Carl N. Morris
Joan Garfield's comments are so important. I have tried to implement some of the things she said in my graduate classes, and I cannot do it very well. It has to do with the way we were taught. I was taught in the lecture mode, and I find it too easy to slip back into that same mode. I do not know if others here have also had this experience, but I will try again to follow Joan's advice because I think it is terribly important to help make that change. It will change the environment to a much more cooperative one.
I have resided in mathematics departments for much of my career although I have always been a statistician, and that will affect how I interpret things. I worry that we statisticians are running statistics a bit too much like the mathematicians do. However, I have also worked in other kinds of departments. At present I am half-time in a medical school, as well as half-time in the statistics department at Harvard. Before this, I was in the economics department at Rand [Corporation] for six years.
So my background includes having been both an employer, on the side of some of our earlier speakers, and a supplier of talent, in the view of Peter Bickel.
The most important thing teachers do is to decide on curriculum for their classes, to decide what it is that students are going to be taught. I believe this despite what Joan Garfield has said. I always feel that in the making of those decisions is the point when I, as a teacher, truly make a difference. And what all the presentations today have made evident is that some very tough choices must be made. We say that the graduate students in statistics today have to learn everything we did in the past, and that now they have to learn lots of new things, too. Furthermore, even though we have been in the field for more years than our students, few of us know these new things. But somehow the students are supposed to do all that. Thus curriculum choice is terribly important; that is what this symposium is about.
Who should be encouraged to enter the statistics profession? Should the historical mix of skills be changing? Should it move toward people who have other types of skills, sometimes sacrificing some of the more mathematical skills that are usually required right now? If that is the case, are the leading departments in statistics ready to do this? Moreover, what should be taught? Can the needed changes be made? I am pessimistic about this. It is awfully hard to change, because to do so requires performing surgery on ourselves, and that hurts. I will try to address a few of these topics.
Since I am a "respondent," I will review what preceded this. Jon Kettenring opened the symposium. He works at an institution that employs somewhat the same type of people as Rand does and did when I was there, and so I have some experience with that. Such institutions must emphasize interpersonal skills and recruit problem solvers. Those are necessary skills in interdisciplinary situations. At Rand, if people were hired who had good interpersonal skills and were problem solvers, and who were good at statistics, they would create new jobs. If you hire a statistician with the skills described by today's speakers, you will find that next year there will
be a new opening created because somebody else wants a statistician who can help like that. On the other hand, when somebody without the interpersonal skills and natural inquisitiveness is hired, everything closes down for a while.
I am also suggesting that there is more than one dimension to a person's useful skills. Ability involves much more that just IQ; it is at least two-dimensional. When looking at the Graduate Record Exam scores for entering statistics students, the verbal should be considered much more than it has been in the past. I mean that both specifically, and also much more generally. A sense of the applicant's general skills must be obtained. This could change the mix of people who come in to statistics. It might also bring more balance to the profession, perhaps across gender lines.
Peter Bickel listed nine topics that should be covered in graduate training. One he did not mention — nor did anyone else — is almost the most important topic. That topic is model checking. I believe inferences are made by proposing a model and then checking it. Then you adjust it and check it some more. When you have done the best you can with your data and your knowledge, you draw the inference. This is conditional on the model you finally fit, the one you publish. Later, somebody else with better data, or with deeper understanding, might look again at the problem and show how to do a much better analysis. That is great; an evolution has occurred, and public knowledge has been enhanced. Both parties have made important contributions to this evolution. Certainly that point has to be emphasized when students are taught to do statistics.
What about training for the academic market, on which Peter Bickel touched? That involves training students to do something fundamental, and "important." It can be hard to understand the criteria. As a journal editor, I am occasionally told by authors that "this paper (or result) is very important." Sometimes I could not figure out what was important about it at all. I finally decided that when that happened, "important" meant that it was hard to get the result, and perhaps some smart people had tried earlier to get the answer and they could not. A recent example is Fermat's last theorem. Andrew Wiles recently established the truth of Fermat's conjecture (that there are no positive integer exponents n bigger than 2 such that An plus Bn equals Cn). The result will be hailed as very "important'' in mathematics, because mathematicians have been working on it, unsuccessfully, for 350 years. But the world is not going to change much because of it, and I think this use of the term "important" is different from what would be understood by the non-academic market.
