There are two competing philosophies of statistical analysis: the Bayesian and the frequentist. The frequentists are much the larger group, and almost all the statistical analyses which appear in the BMJ are frequentist. The Bayesians are much fewer and until recently could only snipe at the frequentists from the high ground of university departments of mathematical statistics. Now the increasing power of computers is bringing Bayesian methods to thefore.

Bayesian methods are based on the idea that unknown quantities, such as population means and proportions, have probabilitydistributions. The probability distribution for a population proportionexpresses our prior knowledge or belief about it, before we add the knowledge which comes from our data. For example, suppose we want to estimate the prevalence of diabetes in a health district. We could use the knowledge that the percentage of diabetics in the United Kingdom as a whole is about 2%, so we expect the prevalence in our health district to be fairly similar. It is unlikely to be 10%, for example. We might …