Instead of completely rewriting the primer, producing a thicker report which would have been harder to read sequentially, I have divided the text into three parts.
This structure inevitably leads to some repetition, which I have tried to keep to a minimum. In any case, repetita juvant, especially in this subject where the real difficulty is not understanding the formalism, but shaking off deep-rooted prejudices. This is also the reason why this report is somewhat verbose (I have to admit) and contains a plethora of footnotes, indicating that this topic requires a more extensive treatise.
A last comment concerns the title of the report. As discussed in the last lecture at CERN, a title which was closer to the spirit of the lectures would have been ``Probabilistic reasoning ... ''. In fact, I think the important thing is to have a theory of uncertainty in which ``probability'' has the same meaning for everybody: precisely that meaning which the human mind has developed naturally and which frequentists have tried to kill. Using the term ``Bayesian'' might seem somewhat reductive, as if the methods illustrated here would always require explicit use of Bayes' theorem. However, in common usage `Bayesian' is a synonym of `based on subjective probability', and this is the reason why these methods are the most general to handle uncertainty. Therefore, I have left the title of the lectures, with the hope of attracting the attention of those who are curious about what `Bayesian' might mean.