An Accidental Statistician

by George E P Box

  There were however some more serious complications. I was already in the United States, but Joan was to come somewhat later with our three-month-old baby, Helen, who had been born in England. Helen, of course, did not possess an alien registration card, so beginning in May 1960, five months before the baby's birth, I inquired whether my daughter would need a visa to enter the United States. This began considerable correspondence.

  I first wrote to the American Council for Nationalities Service in New York and received a long reply dated May 16, 1960, the meaning of which I found impossible to fathom. This quoted State Department Regulation 22 C.F.R. Section 42.36. I later wrote a letter to the Department of State in Washington and received another lengthy letter, dated June 10. This said that regulation 22 C.F.R. Section 42.36 would not be applicable to the baby's situation. Finally, on February 2, 1961, I received a second letter from my first correspondent from New York that seemed also to contradict the previous one.

  In the end, Joan flew to the United States. with the baby in a basket, and she passed through the immigration and customs process with no difficulty. Afterward I inquired how I could legalize her status in the United States. I received an alarming reply informing me that there was a good chance the baby was in the country illegally and that we would have to leave and then cross back over the border to establish legality. Luckily, after more bureaucratic exchange, I was eventually able to add Helen to my passport, finally putting an end to her unintended life of crime.

  Many years later, I had a similarly vexing experience with U.S. immigration authorities. The American government had decided that all resident aliens needed to be fingerprinted. The nearest immigration office was in Milwaukee, 70 miles from Madison. I went there and waited for what seemed an interminable amount of time. Finally, when it was my turn, the employee who was attempting to take my fingerprints was having trouble and called in another person to help. They both twisted my fingers in every possible direction, but they were unable to obtain prints. I was asked to return to the office on another day, when another attempt would be made but upon my return, the same thing happened. After considerable mulling and muttering, it was determined that I have no fingerprints. Like my infant daughter, I had launched an inadvertent career of crime. I thought immediately of:

  Macavity's a Mystery Cat: he's called the Hidden Paw—

  For he's the master criminal who can defy the Law.

  He's the bafflement of Scotland Yard, the Flying Squad's

  despair:

  For when they reach the scene of crime—Macavity's not there!

  He's outwardly respectable. (They say he cheats at cards.)

  And his footprints are not found in any file of Scotland Yard's…1

  T.S. Eliot

  My son Harry was born in Madison on May 13, 1962, becoming the only U.S. citizen in the family (Figure 7.1). We lived close to Lake Mendota in Shorewood Hills, an attractive village in the middle of the city of Madison. As they grew up, the children went to Shorewood School, the public school nearby, where they had the advantage of meeting other children of diverse ethnic backgrounds. Close by was university housing for visiting faculty and graduate students who came from all over the world. The children of these families made Shorewood School as international a place as the university campus.

  Figure 7.1 Harry, Helen, and our dog Victor.

  Madison is a city of lakes, and families take advantage of this whatever the season. When the children were young, I bought a small sailboat and Helen and Harry learned to be proficient sailors. Winter also invited us onto the lakes. Once when Helen was a toddler, she and I took a walk on frozen Lake Mendota. We passed many ice fishermen, and Helen peered into each of their buckets to see what they had caught. Whenever she saw an empty pail, she exclaimed rather loudly, “This one hasn't caught anything! And this one hasn't caught anything either!” I thought we'd get shot.

  Joan attended the university where she studied in the English Department. She earned an honor's degree in English and a master's degree in the History of Science (Figure 7.2). In 1978, she wrote a highly praised biography of her father, R.A. Fisher: The Life of a Scientist, which was published by Wiley.

  Figure 7.2 Joan getting her degree with Helen and Harry.

  Both Joan and I enjoyed Shakespeare, and in the summer we would drive with the children to the Shakespeare Festival at Stratford, Ontario. Joan missed England, and Stratford had a bit of England about it, with its parks and gardens and places that served tea. Many of the actors were British, chief among them Alec Guiness, who was there in the earliest days of the festival.

  In the mid–1960s, I received an invitation to be a visiting professor at the Harvard Business School. We packed up our car, and with our two small children in the back, set out for Massachusetts. Midway on our journey, we stopped at a motel. Joan and I busied ourselves removing the luggage from the car. It hadn't been a minute when we heard a happy voice exclaiming from a distance, “I like it! I like it!” There was Helen, arms extended, flying down a very tall slide and into the motel swimming pool. She hadn't yet learned to swim, so Joan leapt into the pool fully clothed to rescue her. With half of us wet through, we entered the lobby and checked in.

  Near Boston we rented a large, dark, and spooky old house with turrets and extensive grounds that belonged to a professor of French who was on leave. Stories about the place abounded: A former owner had once kept 50 cats there. And some years before, a number of valuable paintings stored in the barn had been stolen. The heating system, which relied on several thermostats, was incomprehensible; some rooms were icy, while others were tropical.

  There were numerous trees on the property, and one autumn day, Joan raked the fallen leaves into an enormous pile and made a bonfire as she would have done in England. Within minutes, and to the delight of my small son, the fire brigade roared up and extinguished the burning pile.

