在的曼彻斯特非常近，如果我想离开这里去听讲座或参加研讨会之类的，我甚至不需要告诉任何人我要去哪里；我只需要直接去。很快，我就认识了Bartlett。那时我常去曼彻斯特参加研讨会，那里总会有一杯茶，他会鼓励和欢迎我，问我在做什么等等。我可以和他交流。Bartlett是一位统计学家，我发现他的话总是让人容易理解。后来，我报名了他的多元分析课程。他有很强的几何倾向，而我发现这正是我想要的，因为它能让我更好地理解一些概念，几何之后，代数的思想就自动跟着来了。此后，我认为自己对几何有了更深的理解。我一直觉得，如果能从几何角度看东西，人们对它的理解会比其他任何方式都要深刻。
In the early days, Cullumbine and Gaddum and Cameron were very encouraging to me. I didn't have a very good opinion of myself in those days; certainly, I didn't think that I could do anything very much. My family was very poor and a university education cost money, so I wasn't thinking very much in terms of even that early on. And then I gradually got used to the idea that I could perhaps do something at the university. But certainly the idea of ever being a professor or anything like that never occurred to me. I think I needed some encouragement at that stage and these people gave it to me. George Barnard in particular is a wonderful person because he is completely without any feeling of the "You're a student, I'm a professor" type of thing. I can remember from the very earliest times, I was always his friend. And it was always exciting to be with George because he'd say, "Where are you going now?" And I'd say, "Well, nowhere in particular." And he'd say, "Well, I've got my van outside so let's go and have dinner somewhere," or "Why don't you come home and we'll eat there." He'd stop the van and go and get a bottle of wine or something on the way home. It just felt very good, and it was a surprise to me to discover that some of the ideas I had were of interest to someone like George Barnard.
在早期，卡伦宾（Cullumbine）、加德姆（Gaddum）和卡梅伦（Cameron）对我来说是极具鼓舞性的的。在那些日子里，我对自己的认识不太乐观；当然，我不认为我能真正做些什么。我的家庭非常贫穷，而大学教育需要钱，所以，在早期我并没有过多考虑这个问题。后来，我逐渐习惯了这样的想法：也许我可以在大学里做点什么。当然，我从来没有想过成为一名教授或类似的职位。我想在那个阶段我需要一些鼓励，这些人给了我鼓励。George Barnard尤其是一个了不起的人，因为他完全没有“你是学生，我是教授”之类的感觉。我记得从最早的时候起，我就一直是他的朋友。和George在一起总是令人兴奋的，因为他会说，“你现在要去哪里？”我会说，“好吧，没什么特别的。”他会说，“好吧，我的货车在外面，我们去什么地方吃晚饭吧，”或者“你为什么不回家，我们在那里吃饭。”在回家的路上，他会停下货车，去喝一瓶酒或别的什么。我感觉很好，我很惊讶地发现我的一些想法对像George Barnard这样的人很感兴趣。
DeGroot: Were you fairly unique in being an industrial statistician in England at that time?
DeGroot: 你当时在英国做工业统计学家是不是很独特？
Box: No, I don't think so. I think a number of people went into industry. I thought, "Well, I know something about chemistry and I'm getting qualified in statistics, so what would I do?" The chemical industry seemed appropriate, and in England at that time the chemical industry meant ICI. It pretty much dominated the whole place.
Box: 不，我不这么认为。我想很多人都进入了这个行业。我想，“嗯，我懂一些化学知识，而且我在统计学方面也越来越合格，那我该怎么办呢？”化学工业似乎是合适的，而在当时的英国，化学工业指的是ICI。它几乎控制了整个地方。
DeGroot: You mentioned your childhood just in passing. Tell me a little bit about your childhood, and how you came to go to the university.
DeGroot: 你顺便提到了你的童年。告诉我一些关于你的童年，以及你是如何进入大学的。
Box: My grandfather was a merchant who had a shop that was something like a hardware store. It was in a place called Gravesend in England. It's about 20 miles east of London on the Thames. At one time my grandfather was quite prosperous. He had a family of boys and a couple of girls. The eldest boy was Bertie. In those days it wasn't a question of money, and my Uncle Bertie went to Oxford and did very well. He went into the church and became a Professor of Theology. He was an expert on Greek and Hebrew and stuff, and actually wrote things for the Encyclopedia Britannica. I had another uncle who came to the United States and became somebody who was quite important on the railway and lived near Chicago. My father was the youngest son, and at about this point my Grandfather's business went bang. He didn't go bankrupt; he paid off all his debts, but there wasn't any money. So my father never got a chance to get much of an education. He was a person whom I loved very dearly, and he was a very interesting man. But he didn't have a chance, really. So he worked in a shop, as sort of a shop assistant, I guess. I did very well at the elementary school I went to. The only way that you could get out of that rut in those days was to win scholarships, and there weren't very many of them; but I did. I went to a grammar school, and then from grammar school I went to a polytechnic and studied chemistry.
