Central to Bayesian methods is a theorem from probability theory known as Bayes' theorem.  Relative to a prior probability distribution over hypotheses, and the probability distributions over sample space for each hypothesis, it tells us what the adequate posterior probability over hypotheses is. More precisely, let \(s\) be the sample and \(S\) be the sample space as before, and let \(M = \{ h_{\theta} :\: \theta \in \Theta \}\) be the space of statistical hypotheses, with \(\Theta\) the space of parameter values. The function \(P\) is a probability distribution over the entire space \(M \times S\), meaning that every element \(h_{\theta}\) is associated with its own sample space \(S\), and its own probability distribution over that space. For the latter, which is fully determined by the likelihoods of the hypotheses, we write the probability of the sample conditional on the hypothesis, \(P(s \mid h_{\theta})\). This differs from the expression \(P_{h_{\theta}}(s)\), written in the context of classical statistics, because in contrast to classical statisticians, Bayesians accept \(h_{\theta}\) as an argument for the probability distribution. 