In previous chapters we have applied the Bayesian and the frequentist approach to some basic problems. The key differences of the two approaches are summarized in Table 20.1. The last two rows deserve additional remarks, which will be given in the following sections.

Prior knowledge is prior data

In scientific problems the present data are certainly not the only information that is known for the problem under consideration. Usually, there exists a wealth of knowledge in the form of previous experimental data and theoretical facts, such as positivity constraints, sum rules, asymptotic behaviour. A scientist is never in the situation that only the current data count. The Bayesian approach allows us to exploit all this information consistently. It has been criticized that priors are a subjective element of the theory. This is not really correct, as the Bayesian approach is internally consistent and deterministic. The only part that could be described as subjective is the knowledge that goes into the prior probabilities. But this degree of subjectivity is actually the foundation of all science. It is the expertise that exists in the respective discipline. The generation of experimental data is based on the same subjectivity, as it is generally motivated by prior knowledge in the form of previous data or theoretical models.

A great part of the prior knowledge is a summary of a conglomeration of previous measurements, with completely different meanings and sources of statistical errors.