Box: 我祖父是个商人，他开了一家类似五金店的商店。那是在英国一个叫格雷夫森德（Gravesend）的地方。它在伦敦以东约20英里的泰晤士河上。我祖父曾一度相当富裕。他有一个男孩和两个女孩的家庭。最大的男孩是伯蒂（Bertie）。在那些日子里，这不是钱的问题，我的Bertie伯伯去了牛津，成绩很好。他进了教堂，成为了一名神学教授。他是希腊语和希伯来语等方面的专家，实际上为《大英百科全书》写了一些东西。我还有一个伯伯，他来到美国，成为铁路上的重要人物，住在芝加哥附近。我父亲是最小的儿子，大约在这个时候，我祖父的生意一帆风顺。他没有破产【译者注：这句上下文有些矛盾】；他还清了所有的债务，但没钱了。所以我父亲从来没有机会接受过很多教育。他是一个我深爱的人，他是一个非常有趣的人。但他没有机会，真的。所以他在一家商店工作，我猜他是个店员。我在上小学时成绩很好。在那些日子里，你能摆脱这种乏味生活的唯一方法就是获得奖学金，而奖学金并不多；但我做到了。我上了一所文法学校，然后从文法学校上了一所理工学院，学习化学。
DeGroot: Where was that?
DeGroot: 那是哪里？
Box: That was in Kent. I was studying chemistry there when the war broke out. so then after that, as I told you, I went to London University.
Box: 那是在肯特（Kent）。战争爆发时我正在那里学习化学。那之后，正如我告诉你的，我去了伦敦大学。
DeGroot: Tell me a little about your relationship with Fisher. You said that you met him again later on.
DeGroot: 告诉我一些你和Fisher的关系。你说你后来又见到他了。
Box: I don't think I ever had a terribly close relationship with Fisher, although I knew him quite well later on. I never knew that he thought well of me, for example, except that I would sometimes hear it from somebody else. There was a paper-I think it was the paper with Sigurd Andersen-in which I took a certain point of view about something and Yates said that he thought that wasn't right. And I heard later on from George Barnard, who was there, that when this came up in a discussion Fisher said, "No, I think George is right about that." But he never actually said anything like that to me. The kind of thing that would happen was that I was at a meeting one day and Fisher just came over to me and said, I'm putting you up for the ISI. Is that all right?" And just walked away again. Now presumably if Fisher wanted to put someone up for the International Statistical Institute, he must have thought well of them. But he never said so.
Box: 我不认为我曾经和Fisher有过非常亲密的关系，尽管我后来很了解他。比如说，我从来不知道他对我的评价很好，只是有时候我会听到别人这么说。有一篇论文，我认为是关于西古德·安徒生（Sigurd Andersen）的论文，我对某些事情持某种观点，而耶茨（Yates）说他认为这是不对的。后来我从在场的George Barnard那里听说，在一次讨论中提到这一点时，Fisher说，“不，我认为George是对的。”但他从来没有对我说过这样的话。可能会发生的事情是，有一天我在开会，Fisher走过来对我说，我要把你推荐给ISI。 可以吗? ”然后又走开了。现在想必，如果Fisher想为国际统计研究所推荐某人，他一定对他们考虑得很好。但他从来没有这样说过。
George Box as a young child with his elder brother and sister
图5:乔治·博克斯小时候和他的哥哥姐姐在一起
I never got into a big fight with him over anything, although many people who knew him did. I've heard stories that there were times that he got unreasonable and blew up, but he never did with me. We may have come very close, I think, once or twice. When I got interested in Bayes I remember the point that we stuck at was about flat priors, because he said to me that knowing that things are equally probable, and not knowing what the probabilities are, are two totally different things. I realized at that point that I'd better leave the subject there, and I did. [Laughs] I remember that when I started getting interested in time series I told him, and he sounded rather disappointed and said, "Oh I don't think there's much in that." He wasn't all that enthusiastic about time series. [Laughs]
我从来没有因为任何事情和他大吵过一架，尽管很多认识他的人都这么做了。我曾听说过这样的故事，有几次他变得无理取闹，脾气暴躁，但他从来没有对我这样做过。我想，有一两次我们可能已经非常接近了。 当我开始对贝叶斯感兴趣的时候，我记得我们停留在平坦先验【译者注：flat priors不知道如何翻译】上，因为他对我说，知道事物的概率相等，和不知道概率是什么，是完全不同的两件事。我意识到我最好把这个话题打住，我也这样做了。[笑]我记得当我开始对时间序列感兴趣时，我告诉了他，他听起来很失望，说：“哦，我觉得这没什么。”他对时间序列并不那么热情。[笑]
DeGroot: You were married to his daughter, Joan. How did you meet her?
DeGroot: 你和他的女儿琼（Joan）结婚了。你是怎么认识她的？
Box: Well, it hadn't anything to do with knowing Fisher. What happened was that when I went over to Princeton and started the Statistical Techniques Research Group, we didn't have a secretary. Around about then, John Tukey was going to England and was going to see Fisher about something. Joan was there and he happened to mention that there was a job for a secretary. Joan had taken some secretarial training, and she decided to come over and that's how we met.
Box: 嗯，这和认识Fisher没有任何关系。当时发生的事情是，当我去普林斯顿开始统计技术研究小组时，我们没有秘书。大约在那个时候，John Tukey要去英格兰，要去跟Fisher谈些事情。Joan在那里，他碰巧提到有一份秘书的工作。琼接受了一些秘书培训，她决定过来，我们就是这样认识的。
DeGroot: Tell me about your current research interests.
