Nancy Reid, Nancy Reid is Professor of Statistics Statistics Department, University of Toronto, 100 St. George Street, Toronto, Ontario, Canada M5S 1A1.
Nancy Reid，Nancy Reid，多伦多大学统计统计系教授，安大略多伦多市圣乔治街100号，加拿大M5S 1A1。
Abstract.
David Roxbee Cox was born in Birmingham on July 15,1924 He attended Handsworth Grammar School and St. John's College, Cambridge. From 1944 to 1946 he was employed at the Royal Aircraft Establishment, and from 1946 to 1950 he was employed at the Wool Industries Research Association in Leeds. He obtained his Ph.D. from the University of Leeds in 1949. He was an assistant lecturer at the University of Cambridge from 1950 to 1955, and then visited the United States for 15 months, mainly at the University of North Carolina. From 1956 to 1966 he was Reader and then Professor of Statistics at Birkbeck College, London, and from 1966 to 1988 was Professor of Statistics at Imperial College, London. In 1988 he moved to Oxford to become the Warden of Nuffield College, a post from which he retired on July 31,1994 . He is now an Honorary Fellow of Nuffield College and a member of the Department of Statistics at the University of Oxford. In 1947 he married Joyce Drummond. They have four children and two grandchildren.
David Roxbee Cox 于1924年7月15日出生于伯明翰，他就读于剑桥汉兹沃思文法学校(Handsworth Grammar School)和圣约翰学院(St. John's College)。1944年至1946年，他受雇于皇家飞机公司(the Royal Aircraft Establishment)，1946年至1950年，他受雇于利兹羊毛工业研究协会(the Wool Industries Research Association in Leeds)。他获得了博士学位。来自1949利兹大学。他是1950至1955年间在剑桥大学的助理讲师，然后在美国访问了15个月，主要是在北卡罗来那大学。从1956年到1966年，他是伦敦伯克贝克学院的读者和统计学教授，从1966年到1988年，他是伦敦帝国理工学院的统计学教授。1988年，他搬到牛津大学，成为纳菲尔德学院的院长，1994年7月31日，他从该学院退休。他现在是Nuffield学院的名誉研究员，也是牛津大学统计系的成员。1947年，他与Joyce Drummon结婚。他们有四个孩子和两个孙子。
Among his many honours, Sir David has received to date 10 honorary doctorates, an honorary fellowship from St. John's College, Cambridge, and honorary membership in four international academies. He has been awarded the Guy medals in Silver (1961) and Gold (1973) by the Royal Statistical Society. He was elected Fellow of the Royal Society of London in 1973 and was knighted in 1985. In 1990 he won the Kettering prize and gold medal for cancer research.
在他的众多荣誉中，大卫爵士迄今已获得10个荣誉博士学位、剑桥圣约翰学院的荣誉奖学金以及四所国际学院的荣誉会员资格。他被英国皇家统计学会授予盖伊银牌（1961年）和金牌（1973年）。1973年，他被选为伦敦皇家学会会员，1985年被授予爵位。1990年，他获得凯特林奖和癌症研究金奖。
He has authored or coauthored over 200 papers and 15 books. A list of his publications through 1988 is included in Hinkley, Reid and Snell (1991). From 1966 through 1991 he was the editor of Biometrika. He has supervised, encouraged and collaborated with innumerable students, postdoctoral fellows and colleagues. He has served as president of the Bernoulli Society and the Royal Statistical Society, and he is presidentCox：elect of the International Statistical Institute.
他撰写或合著了200多篇论文和15本书。辛克利、里德和斯奈尔（1991年）收录了他1988年的出版物清单。从1966年到1991年，他是Biometrika的编辑。他监督、鼓励并与无数学生、博士后研究员和同事合作。他曾担任伯努利学会和皇家统计学会主席，并当选为国际统计学会主席。
This conversation took place in Sir David's office at Nuffield College on October 26 and 27,1993.
这次谈话于1993年10月26日和27日在纳菲尔德学院大卫爵士的办公室进行。
Reid ：I'd like to ask you about your work early in your career at the Wool Industries Research Association. What kind of a place was it, and what kind of position had you there?
Reid ：我想问一下你职业生涯早期在羊毛工业研究协会的工作情况。那是一个什么样的地方，你在那里的职位是什么？
Cox： Well, Henry Daniels has described it a bit in a recent interview (Whittle, 1993 ). It was a type of organization that was very common in the U.K. at that time, funded by government and by money obtained from a levy on the industry, to do basic research on problems to do with the industry; and it had at that time a remarkable director who simply had the idea that you get people and largely let them get on with it, with encouragement. I went there because with the previous job I had I'd worked on a problem to do with the strength of spot-welded joints and I just happened to read in the library a marvellous related paper by Henry Daniels. Then as I went out of the library there was an advertisement of a job to go and work with Henry. The war had just ended and I was free to move, so instead of going back to Cambridge to complete my BA, which f'd normally have done, went to work with him.
Cox： 亨利·丹尼尔斯在最近的一次采访中对此进行了描述（惠特尔，1993）。这是一种在英国很常见的组织，当时由政府出资，并从该行业的税收中获得资金，对与工业有关的问题进行基础研究；当时有一位杰出的导演，他只是有一个想法，那就是你能吸引人们，并在很大程度上让他们在鼓励下继续工作。我去那里是因为在我以前的工作中，我研究了一个与点焊接头强度有关的问题，我碰巧在图书馆里读到了亨利·丹尼尔斯（Henry Daniels）的一篇精彩的相关论文。然后，当我走出图书馆时，看到一则招聘广告，招聘我和亨利一起工作。战争刚刚结束，我可以自由地搬家了，所以我没有回到剑桥完成我的文学学士学位（通常f都会完成），而是和他一起工作。
In wool textiles, you see, you've got everything from the biology and the nutrition of the sheep through the chemistry and physics of various processes, to the operational research side, the engineering side and the economic side. So there was an enormous range of problems and extremely good people working there from whom I learned an enormous amount. I did some design of experiments and some analysis of data. People would come along with their split split plot experiments, or their analysis of covariance, and they'd say, "Oh, there's no hurry, tomorrow afternoon will do." I hadn't the remotest idea of how to analyse these things. There weren't really any books so one had to struggle to find out what to do. In addition I worked on more basic, longer term, problems. In fact I did a lot of work which was never published: more applied mathematics; theory of elasticity, large extension elasticity theory, things like that. I wasn't terribly good at it, but I did do a great deal of work.
在羊毛纺织品方面，你看，从绵羊的生物学和营养，到各种过程的化学和物理，到运筹学方面，工程方面和经济方面，无所不包。因此，那里存在着大量的问题和非常优秀的工作人员，我从他们那里学到了很多东西。我做了一些实验设计和数据分析。人们会带着他们的裂区实验或协方差分析来，他们会说，“哦，不用急，明天下午就可以了。”我一点也不知道如何分析这些东西。实际上没有什么书，所以人们不得不努力找出该做什么。此外，我还研究了更基本、更长期的问题。事实上，我做了很多从未发表过的工作：更多的应用数学；弹性理论，大延伸弹性理论，诸如此类的东西。我不太擅长，但我确实做了很多工作。
Reid ：Did you save all your papers?
Reid ：你把所有的文件都存起来了吗？
Cox： Yes, they're around here somewhere. [Looking around vaguely.]
Cox： 是的，他们就在附近的某个地方。[模糊地环顾四周。]
Reid ：So the work in your paper "The theory of drafting wool slivers: I" [1], that was more or less part of your job.
Reid ：因此，你的论文《羊毛条牵伸理论：I》[1]中的工作或多或少是你工作的一部分。
Cox： Yes.
Cox： 对
Reid ：Plus no doubt a few evenings here and there.
Reid ：毫无疑问，这里和那里还有几个晚上。
Cox： [Laughs.]
Cox： [笑.]
Reid ：Are parts 2 and 3 somewhere?
Reid ：第二部分和第三部分在什么地方吗？
Cox： No; that's an important moral, you see, which I should have learned from Henry Daniels. His paper is "Theory of strength of bundles part 1," 1944, Proceedings of the Royal Society, and part 2 is still anxiously awaited.
Cox： 不你看，这是一个重要的道德准则，我应该从亨利·丹尼尔斯那里学到。他的论文是1944年的《捆绑力量理论第一部分》，皇家学会学报，第二部分仍在焦急等待。
Reid ：Presumably you got your Ph.D. at the University of Leeds because it was nearby?
Reid ：大概你拿到了博士学位。在利兹大学，因为它就在附近？
Cox： Right. At that time anybody who worked in the city of Leeds and had a degree from anywhere could register for a Ph.D.
Cox： 正当当时，任何在利兹工作并在任何地方获得学位的人都可以注册博士。
Reid ：Was there any particular advantage to you at that time to have a Ph.D.? Why did you go to the trouble?
Reid ：你当时有没有什么特别的优势来获得博士学位。？你为什么要找麻烦？
Cox： I think Henry must have suggested it. I suspect (perhaps it's an arrogant thing to say but I don't mean it that way) that the director of research thought this would tie me to Leeds for a few years, which in a sense it did.
Cox： 我想一定是亨利建议的。我怀疑（也许这是一个傲慢的说法，但我不是那个意思）研究总监认为这会把我和利兹联系几年，从某种意义上说确实如此。
Reid ：Was your "wool" paper [1] your dissertation for your Ph.D?
Reid ：你的“羊毛”论文是你的博士论文吗？
Cox： That was a bit of it, that was a chapter basically. There was also a chapter on long-range dependence, and various other things.
Cox： 这是一点，这基本上是一个章节。还有一章是关于长期依赖和其他各种事情的。
Reid ：Your book on statistics and textiles [2] went to a fifth edition, in 1960
Reid ：你关于统计和纺织品的书在1960年出版了第五版
Cox： Oh, but that was just an account of very elementary methods for quality control.
Cox： 哦，但那只是对质量控制基本方法的说明。
Fig. 1. At Storrs University, Connecticut, February 1994, to be videotaped for the American Statistical Association's distinguished lecturer series.
图1。1994年2月在康涅狄格州斯托尔斯大学，为美国统计协会的杰出讲师系列录制。
Reid ：Yes, but it's very elegant. There was recently a suggestion that we should have a list of the good cookbooks, cookery books you call them over here, and I was thinking it should be on the list.
Reid ：是的，但它很优雅。最近有人建议我们应该有一份好的烹饪书的清单，你们称之为这里的烹饪书，我想它应该在清单上。
What about your time at Cambridge as a student: did you learn any statistics?
作为一名学生，你在剑桥的时光怎么样：你学过什么统计数据吗？
Cox： The short answer is no. Harold Jeffreys gave a short course which was intriguing, but almost totally incomprehensible. I sat in on a rather longer course that J. O. Irwin gave, where he was essentially reading Wishart's lecture notes because Wishart was away on war service. This calculated the moments about the origin, about the mean, the factorial moments, the cumulants and the factorial cumulants, of a considerable number of known distributions. It wasn't terribly inspiring. Although in a certain way it was a very systematic course, and there was more to it than I just described.
Cox： 简而言之，答案是否定的。哈罗德·杰弗里斯（Harold Jeffreys）的课程很短，很有趣，但几乎完全无法理解。我旁听了J.O.Irwin教授的一门较长的课程，他主要是在读Wishart的讲稿，因为Wishart外出服役了。这计算了大量已知分布的原点、均值、阶乘矩、累积量和阶乘累积量的矩。这并不太鼓舞人心。虽然在某种程度上，这是一门非常系统的课程，而且比我刚才描述的要多。
During the war people came round to the universities and decided whether you went into the army or air force or went to a research establishment. There was an enormous shortage of statisticians, and the notion was that anyone doing a mathematics degree and doing reasonably well knew something about statistics or could learn it very quickly-a totally false assumption. I was sent as a statistician a' though I didn't know any statistics.
战争期间，人们来到大学，决定你是进入陆军还是空军，还是进入研究机构。统计学家严重短缺，这种观念认为，任何拥有数学学位并做得相当好的人都对统计有一定的了解，或者可以很快学会统计——这是完全错误的假设。我被派去当统计员，虽然我不知道任何统计数字。
Reid ：So you were sent to the Royal Aircraft Es tablishment as part of your draft work or war commission. How is it that you have an MA after just two years as an undergraduate?
Reid ：所以你被送到皇家飞机公司，作为你征兵工作或战争委员会的一部分。你怎么会在仅仅读了两年本科之后就获得了文学硕士学位？
Cox： Under the war regulations, you see, you could get a degree in two years. Then Oxford and Cambridge have this strange system: once you've got a Bachelor's degree you can get a Master's degree automatically a certain number of years after your BA.
Cox： 根据战争条例，你看，你可以在两年内拿到学位。牛津和剑桥有一个奇怪的体系：一旦你获得学士学位，你可以在获得学士学位后的若干年内自动获得硕士学位。
Reid ：What kind of problems did you work on in the Royal Aircraft Establishment?
Reid ：你在皇家飞机公司处理过什么问题？
Cox： I was in a department of structural and mechanical engineering: it was mostly strengths of materials. They did testing components of aircraft and to a certain extent testing whole pieces of aircraft: they used to break aircraft wings. But there were also miscellaneous other things like where German rockets landed, and a big thing on aircraft accident rates.
Cox： 我在结构和机械工程系工作：主要是材料的强度。他们测试了飞机的部件，并在一定程度上测试了飞机的整体部件：他们用来折断飞机的机翼。但也有其他杂七杂八的事情，如德国火箭降落的地点，以及飞机事故率的一个大问题。
Reid ：Were there other statisticians working there?
Reid ：还有其他统计员在那里工作吗？
Cox： No.
Cox： 不
Reid ：The opportunities that you had to be so involved with applications in these early years seem to me to have influenced all your later work.
Reid ：在我看来，你早年参与申请的机会影响了你以后的工作。
Cox： I was involved in all these applications but it wasn't what I was interested in. I was interested in mathematics. I wanted to be either an analyst or possibly a mathematical physicist-I didn't want to be a statistician. I mean I don't regret being one, but that was what I was interested in, for quite a while.
Cox： 我参与了所有这些应用程序，但这不是我感兴趣的。我对数学感兴趣。我想成为一名分析师，或者可能是一名数学物理学家——我不想成为一名统计学家。我的意思是，我并不后悔成为一个这样的人，但这正是我感兴趣的一段时间。
Reid ：Where did that come from, that interest?
