15 March 2006
Statistics and probability are the complementary disciplines of the science of uncertainty, but many of us are still uncertain about why we might need them.
But more careful thought suggests that there is often a gap between the physical reality and the physical law. That gap is a very narrow one in the ‘A’ level physics lab, but becomes greater and more important as scale becomes larger, observation becomes more difficult, or knowledge becomes weaker.
For example, the atmosphere and the Earth’s interior are physical systems, much-studied and rather well understood, yet neither hurricanes nor earthquakes can be predicted accurately enough to protect life from disaster. In the biological and medical worlds, there are much greater uncertainties still, and even with fantastically increasing knowledge of genetics and microbiology, we are hugely ignorant of many aspects of animal development and growth, evolution, or disease susceptibility.
On average, you don’t get up late, and on average the bus isn’t early, but you are still sometimes late for work.
Modern statistics is about quantifying uncertainty in all sorts of system. It addresses the knowledge we think we have, the knowledge we know we don’t have, and perhaps even the knowledge we don’t know we don’t have. That is, it deals both with systems that are intrinsically uncertain – the choice of a gene passed at random from parent to child – and with systems we believe not to be random but which are too complicated to model exactly – the atmosphere. It handles the uncertainty that comes from not being able to measure a phenomenon accurately, so that times, distances, disease symptoms or weather records are imperfectly recorded. The special characteristic of complex stochastic models is that they give us a way to bring all these different sources of uncertainty about a system into consideration simultaneously, because it is often the interplay between these factors that governs behaviour. (On average, you don’t get up late, and on average the bus isn’t early, but you are still sometimes late for work.)
What I find compelling about working in this area is that I can use a combination of statistical, mathematical and computational skills, in a creative way, to help to understand uncertainty. That is already fascinating, but then I get the chance to apply that understanding and the tools I have developed, in solving problems in science, technology, medicine, and in society itself. In just a few short months I have worked on genes and disease, on badgers and TB, on forensic science, on astronomical measurements, and on credit card encryption. In fact, what is most uncertain of all is where my research will take me next!