DeGroot: 告诉我你目前的研究兴趣。
Box: For the last three years or so, I've become extremely interested in this quality movement. I was always very interested in design of experiments and industrial statistics; that was my first love, so to speak. And now there seems to be a new movement. Quite honestly, I thought that the old kind of quality control was a bit of a bore. I mean there wasn't anything very exciting about it. But the new ideas are different. The idea is to try to design products and processes so that you don't have a quality problem further down the line. You should be making things that just don't go wrong and should be using experimental design to help do that. It seems to me to be a fascinating idea. Taguchi is a very controversial name but I think that his quality engineering ideas are very important——ideas of using experimental design to reduce variance, to get products robust to environment variation, and robust to component variation. The whole situation is confused by the fact that Taguchi's statistics is often not very good. In fact, a statistician reading Taguchi might dismiss it because the statistics is pretty bad. But that can be fixed up, and there are some good ideas there.
Box:在过去三年左右的时间里，我对这场高质量的运动非常感兴趣。我一直对实验设计和工业统计非常感兴趣；可以说，那是我的初恋。现在似乎出现了一场新的运动。老实说，我认为传统的质量控制有点令人厌烦。我的意思是，它没有什么令人兴奋的地方。但新的想法是不同的，我们的想法是尝试设计产品和流程，这样你就不会再有质量问题了。你应该做一些不会出错的事情，并且应该使用实验设计来帮助你做到这一点。在我看来，这是一个迷人的想法。田式（Taguchi）是一个非常有争议的名字，但我认为他的质量工程思想对于使用实验设计来减少差异、使产品对环境变化和部件变化具有鲁棒性非常重要。Taguchi的统计数据往往不是很好，这一事实使整个情况变得混乱。事实上，一个阅读Taguchi的统计学家可能会忽略它，因为统计数据非常糟糕。但这是可以解决的，有一些好主意。
And there are some new problems in experimental design and in the analysis of data which come out of this thing, some new theoretical problems. For example, as soon as you start to consider the analysis of the mean and the standard deviation (or some other measures of location and spread) simultaneously, the problem about transformation becomes very important; because if you're, so to speak, in the "wrong" metric then dependence between location and spread can produce "pseudo" dispersion effects induced by location effects. If you were in the "right" metric, they wouldn't be there. So there are interesting problems in analysis. There are also interesting problems in experimental design. For example, the "inner" and "outer" arrays to accommodate design variables and environmental variables can involve prohibitively large numbers of experiments. It may be possible to reduce those numbers by employing somewhat new ideas about fractionation and so forth.
在实验设计和由此产生的数据分析中，存在着一些新的问题，一些新的理论问题。例如，一旦开始考虑均值和标准偏差（或其他位置和扩展的其他度量）的分析，转换问题就变得非常重要；因为，可以说，如果你使用了“错误”的度量，那么位置和传播之间的依赖性可能会产生由位置效应引起的“伪”分散效应。如果你在“正确”的尺度，他们就不会在那里。所以在分析中有一些有趣的问题。在实验设计中也有一些有趣的问题。例如，容纳设计变量和环境变量的“内部”和“外部”数组可能涉及大量的实验。通过采用一些关于分馏等的新想法，可以减少这些数量。
DeGroot: Have you been working with particular industries?
DeGroot: 你曾在特定行业工作过吗？
Box: We have a National Science Foundation grant which is joint between AT&T and Bell Labs. Last summer we made a trip to Japan together, for example, some people from Bell Labs and Jeff Wu and I from the University of Wisconsin.
Box:我们有一个国家科学基金资助，它是在AT&T和贝尔实验室之间的合作项目。去年夏天我们一起去日本旅行，比如贝尔实验室和Jeff Wu和我从威斯康星大学来的一些人。
DeGroot: Do you have any books currently underway?
DeGroot: 你有没有正在出版的书？
Box: There's a book that's just come out on response surfaces which Norman Draper and I had been writing for a very long time. [Empirical Model Building and Response Surfaces. Wiley, New York, 1987.] It finally got done. There is quite a lot in there about transformations, which I think is an important subject.
Box: 我和Norman Draper已经写了很长时间了，有一本书刚刚在回应面【译者注：surfaces的翻译不太准确】上出版。[经验模型构建和响应面，威利，纽约，1987年]终于完成了。其中有很多关于转换的内容，我认为这是一个重要的主题。
DeGroot: Your interest in transformations goes way back, too. There was at least one well-known paper on that topic in which you were involved.
DeGroot:您对转换的兴趣也可以追溯到很久以前。至少有一篇关于这个话题的著名论文你也参与其中。
Box: Yes. The story about that goes back to the time when I was still in England, and David Cox and I were both on the research committee of the Royal Statistical Society. Various people remarked on the fact that Box and Cox were both on the committee and said that we should write a paper together. My recollection is that either David said to me or I said to David, "You know, perhaps we ought to take them up on that." And so, "Yes, OK, let's do that. And what should it be about?" Well, we both knew the story about Box and Cox. This is a story about Box living in a room during the day and Cox living in the same room during the night, and neither of them knew that the landlady was giving the room to two people and getting two rents rather than one. So we said, "Well, obviously the thing to write about is transformations." And that was all we had to begin with. [Laughs] We did something about it. We got as far as the part about the Jacobian, and if you've read that paper ["An analysis of transformations," J. Roy. Statist. Soc. Ser.