Reid：那是从哪里来的，那种兴趣？
Cox： This is part of the Cambridge tradition; and I went to lectures by several great mathematicians. On the whole not very good lecturers, but inspiring.
Cox： 这是剑桥传统的一部分；我去听了几位伟大数学家的讲座。总的来说，不是很好的讲师，而是鼓舞人心的。
Reid ：Did you always have a notion that you would get this practical work out of the way and get back to mathematical physics?
Reid ：你是否一直有这样一种想法，你会把这项实际工作抛到脑后，回到数学物理上来？
Cox： Oh, as I got older, I got more and more interested in applications. But as late as 1955, certainly as late as 1950 , I would have still seriously considered giving up statistics. Partly because the career opportunities in statistics at that time seemed terrible. There was this burst of activity during the war and immediately following, but at one point there were only two or three professorships of statistics in the whole of the country and the possibility of ever becoming a full professor in the university system seemed very remote indeed.
Cox： 哦，随着年龄的增长，我对应用越来越感兴趣。但直到1955年，当然是1950年，我仍然会认真考虑放弃统计。部分原因是当时统计行业的就业机会似乎很糟糕。在战争期间和战争之后都有这样的活动爆发，但在某一点上，全国只有两三名统计学教授，成为大学系统正式教授的可能性似乎非常渺茫。
Reid ：Was that your goal at that time?
Reid ：那是你当时的目标吗？ Cox： [Laughs.] No, no, not at all. The goal was to survive, get enough to eat, somewhere to live; survive. No. no, no: that wasn't a goal at all. I never really thought much about goals. Except one thing I would really like to do is to make a contribution to probability and the foundations of quantum mechanics. But I don't think I'll ever do that. Partly because it's too difficult. Primarily because it's too difficult.
Cox： [笑]不，不，一点也不。目标是生存，获得足够的食物，有地方住；幸存不，不，不：那根本不是一个进球。我从来没有认真考虑过进球。除了我真正想做的一件事，就是为概率论和量子力学的基础做出贡献。但我想我永远不会那样做。部分原因是太难了。主要是因为太难了。
Reid ：You left the Wool Industries Research Association to go to Cambridge as a lecturer?
Reid ：你离开羊毛工业研究协会去剑桥当讲师？
Cox： Assistant lecturer.
Cox： 助理讲师。
Reid ：What was Cambridge like then, going back as a lecturer?
Reid ：那时候剑桥是什么样子的，回去当讲师？
Cox： Scientifically, fantastic. Personally, terrible.
Cox： 科学地说，太棒了。就我个人而言，很糟糕。
Reid ：Please elaborate.
Reid ：请详细说明。
Cox： Well, first of all, scientifically, I mean, marvellous, absolutely first class students; and excellent colleagues: Wishart, who was not really very active scientifically, was a very good director of the laboratory. Daniels, Anscombe, Lindley, and then lots of visitors. From that point it was absolutely marvellous. Personally, well, one was very badly paid. My wife and I had two young children and certainly couldn't afford a car, couldn't really heat the house properly and so on. I had a post that was limited to five years and that was unsettling and very discouraging.
Cox：首先，科学上，我的意思是，非常好，绝对一流的学生；还有优秀的同事：威斯哈特在科学上并不十分活跃，他是一位非常出色的实验室主任。丹尼尔斯，安斯科姆，林德利，还有很多游客。从那一点上说，这绝对是了不起的。就我个人而言，有一个薪水很低。我妻子和我有两个小孩，当然买不起汽车，也不能给房子供暖等等。我有一个职位被限制在五年内，这是令人不安和非常沮丧的。
Reid ：How did you come to have such a terminal post?
Reid ：你怎么会有这样一个终点站？
Cox： That's all there was available.
Cox： 这就是所有可用的。
Reid ：Even for the best and the brightest?
Reid ：即使是最优秀和最聪明的人？
Cox： Basically any post that became available in mathematics that I might have been appointed to would have been filled by a pure mathematician. I didn't take it personally, but it was just unsettling. At the end of the five years it seemed I had really no option but to go to the United States, which was an extremely fortunate thing to do.
Cox： 基本上，任何我可能被任命的数学职位都会由一位纯粹的数学家来填补。我并不认为这是我个人的事，但这只是令人不安。五年后，我似乎真的别无选择，只能去美国，这是一件非常幸运的事情。
FIG.
图$2。$这幅由马丁·詹宁斯（Martin Jennings）创作的铜像由牛津大学纳菲尔德学院的研究员委托制作，陈列在学院的高级休息室。
As I say, scientifically it was fantastic and yet going to the United States was a revelation. Not just the physical standard of living, but the enthusiasm of the people was very encouraging. There were even people that had read papers that I wrote. For example, I gave a lecture at Princeton on conditioning; if P'd given that lecture in London, oh, I don't mean people wouldn't have been interested, pleasant and encouraging, but there wouldn't have been any sense of vigour.
正如我所说的，从科学上讲，这是一次奇妙的经历，然而去美国却是一次启示。不仅是物质生活水平，而且人们的热情非常令人鼓舞。甚至有人读过我写的论文。例如，我在普林斯顿做了一个关于条件反射的讲座；如果P在伦敦演讲，哦，我不是说人们不会感兴趣、愉快和鼓励，但也不会有任何活力。
Reid ：Yes, I think I know what you mean.
Reid ：是的，我想我知道你的意思。
Cox： You know what I mean I'm sure; and it was more noticeable in those days. Without going into the sociology of it, I think the attitude in the United States then was that everything is possible. Now a sort of British cynicism is to some extent apparent and people in the United States see the difficulties rather more than they did then.
Cox： 你知道我的意思，我确信；在那些日子里，它更引人注目。如果不深入社会学，我认为美国当时的态度是一切皆有可能。现在，某种程度上英国人的愤世嫉俗是显而易见的，美国人比他们当时更能看到困难。
Reid ：It was economically a tremendously rich time for the United States.
Reid ：对美国来说，这是一个经济上极其富裕的时期。
Cox： Yes, that's right; and people were enormously helpful and pleasant and encouraging.
Cox： 是的，没错；人们非常乐于助人，令人愉快，令人鼓舞。
Reid ：You mentioned once that you might have stayed.
Reid ：你曾经提到你可能会留下来。
Cox： Yes, very easily.
Cox： 是的，很容易。
Reid ：How close did you come?
Reid ：你离得有多近？
Cox： Oh, very close.
Cox： 哦，非常接近。
Reid ：And how did you come to come back?
Reid ：你是怎么回来的？
Cox： Well, suddenly there started to be all sorts of jobs appearing. I had accepted a job in the U.S. and then was offered the Birkbeck job, which was in many ways very nice indeed. For the next few years, I had a succession of very tempting offers in the U.S. to which Joyce and I could have very easily succumbed-which would have been marvellous, I'm sure. I don't in any way whatever regret staying in the U.K., but I'm sure I'd have been very happy in many places in the United States.
Cox： 突然，各种各样的工作出现了。我在美国接受了一份工作，然后得到了伯克贝克的工作，这在很多方面都非常好。在接下来的几年里，我在美国收到了一系列非常诱人的邀请，乔伊斯和我本可以很容易地接受这些邀请，我相信这会是一件了不起的事情。我不后悔在英国呆在哪里，但我相信在美国很多地方我都会很开心。
Reid ：Your 1958 paper on conditioning [6] was presented when you were in North Carolina?
Reid ：你1958年关于调节的论文[6]是你在北卡罗来纳州时发表的？
Cox： Well, it was actually presented in Princeton. I was visiting North Carolina at the time.
Cox： 嗯，它实际上是在普林斯顿上演的。当时我正在访问北卡罗来纳州。
Reid ：Was it considered controversial by the audience, do you remember?
Reid ：你还记得吗，观众们认为它有争议吗？
Cox： Yes. It's the only occasion I've ever given a lecture where people came up and were still talking to me about two and a half hours later-Allan Birnbaum in particular.
Cox： 对这是我做过的唯一一次演讲，人们来到我面前，并且在两个半小时后仍在与我交谈，尤其是艾伦·伯恩鲍姆（Allan Birnbaum）。
Reid ：Talking about?
Reid ：谈论什么？
Cox： The implications of conditioning, although there's a lot more in the paper than the conditioning, things about the difference between
Cox： 条件作用的含义，虽然在论文中比条件作用有更多的内容，但是关于$p$值和假设检验之间的差异，例如。
Reid ：Your weighing machine example introduced in that paper is possibly the only thing about conditional inference that everybody at least thinks they understand. Why is conditional inference so difficult?
Reid ：那篇文章中介绍的称重机示例可能是关于条件推理的唯一一件事，至少每个人都认为他们理解。为什么条件推理如此困难？
Cox： Well, there are two aspects, aren't there: is it conceptually difficult, and is it mathematically difficult. It seems to me that conceptually it's not difficult, it's a very clear consequence of wanting to make long-run probability calculations relevant to the interpretation of sets of data. Of using physical probability epistemologically. Of calculating confidence coefficients and significance levels whose interpretation is based on long-run frequency but which you want to be relevant to a particular set of data. How does the long run become relevant to a particular set of data? Well, by being suitably conditioned. The arguments for this seem to me absolutely overwhelming; but to convert that idea into definitions, formulae, algorithms and so forth, then it gets much more difficult. I think that's the point at which people find it hard going. I find it hard going. [Pause.] Yet it's strange, isn't it, that an enormous number of peo. ple must learn about statistics and perhaps even do Ph.D.'s in statistics and not think about this at all.
Cox： 嗯，有两个方面，不是吗：概念上的困难，数学上的困难。在我看来，从概念上讲，这并不困难，这是一个非常明显的结果，因为我想进行与数据集解释相关的长期概率计算。在认识论上使用物理概率。计算置信系数和显著性水平，其解释基于长期频率，但您希望与特定数据集相关。长期运行如何与特定数据集相关？好吧，通过适当的调节。在我看来，这方面的论据绝对压倒一切；但要将这个想法转化为定义、公式、算法等等，就变得困难得多。我想这就是人们觉得很难做到的地方。我觉得这很难。[停顿]但奇怪的是，这么多人。ple必须学习统计学，甚至可以攻读统计学博士学位，而不要去想这些。
Reid ：Well, I guess that might partly be the American training.
Reid ：嗯，我想部分原因可能是美国的训练。
Cox： Oh, I don't think it's as nationalistic as that.
Cox： 哦，我不认为这是民族主义。
Reid ：Was your paper written to make a statement against decision theoretic formulations?
Reid ：你的论文是为了发表反对决策论公式的声明吗？
Cox： I think partly, yes. I don't exactly recall how it came about but the background, more or less, is that in the 1950 's, particularly in Cambridge, there was intense interest in these philosophical issues. Fisher gave three famous public lectures (well, one was a vote of thanks to somebody else and the two others were lectures) in which he put forward the ideas that to some extent appeared in his last book. There was an enormous amount of discussion of this. Of course Don Fraser was active in these things at that time as well. Then I got to the United States and I was invited to give I think it was a special IMS lecture, or one of these things, and I hadn't the remotest idea of what to talk about. I thought, well, perhaps this would be a good topic. With the weighing machine example, you see,
Cox： 我想部分是的。我不清楚它是如何产生的，但背景或多或少是，在20世纪50年代，特别是在剑桥，人们对这些哲学问题产生了浓厚的兴趣。费舍尔做了三次著名的公开演讲（一次是对其他人的感谢，另外两次是演讲），他在演讲中提出了在某种程度上出现在他上一本书中的观点。对此进行了大量的讨论。当然，当时唐·弗雷泽也积极参与这些事情。然后我到了美国，我被邀请做一个特别的IMS讲座，或者是其中的一个，我一点也不知道该谈什么。我想，也许这是个好话题。以称重机为例，你看，$I$试图将论点简化为其绝对最简单的情况：这是一个教育学的例子，试图将论点简化为最简单的形式。
Reid ：And when you get to the examples that are somehow not so clear-cut, getting back to your com- ment that vou want the long-run freauency to be relevant to the data at hand: it seems terribly difficult to mathematize that.
Reid ：当你谈到一些不那么清晰的例子时，回到你的观点，你希望长期的频率与手头的数据相关：似乎很难将其数学化。
Cox： Yes.
Cox： 对
Reid ：Is that just the state of affairs or are we all missing something?
Reid ：这只是事态发展还是我们都遗漏了什么？
Cox： Oh, I expect we're all missing something, but I don't know what it is. [Laughs.]
Cox： 哦，我想我们都错过了什么，但我不知道是什么。[笑]
Another aspect is to minimize differences from Bayesian arguments, particularly with standardized priors, which is how I first learned about statistics in Jeffreys' lectures. I feel the differences between the various schools of inference are emphasized too much and the similarities not enough. Bayesians will achieve this conditioning automatically, so as compared with unconditional Neyman-Pearson, say, conditional inference is going some step towards Bayesian conditioning without having to bring in priors
另一个方面是最小化与贝叶斯论点的差异，特别是与标准化先验的差异，这是我在Jeffreys的讲座中第一次学习统计学的方法。我觉得各种推理流派之间的差异被强调得太多，而相似性却不够。Bayesian将自动实现这种条件化，因此与无条件Neyman-Pearson相比，条件推理在不必引入先验的情况下向Bayesian条件化迈进了一步。
Reid ：And is that the right direction, towards Bayesian inference?
Reid ：这是朝向贝叶斯推理的正确方向吗？
Cox： Well, yes; but in talking about Bayes, I feel one has to distinguish very sharply personalistic priors from standardized priors. Personalistic priors have a role, if you are strongly interested in the aspects of how personal judgment enters into analysis, but most of the problems I look at are not like that. To me Bayes with some sort of reference prior seems quite appealing, although I don't regard it as the absolutely ultimate criterion. All these things are essentially measuring devices for measuring how much information there is in data, and you test a measuring device by seeing how it works when you use it. From that point of view the absolutely ultimate criterion must be some sort of notion of probability of correctness
Cox： 嗯,对,；但在谈到Bayes时，我觉得必须非常明确地区分个人化先验和标准化先验。如果你对个人判断如何进入分析的各个方面非常感兴趣，那么个人化的先验论就有一定的作用，但我看到的大多数问题都不是这样的。对我来说，带有某种参考的Bayes似乎很有吸引力，尽管我并不认为它是绝对的终极标准。所有这些基本上都是测量设备，用于测量数据中有多少信息，您可以通过查看测量设备在使用时的工作方式来测试它。从这个观点来看，绝对的终极标准必须是某种正确概率的概念
Reid ：In a long-run frequency sense.