  As a small boy, Harry liked cars and trains and planes. One Christmas when he was three or four, we gave him a bright red pedal car. He liked it so much that we could not extricate him for hours and we had to bring him his breakfast in the car.

  Later, when he was about seven, I happened to see an advertisement in the paper for a Lionel train set, so I went to look at it. It was a beauty with a locomotive that smoked; a number of cars, tracks, and switches; and a station. The man who was selling the set explained that he had bought it for his daughter but she wasn't interested. So I bought it, and Harry and I got a very large plywood base on which we set up a simple system. It ran perfectly.

  Now I can't remember how it happened, but at that time we got to know an elderly man called Mr. Fischer, who had retired from his job at the Oscar Meyer plant on the north side of Madison. He had an extremely elaborate model railway in his basement. He had switches and sidings and crossovers and bridges, and he taught us all the things we needed to know about model trains. He became very fond of Harry, so we visited him on most Saturday mornings, and he would make extremely generous “swaps” with pieces of equipment. We felt a bit embarrassed by his generosity, but as a small token of our thanks, we always took him a six pack of his favorite beer.

  The Lionel train people had introduced something new every Christmas, and Mr. Fischer had it all. He had a circus train where the giraffe automatically bent over when the train entered a tunnel. Also, on command, the train would stop to have its cars loaded with logs and could be made to halt automatically at stations.

  Eventually our system also became very complex with many switches and all the other electronically driven devices. Harry got to be quite an expert with electric circuitry, and he has been so ever since.

  Helen and Harry were about four and six, respectively, when the circus came to Madison. The performance they liked the best was by the elephants and the elephant trainer. He was tall and handsome and beautifully dressed in silver and gold. It was a bitterly cold day, and when the show was over, we spent a long time trying to get our car started. Eventually we were alone in t
he car park, cold and dispirited. Seeking help, or perhaps a phone, we walked over to a very large wooden building that was there on the grounds. We opened a door, and there, in all his gold and silver finery, was the elephant man! Further down the room were two elephants. We explained what had happened to us. He was very sympathetic, and while we admired the elephants, he found a can and siphoned it full of gas. Then he walked to our car in the freezing cold, filled our tank, made sure that we were okay, and waved to us as we left. When we got home, the children mentioned the circus, but by far the best, and what they wanted to tell about, was our personal adventure with the elephant man.

  Over the years, we had several live-in nannies who looked after Helen and Harry. By far the best was Jean Thain, who had come from England with the recommendation of Harry Fisher's ever-capable neighbor, Mrs. Hester. My daughter, who was five when Jean arrived, is sure that the latter was the incarnation of Mary Poppins. Jean was indeed extremely competent and good with children, and she remained with us for a number of years. Her departure was entirely my doing, although it was for the best of reasons.

  My brother Jack had two sons, Michael and Roger. Michael was quite brainy, received a good degree from the university, and he too got a job with ICI. His brother, Roger, had a very inferior job in the same department and became quite depressed. I did what I could to help him, but because I was in the States, I had to do this from a distance. I bought two small reel-to-reel tape recorders, and I sent one to him and we corresponded that way. He told me about his troubles, and I sent him encouraging messages. Roger had a respectable degree in mathematics, so I told him that he did not have to be miserable at ICI working for his brother, that he had a choice in the matter, and that people like him were needed all over the world. Canada, Australia, and New Zealand were possibilities.

  It later occurred to me that Roger might get a job in the United States. At that time, we had a large computer center in Madison that my friend Merve Muller directed. He was in need of help, so Merve offered Roger a job. Roger quit his job at ICI, flew over, lived with us, and did well in his new position.

  After getting to know one another, Roger and Jean fell in love and eventually married. They moved to Melbourne, Australia, and when we visited them, they were thriving.

  Just as my family grew, so did the Statistics Department. By 1968, we had 17 faculty members. Their names and their specialties are listed below:

  George Box—Design of Experiments and Time Series

  John Gurland—Mathematical Statistics and Medical Applications

  Norman Draper—Design of Experiments

  Irwin Guttman—Mathematical Statistics

  George Tiao—Economic Applications

  Sam Wu—Mechanical Engineering

  Bill Hunter—Chemical Engineering

  Donald Watts—Electrical Engineering-Signal Processing

  Jerome Klotz—Mathematical Statistics

  Bernard Harris—Mathematical Statistics

  George Roussas—Design of Experiments

  Richard Johnson—Mathematical Statistics

  Gouri Bhattacharyya—Mathematical Statistics

  Asit Basu—Mathematical Statistics

  Stephen Stigler—Mathematical Statistics and History of Statistics

  Grace Wahba—Mathematical Statistics

  John Van Ryzin—Mathematical Statistics

  Joseph Sedransk—Mathematical Statistics

  We also had a number of distinguished visitors, including G. M. Jenkins, R. A. Fisher, G. A. Barnard, D. V. Lindley, J. Durbin, M. Stone, H. Raiffa, R. Schlaiffer, F. Mosteller, J. W. Tukey, F. Anscombe, D. J. Fraser, S. Geisser, and A. Zellner.