Box: 对这个故事可以追溯到我还在英国的时候，我和大卫·考克斯（David Cox）都是英国皇家统计学会研究委员会的成员。许多人评论说，Box和Cox都是委员会成员，并说我们应该一起写一篇论文。我记得要么是大卫对我说，要么是我对大卫说，“你知道，也许我们应该向他们提出这个问题。”然后，“是的，好吧，让我们这样做。那应该是关于什么的？”嗯，我们都知道关于Box和Cox的故事。这是一个关于Box白天住在一个房间里，Cox晚上住在同一个房间里的故事，他们都不知道房东太太把房间给了两个人，并得到了两份而不是一份租金。所以我们说，“很明显，我们要写的是转换。”这就是我们开始要做的。[笑]我们做了些什么。我们已经谈到了关于雅可比矩阵的部分，如果你读过那篇文章[《变换分析》，J.Roy.Statist.Soc.Ser.B26（1964）211-252]，你就会知道这部分有点棘手，甚至有争议。我们不太知道如何处理这一点，所以它被搁置一边。时光流逝，岁月流逝；我去了普林斯顿，然后去了麦迪逊。我在麦迪逊呆了一段时间后，我记得大卫给我写了一封信，说，“嘿，你知道我们在做什么吗？我想如果我们走这条路，我们就能做到。”然后我回信说，“是的，我想是的，”然后这个怎么样，那个怎么样，等等。于是我们又开始合作，最后我们把论文发表了。
DeGroot: A classic paper. So it really did start with just the authors' names and built up from there.
DeGroot: 一篇经典的论文。因此，它确实是从作者的名字开始，并从那里建立起来的。
Box: Yes. I think we also had sort of a slight conspiracy because I think we both felt it was a bit funny about the Box and Cox notion. David was keener on the likelihood approach and I was keener on the Bayesian approach. So we put both in, and when the discussion came up various people said, "Perhaps the authors would like to say whether they both agree on this" and we were careful not to say. So there was sort of a slight Box-Coxish uncertainty about the whole thing which we thought was amusing.
Box: 对。我想我们也有点小阴谋，因为我想我们都觉得Box和Cox的概念有点滑稽。David更热衷于似然方法，而我更热衷于贝叶斯方法。所以我们把两者都放进去，当讨论开始时，很多人说，“也许作者想说他们是否都同意这个观点”，我们小心翼翼地不说。所以整个事情有一种Box-Coxish式的不确定性，我们觉得很有趣。
DeGroot: You have received many honors during your career. Are there some that you particularly value or appreciate more than others?
DeGroot: 在你的职业生涯中，你获得了许多荣誉。是否有一些你比其他人更看重或欣赏？
Box: The one that I value the most is the Royal Society.
Box: 我最看重的是皇家学会。
DeGroot: Becoming a Fellow of the Royal Society.
DeGroot: 成为皇家学会会员。
Box: Yes. I don't know why that is exactly; I suppose it's my English background. It just seemed to me to be something that's pretty special.
Box:对我不知道这到底是为什么；我想这是我的英语背景吧。在我看来，这是一件非常特别的事情。
DeGroot: Even in America we recognize it as such.
DeGroot: 即使在美国，我们也承认这一点。
Box: It was somewhat of a surprise, but anyway...
Box: 这有点令人惊讶，但无论如何...
DeGroot: How does that come about?
DeGroot: 这是怎么发生的？
Box: Well, your name gets on the list. It stays on for a certain number of years, and at some point if enough people decide they want you to be a Fellow, then I guess you become a Fellow. But the thing that is most impressive about it, as I found when I went to the Royal Society to be made a Fellow, is that there's a book which has all the names of the Fellows ever since the Society was founded by Charles II around 1660 . There were about six other people that were being made Fellows at the same time as me, and the librarian brought out this book and took us through it page by page. There are 6000 names in the book, from the time of its inception to the present day. So he said, "Well, there's Isaac Newton and this is Charles Darwin...." Isaac Newton had a very small signature, as l recall. So you go through, and if there's anyone that you are particularly interested in you can look him up. He took us through page by page, and it took us the best part of an hour to get through. The librarian had these old-fashioned pens with real ink and a nib to sign with, and he made us practice to make sure that we didn't blot the book. Each time there's a new monarch they start a new page, and whoever is the king or the queen signs the top of that page. In more recent years it's become an illuminated page. But there's just this one book.