Reid ：在长期频率意义上。
Cox： Well, in some sense-yes, in a frequency sense: that if hypothetically we were to use this procedure again and again, then its properties would be reasonable. That's much weaker than saying, you know,
Cox： 在某种意义上，是的，在频率意义上：假设我们一次又一次地使用这个过程，那么它的性质是合理的。这比说，你知道，95%$的覆盖率才是最重要的要弱得多。但它是说，如果你有一个程序，在假设的重复中做得不好，它不可能是一个好的程序。如果有一个最终的测试，那就是。
Reid ：Could I come back to the talk that you gave, that the paper is based on-you said it generated a lot of discussion. Was it well-received and was the discussion friendly but puzzled or was it hostile?
Reid ：请允许我回到你的演讲，那篇论文是基于你说的，它引起了很多讨论。它是否受到欢迎，讨论是否友好但令人困惑，还是充满敌意？
Cox： It was in no sense hostile; and it wasn't discussion, it was six people gathered around a blackboard after the lecture. It wasn't discussion in anything like the normal sense of a scientific meeting. For one thing, for some strange reason it was held in the evening, something like seven o'clock in the evening.
Cox： 这一点也不敌对；这不是讨论，而是六个人在演讲结束后聚集在黑板旁。这不是一般意义上的科学会议讨论。首先，出于某种奇怪的原因，它是在晚上举行的，大约是晚上七点。
Reid ：Do you remember who the six people were?
Reid ：你还记得那六个人是谁吗？
Cox： Not very clearly. I know that Arthur Dempster was there, I can't remember whether he took part in this discussion. Allan Birnbaum was the main person. [Laughs.] I'm probably offending somebody by leaving them out-they were all people who then and now are quite well known. It's a long time ago. But in no sense was it a hostile discussion.
Cox： 不太清楚。我知道阿瑟·登普斯特当时在场，我记不起他是否参加了这次讨论。艾伦·伯恩鲍姆是主要人物。[笑]我可能是因为把他们排除在外而得罪了他们都是当时和现在都很有名的人。那是很久以前的事了。但这绝对不是一场敌对的讨论。
Reid ：How long were you in the U.S. at that time?
Reid ：那时你在美国呆了多久？
Cox： Fifteen months-Princeton, North Carolina and Berkeley.
Cox： 15个月普林斯顿、北卡罗来纳和伯克利。
Reid ：It must have been a busy 15 months.
Reid ：这15个月一定很忙。
Cox： Yes, and very exciting.
Cox： 是的，非常激动人心。
Reid ：Who were the people you interacted with the most?
Reid ：与你互动最多的人是谁？
Cox： Well, John Tukey very particularly, John perhaps more than anybody and very intensively. Martin Wilk arrived in Princeton the same day that Joyce and I did. He had just finished at Iowa State, and I had many discussions with Martin. Bernard Greenberg, who was the head of the Biostatistics group at Chapel Hill, I couldn't say I had many technical discussions with him, but he was enormously helpful to me. At Berkeley, I don't remember scientific discussions, with particular people there, although I took part in all sorts of seminars. I suppose, if anybody, it would have been Mr. Neyman.
Cox： 嗯，约翰·图基，非常特别，约翰可能比任何人都要强烈。马丁·威尔克和乔伊斯到达普林斯顿的同一天。他刚在爱荷华州毕业，我和马丁进行了多次讨论。Bernard Greenberg是Chapel Hill生物统计学小组的负责人，我不能说我和他进行了很多技术讨论，但他对我帮助很大。在伯克利，虽然我参加了各种各样的研讨会，但我不记得与那里特定的人进行过科学讨论。我想，如果有人的话，应该是内曼先生。
Reid ：Your whole approach is so different than the American school of the fifties.
Reid ：你的整个方法与50年代的美国学校大不相同。
Cox： Yes. [Laughs.] I can remember Mr. Neyman telling me off, in a very nice way. I gave a talk in his seminar about some problem in stochastic processes and I used Dirac delta functions and he came up to me afterwards and said, "Yes, that really was quite interesting, but we don't do that sort of mathematics here." But the irony was that a few years later Laurent Schwartz visited Berkeley and, of course, after that it was perfectly respectable. But Mr. Neyman was very nice about it.
Cox： 对[笑]我记得内曼先生以一种非常好的方式对我指手画脚。我在他的研讨会上讲了一个关于随机过程中的一些问题，我使用了狄拉克三角函数，他后来找我说，“是的，这真的很有趣，但我们这里不做那种数学。”但讽刺的是，几年后，劳伦特·施瓦茨访问了伯克利，当然，从那以后，这是非常体面的。但内曼先生对此很好。
[Schwartz's books (Schwartz, 1950, 1951) established a mathematical foundation for the study of Dirac delta functions.]
[Schwartz's books (Schwartz, 1950, 1951)建立狄拉克δ函数研究的数学基础.]
Reid ：Was your 1958 paper your first paper on pure theoretical statistics, so to speak?
Reid ：可以说，你1958年的论文是关于纯理论统计的第一篇论文吗？
Cox： I'm not quite sure, but I think it must have been. Yes, and forced on me by having nothing better to talk about.
Cox： 我不太确定，但我想一定是这样。是的，我没有更好的话题要谈，这迫使我这么做。
Reid ：Could we turn to your 1955 paper that you read to the RSS [3]? That was the work you'd done at WIRA and Cambridge?
Reid ：我们可以看看你1955年的论文吗？你在RSS上读到了？那就是你在WIRA和剑桥做的工作？
Cox： Well, some of it was done in the period from 1946 to 1950 , and then it continued on at a lower level of intensity between 1950 and 1954. The trouble with the paper is that there is far too much in it. Doubly stochastic Poisson processes, all sorts of tests to do with empirical series of point events, a certain amount about unbalanced variance components, a certain amount about overdispersion in Poisson models and quite a bit about some of the peculiar sampling problems that come up in those sorts of studies. That makes it all a bit of a mish-mash. There was even more in the original version. In those days you didn't submit something to the RSS for reading until you really felt you had spent a long time on it. That was the idea I picked up anyway; I don't know how true it really was.
Cox： 有些是在1946年至1950年期间完成的，然后在1950年至1954年期间以较低的强度继续进行。这张纸的问题是里面的东西太多了。双随机泊松过程，各种与点事件的经验序列有关的测试，一定量的不平衡方差分量，一定量的泊松模型中的过度分散，还有很多关于这些研究中出现的一些特殊抽样问题。这让这一切有点混乱。原始版本中甚至还有更多。在那些日子里，直到你真的觉得自己花了很长时间才把东西提交给RSS阅读。不管怎样，这就是我的想法；我不知道这到底有多真实。
Fig. 3. With Nancy Reid and David Hinkley at CIMAT (Centro de Investigaćion en Matemáticas), Guanajuato, Mexico, March
图3。与南希·里德和大卫·辛克利在墨西哥瓜纳华托CIMAT（数学研究中心），1993年3月。
Reid ：Almost all your early work that wasn't in design was in stochastic processes; you have several books
Reid：几乎你所有的早期工作都不是在设计中，而是在随机过程中；你有几本书，$[9,10,12,13]$是1955年报纸[3]上的。
Cox： Well, in some ways preceding the 1955 paper. When I first went to work with Henry Daniels he said the up-and-coming subject of the next umpteen years is stochastic processes, and he even arranged for me to go across from Leeds to Manchester every other week to listen to Maurice Bartlett's lectures. Leeds to Manchester is about 70 kilometers but in those days that was a major journey, like going to the North Pole, particularly going from Yorkshire to Lancashire. Then he gave me various suggested readings: Chandrasekhar's famous paper [Chandrasekhar, 1943] and S. O. Rice's papers [Rice, 1944,1945 ] and Bartlett. There wasn't much else, you see. It was the idea then that if you're a statistician, you'd jolly well better be interested in stochastic processes. So 1 had never thought of stochastic processes as separate from statistics. Just as I don't think of time series as separate from stochastic processes or from statistics.
Cox： 嗯，在1955年的论文发表之前的某些方面。当我第一次与亨利·丹尼尔斯合作时，他说未来几十年的新兴学科是随机过程，他甚至安排我每隔一周从利兹到曼彻斯特听莫里斯·巴特利特的讲座。利兹到曼彻斯特大约有70公里，但在那些日子里那是一次重要的旅行，就像去北极一样，特别是从约克郡到兰开夏郡。然后他给了我各种建议阅读：钱德拉塞卡的著名论文[Chandrasekhar，1943]和s.O.Rice的论文[Rice，19441945]和Bartlett。你看，没有什么别的了。当时的想法是，如果你是一名统计学家，你最好对随机过程感兴趣。所以我从来没有想过随机过程与统计学是分开的。正如我不认为时间序列与随机过程或统计分开一样。
Now, there were various problems in my thesis about time series and stochastic processes. There was a textile problem of a queuing kind that led to my interest in queuing theory. So I was quite interested in stochastic processes by the time I went to Cambridge in 1950 , and that interest has continued. In those days, while it was a difficult subject to work in, it wasn't highly technical. I mean, you needed to know some matrix algebra and some differential equations and preferably some partial differential equations and Laplace transforms-the standard elementary techniques of mathematical physics-and I did know that, that was what my training was. Of course, if you were like Henry and were a wizard at saddlepoints and so forth, all the better. All the same the subject wasn't highly technical. You looked at a particular scientific problem, you saw if you could formulate it somehow or other as a Markov process and you set up your differential equations and you had a go at solving them. You had better solve them analytically because unless they were very simple, solving them numerically would have been a bit of a pain. It's the sort of mathematics I like doing and the concepts are fairly straightforward. Some of the more theoretical work on stochastic processes that I did in a couple of papers in the Proceedings of the Cambridge Philosophical Society
现在，我的论文中有很多关于时间序列和随机过程的问题。有一个排队的纺织问题引起了我对排队论的兴趣。所以我在1950年去剑桥的时候对随机过程很感兴趣，而且这种兴趣一直在持续。在那些日子里，虽然这是一个很难研究的课题，但技术性不强。我的意思是，你需要知道一些矩阵代数和微分方程，最好是一些偏微分方程和拉普拉斯变换，数学物理的标准基本技术，我确实知道，这就是我的训练。当然，如果你像亨利一样，是一个巫师在鞍点等等，那就更好了。尽管如此，这个主题的技术性并不强。你看了一个特殊的科学问题，你看到了，你是否可以用马尔可夫过程来描述它，你建立了你的微分方程，你试着去解决它们。你最好用解析的方法来求解，因为除非它们非常简单，否则用数值的方法来求解会有点痛苦。这是我喜欢做的那种数学，而且概念相当简单。我在《剑桥哲学学会会刊》[4,5]$上的几篇论文中所做的一些关于随机过程的理论工作基本上是关于如何将非马尔可夫过程构建成马尔可夫过程。
It seems to me that if you look now at even relatively elementary books on stochastic processes, they require very heavy apparatus. Things like Itô calculus and so forth that seem to demand a lot of what I would regard as heavy mathematical background. I'm not convinced they really do need all that paraphernalia-that one couldn't study stochastic processes more in the spirit of Bartlett's great masterpiece [Bartlett, 1955], which is difficult reading but not because of an overelaborate mathematical formalism. Anyway, I've always been interested in stochastic processes from that point of view, and at that mathematical level. Nowadays I feel out of touch. If I went to one of the meetings of the Stochastic Processes Group of the Bernoulli Society, I suspect I wouldn't understand anything. It's all so dressed up in this great apparatus. Which has a beauty of its own, I'm not debunking it in any sense, it's great stuff, but is it really necessary for looking at scientific problems, if that's what one wants to do. I don't know.
在我看来，如果你现在看一看关于随机过程的相对初级的书籍，它们需要非常重的设备。像微积分之类的东西似乎需要很多我认为很重的数学背景。我不相信他们真的需要所有的工具，人们无法按照巴特利特的伟大著作[Bartlett，1955]的精神来研究随机过程，这本书读起来很难，但不是因为过于复杂的数学形式主义。不管怎样，我一直对随机过程感兴趣，从这个角度来看，在数学层面上。现在我觉得失去了联系。如果我去参加伯努利学会随机过程小组的一次会议，我想我什么都不懂。在这台伟大的仪器里，一切都那么华丽。它有它自己的美，我不是在任何意义上揭穿它，它是伟大的东西，但它真的有必要去研究科学问题吗，如果这是一个人想要做的。我不知道。
The main area that
我继续做的主要工作是我主要与Valerie Isham一起做的工作。我们解决了一个长期存在的问题，这个问题与物理学中所谓的协方差计数有关[18]。这是一种计算粒子数的方法，它依赖于观察重叠周期内观察到的粒子数之间的相关性。这是一种阻塞问题。曾经有过各种各样的尝试来解决这个问题，但都没有成功。
And then more recently we've worked with hydrologists on marked point process models for rainfall [21-23]. There again we used the traditional kind of mathematics and my book with Valerie on point processes [19], while we range over a pretty wide variety of models and there are various new things in there, I think, it's not done by bringing a vast mathematical armoury to bear.
最近，我们与水文学家合作建立了降雨的标记点过程模型[21-23]。在那里，我们再次使用了传统的数学和我与Valerie合著的关于点过程的书[19]，而我们的研究范围非常广泛，有各种各样的新事物，我认为，这不是通过带来一个庞大的数学武器库来完成的。
And there is a close connection between all that and the proportional hazards model. Particularly in point processes one naturally thinks of saying, "Here we are now, and we've got a certain history; what's the probability of an event in the next short element of time?" Now the mathematicians make a great hooha about setting up such a function, but it's physically absolutely obvious that such a thing uniquely defines a point process and it takes half a sentence to say so and Bartlett said so many, many years ago. That's the kind of thing that rather worries me; the notion that you can't just set up a complete intensity function or whatever you like to call it without a great mathematical paraphernalia of filtrations, and this and that. If you want a very general mathematical theory, it's clear that's the way to do it; but all I'm saying is that it should be legitimate to treat the subject at this more informal level as well. I'm not saying that it isn't valuable to have the very general theory; I think it is, but not everybody has to go that way. And if it means that you get a situation where lots of statisticians don't know anything about stochastic processes because they haven't the time to master all the elaborate apparatus, then that's bad news.
