Bayesian statistics is first introduced in the context of a finite set of hypotheses, after which a generalization to the infinite case is provided. Assume the prior probability \(P(h_{\theta})\) over the hypotheses \(h_{\theta} \in M\). Further assume the likelihoods \(P(s \mid h_{\theta})\), i.e., the probability assigned to the data \(s\) conditional on the hypotheses \(h_{\theta}\). Then Bayes' theorem determines that  \[ P(h_{\theta} \mid s) \; = \; \frac{P(s \mid h_{\theta})}{P(s)} P(h_{\theta}) . \]  Bayesian statistics outputs the posterior probability assignment, \(P(h_{\theta} \mid s)\). This expression gets the interpretation of an opinion concerning \(h_{\theta}\) after the sample \(s\) has been recorded accommodated, i.e., it is a revised opinion. Further results from a Bayesian inference can all be derived from the posterior distribution over the statistical hypotheses. For instance, we can use the posterior to determine the most probable value for the parameter, i.e., picking the hypothesis \(h_{\theta}\) for which \(P(h_{\theta} \mid s)\) is maximal.