Box: 嗯，你的名字在名单上。它会持续若干年，在某个时刻，如果有足够多的人决定让你成为一个成员，那么我猜你会成为一个成员。但最令人印象深刻的是，当我去皇家学会成为一名会员时，我发现有一本书记载了自1660年左右查尔斯（Charles）二世建立该学会以来所有会员的名字。当时，大约有六个人和我同时成为研究员，图书管理员拿出这本书，带我们一页一页地阅读。书中有6000个名字，从创始到现在。所以他说，“这是艾萨克·牛顿（Isaac Newton），这是查尔斯·达尔文（Charles Darwin）……”艾萨克·牛顿有一个很小的签名，我记得。所以，如果有任何你特别感兴趣的人，你可以去找他。他带我们一页一页地看，我们花了大半个小时才看完。图书管理员有这些老式的钢笔，上面有真墨水，还有一个笔尖可以签字，他让我们练习确保我们不会弄脏书。每当有新的君主，他们都会翻开新的一页，无论谁是国王或王后，都会在这一页的顶部签名。近几年来，它已成为一个发光的页面。但只有这一本书。
DeGroot: Was there a formal induction ceremony?
DeGroot: 有正式的入职典礼吗？
Box: Well, your name is called and you go up and sign the book, and then there's a mace, a gold mace, about four feet long given by Charles to the Society. So you have to put your hand over the mace and take hold of the president's hand, and then he inducts you into the Society. That's sort of an impressive ceremony. When the president looked over the top of his glasses at me and said the magic words I did feel that that was something special.
Box: 有人叫你的名字，你上前在书上签名，然后有一个权杖，一个金权杖，大约四英尺长，是Charles送给协会的。因此，你必须把手放在权杖上，握住会长的手，然后他引导你进入协会。那是一个令人印象深刻的仪式。当会长从眼睛上方望向我并说出这些神奇的话时，我确实觉得这是一件特别的事情。
DeGroot: What is your assessment of the current health of the field of statistics? Where do you see it heading, and where do you think it should be heading?
DeGroot: 您如何评价当前统计领域的健康状况? 你认为它将走向何方，你认为它应该走向何方?
Box: Well, I'm very encouraged. Looking back over a period of years, there does seem to be a greater readiness to realize that innovation very often comes from some kind of interaction between theory and practice. And more people who have some real understanding of statistical theory are becoming interested in real problems. I do believe that the really new things in statistics very often come in the first place from some application, but you do have to have people who know enough about science as well as statistics so that they can understand what they've got, so to speak. I worry sometimes because although there are more people like this than there were, we could do with more who are prepared to get their hands dirty. Fisher once told me about knowing that you know, and knowing that you don't know, and not knowing you know, and not knowing you don't know. The last category is the one to avoid, of course, because there's no way of escaping from it. Sometimes people who know a lot of statistical theory think they understand statistics when they really don't and they are liable to believe they can give flip answers when somebody comes with a problem. They don't always realize that the person with the problem may not know very much about statistics, but he may know a great deal about medicine or about economics or about production, or whatever area the problem is in. They have to take a very humble attitude and listen very carefully to what the person has to tell them in order to be of any use at all. I still think there's not enough appreciation that one has to do that, and not necessarily think in terms of standard solutions.
Box: 我很受鼓舞。回顾过去几年，人们似乎更愿意认识到，创新往往来自理论与实践之间的某种互动。越来越多对统计理论有真正理解的人开始对实际问题感兴趣。我确实相信统计学中真正的新事物往往首先来自于一些应用，但你确实需要有足够的科学和统计学知识的人这样他们才能理解他们所得到的，可以这么说。 我有时会担心，因为虽然像这样的人比以前多了，但我们可以有更多准备动手的人。Fisher曾经告诉我知道你知道，知道你不知道，不知道你知道，不知道你不知道。当然，最后一类是要避免的，因为无法逃避。有时，知道很多统计理论的人认为他们理解统计，而实际上他们并不理解，当有人遇到问题时，他们很容易相信自己能给出草率的答案。他们并不总是意识到有问题的人可能不太懂统计学，但他可能对医学、经济学、生产或问题所在的任何领域都了解很多。他们必须采取非常谦虚的态度，非常仔细地倾听对方所说的话，这样才会有用。我仍然认为没有足够的认识到人们必须这样做，而不一定要考虑标准的解决方案。
DeGroot: Is there some way we could improve our educational programs, our training of students, to increase that appreciation?
DeGroot: 我们有什么方法可以改进我们的教育计划，我们对学生的培训，以增加这种欣赏？
Box: Well, I think that the more we try to get students exposed to real consulting experiences the better. Since I've been at Madison I've run a thing called a Monday night beer session. This is simply a session which takes place at my house, where people come with a problem and we just kick it around.
Box: 我认为，我们越努力让学生接触到真正的咨询经验，效果就越好。自从我来到麦迪逊，我就开了个周一晚上的啤酒会。 这是一个简单的会议，在我家里举行，人们带着一个问题来，我们只是讨论它【译者注：这句话不太通顺】。
DeGroot: Who comes with the problem?
DeGroot: 谁来解决这个问题？
Box: Recently it's become sort of a quality seminar, or a quality beer session, but up until recently it could be anything. One of the graduate students would usually be in charge of the seminar and they would be on the lookout for people with problems, perhaps from engineering or perhaps from the medical school, or wherever it might be. And they'd say, "Well, this one looks like one we could kick around in the Monday night beer session." So they would come and talk, and we would ask them if they'd explain various things a little more, and try to figure it out. Probably the thing would go on for two and a half hours or three hours, from about seven-ish to about ten-ish, and we'd have a little beer in the middle and at the beginning, and little breaks here and there.