所有这些与比例风险模型之间有着密切的联系。特别是在点过程中，人们会自然而然地想到：“我们现在在这里，我们已经有了一定的历史；在下一个短时间内发生事件的概率是多少？”现在数学家们对建立这样一个函数非常高兴，但从物理上看，这是绝对明显的，这样一个东西唯一地定义了一个点过程，它需要半句话来表达，巴特利特在很多很多年前就说过。这正是我比较担心的事情；如果没有过滤的数学工具，你就不能建立一个完整的强度函数，或者你想叫它什么的，等等。如果你想要一个非常一般的数学理论，很明显这就是方法；但我想说的是，在这个更非正式的层面上处理这个问题应该是合法的。我并不是说拥有非常普遍的理论是没有价值的；我想是的，但不是每个人都必须走那条路。如果这意味着很多统计学家对随机过程一无所知，因为他们没有时间掌握所有精密的仪器，那么这是个坏消息。
Reid ：Could I go back in time and ask things I thought of when you were talking earlier? For example, you went to Bartlett's lectures; were they enlightening?
Reid ：我能不能回到过去问问你刚才谈话时我想到的事情？例如，你参加了巴特利特的讲座；他们有启发性吗？
Cox： That's a very difficult question. I suspect they were highly enlightening. They were not particularly easy. I mean, my admiration for his work is enormous. I think his book's a great masterpiece and
Cox： 这是一个非常困难的问题。我怀疑他们很有启发性。他们并不特别容易。我是说，我对他的工作非常钦佩。我认为他的书是一部伟大的杰作，我很震惊现在自称随机过程专家的人很少读过这本书。我原以为这是过去50年来我们这个领域最重要的书籍之一：每页的想法数量令人难以置信。
Reid ：And how did you get interested in the rainfall work, in particular?
Reid ：你是如何对降雨工作产生兴趣的？
Cox： Very soon after I went to Imperial College I had some contact with hydrologists and that led to a Ph.D. student, Gideon Weiss, who did some nice hydrological work on runoff modeling. Beyond this sort of vague interest I didn't do anything very much until I went once to Caracas, really to meet someone else. I met there a famous hydrologist, Ignacio RodriguezIturbe, who had worked on point process models in rainfall. We developed a collaboration following from this. It really was a kind of accident arising out of visiting Caracas.
Cox： 在我进入帝国理工学院后不久，我与水文学家进行了一些接触，并因此获得了博士学位。学生Gideon Weiss在径流建模方面做了一些很好的水文工作。除了这种模糊的兴趣之外，我什么也没做，直到有一次我去加拉加斯，真的是去见另一个人。我在那里遇到了一位著名的水文学家，伊格纳西奥·罗德里格齐特贝，他曾研究过降雨的点过程模型。我们在此基础上开发了一个合作项目。这真的是一种因访问加拉加斯而引起的意外。
Reid ：A happy accident.
Reid ：一个愉快的意外。
Cox： Yes, indeed extremely.
Cox： 对,确实非常。
Reid ：There's an enormous literature on rainfall in the physical literature. How did you avoid being swamped by that and just getting on with something new?
Reid ：物理文献中有大量关于降雨的文献。你是如何避免被这件事所困扰，而只是去做一些新的事情的？
Cox： Well, really by drawing on Ignacio's deep knowledge of that. I mean I have talked to meteorologists and hydrologists a bit as well, but it's largely Ignacio.
Cox： 好吧，真的是利用伊格纳西奥对这方面的深刻了解。我的意思是，我也和气象学家和水文学家谈过一点，但主要是伊格纳西奥。
Reid ：Are you still working on it?
Reid ：你还在努力吗？
Cox： Yes, but it goes very slowly. I'm working with Valerie on it; in fact we gave a paper at a conference three or four weeks ago on extending the sort of models we had in the earlier papers to several sites.
Cox： 是的，但进展很慢。我正在和瓦莱丽一起工作；事实上，我们在三四周前的一次会议上发表了一篇论文，讨论了如何将早期论文中的模型扩展到多个站点。
Reid ：Design of experiments was another part of your work at the Wool Industries Research Association.
Reid ：实验设计是你在羊毛工业研究协会工作的另一部分。
Cox： Yes, there was a fair amount of use of balanced designs in the textile industry. Henry Daniels had persuaded a lot of people that this was more or less inevitable. So I was interested while I was in Leeds, and when I went to Cambridge I was also involved with agriculturists and others. I also taught a course in design for two or three years. I had an interest in both the practical and theoretical side.
Cox： 是的，在纺织工业中有相当数量的平衡设计的使用。亨利·丹尼尔斯说服了很多人，这或多或少是不可避免的。所以我在利兹的时候很感兴趣，当我去剑桥的时候，我也参与了农业家和其他人的活动。我还教了两三年设计课程。我对实践和理论都感兴趣。
Reid ：Had you ever had to design an experiment?
Reid ：你曾经设计过实验吗？
Cox： Oh yes many. Not recently, unhappily. It's the most interesting side of statistics in some ways.
Cox： 哦，是的，很多。不幸的是，不是最近。在某些方面，这是统计学最有趣的一面。
Reid ：Is Planning of Experiments [7] based on your lecture notes?
Reid ：实验计划[7]是基于你的课堂讲稿吗？
Cox： No, not at all. The lecture notes are mathematical, about things like Galois fields and combinatorics and the derivations of various standard designs, fractional replication and so on.
Cox： 不，一点也不。课堂讲稿是数学的，关于伽罗瓦场、组合学、各种标准设计的推导、分数复制等等。
Reid ：I guess you would have had to be quite mathematical in the mathematics department.
Reid ：我猜你在数学系一定是个数学高手。
Cox： Not necessarily, although the students would have expected a fairly mathematical treatment. It was something like 24 hours of lectures, and the pace of lecturing in Cambridge in those days was very fast. Some people could do it by writing on a blackboard with their right hand and rubbing off with their left hand while they were talking about a third thing. I could never master that technique, but I lectured pretty quickly.
Cox： 不一定，尽管学生们希望得到一个相当数学化的处理。这就像是24小时的演讲，而在剑桥的演讲速度在那些日子里是非常快的。有些人可以用右手在黑板上写字，在谈论第三件事时用左手摩擦。我永远也不会掌握那种技巧，但我讲得很快。
Reid ：What was the context for writing the book?
Reid ：写这本书的背景是什么？
Cox： I'm not absolutely sure, but I think I had the sort of vague idea of writing up something like the lecture notes as a theoretical book on design of experiments. Then I decided for some reason that it would be much more difficult and much more useful to write something that was aimed at scientists with a minimum of technical statistical analysis, and so I tried to do that. In particular there are very few formulae, and the handful of formulae are written in words. You could call it a gimmicky thing, if you like, but it was meant as a way of saying no working scientist should be put off by the fear that they don't know enough mathematics. And yet at the same time it's an attempt to explain things, not to just say dogmatically, "Randomize," but to explain why you should randomize.
Cox： 我不是绝对肯定，但我想我有一种模糊的想法，就是把课堂讲稿写成一本关于实验设计的理论书。然后，出于某种原因，我决定写一篇针对科学家的文章，用最少的技术统计分析，会更加困难，也更加有用，所以我试着这么做。特别是公式很少，少数公式是用文字写的。如果你愿意的话，你可以称之为噱头，但它的意思是说，任何在职科学家都不应该因为担心他们不懂足够的数学而被吓倒。但同时，这也是一种解释事物的尝试，不是教条式地说“随机化”，而是解释为什么你应该随机化。
Reid ：It's a lovely book, and quite unusual now: was it pretty unusual at the time as well?
Reid ：这是一本可爱的书，而且现在很不寻常：它在当时也很不寻常吗？
Cox： Yes. It isn't a textbook, you see. In fact in a certain way none of the books I've written are textbooks. None of the books I've written are other than extremely indirectly based on lectures, they're not really meant to teach courses from. They are attempts to write down a subject that I've thought about for a while, as it seems to me, or whoever I've been working with, and I've been very very fortunate in the people I've worked with. Maybe it would have been better if they had been textbooks, but they aren't. The publishers may pretend they are, but they aren't.
Cox： 对你看，这不是教科书。事实上，在某种程度上，我写的书都不是教科书。我写的书中没有一本是以讲座为基础的，它们并不是真正用来教授课程的。他们试图写下一个我已经思考了一段时间的主题，在我看来，或者是和我一起工作的任何人，我在与我一起工作的人中非常幸运。如果它们是教科书也许会更好，但它们不是。出版商可能会假装他们是，但事实并非如此。
Reid ：Even Theoretical Statistics [16]?
Reid ：即使是理论统计[16]？
Cox： Well, that's a slight exception. I used to give 12 hours of lectures on that material and cover quite a lot of it. [Laughs.] So you could say it grew out of some lectures, but only in the most tenuous sense; and it's not an easy book to teach from, I would imagine.
Cox： 嗯，这是一个小小的例外。我曾经就这些材料做过12个小时的讲座，涵盖了相当多的内容。（笑）所以你可以说它是从一些讲座中产生的，但只是在最微妙的意义上；我想这不是一本容易教的书。
Reid ：I can attest it's not an easy book to teach from.
Reid ：我可以证明这不是一本容易教的书。
Cox： I've never attempted it; I wouldn't dream of doing so. The publishers ask for comments on books and David and I did get the comment that the book should be totally rewritten in the form of theorems and proofs. I'm afraid I sent a rather sour answer to that, which I hope reached the stupid person who made that remark. I mean, I understand why the remark was made, but all the same...
Cox： 我从未尝试过；我做梦也想不到这样做。出版商要求对书籍发表评论，大卫和我得到的评论是，这本书应该以定理和证明的形式完全重写。恐怕我给了一个相当尖刻的回答，我希望这个回答能传到那个愚蠢的人那里。我的意思是，我理解为什么会有这样的评论，但仍然。。。
Reid ：Just to get back to Planning of Experiments: do you remember how it was received at the time?
Reid ：回到实验计划上来：你还记得当时是怎么收到的吗？
Cox： I don't really remember how it was received Most of the reviews were reasonably favourable. I do remember one by a mathematician that said something like, "This book is on the whole a competent account of principles of experimental design for nonmathematicians. What a pity that biologists and others don't learn more mathematics so that such books would be unnecessary." I thought that missed the point rather dramatically. This is an underlying point about all sorts of statistical issues: to what extent these matters are really mathematical, and to what extent the important things are concepts which then have to be translated into mathematics. The other thing about the book is the pattern of sales was very curious because it sold extremely well, by my perception (Wiley might think differently), for almost 30 years and then suddenly the sales dropped off. So that would suggest that the reception was reasonable.
Cox： 我真的不记得它是怎么收到的大多数评论都是相当好的。我确实记得一位数学家说过这样的话：“这本书大体上是对非数学家的实验设计原理的有力说明。生物学家和其他人没有学到更多的数学知识，这样的书就没有必要了，这是多么遗憾啊。”我认为这一点相当明显地漏掉了。这是关于各种统计问题的一个基本观点：在多大程度上，这些问题是真正的数学问题，在多大程度上，重要的问题是必须转化为数学的概念。关于这本书的另一件事是它的销售模式非常奇怪，因为它在我看来（威利可能会有不同的想法）销售非常好，持续了将近30年，然后销售突然下降。因此，这表明接待是合理的。
FiG. 4. With George Box and Stu Hunter in front of Meadow Brook Hall, Oakland University, Rochester, Michigan, in June
图4。1986年6月，乔治·博克斯和斯图·亨特在密歇根州罗切斯特的奥克兰大学梅多布鲁克大厅前
Reid ：Perhaps what the reviewer meant was that there are occasions when it is nicer to see a formula than to see a formula written in words.
Reid ：也许评论员的意思是，有时，看到公式比看到用文字书写的公式更好。
Cox： On that particular bit yes of course, but I don't think that's what he meant. No, I think he meant that we have a book on the mathematical theory of design of experiments and that's it, and everything else is deduction from this.
Cox： 在那一点上当然是的，但我不认为他是这个意思。不，我想他的意思是，我们有一本关于实验设计的数学理论的书，就这样，其他一切都是从这本书中推导出来的。
Reid ：You wanted to talk about split plots.
Reid ：你想谈谈分裂阴谋。
Cox： Partly in connection with Planning of Experiments. One of the advantages of writing in a nonmathematical style is that it forces one to explain, in qualitative terms, absolutely crucial, vital issues which everybody has to understand about split plot experiments. Why certain contrasts have different errors from other contrasts. This isn'tjust a question of deducing it from some model that one's plucked out of the air, but in seeing why physically this is so. And then once you've mastered the split plot experiment of course you can go on to the split split plot, or the split split-split-split-split plot, with no further problems other than a certain messiness.
Cox： 部分与实验计划有关。以非数学风格写作的优点之一是，它迫使人们用定性的术语解释每个人都必须理解的关于裂区实验的绝对关键、至关重要的问题。为什么某些对比与其他对比有不同的误差。这不仅仅是一个从空气中提取的模型中推断出来的问题，而是看看为什么在物理上如此。一旦你掌握了分裂图实验，你当然可以继续分裂图，或者分裂图，除了某种混乱之外没有其他问题。
But the importance of it goes beyond design of experiments because it does bring home in its simplest form the point about hierarchical error structures. There is a tendency if you see random variation on different individuals, to model it by iid random variables. The split plot is a warning against this: there may well be correlational structures or hierarchical structures in the error which mean that some comparisons have quite different precision than others. That's a point of importance far beyond just the classical design of experiments. Although one could have a working life and never come across a split plot design, there are other areas where it's a wholly natural design and there are other areas where it's being used implicitly, without people quite understanding that this is what is being done, and getting incorrect estimates of precision. So I think the moral is that these very important, absolutely central issues, like the split plot, have to be understood, and it's more important to understand them at a qualitative level than it is to plough through a lot of algebra.