Often, however, even in statistics, the person whose genius establishes the statistical equivalent of the Wiles-Fermat Theorem still would be hired. Probably that is as it should be. But I am suggesting that more weight be given, in criteria for promotion and hiring of our faculty, to the needs for producing research and students that are important to the outside world.
Phillip Ross discussed expediency versus quality. The key sometimes is that the employer wants a fast answer, even if it is just a hunch and possibly not very good. That is acceptable practice so long as the statistician can say: "Here is a fast answer. It may not be very good, and I really need more time. We see this problem repeatedly, and because it will come up again, I must take some time to work on it and understand it for the next time." That is what statistics is about: getting important ideas that are used more than once, perhaps even in different fields, and abstracting them, developing them.
An illustration of this involves the widely used method of "regression" that was developed to learn how sons' heights regressed from fathers' heights toward the mean height. The word "regression" now refers to the method, rather than to the motivating application. I once had a similar experience with Brad Efron when we developed a method for shrinkage. We called it the "toxo" method, because we first tried it out on toxoplasmosis data. It was hard later to stop calling everything we did with that method the "toxo method.''
I am trying to exemplify that in statistics we often do something to solve a special problem, but it really solves many other problems, too. That is something very worthwhile that statisticians do, and it is why statistics departments are so valuable. But statistics departments must communicate with other departments and with other research units to realize this value. Our statistics departments must do whatever is necessary to effect and preserve this communicating, using joint appointments, and so on, to nurture communication and interdisciplinary research.
John Bailar said that the supply right now exceeds the demand for theoretical statisticians. I agree. But I personally would rather not separate theory from application. I do not see how one can. I can think of few interesting applied problems that do not have theoretical components, or of any interesting statistical theory that has no applications. I abhor the sometimes-stated idea that one researcher is better than another because he is more "theoretical." Statistics students must be trained so as to be acquainted with both aspects, and to understand theory partly through applications, and application with theory.
Recently I have hit an impasse in trying to determine how to forecast future work load in Veterans Administration hospitals. Since I, thus far, cannot get the modeling of the data correct, I cannot get the estimates to come out right. This problem, which will have a big payoff, will take significant theoretical talent to solve. It is a theoretical problem, besides being an applied problem.
John Bailar also discussed bias. There are many important problems that can be looked at only if bias can be eliminated. For example, how can data be used to determine the relative benefits of one medical therapy versus another when the data were not randomized? There would be enormous amounts of data for doing that, if only the physicians applied the treatments at random.
I love Jean Thiebaux's idea of the collective scientific mind, that none of us is big enough to understand all the science but that somehow there still exists a collective mind that is the union of all of this. Perhaps some scientists do actually try to get an overview, just as a head of state cannot understand everything that is going on in the government but might have an overview of the government without knowing all the details. But I think the collective mind goes on within statistics, as well as across fields. Both Peter Bickel and John Lehoczky noted that graduate school cannot teach everything about statistics. So, there may have to be a collective statistics mind. Perhaps not every student can learn about sequential analysis. Instead, people will have to work together and to share knowledge. Thus Joan Garfield's cooperative role is appropriate in this context, too.
Ideally, I view statistics departments through a hub-and-spoke metaphor. In it, statistics sits at the center of the university, as the hub, and the other departments that use statistics are the spokes. The statistics department is in contact with every other department. Joint
appointments help to do that, but there are many other ways to facilitate that communication, including communication through statistics students.
We learn from the other departments, and they learn from us. Statistical information flows between departments, often first through the statistics hub. The statisticians learn something from one department, they talk to other statisticians, and later a statistician who is working with yet another department spins the information back out, perhaps assisted by an abstraction of the methodology. Many mathematical ideas, such as regression, do not have to be rediscovered in every field. But somebody does have to communicate the idea.