Box: 最近，它变成了一个质量研讨会，或者一个质量啤酒会议，但直到最近它还可以是任何东西。其中一名研究生通常会负责研讨会，他们会密切关注有问题的人，可能来自工程学院，也可能来自医学院，或者其他任何地方。他们会说，“嗯，这个看起来像是我们可以在周一晚上的啤酒会议上玩的。”所以他们会来聊天，我们会问他们是否能多解释一些事情，并试着弄清楚。大概会持续两个半小时或三个小时，从七点到十点左右，中间和开始的时候我们会喝点啤酒，几乎都不休息【译者注：little breaks here and there，翻译得不太准确】。
DeGroot: That's a nice idea.
DeGroot: 这是个好主意。
Box: In the end, we'd get some understanding for what this chap was trying to do. There is no credit for this session. It's purely a voluntary thing and anyone can come. They can come once or they can come every time, or whatever they want, and anybody on the faculty can come if they want to. Whatever the topic is going to be is up on the notice board. It does seem as if these sessions help students get the right idea Sometimes one of the graduate students would become very interested in a problem and say he wants to give this guy some more help and work with him. So we get something going and then, perhaps two or three months later, they come back again and say, "We've got to this point now," and everyone is sort of interested in how they are getting on, and did that work out, and things like that.
Box:最后我们会对这个家伙试图去做的事情有所了解。本课程没有学分，这纯粹是自愿性的，任何人都可以来。他们可以来一次，也可以每次来，或者他们想来什么时候来都行，任何教职人员都可以来，只要他们愿意。无论主题是什么，都在布告栏上。似乎这些课程确实能帮助学生们获得正确的想法，有时一个研究生会对一个问题非常感兴趣，并说他想给这个家伙更多的帮助，和他一起工作。所以我们做了一些事情，然后，也许两三个月后，他们再次回来说，“我们现在已经到了这一点，”每个人都对他们的进展感兴趣，他们做了什么，诸如此类的事情。
DeGroot: That's very good. The difficulty is that not every department has a George Box to point the way.
DeGroot: 那太好了。困难在于，并非每个部门都有George Box指路。
Box: I don't think there's any magic about it. The only thing is to try to persuade people not to jump in too quickly with solutions. I mean, let's hear all about it. Let's ask the right questions. Let's not be saying, "Oh yes, you should do this and that," too early on. We should be trying to make sure we really understand what the fellow is trying to do. It takes a good deal of time to do that. It's interesting because a good statistician gets to know everybody else's business, and you find there are all kinds of fascinating things going on in the university that you didn't know about.
Box: 我不认为这有什么魔力。唯一要做的就是说服人们不要太快地提出解决方案。我是说，让我们听听，让我们提出正确的问题。我们不要过早地说：“哦，是的，你应该做这个和那个。”。我们应该努力确保我们真正理解这个家伙想要做什么。这样做需要很多时间。这很有趣，因为一个好的统计学家可以了解其他人的业务，你会发现在大学里有很多你不知道的有趣的事情。
DeGroot: Sure. That's really the fun of being a statistician-you get to learn about so many different areas. You mentioned Bayes several times during this conversation. Do you still regard yourself as a Bayesian?
DeGroot: 当然。 这就是做统计学家的乐趣所在——你可以了解这么多不同的领域。 你在谈话中多次提到贝叶斯。 你还认为自己是贝叶斯学派吗?
Box: Well, I think it's an unfortunate idea, this idea of being a Bayesian. It makes it sound like a Christian or something like that, a unique thing. I don't know why it is that people like to have a oneness about things. I mean there are many important things that depend on twoness. And there are things that depend on threeness, and so on. So why we should always be striving for oneness, I don't know. And, of course, if you're looking for oneness when you've got twoness, you may make a number of errors. For example, if Martians came down and they didn't know that there were men and women on the planet, and were trying to explain everyone's behavior in terms of a single sex, they would have some very difficult problems to explain. Perhaps I can say this-I've said it in print but I'll say it again. I believe that there are not one but two quite different types of inference necessary to scientific investigation. One is like addition, in which you are adding a model to the data. You're saying, given that this is the model and given that these data are generated by this model, then taking the two together what can we say about this situation. That problem is, I think, best treated by Bayes. But it doesn't say anything about whether the model is appropriate for the data. There's a quite different thing, which instead of a model plus data, is a model minus data from which residual analysis, tests of fit, diagnostics, and so forth comes. I think this part really has to be based on an idea of repeated sampling because that's the only way that in any absolute sense you can discredit the model. So I'm only half Bayesian, in the sense that I think that the best way to do the first bit-combine data with the model-is to do it with Bayes. But you could argue that the other part is even more important, because the other part is the more creative part. When you look at residuals or you look at discrepancies between what you thought and what happened, that's the part where you say, "Aha, it's clear that what I was thinking was wrong, and it's wrong in the following kinds of ways; which suggest to me (or suggest to this guy I'm working with, who's an engineer and understands these things) that perhaps this is what's happening." And so we have to go and do something else, and perhaps run experiments on variables that we have never even considered before. So in a sense this is the only part where something really new is created. Everything else is just deduction-finding things which were latent in what you already knew. The creative part is looking (or getting your scientific partner to look) at the discrepancies; which you hope may ignite the tinder which is the knowledge that he has about chemistry or engineering or whatever it is that you're trying to do. I think that statisticians haven't thought about this enough. And to the extent they haven't, they have not served science very well because this is the most important node in the scientific process.