但它的重要性超出了实验设计，因为它确实以最简单的形式阐明了关于分层误差结构的观点。有一种趋势，如果你看到不同个体的随机变化，就用iid随机变量来建模。分裂图是对这一点的警告：误差中很可能存在相关结构或层次结构，这意味着某些比较与其他比较具有完全不同的精度。这一点的重要性远远超出了经典的实验设计。虽然一个人可能有一个工作的生活，从来没有遇到过分割区设计，但在其他一些领域，这是一个完全自然的设计，在其他一些领域，它被隐式地使用，而人们不太理解这就是正在做的事情，并且得到了错误的精度估计。因此，我认为寓意在于，这些非常重要、绝对核心的问题，比如分裂情节，必须被理解，从定性的角度理解它们比钻研大量代数更重要。
Reid ：And some areas where it comes up all the time?
Reid ：有些地方经常出现这种情况？
Cox： In all sorts of contexts where you can have repeat measurements, whether it's an experiment or observational study: agriculture, of course, where it originated; any multistage industrial process or physical process where let's say, simplest case, you have two stages of processing some material. You are interested in a factorial experiment where you make some changes in stage A, and some changes in stage
Cox： 在各种各样的情况下，你可以重复测量，无论是实验还是观察研究：当然，农业，它起源于哪里；任何多阶段的工业过程或物理过程，比如说，最简单的情况下，处理某些材料有两个阶段。你对阶乘实验感兴趣，你在a阶段做了一些改变，在B阶段做了一些改变，对a阶段的材料进行设计是完全自然的，a阶段处理，加工并产生一些材料，然后将其分为若干部分，并在B阶段以不同的方式进行处理。这种方式几乎是必要的。
Then there's the possibility that you have factorial experiments where certain kinds of adjustment to a process or a system are extremely difficult or expensive to make and other adjustments are very easy to make. Then it would be natural to hold the expensive factor fixed for a certain length of time, have a number of runs in which the inexpensive factor is varied and then switch your expensive factor and do some more. Certain areas of experimental psychology as well. Mostly when it does arise, it arises inevitably from the nature of the constraints on the way the experiment has to be set up. I don't think it's very often imposed. It's more often that the physical constraints of the experiment dictate that a split plot structure is used.
还有一种可能性是，你有阶乘实验，在那里对一个过程或系统进行某些类型的调整是非常困难或昂贵的，而其他调整是非常容易的。然后很自然地将昂贵的因素固定一段时间，进行多次跑步，其中便宜的因素是不同的，然后切换昂贵的因素并做更多的事情。实验心理学的某些领域也是如此。大多数情况下，当它确实出现时，它不可避免地来自于对实验设置方式的限制的性质。我不认为这是经常强加的。更常见的是，实验的物理限制决定了使用分割图结构。
Reid ：Perhaps it needs a better name.
Reid ：也许它需要一个更好的名字。
Cox： I used to think it didn't matter what things were called, but that's a very mistaken view; there is a certain skill in naming things and methods in a way that will make them attractive. Well, I've had my say about split plots and even split split-split plots.
Cox： 我曾经认为，事物的名称无关紧要，但这是一个非常错误的观点；在命名事物和方法时有一定的技巧，可以使它们具有吸引力。好吧，我已经有了关于分裂图谋的发言权，甚至分裂图谋。
Reid ：I was wondering what your thoughts are on sequential design and analysis?
Reid ：我想知道你对顺序设计和分析有什么想法？
Cox： Perhaps I could ramble on a bit about my interest in sequential analysis. I first came across this when I was at the Royal Aircraft Establishment and Wald's secret report was circulated to government research scientists. And in the department of structural and mechanical engineering, people were very interested, because the claim was that you could halve the amount of testing. One of the really expensive things they did was to take whole aircraft wings and load them until they broke, measuring all sorts of things, strain gauges all over the place. Being very good engineers they
Cox： 也许我可以谈谈我对序列分析的兴趣。我第一次遇到这个问题是在皇家飞机公司，瓦尔德的秘密报告被分发给了政府的研究科学家。在结构和机械工程系，人们非常感兴趣，因为他们声称可以将测试量减半。他们做的一件非常昂贵的事情是把整个机翼都装上，直到它们断裂，测量各种各样的东西，到处都是应变计。作为一名非常优秀的工程师，他们总是花费d$来折断两个机翼，这是一项非常昂贵的业务。我记得一个小组的一位负责人对我说，“也许这意味着我们只需要折断一个机翼。”他稍微说服了我，这并不完全是沃尔德工作的含义。我参加的第一次皇家统计学会会议也是在战争期间，乔治·巴纳德发表了讲话。他开发了一种与瓦尔德的作品非常相似的东西，但用了非常不同的方式，在一些军火工厂中得到了广泛的应用。所以当我去WIRA的时候，我对顺序抽样很感兴趣，我确实有意识地四处寻找应用程序，那里的人非常接受新的想法，而人们并不总是这样。有一两件事我们尝试了一些简单的顺序测试，但很明显，它实际上根本没有效果。最近发生的事情似乎是，医学统计学家对这一课题产生了极大的兴趣，我认为，部分原因是由于伦理问题，即在涉及重大生命威胁事件的试验中，没有超过必要的时间继续进行。所以这个主题有一个非常有趣的更新。
Why was the previous work pretty ineffective? Too slanted to simple decisions like accept/reject (which is after all what it was set up for) rather than measuring things, estimating things. And when you come to sequential estimation, what the sequential method does, and it can be very important, is adjust the sample size to the requirement of the precision that you want. It's not a question exactly of saving observations, but more a question of getting the precision that you need.
为什么以前的工作效率很低？过于倾向于简单的决定，比如接受/拒绝（这毕竟是它的初衷），而不是衡量事物、估计事物。当你谈到序贯估计时，序贯方法所做的，而且可能是非常重要的，就是调整样本大小，使之符合你想要的精度要求。这不是一个保存观测数据的问题，而是一个获得所需精度的问题。
Reid ：When you said that recently there's been quite a bit of development in medical applications, do you mean in the last 15 to 20 years, or in the last 5 with the AIDS crisis?
Reid ：当你说最近在医学应用方面有了很大的发展，你是说在过去15到20年里，还是在过去的5年里，在艾滋病危机中？
Cox： No, AIDS is just one aspect of it. Work on group sequential sampling seems to be being used, and very interesting: and adaptive randomization.
Cox： 不，艾滋病只是其中的一个方面。关于群体序贯抽样的工作似乎正在使用，而且非常有趣：和自适应随机化。
But even in a major clinical trial, where sequential stopping may be a very relevant and contentious issue, the most you can look for is reasonable advice as to when one should think seriously about stopping. I think a decision about stopping is always going to be taken on grounds that are statistical and ethical, involving prior knowledge and perhaps even political considerations, quite properly. And for a statistician to' come up with a procedure to simply say you stop now or you must continue, is a misformulation.
但是，即使在一个重要的临床试验中，顺序停药可能是一个非常相关和有争议的问题，你能找到的最多的是关于何时应该认真考虑停药的合理建议。我认为关于停止的决定总是基于统计和道德的理由做出的，涉及到事先的知识，甚至是政治考虑，这是非常恰当的。而对于一个统计学家来说，“想出一个程序，简单地说你现在停止或者你必须继续，这是一个错误的公式。”。
Reid ：I'd like to ask you about binary data. I think that your first binary data paper was
Reid ：我想问你关于二进制数据的问题。我认为你的第一篇二进制数据论文是1958年[8]，而调节论文是1958年，所以你在IMS会议上确实有其他的话题要谈。
Cox： Well, the IMS meeting was in 1956, you see. The Annials didn't actually leap at the thought of publishing this paper.
Cox： 嗯，国际监测系统会议是在1956年，你看。周年纪念实际上并没有想到要发表这篇论文。
Reid ：Really, you went several rounds with the editors, did you?
Reid ：真的，你和编辑谈了好几次，是吗？
Cox： Well, if you look at other papers in the
Cox： 好吧，如果你看看其他的报纸，在当时的$A n$nals，这根本不是传统的编年史风格。我不是说他们脾气暴躁或不讲理，但这需要一段时间。
I think the binary data work was partly motivated by things in Chapel Hill, but more particularly by going to Birkbeck College, London. There was a very strong psychology department, mainly experimental psychology, and they were very concerned about analysing binary data.
我认为二进制数据工作的部分动力来自教堂山的事情，但更特别的是来自伦敦伯克贝克学院。有一个非常强大的心理学系，主要是实验心理学，他们非常关心分析二进制数据。
Reid ：And what was available before your 1958 paper?
Reid：在你1958年发表论文之前有什么可用的？
Cox： I'm very unclear about the history. Analvsis of binary data l think was often thought of as chi-squared basically. You find observed frequencies and you find fitted frequencies and you compute observed minus fitted squared over fitted; you forced it into that mold. Now that isn't totally true, because contrasted very much with that was Finney's work on probit analysis. And I think historically, I don't know who first did logistic regression, but quite possibly it was Jerry Cornfield on the Framingham study a few vears before 1958. Possibly Nathan Mantel would have been involved. I certainly met Cornfield, so whether I was influenced by him is entirely possible, but I don't remember. What I was trying to do was set out a systematic framework for analysing binary data that is somewhat analogous to least squares regression.
Cox： 我对历史很不清楚。我认为二进制数据的分析通常被认为基本上是卡方的。你们找到观测到的频率，你们找到拟合频率，你们计算观测到的负拟合平方和过拟合；你强迫它进入那个模子。这并不完全正确，因为芬尼在概率分析方面的工作与之形成了很大的对比。我想从历史上看，我不知道是谁首先做了逻辑回归，但很可能是1958年前几次弗雷明翰研究中的杰里·康菲尔德。内森·曼特尔可能也参与其中。我当然见过康菲尔德，所以我是否受到他的影响是完全可能的，但我不记得了。我试图做的是建立一个分析二进制数据的系统框架，这在某种程度上类似于最小二乘回归。
Reid ：Which you did, beautifully. I was a little bit surprised when l read the paper to see you derive in detail conditioning on a sufficient statistic for the nuisance parameter in a canonical exponential family; would that have been relatively new at the time?
Reid ：你做得很漂亮。当我读到这篇文章时，我有点惊讶，看到你详细地推导了正则指数族中讨厌参数的充分统计条件；那在当时会是相对较新的吗？
Cox： Well, I thought it was new, and the motivation was new but of course as probably somebody pointed out in the discussion, it was regions of Neyman structure; from the Neyman-Pearson point of view it would have been orthodox. But the justification I gave for it was not a Neyman-Pearson justification. It was Fisherian in the sense of saying this part of the sufficient statistic doesn't tell us about the parameter of interest and so we'll condition on it. It's a nice question, I'm very unclear about it, as to whether that isn't really a better justification for conditioning than achieving exact similarity.
Cox： 嗯，我认为这是新的，动机也是新的，但当然，正如可能有人在讨论中指出的，这是内曼结构的区域；从内曼·皮尔森的观点来看，这是正统的。但我给它的理由不是内曼·皮尔森的理由。这是费舍尔式的，意思是说，这部分充分的统计数据并没有告诉我们感兴趣的参数，所以我们将以它为条件。这是一个很好的问题，我很不清楚，这是否真的比获得精确的相似性更好地证明了条件作用。
Reid ：It's still not clear to me why you're so sure that there's no information about the odds ratio in the distribution of the marginal total.
Reid ：我仍然不清楚，为什么你这么肯定，在边际总数的分布中，没有关于优势比的信息。
Cox： Well, I'm not sure. Efforts still continue to define that elusive notion. [Laughs.]
Cox： 嗯，我不确定。人们仍在努力界定这一难以捉摸的概念。[笑]
Reid ：That was a read paper, to the Royal Statistical Society. Was it your impression that it was well received? Those discussions to me always sound terribly critical: what was your feeling at the time?
Reid ：这是一篇致皇家统计学会的阅读论文。你的印象是它很受欢迎吗？对我来说，这些讨论听起来总是非常关键：你当时的感觉如何？
Cox： Well, in those days, it's probably changed now, you offered a paper for reading after working on it for some years. It was not something you did lightly, and you expected an onslaught. My impression is that it was much better received than I expected it to be. Well, there are one or two quite inaccurate comments on it, which is inevitable because people had a very short time to read the paper. I think it was reasonably favourably received.
Cox： 好吧，在那些日子里，它现在可能已经改变了，你在写了几年之后提供了一篇论文供阅读。这不是你轻易做的事，你期待着一场猛烈的攻击。我的印象是，它比我预期的要好得多。嗯，有一两个相当不准确的评论，这是不可避免的，因为人们阅读报纸的时间很短。我认为它受到了合理的欢迎。
Reid ：Your 1970 book on binary data came more or less from that binary data paper, I guess?
Reid ：我想，你1970年写的关于二进制数据的书或多或少是从那本二进制数据的论文中来的吧？
Cox： Yes, it should have been written in 1960 ; that was a mistake. I don't know quite why I didn't write it then.
Cox： 是的，它应该写于1960年；那是个错误。我不知道为什么我当时没有写。
Reid ：Why do you say it was a mistake?
Reid ：你为什么说这是个错误？
Cox： Well, it's more like a book. Computing was changing extremely rapidly at that time. You see in 1960 computers were there and all sorts of things could be done but only with enormous struggle. By 1970 things were much more standardized. I mean nothing like they are now, but things were much easier. And things like the emphasis on weighted least squares, which was perfectly appropriate in 1960 , was a bit old hat by 1970 . In any case I had all the material; in fact I had lectured on most of it here and there. It was stupid not to write it down.
Cox： 嗯，它更像一本书。当时，计算机技术的变化非常迅速。你看，在1960年，计算机就在那里，各种事情都可以做，但都需要付出巨大的努力。到1970年，事情变得更加标准化。我指的不是现在的情况，但事情要容易得多。比如强调加权最小二乘法，这在1960年非常合适，到1970年已经有点过时了。无论如何，我拥有所有的材料；事实上，我已经在这里和那里讲授了大部分内容。不把它写下来是愚蠢的。
Reid ：You might have been too busy writing all your other books.
Reid ：你可能正忙着写其他的书。
Cox： [Laughs.] Could be.
Cox： [笑]可能是。
Reid ：I don't remember seeing in the paper analysis of binomial data, but there's a lot of that in the book.
