Prologue

Almost all my professional life has been spent in academe as a statistician. In my first appointment in Cambridge, I was required to lecture for 6 hours each week during half of the year and personally to supervise some students. Admittedly, the preparation of new lecture courses took a lot of time, one occupying the whole of the 4 month summer vacation, but these duties did not constitute a reasonable workload. To fill the gap, one was expected to do exactly what I wanted to do, conduct research. As I moved to become professor and head of department, first in Aberystwyth and then at University College London, other duties, principally administrative, crowded in upon me and there was less time for research. But still it got done, because I wanted it to get done, often in conjunction with good, graduate students.

Research, at least in my case, consists of taking questions that interest one and to which you feel you might, given enough time and effort, be able to find an answer; working on them, producing an answer, which often turns out to be quite different from the form originally anticipated, and publishing the results for others to read. There are many aspects to this creative work but the one to be emphasized here is that the questions I chose to answer were selected by me. There was no superior, as there would have been in industry, posing me problems and expecting answers. There was no deadline to be met. This was freedom of thought in its true sense, requiring little more than a comfortable office, a good library, and, most important of all, time in which to think deeply about what interested you. Good answers produce rewards in promotion and more money but that is not the real motivation, which comes instead from the excitement of the chase, to explore where no one has been before, to think deeply, and to come up with something that is genuinely new. And all this free from the interference of others except those you wish to consult. That is true academic freedom that dictators hate so much.

At least during the first 20 years of my researches, I do not recall ever asking myself or being asked by others, whether what I was doing was worthwhile. Society paid me a salary that provided a comfortable living for myself and my family, giving me enough time to think and write, yielding appreciation from the few people who bothered to read my answers. I suppose if someone had asked me to justify my salary, I should have mumbled something about the training in statistics I had given to many students and the value of statistics in society. But nobody did ask and my conscience did not bother me; it was the chase that mattered. Later, however, as I began to sit on committees and come into more contact with life outside the university, I did wonder about the relevance to society of the answers I had given to questions I had chosen and, more widely, about the value of statistical ideas and methods produced by others. When I thought about this, the answers were not terribly encouraging, for admittedly the discovery of the harmful effects of smoking was mostly due to statistical analysis, and statisticians had played an important role in the breeding of new plants and animals, but I had had little to do with these activities and few had attempted to use the answers my research had provided, let alone succeeded. It had been a good life for me but had it been a worthwhile one from the viewpoint of society?

Research, especially in disciplines that use a lot of mathematics, is a young person's game and after early retirement I did little research but began to read more widely and consider problems that had not seriously entered into my comfortable research world. And I made a discovery. There were people out there, like politicians, journalists, financiers, lawyers, and managers, who were, in my opinion, making mistakes; mistakes that could have been avoided had they known the answers to the questions pondered in my ivory tower. In other words, what I had been doing was not just an exercise in pure thought, but appeared to have repercussions in the world that could affect the activities of many people and ultimately all of us. This is a phenomenon that has been observed repeatedly; namely that if people are given the freedom and opportunity to use their reasoning abilities to explore without any application in mind, what is termed pure research, they often come up with results that are applicable. Ivory towers can yield steel and concrete, produce food and shelter. This book is an attempt to explain in terms that motivated, lay persons can understand, some of the discoveries about uncertainty made in academe, and why they are of importance and value to them, so that they might use the results in their lives. In a sense, it is a justification for a life spent in academe.

The preceding paragraphs are too personal and for clarification it is necessary to say something more about scientific research. Research is carried out by individuals and often the best research is the product of one person thinking deeply on their own. For example, relativity is essentially the result of Einstein's thoughts. Yet, in a sense, the person is irrelevant, for most scientists feel that if he had not discovered relativity, then someone else would; that relativity is somehow “out there” waiting to be revealed, the revelation necessarily being made by human beings but not necessarily by that human being. This may not be true in the arts, so, for example, if Shakespeare had not written his plays, it would not follow that someone else would have produced equivalent writing. Science is a collective activity, much more so than art, and although some scientists stand out from the rest, the character of science depends to only a very small extent on individuals and what little effect they have disappears over time as their work is absorbed into the work of others. There are two lessons to be learnt from this as far as this book is concerned. First, my contribution to the results described herein is very small and is swamped by the work of others. It is as if I had merely added a brick or two to the whole building. Second, I have not thought it advisable in a book addressed to a general audience to attribute ideas to individuals. Our concern with individual scientists is often misplaced, because it is the collective wisdom that is important. The situation is made worse by the fact that the ideas are often attributed to the wrong individual. The ideas with which this work is usually associated are termed Bayesian, after Thomas Bayes, who had hardly anything to do with them. Generally, there is Stigler's law of eponymy that says that a scientific notion is never attributed to the right person; in particular, the law is not due to Stigler. Some scientists are named in the book because results are universally named after them—Bayes rule, for example, or de Finetti's theorem.

Here is a book about uncertainty, showing how it might be measured and used in your life, especially in decision making and science. It tells the story of great discoveries made in the twentieth century that merit dispersal outside the narrow community where they were developed. New ideas need new forms of exposition, so after a collection, in Chapter 1, of examples of where uncertainty impinges on our lives, Chapter 2 is concerned with certain stylistic questions, including the thorny subject of mathematics; it is only in Chapter 3 that the discoveries really begin.