Box: 我认为，成为一个贝叶斯学派的想法，听上去是一种很不幸的想法。因为它听起来像是基督徒之类的很单一化的东西。 我不太理解，为什么人们总期望事物是有同一性的。我的意思是，有很多重要的事都依赖二重性。还有一些事依赖于三重性，等等。所以，我们为什么要一直努力追求同一性呢？我不知道。当然，如果你在寻找一的同时又有了二，你可能会犯很多错误。例如，如果火星人来到地球上，他们不知道地球上有男人和女人，并且试图用一种性别来解释每个人的行为，那么他们将有一些很难解释的问题。也许——我已经说过了，但我会再说一遍。我相信，科学研究所需要的不是一种而是两种截然不同的推理。一种类似于加法，我们将模型添加到数据中。也许你会说，假设这是一个模型，假设这些数据是由这个模型生成的，那么把这两者结合起来，我们能对这种情况说些什么呢？ 我认为贝叶斯能最完美地解决这个问题， 但它没有说明这一模型是否适合这些数据。这是一个完全不同的问题，它不是一个可以增加数据的模型，而是一个需要减去数据的模型，对应的方法包括残差分析，拟合测试，诊断等等。我认为，这一部分真的必须基于重复抽样的思想，因为这是唯一一种在任何绝对意义上都可以怀疑模型的方法。所以，我只是半个贝叶斯学派。从某种意义上说，我认为，把数据和模型结合起来的最好方法就是用贝叶斯。但是，你可以说另一部分更重要，因为另一部分更具创造性。当你看到残差或者你看到你的想法和发生的事情之间的差异时，你会说，“啊哈，很明显我所想的是错的，在以下几种方面是错的；这对我来说是错的。这对我(或者对我的同事，他是一名工程师，了解这些事情)意味着，也许这就是正在发生的事情。”因此，我们必须去做一些其他的事情，也许在我们以前从未考虑过的变量上进行实验。因此，从某种意义上说，这是唯一一个创造出新东西的地方。 其他的一切都只是演绎，寻找隐藏在你已经知道的东西里的东西。 创造性的部分是寻找（或者让你的科学伙伴看看）差异，你希望这些差异会点燃一个火种，那就是他对化学或工程学的知识，或者你正在尝试做的任何事情。我认为统计学家对这一点考虑得不够。在某种程度上，他们没有很好地为科学服务，因为这是科学过程中最重要的节点。
DeGroot: Let's shift gears a little bit. What do you like to do when you are not doing statistics?
DeGroot: 让我们稍微换挡吧。当你不做统计时，你喜欢做什么？
Box: I like to walk. I'm sort of an assistant gardener. My wife is a gardener, but I help her a little bit. And I sometimes write songs and I watch movies. I don't do anything very energetic. I like to swim.
Box:我喜欢走路。我算是个助理园丁。我妻子是个园丁，但我帮了她一点忙。我有时写歌，看电影。我不做任何精力充沛的事情。我喜欢游泳。
DeGroot: Well, I've heard at least one of your songs on various occasions, "There's No Theorem Like Bayes' Theorem." How did that come about?
DeGroot:我在不同的场合听过你的一首歌，“没有比贝叶斯定理更好的定理。”这是怎么发生的？
Box: We have a Christmas party at Madison, and that's become a tradition too. Except for a couple of years, it's always been at my house. The party is actually put on by the students and we lend our house to them. They collect a little money from everyone, and they put on the party. The big event of the evening is when the students put on a skit and then the faculty put on a skit. And also there are songs. So around about November one starts to think about whether we are going to have a song that year. Norman Draper has also written some good songs. There was one he wrote that was very good, "The Chairman's Lot Is Not a Happy One" from "The Policeman's Lot Is Not a Happy One." And at one point we had three exchairmen all singing "The Chairman's Lot Is Not a Happy One." But anyway, one year I guess I was thinking about Bayes, and it suddenly struck me about "no theorem like Bayes' theorem." And then everytime I'd be driving some place in my car that I'd driven before, so it was sort of a boring thing, I'd think of another little verse. And as soon as I got out of the car, I'd write it down.
Box:我们在麦迪逊有一个圣诞晚会，这也成为了一个传统。除了这几年，它一直在我家。这个聚会实际上是学生们举办的，我们把房子借给他们。他们从每个人身上收了一点钱，然后举办了聚会。当晚的大事是学生们表演一个短剧，然后老师们表演一个短剧。还有一些歌曲。所以大约在11月左右，人们开始考虑我们是否会在那一年有一首歌。Norman Draper也写了一些不错的歌曲。有一个他写的很好，是《警察的命运不快乐》中的《主席的命运不快乐》。有一次我们有三个执行主席都在唱“主席的命运不快乐”。但无论如何，有一年我想我在想贝斯，突然我想到了“没有比贝叶斯定理更好的定理”。然后每次我开车去我以前开过的地方，那是一件很无聊的事情，我就会想另一首小诗。【译者注：这句话不太通顺】 我一下车，就会把它写下来。
DeGroot: Is it still evolving or is it fixed now?