Reid ：我不记得在论文中看到过对二项式数据的分析，但书中有很多。
Cox： No, that's in the book. That's almost in the 1955 paper [3], although for the Poisson case rather than the binomial case.
Cox： 不，那在书里。这几乎出现在1955年的论文[3]中，尽管是针对泊松情形而不是二项式情形。
Reid ：The binary data paper in many ways is quite similar to your 1972 [15] paper in that it highlights features appearing in a number of applications and then presents a relatively simple systematic way of approaching it. And yet the 1972 paper shot to meteoric fame, and I'm not sure the binary paper did.
Reid ：二进制数据文件在许多方面与您1972年[15]的论文非常相似，因为它突出了许多应用程序中出现的特征，然后提出了一种相对简单的系统方法来处理它。然而1972年的那篇论文却一炮而红，我不确定那篇二元论文有没有。
Cox： No, and I think it's related to what I was saying about computing. Nobody took much notice of the 1972 paper for a while, until various people started to write software which was widely useful.
Cox： 不，我想这和我刚才说的计算有关。有一段时间没有人注意到1972年的论文，直到许多人开始编写广泛有用的软件。
Reid ：It was pretty fast, I think.
Reid ：我想这相当快。
Cox： Yes, it was 6 or 7 years.
Cox： 是的，那是六七年。
Reid ：At Oxford they did the software before you gave the talk, I think. Peto mentions it in the discussion.
Reid ：我想，在牛津大学，他们在你演讲之前做了软件。佩托在讨论中提到了这一点。
Cox： Ah but there's a difference: I had the software to do the examples but there is a difference between just writing the program to do an example and having something polished enough to distribute around the world.
Cox： 啊，但是有一个区别：我有软件来做示例，但是仅仅编写程序来做示例和有足够完善的东西在世界各地分发是有区别的。
Reid ：Could you describe the background for your 1972 paper [15]?
Reid ：你能描述一下你1972年论文的背景吗？
Cox： Quite a few people-I think particularly of Peter Armitage and Ed Gehan and Marvin Zelen, and I think there were others-said they were getting a certain kind of data, censored survival data, with a lot of explanatory variables. Nobody knew quite how to handle this sort of data in a reasonably general way, and there seemed to be dissatisfaction with assuming an underlying exponential distribution or Weibull distribution modified by some factor. It seemed that something slightly more general was called for. Well, in the light of all sorts of things I'd done in stochastic processes it's entirely natural to approach this in terms of hazard. So the specification of some basic function of the underlying time scale, multiplied by a factor, that's sort of immediate and obvious really. I don't know whether it's new to that paper, I think probably it is, but anyway it's sort of immediate.
Cox： 相当多的人——我特别想到彼得·阿米蒂奇、埃德·格汉和马文·泽伦，我想还有其他人说他们得到了某种数据，经过审查的生存数据，有很多解释变量。没有人知道如何以一种相当普遍的方式处理这类数据，人们似乎不满意假定一个潜在的指数分布或由某些因素修正的威布尔分布。似乎需要一些更一般的东西。鉴于我在随机过程中所做的各种事情，从危险的角度来看待这一点是完全自然的。所以，对基本时间尺度的一些基本函数的说明，乘以一个因子，这有点直接和明显。我不知道这篇文章是否是新的，我想可能是的，但不管怎样，它有点直接。
Then the question was how to actually do the statistical analysis. I wrote down the full likelihood function and was horrified at it because it's got exponentials of integrals of products of all sorts of things, unknown functions and so forth. I was stuck there for quite a long time-I would think the best part of five years or maybe even longer. Then suddenly I thought that the obvious thing to do was to concentrate on the part of the likelihood that actually gave you the information about the regression coefficients that you were interested in. It was absolutely obvious how to do that, and so just write down the answer. It occurred to me while I had a high temperature and was in bed with flu. It suddenly struck me that you could do this, and then when I felt better I tried to recover the argument and couldn't. But I was so convinced that when I was ill I had done this, that I tried again and then I saw what it was that I'd done.
然后问题是如何实际进行统计分析。我写下了全似然函数，并对它感到震惊，因为它有各种各样的乘积的指数积分，未知函数等等。我被困在那里很长一段时间——我想这是五年中最好的一段时间，甚至更长。然后我突然想到，显然要做的事情是专注于可能性的一部分，它实际上给了你关于你感兴趣的回归系数的信息。这是非常明显的怎么做，所以只要写下答案。当我发高烧和患流感躺在床上时，我突然想到了这一点。我突然意识到你可以这样做，然后当我感觉好点的时候，我试着恢复论点，但做不到。但我坚信，当我生病的时候，我做了这件事，我再试了一次，然后我看到了我做了什么。
Then, of course, the paper has a lot of other things in it, which came later: particularly the numerical example, and the idea of time-dependent covariates, and multivariate generalizations and so on. But the key thing was to see that it was obvious that you just ignored parts of the likelihood. Now of course that did raise the question of whether when you'd thrown away certain factors of the likelihood, you could still apply standard maximum likelihood results. Somehow or other, I don't exactly remember how, I persuaded myself that it was quite clear that the results did apply. So the paper just says that and doesn't really give any careful justification.
当然，这篇论文还有很多其他的东西，都是后来才出现的：特别是数值例子，时间相关协变量的概念，以及多元推广等等。但关键是要看到，很明显，你忽略了部分可能性。当然，这确实提出了一个问题，当你抛开某些可能性因素后，你是否仍然可以应用标准的最大可能性结果。不知怎么的，我不记得我是如何说服自己，很明显，结果确实适用。所以这篇文章只是说了这一点，并没有给出任何仔细的理由。
Reid ：I think you used the word martingale in the paper.
Reid：我想你在报纸上用了鞅这个词。
Cox： Did I? Well, I was well aware it was connected with martingales. I'd been influenced by David Silvey [Silvey (1961)] who I think fifteen years before that had pointed out that there is a very strong connection between maximum likelihood estimation with dependent random variables and martingales. Anyway, I didn't spell it out in any detail: that was done two or three years later in a Biometrika paper which sets out the idea a bit more systematically
Cox：是吗？我很清楚这和鞅有关。我受到了David Silvey[Silvey（1961）]的影响，我认为他在15年前就指出了相依随机变量的最大似然估计和鞅之间有着非常紧密的联系。无论如何，我没有详细说明：这是在两三年后的一篇Biometrika论文中完成的，该论文更系统地阐述了这一想法。我在1972年的论文中将这件事称为$a$条件可能性，我被许多人指责，他们说这不是条件可能性，我认为这很奇怪。这真的是一美元一美元的条件；这是一种条件可能性。
So that's the essence of it. It didn't come from one particular application, but it came from perceiving, on the advice of others, that in medical statistics people were getting a certain kind of data that they didn't know how to analyze. And I think, though it's a long time ago and I don't remember too clearly, I could conceive that in industrial reliability and perhaps other fields essentially the same problems were arising.
这就是它的本质。它不是来自某个特定的应用程序，而是来自于根据其他人的建议感知到，在医学统计中，人们得到了某种他们不知道如何分析的数据。我想，虽然这是很久以前的事了，我记不太清楚了，但我可以想象，在工业可靠性和其他领域，基本上也出现了同样的问题。
Reid ：Between the time that you suddenly realized how to do the likelihood and you finished the paper-about how long was that?
Reid ：从你突然意识到如何做这个可能性到你完成这篇论文有多长时间？
Cox： I don't remember; it wouldn't have been very long. Not more than a few months.
Cox： 我不记得了；不会太久的。不超过几个月。
Reid ：At that point did you have a feeling of excitement that one assumes goes with a great discovery?
Reid ：在这一点上，你是否有一种兴奋的感觉，人们认为这是一个伟大的发现？
Cox： Yes, I think so, because I'd had this problem at the back of my mind for a long time, and it was awfully nice to feel that l'd got somewhere with it.
Cox： 是的，我想是的，因为这个问题在我的脑海里已经存在很长时间了，感觉到我已经找到了解决这个问题的方法，真是太好了。
Reid ：I think that comes across in the paper; it almost seems to have been written in one go.
Reid ：我认为这在报纸上出现了；它几乎像是一下子写出来的。
Cox： It would have been written extremely quickly, yes.
Cox： 是的，它会写得非常快。
Reid ：How do you feel about the cottage industry that's grown up around it?
Reid：你觉得在它周围成长起来的家庭手工业怎么样？
Cox： Don't know, really. In the light of some of the further results one knows since, I think I would normally want to tackle problems parametrically, so I would take the underlying hazard to be a Weibull or something. I'm not keen on nonparametric formulations usually.
Cox： 不知道，真的。鉴于人们知道的一些进一步的结果，我认为我通常希望以参数化的方式解决问题，因此我认为潜在的危险是威布尔或其他什么。我通常不喜欢非参数公式。
Reid ：So if you had a set of censored survival date today, you might rather fit a parametric model, even though there was a feeling among the medical statisticians that that wasn't quite right.
Reid：因此，如果你今天有一组经过审查的存活日期，你可能更愿意拟合一个参数模型，尽管医学统计学家认为这不太正确。
Cox： That's right, but since then various people have shown that the answers are verv insensitive to the parametric formulation of the underlyıng distribution [see, e.g., [20], Chapter 8.5]. And if you want to do things like predict the outcome for a particular patient, it's much more convenient to do that parametrically.
Cox： 这是对的，但从那时起，各种各样的人已经证明，答案对潜在的ıng分布的参数公式非常不敏感[参见，例如[20]，第8.5章]。如果你想做一些事情，比如预测某个病人的结果，那么用参数化的方法来做就方便多了。
Reid ：The paper has had an enormous impact, as you know, in many different directions. What do you think are the most positive benefits of the work?
Reid ：正如你所知，这份文件在许多不同的方面产生了巨大的影响。你认为这项工作最积极的好处是什么？
Cox： Handling in-study covariates, that is, timedependent covariates, I think is rather importantand the fact that it's readily adapted to multiple events, what the sociologists call event history analysis, for instance. It's the basis for really lots of further things in a fairly immediate way. Of course, another issue is the physical or substantive basis for the proportional hazards model. I think that's one of its weaknesses, that accelerated life models are in many ways more appealing because of their quite direct physical interpretation, particularly in an engineering context.
Cox： 在研究中处理协变量，也就是时间相关的协变量，我认为是相当重要的，而且事实上它很容易适应多个事件，比如社会学家称之为事件历史分析。它是以相当直接的方式进行大量后续工作的基础。当然，另一个问题是比例危险模型的物理或实质基础。我认为这是它的弱点之一，加速寿命模型在许多方面更具吸引力，因为它们的物理解释相当直接，特别是在工程环境中。
Reid ：We did talk about your books to some extent when you mentioned earlier that none of your books are textbooks. I've always thought of Theoretical Statistics
Reid ：当你之前提到你的书都不是教科书时，我们确实在某种程度上谈论过你的书。我一直认为理论统计学$[16]$是一本教科书，而Pve使用了部分随机过程[12]作为教科书。
Cox： Yes, Stochastic Processes would be the nearest. But although it now looks very elementary, there was quite a bit of new material in it, both of Hilton's and mine.
Cox： 是的，随机过程是最接近的。虽然现在看起来很简单，但里面有很多新材料，包括希尔顿和我的。
It might help explain my attitude to these books to point out the traditional British method of university teaching, though I don't say this is good or that I altogether approve of it. You see, although Pve taught quite a wide range of courses at one time or another, I've only once ever used a textbook. I would not normally, even for a moment, consider using a textbook in a course of lectures. I would refer the students to several different books, and see the role of books as backup for the teacher of a course, the opportunity to choose what he or she thought was important. Not to set out an exact prescription for somebody to follow. And that's whv, perhaps. my co-workers and 1 have written books in the particular way we have. So, the serious point is the attitude to textbooks which is still I think entirely different in the U.K. than in the U.S. I don't say that in any spirit of thinking the U.K. system is better, just totally different. And I guess the best method is somewhere in between.
指出英国传统的大学教学方法可能有助于解释我对这些书的态度，尽管我不认为这是好的，也不认为我完全赞同。你看，虽然Pve在某个时候教过很多课程，但我只使用过一次教科书。我通常不会，甚至在一段时间内，考虑在讲课中使用教科书。我会让学生看几本不同的书，并将书的作用视为一门课程的老师的后盾，让他们有机会选择他或她认为重要的内容。不是给某人开一个确切的处方。也许这就是whv。我和我的同事以我们特有的方式写书。因此，最严重的是对教科书的态度，在英国我认为与美国完全不同，我不认为任何精神上的想法，英国制度更好，只是完全不同。我想最好的方法是介于两者之间。
I've only once taught a course from a textbook, and that was in Berkeley in 1956 , when one of the standard things one did in those days, if one was lucky enough to be invited to Berkeley for the summer, was to teach a summer school course from Mr. Neyman's elementary book on statistics, which I think is no longer in print. At coffee many mornings, Mr. Neyman would say anxiously "Have you done the example on so-and-so?" and he'd mention one of his favorite examples; and I cheated slightly, because I could almost always say, "Yes, I've done that example" but what I didn't tell Mr. Neyman was I often demanded more of the students than he had.
我只教过一门教科书上的课程，那是1956年在伯克利，当时人们做的一件标准的事情，如果有幸被邀请到伯克利过暑假的话，就是教一门内曼先生的《统计学基础》中的暑期课程，我想这本书已经不再出版了。很多早上喝咖啡的时候，内曼先生都会焦急地说：“你做过某某的例子吗？”他会提到他最喜欢的一个例子；我有点作弊，因为我几乎总是可以说，“是的，我做了那个例子”，但我没有告诉内曼先生的是，我经常要求学生比他更多。
Reid ：You're famous for your books being extremely concise.
Reid ：你的书非常简洁而出名。
Cox： Really?
Cox： 真正地
Reid ：[Laughs.] Yes. Is it something you need to strive for or is it something that comes automatically to you?
Reid ：[笑]是的。这是你需要努力争取的东西还是你自然而然想到的东西？
Cox： Well, I'm gradually coming around to the idea, and this is something I've only learnt perhaps in the last year or so, that it's not something to strive for so much as something to fight against. All my inclination, and all my training, is to write with not an unnecessary word.
