Statistical analyses are mainly based today on one of the two major paradigms: frequentist and Bayesian. Bayesian methods provide a complete paradigm for both statistical inference and decision-making under uncertainty. Bayesian methods may be derived from an axiomatic system and provide a coherent methodology which makes it possible to incorporate relevant initial information and solves many of the difficulties faced by conventional statistical methods. The Bayesian paradigm is based on an interpretation of probability as a conditional measure of uncertainty which closely matches the sense of the word “probability” in ordinary language. Statistical inference about a quantity of interest is described as the modification of the uncertainty about its value in the light of evidence, and Bayes’ theorem specifies how this modification should be made. Bayesian methods may be applied to highly structured complex problems, which have been often untractable by traditional statistical methods. The special situation, often met in scientific reporting and public decision-making, where the only acceptable information is that which may be deduced from available documented data, is addressed as an important particular case, often referred to as reference analysis.