2 - Probability

Summary

God does not play dice with the Universe.

(Albert Einstein)

Whether He does or not, the concepts of probability are important in astronomy for two reasons.

1. Astronomical measurements are subject to random measurement error, perhaps more so than most physical sciences because of our inability to re-run experiments and our perpetual wish to observe at the extreme limit of instrumental capability. We have to express these errors as precisely and usefully as we can. Thus, when we say ‘an interval of 10^-6 units, centred on the measured mass of the Moon, has a 95 per cent chance of containing the true value’, it is a much more quantitative statement than ‘the mass of the Moon is 1 ± 10^-6 units’. The second statement really only means anything because of some unspoken assumption about the distribution of errors. Knowing the error distribution allows us to assign a probability, or measure of confidence, to the answer.

2. The inability to do experiments on our subject matter leads us to draw conclusions by contrasting properties of controlled samples. These samples are often small and subject to uncertainty in the same way that a Gallup poll is subject to ‘sampling error’. In astronomy we draw conclusions such as: ‘the distributions of luminosity in X-ray-selected Type I and Type II objects differ at the 95 per cent level of significance.’ Very often the strength of this conclusion is dominated by the number of objects in the sample and is virtually unaffected by observational error.