Cox： 嗯，我逐渐接受了这个想法，这是我在过去一年左右才学到的东西，这与其说是一件需要努力的事情，不如说是一件需要对抗的事情。我所有的爱好，所有的训练，都是用一个不必要的词来写作。
And I suppose it's something about me personally; I find it much easier to understand something that is clearly put with a minimum number of words, when you know you've got to look at each word and think what it means. The notion that if you then double the number of words you make it any clearer, I think is not right. You know, if you double the amount of information or explain something at more length or give an example or something, that's helpful, but.... So I would in principle want to claim maximum conciseness is also maximum clarity.
我想这与我个人有关；我发现，当你知道你必须看每一个单词并思考它的意思时，用最少的字数清楚地理解一些东西要容易得多。我认为，如果你把字数增加一倍，就会使它更清楚，这种想法是不对的。你知道，如果你把信息量翻了一番，或者解释得更详细，或者举个例子什么的，那是很有帮助的，但是。。。。所以原则上我想说，最大限度的简洁也是最大限度的清晰。
There's also the psychological point. I find the notion of trying to explain a certain moderately advanced subject in a couple of hundred pages, the essence of it, much more appealing than the 800 -page encyclopedia on something. In certain very particular subjects there's a need for an encyclopedic treatment but I don't think very many. I mean one could write a book a thousand pages long. on the linear model, but would it be a good idea?
还有心理上的问题。我发现试图用几百页的篇幅来解释某个中等程度的高级学科的概念，它的本质，比800页的百科全书更吸引人。在某些非常特殊的学科中，有必要进行百科全书式的治疗，但我认为不太多。我的意思是一个人可以写一千页长的书。关于线性模型，但这是个好主意吗？
Reid ：You said a minute ago that in the last year or two you've come to the notion that you needn't be quite so concise?
Reid：你一分钟前说过，在过去一两年里，你已经意识到你不必如此简洁了？
Cox： Hmmmmm.
Cox： 嗯.
Reid ：Do you have a favorite book? of your own?
Reid ：你有最喜欢的书吗？你自己的？
Cox： Well, either Planning of Experiments [7] or Point Processes [19], I suppose.
Cox： 我想，要么是实验计划[7]，要么是点过程[19]。
Reid ：Any you really don't like or wish you hadn't written?
Reid ：任何你真的不喜欢或希望你没有写的东西？
Cox： No, actually. Perhaps I should have, but I don't. Of course many of my books, and papers, are collaborative efforts. It's been my enormous good fortune to work with a succession of friends with whom collaboration has been both very enjoyable and from my point of view extremely fruitful. But, they're all a considerable pain to write. It's satisfying when it's done and on the whole, if you've thought about a subiect for a considerable time and feel you have something to say about it that isn't in the literature already, it is entirely sensible to write it down as a book of some sort. Whether it is a textbook or not doesn't really matter. But with one exception I think all the books have taken a mighty long time to do, the exception being the little book on renewal theory [10], which took about three months. The slowness comes partly from not concentrating on one thing at a time, but more seriously it comes from a lack of clarity about what you want to say.
Cox： 不，事实上。也许我应该，但我没有。当然，我的许多书和论文都是合作的成果。与一系列的朋友一起工作是我巨大的幸运，他们的合作非常愉快，从我的角度来看，非常富有成效。但是，他们都是一个相当痛苦的写作。当它完成的时候是令人满意的，总的来说，如果你已经思考了一段相当长的时间，并且觉得你对它有一些文献中没有的东西要说，那么把它写成某种书是完全明智的。它是否是教科书并不重要。但是除了一个例外，我认为所有的书都花了很长时间才完成，唯一的例外是关于更新理论的小书[10]，它花了大约三个月的时间。这种迟钝部分是因为没有一次专注于一件事，但更严重的是，它来自于对你想说什么缺乏清晰的理解。
Reid ：Five years you said once, on average it took you to do a book.
Reid ：你曾经说过五年，你平均花了五年的时间写一本书。
Cox： Did I?
Cox： 是吗？
Reid ：Yes, which means you sometimes must have been doing two at the same time. Do you enjoy writing just for the sake of writing?
Reid：是的，这意味着你有时必须同时做两件事。你喜欢仅仅为了写作而写作吗？
Cox： No, I certainly don't. I'd rather look at the problem which somebody brought in this morning, so to speak.
Cox： 不，我当然不知道。可以说，我宁愿看看今天早上有人提出的问题。
Reid ：Before this interview you suggested talking about the motivation of theoretical research.
Reid ：在这次采访之前，你建议谈谈理论研究的动机。
Cox： I think what I had in mind was perhaps this: that people say theoretical work in statistics should be motivated by applications because it's a practical subject, and that of course is true. On the other hand, I think theoreticians have to try and stand back from individual applications. Some of the papers I've written have been very strongly tied to, for example, solving a particular problem in experimental design in a very particular context. Okay, that can be worth doing maybe, but the things that are more likely to be widely useful are those where you stand back from one very particular application and say here's a whole family of problems that arise in applications in several fields, and try to address that. That's a better way to go if you can. And in a sense, you see, the work on conditional inference is one step further back still from that, in that it was very strongly motivated by practical experience and yet on the other hand, I couldn't say it arose from one particular special type of problem. It arose in a sense from all the applied work I'd done to that point.
Cox： 我想我的想法可能是这样的：人们说统计学的理论工作应该以应用为动力，因为它是一门实用的学科，这当然是真的。另一方面，我认为理论家必须试着避开个别应用。我写的一些论文都与，例如，在一个非常特殊的背景下解决实验设计中的一个特殊问题紧密相关。好的，这可能是值得做的，但更可能广泛有用的事情是，你从一个非常特殊的应用程序中退后一步，说在几个领域的应用程序中出现了一系列问题，并尝试解决这些问题。如果可以的话，这是一个更好的方法。从某种意义上说，你看，条件推理的工作比这还要倒退一步，因为它受到实践经验的强烈推动，但另一方面，我不能说它是由一种特殊类型的问题引起的。从某种意义上说，它是从我迄今为止所做的所有应用工作中产生的。
Reid ：Are you saying that you saw something missing from the theory?
Reid ：你是说你看到了理论上的缺失？
Cox： No, but that I felt, for instance, that various aspects of the Neyman-Pearson theory-choose alpha, choose a critical region, reject or accept the null hypothesis-give a rigid procedure, that this isn't the way to do science.
Cox： 不，但我觉得，例如，尼曼-皮尔逊理论的各个方面选择α，选择一个临界区域，拒绝或接受无效假设，给出一个严格的程序，这不是科学的方法。
Reid ：To me it's so obvious that it's not the way to do it, but presumably not at all obvious in the fifties.
Reid ：对我来说，这是如此明显，它不是这样做的方式，但大概在50年代一点也不明显。
Cox： I agree it's obvious but why then do people write books that say this is what you should do? But. Neyman talked a lot about inductive rules of behav- ior, and it seemed to me he took the view that the only thing that you could ever say is if you follow this procedure again and again, then
Cox： 我同意这很明显，但为什么人们写的书说这是你应该做的？但是内曼谈了很多关于行为的归纳规则，在我看来，他认为你唯一能说的是，如果你一次又一次地遵循这个过程，那么95%的时间会有事情发生；你不能说任何关于某个特定实例的事情。现在，我不认为这是他在应用中实际使用统计方法的方式；他采取了更灵活的方式。
But even apart from that, you can say, is this notion of
但除此之外，你可以说，这个5%或95%区域的概念，这仅仅是对95%置信区间的解释吗？一种假设性的解释，如果你这么做，会发生这样那样的事情吗？或者它是关于如何做科学的指导？在我看来，第一次还行，事实上第一次还行，第二次还行。我不认为这一直都很清楚。你这样认为吗？
Reid ：No, I agree not. It always seemed clear to me, if I thought about it, which wasn't terribly often I suppose.
Reid ：不，我不同意。如果我想一想，这对我来说总是很清楚的，我想这并不经常发生。
Cox： Yes, but if you do, if you're involved in doing applied work, you don't necessarily have to think about it but you have to have a broad approach. The theoretician's job is partly to try and capture how you should use these techniques as well as just to form a theoretical basis.
Cox： 是的，但是如果你做了，如果你参与了应用工作，你不一定要考虑它，但你必须有一个广泛的方法。理论家的工作部分是尝试和捕捉你应该如何使用这些技术，以及只是形成一个理论基础。
Reid ：So it really is motivated by applications, or motivated by science.
Reid ：所以它实际上是由应用程序驱动的，或者是由科学驱动的。
Cox： Yes, totally so. But not by saying here is this problem in mineral technology or something to which here is the answer.
Cox：是的，完全是这样。但不是说这里是矿物技术的问题，或者这里是答案。
Reid ：Yes. We seem to hear a lot about this nowadays. Unless you're going to the lab and standing shoulder to shoulder
Reid ：对我们现在似乎听到很多关于这方面的事情。除非你要去实验室并肩站着...
Cox： Well, I'm a terrible experimenter, but I have spent a fair amount of time in labs, although not as much as I would have liked to. But of course some of this discussion has a strong antitheoretical tone to it which seems to me destructive and totally unnecessary: "We're practical chaps and we don't need all this theory. All we need to do is plot a few graphs, and be sensible." Now it's important to plot a few graphs and be sensible-it's important and difficult, but if you remove theory then the whole subject becomes nothing. It becomes a collection of fragmentary tricks.
Cox： 嗯，我是一个糟糕的实验者，但我在实验室里花了相当多的时间，虽然没有我想要的那么多。但当然，其中一些讨论带有强烈的反神学基调，这在我看来是破坏性的，完全没有必要的：“我们是实用主义者，我们不需要所有这些理论。我们需要做的只是画几张图，然后变得理智。”现在画几张图，变得理智很重要，这很重要，也很困难，但是如果你去掉了理论，那么整个主题就什么都没有了。它变成了一堆零碎的把戏。
Reid ：The theory that you're describing where you see a common thread in a variety of applications, it's really rare to see that kind of theoretical work done. And in that sense one can sympathize with the more practical people in that a lot of the theoretical work does seem very self-motivated.
Reid：你所描述的理论，在各种应用中，你可以看到一个共同的线索，这种理论工作很少完成。从这个意义上说，我们可以同情更实际的人，因为很多理论工作似乎都是自我激励的。
Cox： There's nothing wrong with that but different people get their motivation in different ways. I don't think you can lay down any law. And of course, as the subject gets more and more specialized, it's getting more and more difficult for particular individuals to know enough about more than at most one or two fields of application. Forty years ago it was perhaps a bit easier to be wide ranging in applied interests.
Cox：这没什么错，但不同的人有不同的动机。我认为你不能制定任何法律。当然，随着这门学科越来越专业化，对于特定的个人来说，了解最多一个或两个应用领域的知识变得越来越困难。四十年前，在应用兴趣领域广泛开展工作可能要容易一些。
Reid ：Let me ask just one more question on the theory topic. I'm not sure if it has a sensible answer, but what's your favorite part of theoretical statistics?
Reid ：让我再问一个关于理论的问题。我不确定它是否有一个合理的答案，但你最喜欢的理论统计部分是什么？
Cox： I've never thought of that. Well I'm tempted to say, what I'm working on at the moment, but that's a slightly facetious answer. You're thinking now as a teacher?
Cox： 我从来没想过。嗯，我很想说，我现在正在做什么，但这是一个有点滑稽的回答。你现在想当老师？
Reid ：I suppose I mean possibly as a teacher or expositor.
Reid ：我想我的意思可能是作为一名教师或讲解员。
Cox： It's an interesting question. I very much admire subjects like certain areas of pure mathematics, or for that matter certain areas of probability theory, where a seminar can be given in the old style with a very large blackboard, in which the lecture begins in the upper left-hand corner of the blackboard and develops a theme and ends 50 minutes later down in the bottom right-hand corner of the blackboard. Then you've got an area before you-a beautiful painting, almost. It would be excellent to be able to do that with a topic in statistics. I feel it's very hard, partly because the difficult aspects are often more conceptual than mathematical. But if one could think of it, a piece of theory, a new theory that could be laid out like that, I'd find it extremely appealing.
Cox： 这是一个有趣的问题。我非常欣赏一些科目，比如纯数学的某些领域，或者概率论的某些领域，在这些领域里，可以用一块很大的黑板以老式的方式进行研讨会，讲座从黑板左上角开始，展开主题，50分钟后在黑板右下角结束。然后你面前有一块地方——一幅漂亮的画，差不多。如果能以统计学为主题来做这件事，那就太好了。我觉得这很难，部分原因是困难的方面往往是概念性的，而不是数学性的。但是如果有人能想到它，一个理论，一个新的理论，可以像那样展开，我会发现它非常吸引人。
Reid ：Turning from theory to applications, I wondered if you had any specific applications or consulting problems that you especially enjoyed or you thought were particularly well done and useful.
Reid：从理论到应用，我想知道你是否有特别喜欢的或认为做得特别好和有用的具体应用或咨询问题。
Cox： Well, I collaborated when I was in Leeds very closely with a textile physicist. That was very interesting indeed, and I suppose if I had stayed in Leeds we might have developed that a bit further. It was some mixture of physics, statistics and classical applied mathematics. More recently, I tend to get involved in applied problems almost at second hand via other statisticians or epidemiologists or whatever.
Cox： 我在利兹时与一位纺织物理学家密切合作。这真的很有趣，我想如果我留在利兹，我们可能会更进一步。它是物理学、统计学和经典应用数学的混合体。最近，我倾向于通过其他统计学家或流行病学家或其他什么人间接地介入应用问题。
The only clinical trial I've ever been deeply involved with at first hand was a big primary prevention study on hypertension. I was the only nonmedical person on the management committee, and that was extremely interesting. Not perhaps so much from the statistical point of view, although it was reasonably interesting statistically, but to get some insight into how these things go. Otherwise, I've tried to really range as broadly as possible in applications, and I can't immediately think of any particular one that stands out.
