In this characterization of Bayesian statistical inference the probability of the data \(P(s)\) is not presupposed, because it can be computed from the prior and the likelihoods by the law of total probability,  \[ P(s) \; = \; \sum_{\theta \in \Theta} P(h_{\theta}) P(s \mid h_{\theta}) . \]  The result of a Bayesian statistical inference is not always reported as a posterior probability. Often the interest is only in comparing the ratio of the posteriors of two hypotheses. By Bayes' theorem we have  \[ \frac{P(h_{\theta} \mid s)}{P(h_{\theta'} \mid s)} \; = \; \frac{P(h_{\theta}) P(s \mid h_{\theta})}{P(h_{\theta'}) P(s \mid h_{\theta'})} , \]  and if we assume equal priors \(P(h_{\theta}) = P(h_{\theta'})\), we can use the ratio of the likelihoods of the hypotheses, the so-called Bayes factor, to compare the hypotheses.