The use of statistics in astronomy is frequently a rearguard action or a reaction, a response to a need to do something or say something about data that have already been obtained. The application of statistics in astronomy differs in fundamental ways from that of other branches of science: it is impossible to rerun our experiments. Statistical inference should thus be the more important in our lives. It is important to note that we are none of us doing science unless we are deciding things.
Nevertheless, for the most part our ignorance of statistics, statistical inference, signal processing and experimental design remains profound. (5) We are far too busy trying to build and commission telescopes which cost Euro- millions on the ground or Euro-hundreds-of-millions in space without giving thought to whether the data will be used in detection, correlation, model-fitting, hypothesis testing, let alone how the data will be initially massaged, generally processed or ultimately archived. Most modern telescopes receive data at such a rate that some pre-massage is essential; radio astronomers have not seen real data for years (Radhakrishnan 1990). What is happening to these data? Will we know before it is too late?
In other observational subjects, experimental design and inference, and hypothesis testing develop together (cf. genetics, biology). With a few notable exceptions this did not happen in astronomy. Indeed astronomers may not even know enough to feel shame when we ask a statistician an apparently simple question, such as: do these magnitudes differ significantly? We should know enough not to be taken aback at the response which I heard from one eminent statistician: don't ask me - you took the data.
Completion of this short series is due to many colleagues in the astronomy community who berated me to get on with it. On balance I am probably grateful to them. I am certainly grateful to Charles Jenkins who gave this his erudite criticism and in so doing pushed it past the point of no return. I also thank two referees, anonymous and Martin Hendry, who both offered much very constructive criticism which has substantially improved the product.
5 Let me note honourable exceptions. Astronomers involved in stellar kinematics have always known statistics, and for the years prior to 1950 much of the statistics in astronomy was embodied in stellar kinematics. The famous Statistical Astronomy of Trumpler & Weaver (1953) deals with little else. Modern exceptions are listed in the Introduction. In particular, there is a high level of awareness and very sophisticated use of statistical inference in large-scale structure studies. Back.