我第一手参与的唯一一项临床试验是一项大型的高血压一级预防研究。我是管理委员会中唯一一个非医学人士，这非常有趣。从统计学的角度来看，也许不是那么多，虽然这在统计学上是相当有趣的，但是要了解这些事情是如何进行的。否则，我已经尝试在应用程序中尽可能广泛地应用，我无法立即想到任何一个特别突出的应用程序。
Before I came to Oxford I'd had dealings with a lot of people in different areas of work, in the physical and biological sciences, in technology and to a limited extent in some other fields. I hadn't had any very systematic contact with social scientists. One of the appeals of coming to Nuffield College, which is a postgraduate college in the social sciences, was to broaden my applied experience and to get a better idea of what social scientists are up to. I have found that extremely interesting in various ways. It's left me with a great respect for sociologists, in particular, who in the empirical tradition here are very careful about their data collection and their analysis, and cautious in interpretation. And, of course, they are working totally with observational material, whereas I've tended on the whole to work with experimental material. That brings to the forefront issues like to what extent can you draw reliable conclusions from observational data and also this issue of trying to get somewhere vaguely approaching a notion of causality from observational material. It's very interesting and important.
在我来到牛津之前，我曾在不同的工作领域与许多人打过交道，包括物理和生物科学、技术以及一些其他领域。我没有与社会学家进行过任何系统的接触。来到纳菲尔德学院（Nuffield College），这是一所社会科学研究生院，其中一个吸引人的地方是拓宽我的应用经验，更好地了解社会科学家的研究方向。我发现这在很多方面都非常有趣。这给我留下了对社会学家的极大尊重，尤其是，他们在这里的经验传统中，对他们的数据收集和分析非常谨慎，在解释时也非常谨慎。当然，他们完全是在使用观察材料，而我总体上倾向于使用实验材料。这就引出了最前沿的问题，比如你能从观测数据中得出多大程度的可靠结论，以及试图从观测资料中模糊地得出因果关系概念的问题。这是非常有趣和重要的。
Reid ：I'm not sure students get the same exposure to applied problems that you did.
Reid ：我不确定学生对应用问题的接触程度是否与你相同。
Cox： Well I was exceptionally fortunate in most respects. I didn't learn perhaps a great deal at the Royal Aircraft Establishment, although I expect I learned more than I think I did. But WIRA was fantastic experience. And then Cambridge also, there were a lot of people around who were very good scientists who one could talk to, who wanted to have discussion of their problems. There's a great danger I think that statistical consulting, so-called, in universities can end up rescuing not very good or bad doctoral theses in other subjects, rather than talking to the leading scientists in those subjects. It's the second we should be doing, not the first. The first is a kind of moral duty, up to a point, but not at the expense of the second. Too much of the first leads to all sorts of undesirable things; in particular, a certain arrogance amongst some statisticians towards engineers and scientists, which seems to me absolutely ludicrous and very dangerous.
Cox： 我在很多方面都特别幸运。我在皇家飞机公司学到的东西可能不多，尽管我希望我学到的比我想象的要多。但维拉是一次奇妙的经历。剑桥大学也有很多人，他们都是非常优秀的科学家，可以和他们交谈，他们想讨论他们的问题。我认为，大学里所谓的统计咨询有很大的危险，它最终可能挽救其他学科的不太好或不好的博士论文，而不是与这些学科的顶尖科学家交谈。这是我们应该做的第二件事，而不是第一件事。在某种程度上，第一种是一种道德责任，但不会以牺牲第二种为代价。太多的第一个会导致各种不受欢迎的事情；特别是一些统计学家对工程师和科学家的傲慢态度，在我看来，这绝对是荒谬和非常危险的。
Reid ：It's very difficult though, isn't it, that kind of collaboration that you're describing. You need to find the people or they need to find you.
Reid ：不过，你所描述的那种合作很难，不是吗。你需要找到那些人，或者他们需要找到你。
Cox： Yes, it's very very difficult-I'm tempted to say a matter of luck.
Cox： 是的，这很难——我想说的是运气的问题。
Reid ：Do you sit down and fool with data much.
Reid ：你经常坐下来玩弄数据吗。
Cox： I sit down, and [laughs] make suggestions to other people as to what do to and sometimes I hover annoyingly over them while they do it.
Cox： 我坐下来[笑]向其他人提出建议，告诉他们该怎么做，有时，当他们这么做时，我会恼怒地在他们身上徘徊。
Reid ：I wondered what you'd like to say about computing?
Reid ：我想知道你对计算有什么看法？
Cox： Well, in the days of the electric calculator and the old hand Brunsvega, I did an enormous amount of numerical work. Then when computers came along I went to a programming course in London. In those days the notion was you had to learn to program in machine code, before you were let loose on Fortran or anything like that. And I did write a program for linear regression in 1957 . I think I realized at that point that I had to make a choice either to spend a large proportion of the next 20 years on this, and it was obviously going to be extremely important subject, or to spend nothing and just try and follow what was going on so I had an idea what was feasible, what wasn't feasible.
Cox： 嗯，在电子计算器和老手Brunsvega的时代，我做了大量的数值计算工作。后来，当电脑出现时，我在伦敦参加了一个编程课程。在那些日子里，人们的想法是，在使用Fortran或类似的语言之前，你必须学会用机器代码编程。我在1957年写了一个线性回归程序。我想当时我意识到，我必须做出选择，要么在未来20年的大部分时间里花在这件事上，这显然将是一个极其重要的课题，要么什么都不花，只是试着跟踪正在发生的事情，这样我就知道什么是可行的，什么是不可行的。
I decided on the second, and I think for me that was the right decision to make. The whole business is a great miracle and I think people take it for granted. There was a period, perhaps in the late fifties, when if you went to a statistical meeting all you'd hear would be people talking about whether they'd got their regression program to run. I can remember going to one of the leading British computer scientists and saying I was interested in inverting matrices. "Ah, yes," he said. "Can you do a 3 -by- 3 matrix?" I said. "No, not yet. Tomorrow?"
我选择了第二个，我认为对我来说，这是一个正确的决定。整个商业是一个伟大的奇迹，我认为人们认为这是理所当然的。有一段时间，也许是在50年代末，如果你去参加一个统计会议，你会听到人们谈论他们是否已经运行了回归程序。我记得我去英国一位著名的计算机科学家那里，说我对矩阵求逆很感兴趣。“啊，是的，”他说。“你能做一个3乘3的矩阵吗？”我说。“不，还没有。明天？”
I did, with Katherine Booth, construct some designs on the computer in a paper in Technometrics in the late 1950's [11]. I think that might have been one of the first uses of a computer to construct experimental designs. So I'm sort of interested, but also being an extremely impatient person, I still find the fiddley details irritating. People have been saying for 20 years, "Next year everything will be absolutely painless and foolproof, very, very easy to use." Well now what's happened it seems to me is that, although what can be done has increased by a fantastic factor in that period, and it has got easier, it's not got easier enough for the casual user.
20世纪50年代末，我与凯瑟琳·布斯（Katherine Booth）在《技术计量学》（Technometrics）的一篇论文中，在计算机上构建了一些设计[11]。我认为这可能是计算机最初用于构建实验设计的用途之一。所以我有点感兴趣，但作为一个非常不耐烦的人，我仍然觉得这些琐碎的细节令人恼火。20年来，人们一直在说，“明年一切都将绝对无痛、万无一失、非常、非常容易使用。”好吧，现在发生的事情在我看来是，尽管在那个时期可以做的事情增加了一个奇妙的因素，而且变得越来越容易，但对于普通用户来说还不够容易。
I was also very fortunate to spend six months at Bell Labs in 1965 , where the main topic of discussion was in what direction statistical computing was going to go. Martin Wilk, I think, was the driving force behind it. I think the notions of
1965年，我也非常幸运地在贝尔实验室度过了六个月的时间，这里讨论的主要话题是统计计算将走向何方。我认为，马丁·威尔克是背后的驱动力。我认为S和S-PLUS的概念是马丁所预见的。我记得他曾说过，“我们不想要回归和方差分析的软件包，也不想要二进制数据、时间序列和多元分析的软件包；我们想要的是足够普遍的东西，能够看到这些东西中的共同元素，能够从一种计算类型转移到另一种计算类型。”但即使贝尔实验室拥有巨大的资源，它也需要很长时间才能实现。
Reid ：Well, it really sounds like a prescription for object-oriented programming.
Reid：嗯，这听起来像是面向对象编程。
Cox： Yes, almost.
Cox： 是的，差不多了。
Reid ：The only other thing I wanted to ask you about is something that you mentioned to me in a letter a while ago which I think was connected with your knighthood. Your words were roughly that, after feeling when you were younger that you didn't get very much recognition for your work, you now felt you were receiving a "bizarre excess."
Reid ：我唯一想问你的另一件事是你刚才在信中提到的，我想这与你的骑士身份有关。你的话大概是这样的，当你年轻时觉得自己的工作没有得到太多的认可后，你现在觉得自己得到了“奇怪的超额”
Cox： Yes, I think that sums it up adequately. Well, everybody needs encouragement, and of course as you get older you still need encouragement. But the time you most need it is when you're starting. It would be quite wrong to think that people were ever discouraging, they weren't. It was all very low key, typically British understatement sort of thing. You never really knew quite what people thought, despite the relative frankness of RSS discussions. And I'd published a few papers with very little notion of whether anybody had paid any attention to them. Until I first went to the United States, where people would come and say, "Oh, I read that paper, I think we could do so and so." That sort of thing is very encouraging. And then, more recently, I've been absurdly lucky with all these pieces of recognition. Of course the system's a bad one in one sense, that if you get one piece of recognition it's more likely you'l get another. It ought to be the other way around.
Cox： 是的，我想这就足够了。每个人都需要鼓励，当然，随着年龄的增长，你仍然需要鼓励。但是你最需要它的时候是你开始的时候。如果认为人们曾经感到沮丧，那就大错特错了，事实并非如此。这一切都是非常低调的，典型的英国式的轻描淡写。你从来都不知道人们的想法，尽管RSS的讨论相对坦率。我发表了几篇论文，几乎不知道是否有人注意过它们。直到我第一次去美国，那里的人们会说，“哦，我读了那篇文章，我认为我们可以这样那样做。”这种事情非常令人鼓舞。然后，最近，我非常幸运地得到了所有这些认可。当然，从某种意义上说，这个系统是一个糟糕的系统，如果你得到了一个认可，你就更有可能得到另一个认可。应该是相反的。
Reid ：When you were younger and you were not getting initially positive feedback, was that just typical British understatement?
Reid ：当你年轻的时候，你一开始并没有得到积极的反馈，这只是典型的英国人的轻描淡写吗？
Cox： I think so. Well, I don't even remember thinking about it at the time; this is a retrospective feeling. I wouldn't have expected it, but I perceive now that it would have been good.
Cox： 我认为是这样。嗯，我甚至不记得当时有想过它；这是一种回顾性的感觉。我没有料到，但我现在意识到这会很好。
Reid ：You've been very encouraging to young people; I think that's the first thing anyone I speak to about you mentions.
Reid ：你一直在鼓励年轻人；我想这是我跟你谈的第一件事。
Cox： Well, I hope I have been; I've certainly tried. I think because of this perception in my own case that it was important.
Cox： 嗯，我希望我是；我当然试过了。我认为，在我自己的情况下，这是很重要的。
Reid ：Was there a time when you realized that your fortunes had changed?
Reid ：你有没有意识到自己的命运已经改变？
Cox： Well, two occasions I suppose. First of all I bumped into George Barnard in the street and he said something like, "Have Birkbeck put you in for a professorship yet?" He must have known that they were intending to, which I didn't know, and I was absolutely astounded. Years before when I was at Cambridge I would have said my chances of ever getting a full professorship in a British University were virtually nil. So that was one thing. And then Fellowship of the Royal Society-I was astounded to be nominated, and some people go berserk with anxiety over this; it's probably very similar in Canada and the United States, and in other countries. You're nominated and then some years go by, and if you're lucky you suddenly get a message. I just dismissed it from my mind, I thought it would never go through.
Cox：嗯，我想有两次吧。首先，我在街上碰见乔治·巴纳德，他说：“伯克贝克让你当教授了吗？”他一定知道他们打算当教授，我不知道，我完全震惊了。几年前，当我在剑桥大学的时候，我会说我在英国大学获得正式教授职位的机会几乎为零。所以这是一件事。然后是皇家学会的联谊会——我对被提名感到震惊，有些人对此感到非常焦虑；加拿大、美国和其他国家的情况可能非常相似。你被提名，然后几年过去了，如果你幸运的话，你会突然得到一个信息。我只是把它从脑海中抹去，我以为它永远不会过去。
Reid ：But those were, as you describe them, surprising, unexpected encouragements. Was there a time when you suddenly felt you were a Very Important Person?
Reid ：但正如你所描述的，这些都是令人惊讶的、出乎意料的鼓励。有没有一次你突然觉得自己是一个非常重要的人？
Cox： Well, I hope I've never thought so. [Long pause. In a sense, the only thing that matters is if you can look back when you reach a vast, vast, vast age and say, "Have I done something reasonably in accord with my capability?" If you can say yes, okay. My feeling is in one sense, I've done that: in the tangible sense of books and papers, I've done more than I would have expected. In another sense I feel very dissatisfied: there are all sorts of problems that I nearly solved, and gave up, or errors of judgment in doing a little something and not taking it far enough. That I nearly did something you see, this is the irritating thing. You know, if you'd no idea at all, well it doesn't matter, it's irrelevant, but if you feel you were within an inch of doing something and didn't quite do it...
Cox： 嗯，我希望我从来没有这样想过。[长时间的停顿。从某种意义上说，唯一重要的是，当你年事已高，年事已高，回首往事时，你是否会说：“我做了一些我力所能及的事情了吗？”如果你能说是的，好吧。从某种意义上说，我的感觉是，我已经这样做了：从书籍和论文的有形意义上说，我做的比我预期的要多。从另一个意义上说，我感到非常不满意：有各种各样的问题，我几乎快解决了，最终却放弃了，或者在做一点事情而没有走得足够远的时候判断错误。Th我差点做了什么，你看，这是令人恼火的事。你知道，如果你一点都不知道，那没关系，这是无关紧要的，但是如果你觉得你离做某件事只有一英寸的距离，而且没有完全做。。。
Reid ：David, your energy and modesty continue to be an inspiration to a great many people, including myself. Thank you very much for the privilege of this interview.
Reid ：大卫，你的活力和谦虚继续激励着很多人，包括我自己。非常感谢您能有幸接受这次采访。
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