This is why I believe statistics departments are needed; this is their principal role. However, we have sometimes abused our purpose (as mathematics departments, which should have a similar role, have done also). Departments of statistics (and perhaps even more so, our mathematics ancestors) are formed to play this role of contact hub, but once constructed, are tempted to change their mission to one of polishing up what was developed in the past. Instead, the need is to figure out what will be important in the future. Much of that can be discovered through interdisciplinary collaborations.
Concerning John Lehoczky's presentation, I have admired the Carnegie Mellon University graduate statistics program, and have thought that their department is probably the most successful in providing a first-rate statistics education. It is partly because they do the things that John described. They involve their students in many different ways in practice and in theory, and they help their students with communication and the interdisciplinary skills. But I do not see how it all gets done in the two years before the dissertation research commences.
John Lehoczky wondered what might be cut from the existing curriculum. I suggest that we cut many of those special topics courses, and perhaps have the student who is interested in specialization pick them up in the dissertation. This does not mean students cannot get course exposure to such topics. But there would be more learning such as what takes place in the first CMU course John described, where each faculty member lectures once or twice about his or her specialty. We need more courses that give people a feeling for the various topics. It is not necessary to teach everything; we should teach the most general ideas.
Students must be empowered to learn on their own. Joan Garfield touched on that. If it is done properly, they will learn to love the subject. They will be taught to learn on their own by being helped to find and read the literature. And, anyway, that is how we learn, by doing and applying.
It is going to be painful. Parents must forget their own egos as their children grow up. Our children do not have to follow our paths. They have to do what is right for them. There then will be evolution. We, as teachers, have to do the same thing, and teach what is needed. We have to let them do something different. Joan Garfield gave us some keys for that. If we cannot change our teaching styles, then we can at least let the students do more of the teaching, and they will change it for us. We need not replicate ourselves, to use John Bailar's term.
I would like to introduce a principle for statisticians. We must always do what benefits the field, and not our own department. We need to choose people who come into statistics to lead in the field, so as to help the whole field. We must not train students too narrowly, or the field will suffer.
I think the subject of statistics is extremely healthy. There will be ever more data, and data analysis, and computers to help in doing that analysis. When I fear that the field will
suffer, I mean that statisticians will suffer. Many researchers do statistics. The question is, What will our role as statisticians be in the statistics enterprise?
As we consider the question of what hard trade-offs are acceptable, it might not be a bad idea to survey that portion of the statistical community membership that does the hiring. A questionnaire may help them to tell the people who are doing the teaching what they need to teach.
I was going to tell you a bit about the Harvard graduate statistics program. It is a small program with many good features that are quite consonant with the goals that we have laid out here. Only special students will do well at Harvard because students are left on their own a lot, and they do not take lots and lots of courses.
From the perspective of the general statistics department, again, the biggest step in making good curriculum decisions is that we first must make changes in our faculty selection decisions, and we need more joint appointments to facilitate all the things that we are saying. In some ways, smaller programs may find it easier to change than bigger ones because they more easily develop the unanimity that John Lehoczky said has been formed at Carnegie Mellon University. It is hard to agree on curriculum if people are all thinking differently, or if only one or two are thinking this is a good direction for the future. It is hard because there will be pain, loss of favorite courses, having to change research directions, and so on.
Another way all statisticians can affect research is to quit handing out the money for irrelevant projects. This can be done through the recommendations reviewers provide. When research proposals are being evaluated, one must not only evaluate how able the applicant is, but also how much benefit this research will do for the long-term health of the field of statistics. On the other hand, soft money to support applied projects can help a statistics department by keeping the department relevant.
Some of the science of mathematics surely will be preserved for statistics, partly because mathematical modeling is so important. I believe that 75 percent of what statistics does is create good mathematical models to describe the structures of other sciences.
The future of statistics is secure. Statistics departments, however, and statisticians might not be. We risk being ignored if we do not stay relevant. The statistics enterprise must not be allowed to fail because, as in the hub-and-spoke paradigm, it occupies a central, vital communication position that enhances the scientific capability of the entire university. People will truly appreciate what statisticians can do if we do what I know we can.