DeGroot: 它还在发展还是现在已经修复？
Box: Oh, it's fixed. I got fed up with that one, but we've done some others. There's one about robustness.
Box: 哦，修好了。我受够了那个，但我们也做了一些其他的。有一个是关于鲁棒性的。
DeGroot: Really? Would you tell it to me?
DeGroot: 真正地你能告诉我吗？
Box: Well, I can remember,
Box: 嗯，我记得，
John does it.
Hogg does it.
Every statistician who's in vogue does it.
Let's do it.
Let's go robust.
There's one bit I like particularly.
We had our nice observations,
Circumcised from both ends,
Removing all data on which our theory depends.
John这样做【译者注：这句翻译的不太通顺】。
Hogg这样做【译者注：这句翻译的不太通顺】。
每个潮流的统计学家都这么干。
让我们都来做。
一起做鲁棒性的工作。
有一点我特喜欢。
我们很好的观察，
从两头去切割，
删除我们的理论所依赖的所有数据。
DeGroot: [Laughs] That's great.... What does the future hold for George Box?
DeGroot: [笑]太好了。。。。George Box的未来是什么？
Box: Well, we started this Center for Quality at Madison, and I'm the director of research. I'm very happy working with graduate students. The idea of our center is that we think that the quality bit is not just statistics; it's statistics, engineering, and business, particularly organizational development. So what I'd like to be able to do is to help evolve a response to the Japanese initiative which takes statistics into account but isn't solely statistics. I think there's a lot of people in industry at the moment who are very interested in the question, for example, of how to re-educate their engineers; what should they teach them. I don't think that we know, not for sure. We have to think it all out. We'd like simple and efficient techniques. When they're simple to understand for the engineer, it doesn't necessarily mean that there's not a lot of computing behind them, for example. We've got to use the computer and we've got to use a lot of visual things, things that come up on the computer screen that the engineer can look at and understand. So what we've been doing is trying to figure all that out. I've got some very good students, very gung ho. They're very excited about all this, and we have a great time together. I think one of the most pleasant things in my whole life has been my interaction with graduate students. I don't know how many Ph.D. students I've had, but quite a few. So everywhere I go, I keep meeting these people. I'm sure you do, too, and it's very nice. There's a sort of bond with these people; you've been through fire. There was a time when you thought this bloody thing would never work out; but in the end something happened that we finally got something, so it was all right. But it makes a bond, and it's wonderful to see these guys and their wives and children and so forth. I'm always surprised. When somebody graduates, I always think, "Gee, that guy. We're never going to get anyone quite as good as that again." Or sometimes, not as likeable again. And yet, there are always some more. There are always some new people.
Box: 我们在麦迪逊建立了质量中心，我是研究主任。我很高兴和研究生一起工作。我们中心的理念是，我们认为质量比特【译者注：quality bit的翻译感觉有问题】不仅仅是统计数据；它包括统计、工程和商业，尤其是组织发展。所以我想做的是帮助制定一个对日本倡议的回应，该倡议考虑了统计数据，但不仅仅是统计数据。 我想现在业界有很多人都对这个问题很感兴趣，例如，如何重新教育他们的工程师；他们应该教他们什么。我不认为我们知道，也不确定。我们必须想清楚这一切。我们想要简单有效的技术。例如，当工程师很容易理解它们时，并不一定意味着它们背后没有太多的计算。我们必须使用计算机，我们必须使用许多可视化的东西，这些东西出现在计算机屏幕上，工程师可以看到和理解。所以我们一直在努力想办法解决这些问题。我有一些非常好的学生，非常努力。他们对这一切都很兴奋，我们在一起玩得很开心。我认为我一生中最愉快的事情之一就是与研究生的互动。我不知道我有多少博士生，但有很多。所以无论我走到哪里，我都会遇到这些人。我相信你也喜欢，而且非常好。与这些人有某种联系，并一起经历过战火【译者注：这句采用了意译，可能不太合适】。曾经有一段时间，你认为这该死的事情永远不会成功；但是最后发生了一些事情，我们终于得到了一些东西，所以一切都很好。但这是一种纽带，看到这些家伙和他们的妻子孩子等等，真是太好了。我总是很惊讶。当有人毕业时，我总是想，“哎呀，那个家伙。我们再也找不到像他那样优秀的人了。”或者有时候，再也不那么讨人喜欢了。然而，总会有更多的。总有一些新人。
William W. Scherkenbach, W. Edwards Deming, and George Box at Ford Motor Company
William W. Scherkenbach, W·爱德华兹·戴明和乔治·博克斯在福特汽车公司
DeGroot: I don't hear any mention of retirement in there.
DeGroot: 我没听到有人提到退休。
Box: Oh no. I don't know what I'd do if I retired. 1 can't imagine doing anything else but what I do. I really like what I do, so I guess I'll just hang on as long as I can.
Box: 哦，不，我不知道如果我退休了该怎么办。除了我所做的，我无法想象我还能做什么。我真的很喜欢我的工作，所以我想我会尽可能地坚持下去。
DeGroot: Thank you, George.
DeGroot: 谢谢你，George。