  Initially Madison had a department that was like no other, with a proper balance between theory and practice. But after a time the department, which had grown to one of the largest statistics departments in the world by the late 1970s, began to change. Ironically I was partially to blame for this. As the head of the new department from 1960 to 1969, I needed to recruit respected senior staff, and at the time, these were from universities such as Berkeley, which emphasized theoretical statistics. Thus, the available recruits were mostly theoreticians who had a totally different view of what statistics was about. What I thought statistics was about was solving “real-life” problems in engineering, chemistry, biology, agriculture, etc. At the Porton Experimental Station, and then at ICI, my everyday experience had been employing statistics precisely for this purpose. But a 1978 review of the department conducted by a university committee concluded that “the students feel that applied statistics is important, given the current job market. They believe that some theoretical faculty are not aware of the situation in the outside world and hope that recruiting will maintain the current balance [between applied and mathematical statisticians on the faculty].”2 Unfortunately, later on the influence of theoreticians outvoted all attempts to keep the department on its original intended path.

  Meanwhile, there were other changes to worry about. Nobody had told me that being president of the American Statistical Association was a three-year job. First you are president-elect, then you are president, and then you are past president. All three of these offices have duties attached. There were compensations however. I was president-elect in 1977, when Leslie Kish was president. I greatly enjoyed being his right-hand man, and we became close friends. Leslie had had an interesting career. He fought against Franco in the Spanish Civil War. At one point he was wounded by machine gun fire, but he managed to crawl back to his trench. He was in the hospital for some time, and when he was released, he joined the artillery. That particular war was horrible, and the two sides did awful things to each other. But Leslie was one of the kindest and most considerate men I have ever known, and it was a great pleasure to work with him.3

  There is a large committee of 30 or so members elected to run the ASA. They meet under the chairmanship of the president at the annual meeting. Somehow in successive years the duration of the meeting had become longer and longer until during my spell as president-elect, it lasted three days. It was easy to see that the main reason that it took so long was that the committee contained a number of self-important people who loved to hear themselves talk. So I prepared myself for being president by reading Roberts' Rules of Order, and although I didn't always remember it very well, I spoke confidently as if I did. I found that a loud interjection of “You're out of order!” was often enough to dissuade verbosity. So in the year I was president, I got the meeting over in a day and a half. That year we were meeting in Washington, D.C. Having brought things to a close, I pointed out that the Phillips Gallery was just up the road and that the members should not miss its beautiful exhibits and in particular the gorgeous Renoir, “The Boating Party,” at the top of the stairs. I was sure that we would benefit more from this than from further bureaucratic exchange.

  At the annual meeting, I gave the president's address, which provided the opportunity to consider the applied versus theoretical camps in our midst. Although many of the theoretical statisticians at Madison and elsewhere were my friends, I had to speak my mind, although humor has a way of softening even a harsh message:

  When our Executive Director was explaining to me what my presidential duties were, he told me that one of the ‘perks’ associated with this job is that I get to give the annual address to the Association, and I have a captive audience for as long as they are prepared to sit there. Fred said to me, “George, don't give them anything too technical because this is a light occasion and there will be a lot of people that the statisticians have dragged along—husbands, wives, friends—who have had about all the statistics they can take.”

  Well, imagine my disappointment. I had prepared a 50-page draft of my talk. It was called “The Present Status of the One-Armed Secretary Problem: A Decision-Theoretic Approach.” It was all about sigma fields, Hilbert spaces, and all kinds of squiggly letters with dots on. This I reluctantly set aside. (I don't think any of you would have understood it anyway.) I have had to lo
ok for an alternative. I toyed for some time with title, “Whither Statistics?,” subtitled “Perhaps We Shouldn't Start from Here,” but in the end abandoned that too. Eventually it struck me that many of the issues that we face as members of the American Statistical Association are really not very different from those we face as ordinary human beings. This is what my talk is about.

  Some of us have had a preoccupation with optimal or best decision procedures. But the best, of course, is not necessarily very good. For instance, to bring in the aspect of everyday life, if ever I had to decide between cutting my throat with a razor blade or with a rusty nail, I suppose I would choose the razor blade. But, although not strictly relevant to the problem as posed, one question that might cross my mind would be, “Have I considered all my options?”

  A principle that is being given more attention these days is that of ‘robustification.’ Here one doesn't attempt to guarantee that things will be optimal over some tractable, but perhaps very narrow, set of circumstances. Instead one tries to ensure that they will be fairly good over a wide range of possibilities likely to happen in practice. Look at the human hand, for example. I doubt if there is any single thing that the hand does that could not be done better by some special instrument, but it is very good at doing a very large number of things well that arise in the world as it actually is.

  Another way to say this is that there is really nothing wrong with optimization per se, but that we ought to try to optimize over that distribution of circumstances which the world really presents to us. The mistake is choosing the best over too narrow a set of alternatives—suboptimization. It is sometimes argued that by doing simplified exercises, we can at least obtain useful pointers. However, I feel that such pointers are very likely to indicate the wrong direction, as might be true in the case of the razor blade and the rusty nail.