Bayesian statistical methods are often presented in the form of an inference. The inference runs from a so-called prior probability distribution over statistical hypotheses, which expresses the degree of belief in the hypotheses before data has been collected, to a posterior probability distribution over the hypotheses, which expresses the beliefs after the data have been incorporated. The posterior distribution follows, via the axioms of probability theory, from the prior distribution and the likelihoods of the hypotheses for the data obtained, i.e., the probability that the hypotheses assign to the data. Bayesian methods thus employ data to modulate our attitude towards a designated set of statistical hypotheses, and in this respect they achieve the same as classical statistical procedures. Both types of statistics present a response to the problem of induction. But whereas classical procedures select or eliminate elements from the set of hypotheses, Bayesian methods express the impact of data in a posterior probability assignment over the set. This posterior is fully determined by the prior and the likelihoods of the hypotheses, via the formalism of probability theory.